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1808 | 1808.01506_arXiv.txt | Changing gravity in the far infrared emerged as an alternative for addressing the Universe's missing mass problem, which in General Relativity (GR) is modeled as either dark energy or dark matter. This program is fraught with difficulties\footnote{The modifications which never encounter such difficulties seem to be merely different gauges of scalar-tensor gravity, possibly with irrelevant operator corrections. At this point these are clearly less interesting.} with predictivity of the theory in the regime between the cosmological and short-distance scales, which are particularly acute when the modifications break or alter diffeomorphism invariance of GR, which is really a gauge redundancy of the theory. New degrees of freedom may appear lending to all kinds of trouble. A notorious problem are the ghost modes---the excitations with negative kinetic terms---that are commonly encountered on generic backgrounds \cite{deser,Higuchi:1986py,nima}. It now appears that the ghosts are not a showstopper. Frameworks were found where the gauge redundancies are relaxed to allow full massive spin-2 multiplets, yet without propagating ghosts \cite{drgt,fawad}. These models have been applied as approximations to GR in the hope that interesting alternatives to missing mass can be found. If the gravitational field is massive but very light, one might hope that the modifications of the gravitational dynamics, be it at the level of the background or perturbations, could feature new phenomena that can alter cosmological dynamics and compact object fields in interesting ways \cite{guido,mukoh,Comelli:2011zm,koyama}. However these applications run into a problem: the helicity-0 mode of the massive graviton tends to be strongly coupled and its sector runs out of control at very low scales. For example, one may take the mass of the graviton to be $m \sim H_0 \sim 10^{-33} \, {\rm eV}$, in order to defer the deviations from GR to horizon scales, where the dark energy component of the missing mass kicks in. In this case, in vacuum the breakdown happens at typically $\sim 1000 \, {\rm km}$ \cite{nicorata}. In denser backgrounds, this scale can be shorter, as has been noted in \cite{clare}, but it is still very low. These arguments have subsequently been refined and confirmed\footnote{There is an increasing effort underway to address some cosmological problems in massive gravity cosmology by bigravity models.} by various authors \cite{saffin,gaba,javi}. In response it has been proposed that the theory can be improved by embedding massive gravity in warped extra dimensions. It is well known that some of the problems with perturbativity of massive spin-2 modes are relieved in AdS spaces \cite{kogan,maximus,karch}. Therefore it is fathomable to entreat that similar setups can improve massive gravity too \cite{gaba}. In turn, if such frameworks are to be used in phenomenological applications, the extra dimensions either need to be compactified, or a theory of matter needs to be confined to a brane that floats in the higher-dimensional bulk. In the latter case the brane theory needs to be properly covariantized in the massive gravity bulk. This means that terms which add to the usual Gibbons-Hawking action on the boundary are required to ensure that the theory has a well defined action principle and Hamiltonian evolution. In the case of flat bulks this has been considered in an interesting article \cite{Gabadadze:2018bpf}, which summarizes with a call for deployment of the ``machinery" of \cite{sasaki} to study cosmology of such braneworlds and in particular their vacua, given by the geodesic worldvolumes of an empty, but possibly tensional brane in the bulk. This ``machinery", i.e. the formalism of the Gauss-Codazzi-Weingarten equations that yield the tool for determining the intrinsic geometry of a hypersurface in the bulk, is fortunately not necessary when the vacua are maximally symmetric subspaces. Their large symmetry translates into relatively simple embedding equations \cite{weinbergbook}, that provide a shortcut for constructing solutions. Such methods have been employed in the case of bent braneworlds in flat and curved bulks \cite{kaloperlinde,bent}. In the case of massive gravity the same shortcut remains available, with the generalizations of the boundary conditions (a.k.a. Israel junction conditions) outlined in \cite{Gabadadze:2018bpf}. Following this route, in this paper we construct the vacua of an orbifold brane in a flat bulk of massive gravity \cite{drgt} and bigravity \cite{fawad}, where the intrinsic geometry on the brane is de Sitter. We work with a $5D$ bulk and $4D$ brane for simplicity. We impose orbifolding, i.e. identification of the different sides of the brane which serves as a $\mathbb{Z}_2$ mirror. We then compute the relationship between the expansion rate, the tension and the graviton mass with both finite and infinite bulk boundary conditions, the two branches of solutions corresponding to the so called normal and self-accelerating branches in DGP gravity \cite{dgp} (see, e.g. \cite{specters,gkmp} for a review). We find interesting differences between these solutions and the vacua found by similar means in the DGP braneworlds \cite{deffayet}. In particular, the vacua on both branches never feature the self-accelerating limits: the tension can never be zero. However, both branches feature a completely novel behavior for large tension. On the branch where the bulk extends to infinity, when tension is negative, there is a sub-branch where the larger the tension, the smaller the expansion rate on the brane! On the other branch the same happens for positive tension. In other words, the leading order effects of the tension cancel out from the induced curvature. This is reminiscent of degravitation \cite{degrav} and the mechanism of vacuum energy sequester \cite{sequester}. We also find that on both branches of solutions there exists a normalizable $4D$ graviton localized on the brane. This occurs for a very special selection of the bulk mass parameters. The reason is that due to the degeneracy of the bulk mass contributions, the mass of this mode can be tuned to zero, similarly to \cite{peloso,El-Menoufi:2014aza}. These cases cannot be realized as a continuous limit of a massive theory, because of the Higuchi bound \cite{Higuchi:1986py}. The localized graviton is the zero mode of the bulk equation, which means that the tensor sector of the theory does not contain ghosts. In fact, since our starting point is ghost-free massive gravity, this is not surprising: the only possible source of a ghost would be the brane boundary, which might introduce it via the coupling of the brane bending mode with gravity \cite{dgp,specters} in the scalar sector, just like in DGP. While we did not check this explicitly it is likely that since there are two branches of background solutions, the scalar ghost could be absent on at least one of them because its bulk wavefunction is not normalizable. In this case the full nonlinear theory would be ghost-free, and since it contains the massless $4D$ graviton, there would be an enhanced gauge symmetry protecting the special values of the parameters. This is just the usual $4D$ diffeomorphism invariance of GR. A small deviation of the parameters from the special value yields a ghost, which suggests that the perturbation theory will not correct the special value, in order to maintain unitarity. In this case the additional helicities of the localized graviton decouple, since their couplings to matter sources are $\propto m = 0$. Finally we extend the construction of the background to the case of bigravity. The solutions which we provide look very interesting, since the cancellation of the tension contributions from the brane intrinsic curvature may be helpful to attempts for addressing the cosmological constant problem in this setup. At the same time, finding the localized massless $4D$ graviton, and raising the bulk graviton mass ought to improve the range of validity of the low energy theory. However, before these appealing features can be put to a good use, it is necessary to verify that the theory can accommodate consistent low energy dynamics, including $4D$ cosmology. We leave these important questions for the future. | Our construction of de Sitter branes in a $5D$ flat bulk of massive gravity reveals several unusual and interesting features. Let us outline them here: \begin{itemize} \item First, the background solutions do not display the phenomenon of self-acceleration: the brane geometry is de Sitter only for tensions larger in absolute value than a critical value $48 M_5^3 m$; the graviton mass does not drive the `repulsion' required to induce cosmic acceleration. \item Second, on each branch of solutions there is a sub-branch where the tension $\sigma$ (which measures the vacuum energy of a brane-resident QFT) is effectively shielded from curvature: the leading order contribution cancels, leaving only a correction which gives $H \sim 1/|\sigma|$ and a larger tension gravitates less. For the $\varepsilon = +1$ branch this happens for positive tensions, and for the other branch this is true of negative tension, though that may introduce ghost-like instabilities. \item Third, on both branches there is a localized $4D$ massless graviton mode, with only helicity-2 excitations. This requires a special choice of the bulk graviton mass, and may look like fine tuning at first sight. However, the presence of only two propagating helicities indicates that there may be the enhanced gauge symmetry for this mode in $4D$. Indeed, since the bulk theory is ghost-free, if the brane bending mode does not introduce a ghost, the full nonlinear $4D$ effective theory would be ghost free, and contain the zero mode, implying the presence of the same gauge symmetry as in GR. This is circumstantially supported by the fact that the special value of the bulk graviton mass results in the $4D$ graviton mode right in the middle of the Higuchi window, so that infinitesimal changes of the bulk mass would immediately yield ghosts and break gauge symmetry. Radiative corrections don't do this. \item Fourth, our analysis is performed only at the linear level, with traceless transverse spin-2 modes. It may happen that scalars introduce instabilities, which we have not studied here, that undermine the de Sitter brane stability and obstruct this argument. A direct check of what happens would be very interesting. \item Fifth, in both cases of localized $4D$ massless gravitons, when $H/m \ll 1$ their coupling to brane probes is controlled by $M_{Pl}^2 \sim M_5^3/m$. For $M_5 \sim 10^{17} \, {\rm eV}$ and $m \lesssim 10^{-3} \, {\rm eV}$ this might open the road towards a rich gravitational phenomenology if there is a ghost free sector, with signatures which may be within reach of tabletop searches \cite{adelberger}. \item Sixth, it remains to be seen if the constructions which we have found really are good initial points for developing a new thrust into the phenomenological applications of modified gravity. It should be checked that our backgrounds are not infected with scalar ghosts; that they support normal $4D$ cosmology at low energies and late times; and that their low energy phenomenology is within bounds. \item Finally, even if some of the problems emerge, there remain two obvious roads for corrective actions: a) bigravity, and we have provided the de Sitter brane solutions for this framework as well, and b) warping the bulk, and considering massive gravity in AdS spaces \cite{gaba}, by importing the bent brane solutions from RS2 \cite{bent}. \end{itemize} We hope to return to some of these issues shortly. \vskip.75cm {\bf Acknowledgments}: NK would like to thank CERN Theory Division for kind hospitality in the course of this work. This work is supported in part by the DOE Grants DE-SC0009999 and DE-SC0019081. | 18 | 8 | 1808.01506 |
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1808 | 1808.09201_arXiv.txt | Current cosmological constraints on the scalar spectral index of primordial fluctuations $n_{\rm s}$ in the $\Lambda$CDM model have excluded the minimal scale-invariant Harrison-Zel'dovich model ($n_{\rm s}=1$; hereafter HZ) at high significance, providing support for inflation. In recent years, however, some tensions have emerged between different cosmological datasets that, if not due to systematics, could indicate the presence of new physics beyond the $\Lambda$CDM model. In the light of these developments, we evaluate the Bayesian evidence against HZ in different data combinations and model extensions. Considering only the Planck temperature data, we find inconclusive evidence against HZ when including variations in the neutrino number $N_{\rm eff}$ and/or the Helium abundance $Y_{\rm He}$. Adding the Planck polarization data, on the other hand, yields strong evidence against HZ in the extensions we considered. Perhaps most interestingly, Planck temperature data combined with local measurements of the Hubble parameter \citep{R16,riess2018} give as the most probable model an HZ spectrum, with additional neutrinos. However, with the inclusion of polarisation, standard $\Lambda$CDM is once again preferred, but the HZ model with extra neutrinos is not strongly disfavored. The possibility of fully ruling out the HZ spectrum is therefore ultimately connected with the solution to current tensions between cosmological datasets. If these tensions are confirmed by future data, then new physical mechanisms could be at work and an HZ spectrum could still offer a valid alternative. | Current observations of Cosmic Microwave Background (CMB) anisotropies and Large Scale Structure are in good agreement with the hypothesis that cosmic structures originated from tiny density perturbations in the early universe. The inflationary theory (see e.g. \cite{reviews} for reviews) predicts the existence of such perturbations by stretching microscopic quantum fluctuations to cosmological scales \cite{perturbations}. While the exact inflationary mechanism by which these perturbations are generated is not yet known, a general prediction is that their power spectrum can be well described by a power law $A_{\rm s} k^{n_{\rm s}}$ where $A_{\rm s}$ and $n_{\rm s}$ are defined as the primordial amplitude and spectral index while $k$ is the perturbation wavenumber measured in Mpc$^{-1}h$. Furthermore, the value of the spectral index should be nearly one, $n_{\rm s}\sim1$, reflecting the constancy of the Hubble horizon during inflation, but at the same time not exactly one, due to the dynamics of the inflaton field (again, see \cite{perturbations}). An exact value of $n_{\rm s} = 1$ is indeed not expected in inflation and would coincide with the phenomenological model proposed by Harrison \cite{HZ1}, Zel’dovich \cite{HZ2}, and Peebles and Yu \cite{HZ3}, known as Harrison-Zel'dovich (HZ) spectrum, proposed well before the formulation of inflation, and corresponding to perfect scale-invariance of the fluctuations. While it is still possible to have inflationary models with spectral index nearly identical to HZ (see e.g. \cite{fakehz}), a measurement of $n_{\rm s}$ close but different from one should be considered as a further corroboration of inflation. In the past twenty years, CMB measurements made by balloon experiments such as BOOMERanG \cite{deBernardis:2000sbo1,deBernardis:2000sbo2} and satellite experiments such as WMAP \cite{wmap1,wmap2} and, more recently, Planck \cite{planck2013,planck2015}, have provided improving constraints on $n_{\rm s}$. From the constraint of $n_{\rm s}=0.90\pm0.08$ at $68 \%$ credible interval from BOOMERanG \cite{deBernardis:2000sbo2}, we have now $n_{\rm s}=0.9645\pm0.0049$ from the Planck 2015 data release, i.e. an increase by a large factor of $\sim 16$ in the precision of the measurement and a preference over the HZ spectrum at about $7$ standard deviations. This is a success for the theory of inflation and several CMB experiments are now aiming at the measurement of polarization $B$ modes generated by gravitational waves during inflation (see e.g. \cite{kamionkowski}). It is important to stress, however, that the above constraints have been obtained indirectly, assuming the $\Lambda$CDM model based on Cold Dark Matter (CDM) and a cosmological constant ($\Lambda$). Moreover, the unprecedented sensitivity in cosmological experiments is revealing several interesting discrepancies and tensions in the $\Lambda$CDM model. For example, the Planck constraint on the Hubble constant, obtained under $\Lambda$CDM, is about $3.3$ standard deviation from the direct constraint of Riess et al. 2016 \cite{R16} (R16 hereafter), derived from direct observations. The disagreement is even larger, $3.8$ standard deviations, for the new determination of Riess et al. 2018 \cite{riess2018}. Furthermore, the Planck temperature anisotropy power spectrum data seems to suggest an amplitude of gravitational lensing larger than the one expected in the $\Lambda$CDM scenario at about $\sim 2-2.5$ standard deviations (\cite{planck2015,plancklike,planckshift,hulensing}), showing a possible internal tension in the Planck data itself. A greater amount of lensing in the Planck power spectra, parametrized by the $A_{\rm lens}$ factor (see \cite{calens}), puts the Planck cosmology in better agreement with the cosmic shear data from surveys such as the Kilo-degree survey KiDS-450 \cite{kids} and the Dark Energy Survey (DES) \cite{deswl1,deswl2}, as well as with the cosmological parameters derived from WMAP data \cite{bennett}. While the statistical significance of these tensions is mild \cite{heavens}, the possibility of extensions to the $\Lambda$CDM scenario that could explain them is clearly open. For example, an increase in the number density of relativistic particles at recombination $N_{\rm eff}$ or a change in the dark energy equation of state $w$ could both alleviate the current discrepancy on the Hubble parameter (see e.g. \cite{divalentino}). In the past years the possibility of new physics either in the dark energy sector either in the neutrino sector to solve the Hubble tension has been considered in several works (\cite{divalentino,Bernal:2016gxb,Zhao:2017cud,Archidiacono:2016kkh, Ko:2016uft,DiValentino:2017iww,Qing-Guo:2016ykt,Chacko:2016kgg, Lin:2017bhs,Sola:2017znb,Karwal:2016vyq,Brust:2017nmv,Prilepina:2016rlq, Yang:2017amu,Zhao:2017urm,Zhang:2017idq,DiValentino:2017rcr,DiValentino:2017oaw}). It is therefore timely to investigate the robustness of the conclusion that the HZ spectrum is ruled out while considering extended cosmological scenarios, beyond $\Lambda$CDM. A similar analysis has been already performed in recent papers (see e.g. \cite{Benetti:2017juy,Benetti:2017gvm,Benetti:2013wla,Pandolfi:2010dz}). Here we extend these previous analyses by including more data (for example, the Planck polarization CMB data), by considering more parameter extensions and by using a different approach in calculating Bayesian evidence using the MCEvidence code described in \cite{fantaye}. Moreover, when computing Bayesian evidence we will compare the viability of the HZ spectrum not only with respect to $\Lambda$CDM but also to its extensions. As we will see, a crucial point in this investigation is that an HZ model has $n_{\rm s}=1$, i.e. one parameter fewer than standard $\Lambda$CDM. The HZ model is therefore less complicated (from the point of view of the number of parameters) and this may lead to a higher Bayesian Evidence when compared with models where $n_{\rm s}$ is an additional parameter and which produce similar fits to the data. Indeed, Bayesian Evidence weights the simplicity of the model with the Occam factor, the inverse factor by which the prior space collapses when the data arrive. The paper is structured as follows: in the next section we describe the data analysis method, in Section III we discuss the results and in Section IV we present conclusions. | In this paper we have discussed the agreement of a Harrison-Zel'dovich primordial power spectrum with cosmological data under the assumption of extended cosmological scenarios motivated by tensions between current cosmological datasets. This is an important analysis since having very strong evidence against HZ even in extended scenarios would further support inflation. As already pointed out in the literature, we have shown that an HZ spectrum, in the framework of $\Lambda$CDM, is indeed strongly disfavored by Planck temperature and polarization data with very strong evidence against it. However, focusing just on Planck TT data, we have found no significant evidence against HZ when considering variations in the neutrino number $N_{\rm eff}$, in the Helium abundance $Y_{\rm He}$ and in a combination of the two. Furthermore we have found even a positive evidence for HZ with respect to $\Lambda$CDM when R16 is included. The Planck TT result changes with the inclusion of polarization data, which improves the determination of $N_{\rm eff}$, producing now from Planck TTTEEE data strong evidence against HZ with respect to $\Lambda$CDM+$N_{\rm eff}$ and very strong evidence against HZ within $\Lambda$CDM. This is mitigated by the inclusion of R16 data. From the Planck TTTEEE+R16 dataset we found only positive evidence against HZ with respect to $\Lambda$CDM and inconclusive evidence with respect to $\Lambda$CDM+$N_{\rm eff}$ and $\Lambda$CDM+$Y_{\rm He}$. If we include information from BAO, we have found very strong evidence against HZ in all cases with the exception of the $\Lambda$CDM+$N_{\rm eff}$ scenario. Therefore, when considering the $\Lambda$CDM+$N_{\rm eff}$ scenario we can state that R16 and BAO data have opposite effects in ruling out HZ. R16 is in someway reducing the discrepancy with HZ while BAO data increases it. If we include information from cosmic shear, we have found from Planck TT data very strong evidence against HZ assuming $\Lambda$CDM but no significant evidence against HZ in the case of a $\Lambda$CDM+$A_{\rm lens}$ scenario. However, the inclusion of Planck polarization data again works against HZ and we found very strong evidence against HZ from Planck TTTEEE+WL data even when allowing $A_{\rm lens}$ to vary. We have also investigated if further parameter extensions could alter the conclusions. When polarization data are included, there is always a very strong evidence against these extensions with respect to $\Lambda$CDM due to the increased number of parameters, but within these extended parameter frameworks, an HZ spectrum is not yet ruled out, with strong evidence in favor of it when considering the Planck TTTEEE+R16 dataset and the Extended-$10$ scenario. The possibility of fully ruling out the HZ spectrum with very strong evidence is therefore ultimately connected with the solution to the current tension on the Hubble parameter between Planck and R16. If the tension is confirmed by future data, then new physical mechanisms could be at work and an HZ spectrum could still offer a possible alternative. \ | 18 | 8 | 1808.09201 |
1808 | 1808.10195_arXiv.txt | {We report on the discovery by the {\em Nuclear Spectroscopic Telescope Array} (\nustar{}) and the Neutron Star Interior Composition Explorer (\nicer{}) of the accreting millisecond X-ray pulsar \igr{}, detecting coherent X-ray pulsations around 527.4\,Hz (1.9\,ms) with a clear Doppler modulation. This implies an orbital period of $\sim 8.8$ hours and a projected semi-major axis of $\sim1.23$ lt-s. From the binary mass function, we estimate a minimum companion mass of $0.42$ M$_{\odot}$, obtained assuming a neutron star mass of 1.4 M$_\odot$ and an inclination angle lower than 60 degrees, as suggested by the absence of eclipses or dips in the light-curve of the source. The broad-band energy spectrum is dominated by Comptonisation of soft thermal seed photons with a temperature of $\sim 0.7$\,keV by electrons heated to 21\,keV. We also detect black-body-like thermal direct emission compatible with an emission region of a few kilometers and temperature compatible with the seed source of Comptonisation. A weak Gaussian line centered on the iron K$\alpha$ complex can be interpreted as a signature of disc reflection. A similar spectrum characterises the \nicer{} spectra, measured during the outburst fading. } | \label{sec:introduction} Accreting, rapidly-rotating neutron stars (NS) in low mass X-ray binaries have been extensively investigated for almost two decades. This class of objects, also known as accreting millisecond X-ray pulsars (AMXPs), includes at the moment 21 sources with spin periods ranging between 1.7\,ms and 9.5\,ms \citep[see][for extensive reviews]{Burderi13,Patruno12b,Campana2018a}. The characteristic short spin periods observed in AMXPs are the result of long-lasting mass transfer from an evolved sub-Solar companion star via Roche-lobe overflow onto a slow-rotating NS \citep[{\it recycling scenario};][]{Alpar82}, making them the progenitors of rotation-powered millisecond pulsars shining from the radio to the gamma-ray band. Almost a third of the AMXPs are \emph{ultra-compact} binary systems (P$_\mathrm{orb} < 1$ hrs), while the rest show on average short orbital periods (P$_\mathrm{orb} < 12$ hrs), except for the intermittent pulsar Aql\,X$-$1 \citep{Casella08} with $P_\mathrm{orb}\sim18$ hrs \citep{Welsh2000a}. Short orbital periods suggest small low-mass companion stars, consistent with donor masses on average <0.2~M$_{\odot}$. Here, we report on the detection of millisecond X-ray pulsations from \igr{}, an X-ray transient first detected by the INTernational Gamma-Ray Astrophysics Laboratory (\inte{}) during a Galactic Center scanning on 2018 August 10 \citep{Ducci2018aa}. An archival search in the Neil Gehrels Swift Observatory (\swift{}) Burst Alert Telescope data revealed the source to be active since 2018 July 22 \citep{Krimm2018aa}. Pointed \swiftxrt{} observations of the source region, on 2018 August 12, revealed a point-like X-ray source and determined its precise X-ray position \citep{Bozzo2018aa}, which was refined by a \chandra{} observation on 2018 August 23 to be R.A.=$17^h 59^m 02.83^s$ Decl.=$-23^\circ 43' 10.2\arcsec$ (J2000) with an astrometric uncertainty of 0.6\arcsec{} \citep{Nowak2018aa}. On 2018 August 14, the Australia Telescope Compact Array (\atca{}) detected \igr{} with a flux density $S_\nu = 1.09\pm0.02$ $\mu$Jy and $S_\nu = 1.14\pm0.02$ $\mu$Jy (at 68\% c.l.) at 5.5 GHz and 9.0 GHz, respectively, at a position R.A. = $17^h 59^m 02.86^s \pm 0.04^s$ Decl.=$-23^{\circ} 43' 08.3\arcsec \pm 0.1\arcsec$, consistent with the X-ray determinations \citep{Russell2018aa}. In this letter, we describe a coherent timing analysis of the \nustar{} and \nicer{} observations that provided the pulsar spin period and binary ephemeris. We also report on the analysis of the X-ray spectral modelling obtained from \nustar{}, \swift{}, \inte{}, and \nicer{} data. \section[]{Observations and data reduction} \igr{} was observed by IBIS/ISGRI % onboard the INTEGRAL satellite from 2018 August 10 at 15:50 to August 11 at 12:30 UT, for a total exposure time of 66\,ks. We performed reduction and data analysis using the off-line science analysis (OSA) software provided by the \inte{} Science Data Centre. We produced a mosaic image from the combination of the individual images of the available data set, where the source was detected with a significance $>$7$\sigma$ in the 20$-$80\,keV energy band. We extracted the average IBIS/ISGRI spectrum in 8 bins from 25 to 150 keV with equal logarithmic spacing. No JEM-X data were available due to the source location at the edge of its field of view. \nustar{} observed \igr{} (Obs.ID. 90401331002) on 2018 August 13 starting from 22:36 UT for a total exposure of $\sim30$ ks. We performed standard screening and filtering of the events using the \nustar{} data analysis software (\textsc{nustardas}) from \textsc{Heasoft} version 6.24. We extracted source events from a circular region of radius 80\arcsec{} centered on the source position. Due to straylight we extracted the background with a similar extraction area but located in a region far from the source with similar degree of stray-light contamination. The average source count rate per instrument is $\sim9$ counts/s in the energy range 3$-$80 keV. We did not detect any Type-I thermonuclear burst during the observation. We corrected for spacecraft clock drift applying the up-to-date clock correction file (version 84, valid up to 2018-08-14). \swift{} observed \igr{} (Obs.ID. 00010804002) on 2018 August 14 from 00:38 UT for a total of $\sim0.6$ ks with \swiftxrt{} operated in photon counting mode. We reduced and processed the XRT data with \textsc{xrtpipeline} version 0.13.4, extracting source events from a circular region of radius 64\arcsec. We estimated a source count rate of $\sim{1}$ cts/s above the pile-up threshold \citep[see, e.g.][]{Romano2006aa}. Thus, we extracted the source spectrum using an annular region centered at the source position with inner and outer radius of 10\arcsec{} and 64\arcsec, respectively. Similarly, we extracted the background spectrum from an annular region with inner and outer radius of 102\arcsec{} and 230\arcsec, respectively. \nicer{} observed \igr{} on 2018 August 15 from 00:00 to 14:08 UT for a total exposure of $\sim 7.3$\,ks (Obs.ID. 1200310101, hereafter \nicer{}-1), on August 18 from 02:08 to 03:56 UT (exposure of $\sim1.5$\,ks, Obs.ID. 1200310102, \nicer{}-2), on August 23 from 00:58 to 22:57 UT (exposure of $\sim11.5$\,ks, Obs.ID. 1200310103, \nicer{}-3) and on August 24 from 01:51 to 14:44 UT (exposure of $\sim7$\,ks, Obs.ID. 1200310104, \nicer{}-4). We filtered events in the 1--12\,keV band applying standard screening criteria with \textsc{NICERDAS} version 4.0. We removed short intervals showing background flaring in high geomagnetic latitude regions. The spectral background was obtained from blank-sky exposures. We did not detect any Type-I thermonuclear burst during the observations. | \label{sec:discussion} We reported on the newly discovered AMXP \igr{}, for which we detected coherent X-ray pulsations at $\sim527$~Hz in the \nustar{} and \nicer{} observations performed almost 25 days from the beginning of the outburst, with a pulse fraction of 15\%. We modelled the NS spin frequency drift as the Doppler shift induced by the binary orbital motion, discovering the binary nature of the system, characterised by an orbital period of almost 8.8 hours, very similar to the intermittent AMXP SAX J1748.9$-$2021 \citep[see, e.g.][]{Altamirano2008a, Sanna2016a} and the eclipsing AMXP SWIFT J1749.4$-$2807 \citep[see, e.g.][]{Markwardt2010aa, Altamirano2011a, Ferrigno2011a}. \noindent The analysis of the \nustar{} pulse phase residuals revealed the presence of a large spin-up derivative ($2.6\times 10^{-10}$ Hz/s) and an oscillation close to twice the satellite orbital period. We suggest that both effects are associated with the time drift of the internal clock instrument \citep[see, e.g.][]{Madsen15}. Similar spurious frequency derivatives have been reported for \nustar{} observations of AMXPs such as MAXI\,J0911$-$655 \citep{Sanna2017a}, SAX J1808.4$-$3658 \citep{Sanna2017ab} and IGR\,J00291+5934 \citep{Sanna2017b}. Also the large discrepancy on the spin frequency (($\sim1\times 10^{-4}$ Hz) between \nustar{} and \nicer{} is a direct consequence of the \nustar{} clock issue. These considerations are reinforced by the analysis of \nicer{} observations, which does not evidence any significant frequency drift. A spin-up frequency derivative of (2.0$\pm$1.6)$\times 10^{-13}$\,Hz/s is observed from the phase-coherent timing analysis of the \nicer{} observations. For a broad-band (0.1--100 keV) absorbed flux of $\sim7\times10^{-10}$ erg/s/cm$^2$ and a source distance of 8.5 kpc \citep[assumed near the Galactic Center, see, e.g.][]{Kerr1986aa}, we estimate an accretion rate of $\dot{M}\simeq5.2\times10^{-10}$ M$_{\odot}$/yr (for a NS radius and mass of 1.4\,M$_{\odot}$ and 10 km, respectively). Assuming the accretion disc to be truncated at the co-rotation radius, the observed mass accretion rate yields a maximum spin-up derivative of a few $10^{-13}$ Hz/s, fully consistent with the observed one. % A rough estimate of the NS dipolar magnetic field can be obtained by assuming the condition of spin equilibrium for the X-ray pulsar. The magnetic field can then be estimated as: \begin{equation} \label{eq:spineq} B=0.63\,\zeta^{-7/6}\left(\frac{P_{\text{spin}}}{2\text{ms}}\right)^{7/6}\left(\frac{M}{1.4M_{\odot}}\right)^{1/3}\left(\frac{\dot{M}}{10^{-10}M_{\odot}/\text{yr}}\right)^{1/2}10^8 \text{G}, \end{equation} where $\zeta$ represents a model-dependent dimensionless factor (between 0.1--1) corresponding to the ratio between the magnetospheric radius and the Alfv\'en radius \citep[see, e.g.,][]{Ghosh79a,Wang96}, $P_{\text{spin}}$ is the pulsar spin period in ms and $M$ is the NS mass. Assuming a 1.4 M$_\odot$ NS and the value of $\dot{M}$ reported above, we obtain a range for the dipolar magnetic field of $1.4\times10^8<B<8\times 10^{9}$ G, consistent with the average magnetic field of known AMXPs \citep[see, e.g.][]{Mukherjee2015}. From the NS mass function $f(m_2, m_1, i)\sim1.5 \times 10^{-2}$~M$_{\odot}$, we can constrain the mass of the companion star. Since neither total eclipses, nor dips, have been observed in the light curve, we can assume a binary inclination lower than 60 degrees % \citep[see, e.g.][]{Frank02}. As shown in Fig.~\ref{fig:mass}, the upper limit on the inclination angle (represented in blue) allows us to limit the companion star mass $m_2 \gtrsim $0.42~M$_{\odot}$ (for a 1.4~M$_{\odot}$ NS), which increases up to $m_2 \gtrsim 0.52$~M$_{\odot}$ if we consider a 2~M$_{\odot}$ NS. Introducing the contact condition ($R_2\approx R_{L2}$) required to activate Roche-Lobe overflow, we can express the donor radius as a function of its mass as $R_2\simeq 0.87\,m_2^{1/3}\,P_\mathrm{orb,9h}^{2/3}$ R$_{\odot}$, where $m_2$ is the companion mass in units of M$_{\odot}$ and $P_\mathrm{orb,9h}$ represents the binary orbital period in units of 9 hours. In Fig.~\ref{fig:mass}, we report the companion mass-radius relation (black solid line) assuming a 1.4 M$_{\odot}$ NS. For comparison, we show numerical simulated mass-radius relations for Zero-Age Main Sequence stars (ZAMS) \citep[purple crosses; see, e.g.][]{Tout1996aa}, as well as isochrones for stars aged 8 (red diamonds) and 12\,Gyr \citep[blue circles; see, e.g.][]{Girardi2000aa}. From the intersections with the mass-radius companion curve, we can infer that the donor is compatible with either a ZAMS with mass $\sim1.1$ M$_\odot$ (corresponding to an inclination angle of $i\sim24$ degrees) or an old main sequence star with mass 0.85$-$0.92 M$_\odot$ ($i$ ranging between $28$ and $30$ degrees) for a star age between 8 and 12\,Gyr. We note, however, that the \textit{a priori} probability of observing a binary system with inclination $i\leq 30$ degrees is of the order of 13\%. Mass values for which the main sequence radius is smaller than the companion Roche-lobe could still be acceptable if we consider the possibility of a bloated donor star. In that case, the thermal timescale ($GM^2_2/R_2 L_2$) should be much larger than the evolutionary timescale ($M_2/\dot{M_2}$). \begin{figure} \includegraphics[width=0.46\textwidth]{mass_radius_companion} \caption{Radius-mass plane showing the size constraints on the companion star Roche-Lobe of \igr{} (black solid line) obtained from the orbital parameters of the neutron star. The hatched region represents the constraints on the companion mass from the binary mass function, while the blue area defines the mass constraints for inclination angles between 60 and 90 degrees. The other curves represent theoretical mass-radius relations for Zero-Age Main Sequence stars (purple crosses) and isochrones for stars with age of 8 (red diamonds) and 12\,Gyr (blu circles). The top x-axes represents the corresponding binary inclination angle in degrees assuming a 1.4 M$\odot$. } \label{fig:mass} \end{figure} Finally, the broad-band energy spectrum of \igr{} is well described by an absorbed soft black-body like component ($kT\sim 0.8$ keV) with relatively small emitting area compatible with emission from the neutron star surface (or part of it) plus a Comptonised component ($\Gamma \sim 1.8$) with a seed photon temperature compatible with the soft thermal component. The source spectral properties are consistent with other AMXPs observed in the hard state \citep[see, e.g.][]{Falanga05a,Gierlinski2005a, Papitto09, Papitto2013a,Sanna2017a,Sanna2017b}. We found marginal evidence ($\sim4\sigma$, based on an F-test) of a weak emission line compatible with the iron K-$\alpha$ transition. Even if marginally significant, its introduction removes positive residuals around the expected energy and such lines are not unusual for this kind of sources \citep[see, e.g.][]{Papitto09,Papitto2013a, Sanna2017a, Sanna2017b}. From Tab.~\ref{tab:spectral_fit}, we note that at later times, when the source has a re-brightening, the additional black body seems to disappear, while the asymptotic Comptonisation power-law index increases. This might be due to more effective cooling of the seed photons by a thicker accretion stream above the stellar surface. The discovery of another transient by \inte{} and its characterisation as the 22$^\mathrm{nd}$ accreting millisecond pulsar by \nustar{} and \nicer{} enriches the census of these key objects in the understanding of the late stages of stellar evolution. | 18 | 8 | 1808.10195 |
1808 | 1808.10689_arXiv.txt | In a dual-frequency liquid crystal (DFLC), when the frequency of the applied voltage is more than a critical value ($f_c$), the dielectric anisotropy of the material changes from positive to negative. This causes the director to switch its orientation from parallel to the field (for $f < f_c$), to perpendicular to it ($f > f_c$). Hence DFLC can be used in modulating the light by switching the frequency of an externally applied voltage. We present in this work about application of DFLCs in full Stokes polarimetery. A polarization modulator has been worked out based on two DFLCs and two static retarders. The combination of DFLCs' switching and static retarders are chosen such that more or less equal weightage is given to all the Stokes parameters. Initial results on the optimization of position angles of the modulators are presented towards the goal of achieving polychromatic modulator in the wavelength range 600-900 nm. | \label{sec:intro} % Accurate information on the magnetic field, simultaneously at different heights in the solar atmosphere is required to understand many physical processes which take place on the Sun such as explosive events (flares and CMEs), chromospheric and coronal heating, solar wind acceleration and etc. Multi-line spectropolarimetry is a powerful observational tool in remote sensing the magnetic field through Zeeman or Hanle diagnostics for this purpose. Magnetic field measurements at the photosphere have become more or less routine but a similar level of maturity is yet to be achieved with respect to the measurements of the chromospheric magnetic fields\cite{lagg15}. Some of the reasons are the polarization signal in the spectral lines formed in the chromosphere is low (in the order of $10^{-3}$ or less) and interpreting the measurements is challenging as NLTE effects have to be taken into account while modeling the spectral lines\cite{delacruzrodriguez17}. In ground based observations seeing induced spurious polarization is a major obstacle in achieving high precision in polarization measurements. This also known as seeing induced cross-talk \cite{lites87} is caused when consecutive measurements are combined to get the Stokes parameters. A dual-beam setup, in which orthogonally polarized beams are recorded simultaneously on two different detectors or on two different pixels of the same detector, is widely being used for reducing the seeing induced cross-talk. However, dual-beam polarimetry suffers from differential gain effects which is limiting the polarimetric sensitivity to $\approx 10^{-3}$ \cite{snik14}. Moreover, dual-beam setup only helps in reducing the cross-talk from Stokes-$I$ to Stokes-$Q$, $U$ and $V$ and the cross-talk among Stokes~$Q$, $U$ and $V$ still remains. Another way of reducing seeing induced cross-talk is to carry out the measurements with fast modulation. Increase in modulation frequency systematically reduces seeing induced cross-talk \cite{lites87,krishnappa12}. Various modulators are being used such as Piezo-elastic modulators, Liquid Crystal Variable Retarders (LCVRs), Ferro-electric Liquid Crystals (FLCs) as well as rotating waveplate towards achieving fast modulation. Each of these modulators have their own pros and cons (see for e.g. \citenum{snik14}). \citenum{golovin03} and \citenum{Nie06} have shown that the Dual-Frequency Liquid Crystals (DFLCs) can be used as electrically switchable retarders by switching the LC drive frequency. We, in this paper explore DFLCs as potential fast modulators in the context of full Stokes polarimetry. Some of the properties of DFLCs' that motivated us to explore them as modulators are: 1. They switch faster than conventional LCVRs, 2. Unlike FLCs their apertures can be quite large. FLC sizes are limited because they are vulnerable to mechanical stresses which cause defects across the aperture of FLC. | Keeping in view of the potential application of DFLCs in polarimetry as they switch faster than the conventional LCVRs and the apertures can be much larger than the FLCs, a full Stokes polarization modulator based on DFLCs has been worked out. The proposed modulator has two DFLCs interlaced between two static retarders. The modulation scheme presented in this paper is very close to a balanced scheme with 70\% efficiency for Stokes-$Q$ and 50\% efficiency for Stokes-$U$ and $V$. While working out a modulation scheme we have assumed that the retardance of a DFLC varies between 0 (for $f<f_c$) and a finite value ($\delta$: for $f>f_c$). In practice, the molecules close to the surface may not switch completely due to strong anchoring to the substrate plates because of which the retardance may not be completely zero. While designing a modulator this aspect has to be taken into account. A polychromatic design of the modulator based on DFLCs has been presented. It has been found that by optimizing the position angles and the retardances, it is possible to achieve a polychromatic modulator very similar to those based on FLCs \cite{gisler03,tomczyk10} or multiple waveplates \cite{snik12}. The optimization method, which is a direct search method, presented in this paper is very time consuming. We are in the process of adopting a more efficient method for finding the optimum position angles and the retardances of modulator optics. | 18 | 8 | 1808.10689 |
1808 | 1808.10640_arXiv.txt | We study the evolution of binary systems of Ultra-luminous X-ray sources and compute their optical emission assuming accretion onto a black hole via a non standard, advection-dominated slim disc with an outflow. We consider systems with black holes of $20M_{\odot}$ and $100M_{\odot}$, and donor masses between $8M_{\odot}$ and $25M_{\odot}$. Super-critical accretion has considerable effects on the optical emission. The irradiating flux in presence of an outflow remains considerably stronger than that produced by a standard disc. However, at very high accretion rates the contribution of X-ray irradiation becomes progressively less important in comparison with the intrinsic flux emitted from the disc. After Main Sequence the evolutionary tracks of the optical counterpart on the colour-magnitude diagram are markely different from those computed for Eddington-limited accretion. Systems with stellar-mass black holes and $12-20 M_{\odot}$ donors accreting supercritically are characterized by blue colors (F450W -- F555W $\simeq - 0.2 : +0.1$) and high luminosity ($M_{V} \simeq - 4 : - 6.5$). Systems with more massive black holes accreting supercritically from evolved donors of similar mass have comparable colours but can reach $M_V \simeq - 8$. We apply our model to NGC 1313 X-2 and NGC 4559 X-7. Both sources are well represented by a system accreting above Eddington from a massive evolved donor. For NGC 1313 X-2 the agreement is for a $\sim 20M_{\odot}$ black hole, while NGC4559 X-7 requires a significantly more massive black hole. | Ultra-luminous X-ray Sources (ULXs) are non nuclear point-like extragalactic X-ray sources with bolometric luminosity higher than the Eddington limit for a 10$M_{\odot}$ black hole ($L_{Edd} \sim 2 \times 10^{39}$ erg s$^{-1}$; \citealt{1989ARA&A..27...87F}). The majority of them are X-ray binaries with a neutron star (NS) or a black hole (BH), most probably accreting above the Eddington limit. In the past years, there has been an extensive debate on the possibility that the compact object is a stellar or a massive stellar BH accreting above Eddington (\citealt{2009MNRAS.400..677Z,2009MNRAS.395L..71M,2010ApJ...714.1217B,2011NewAR..55..166F}), or an Intermediate mass Black Hole accreting sub-Eddington \citep{1999ApJ...519...89C}. The recent discovery of pulsating ULXs (\citealt{2014Natur.514..202B,2016ApJ...831L..14F,2017Sci...355..817I,2017MNRAS.466L..48I}) led to the conclusion that the accretor can in fact also be a NS. In the last 15 years a significant number of stellar optical counterparts of ULXs have been identified and progressively investigated in detail by several authors (e.g. \citealt{2002ApJ...580L..31L,2004ApJ...603..523Z,2005MNRAS.356...12S, 2007ApJ...658..999M,2008A&A...486..151G,2011ApJ...734...23G}). \cite{2011ApJ...737...81T} and \cite{2013ApJS..206...14G} performed an homogeneous reanalysis of all the available {\it Hubble Space Telescope} ({\it HST}) photometric data of stellar counterparts of ULXs. In the majority of the cases, they appear to be hosted in young stellar environments (e.g. \citealt{2006ApJ...641..241R,2006IAUS..230..293P,2007ApJ...661..165L,2008A&A...486..151G,2011ApJ...734...23G}) and have magnitudes and colours consistent with those of O-B type stars. As for Galactic X-ray binaries, the optical emission of ULX binaries originates from the donor star and the outer regions of the accretion disc. The X-ray flux produced in the innermost regions of the disc can intercept the outer regions and be thermalized, resulting in an enhancement of the optical-IR flux (e.g. \citealt{1993PASJ...45..443S} for standard accretion onto a Schwarzschild BH). The peculiar character of ULX binaries is that X-ray irradiation could be dominant also for massive donors.\\ Comparison of stellar evolutionary tracks of ULXs with the photometric properties of their optical counterparts on the colour-magnitude diagram may be used to constrain the masses of their donor stars (e.g. \citealt{2005MNRAS.356...12S,2005MNRAS.362...79C,2007MNRAS.376.1407C}). \cite{2008MNRAS.386..543P,2010MNRAS.403L..69P} (hereafter PZ and PZ2, respectively) produced evolutionary tracks of ULXs binary systems accreting onto a BH via a standard self-irradiated accretion disc. They showed that a massive donor is needed to fuel persistent ULXs at the required rates (see also \citealt{2005MNRAS.364..344P,2005MNRAS.356..401R}) and provided constrains on both the donor and the BH. Several ULXs are also associated with very extended optical emission nebulae, that give important information on their energetics and lifetime \citep{2002astro.ph..2488P,2003MNRAS.342..709R}. In this work we consider a ULX with a stellar or massive-stellar BH accreting super-Eddington. This configuration can explain some basic facts concerning the X-ray spectral components and the short-term variability at high energies observed in some ULXs (\citealt{2015MNRAS.447.3243M}) and is supported also by the detection of emission lines and blueshifted absorption lines from highly ionized Fe, O and Ne in high-resolution X-ray spectra (\citealt{2016Natur.533...64P}). Super-critical accretion was considered already in \cite{1973A&A....24..337S}, who proposed that in such conditions radiation pressure could originate an outflow from the innermost regions of the accretion disc. \cite{1988ApJ...332..646A} first studied in detail the properties of such optically thick, advection-dominated accretion discs (slim discs). More recently, supercritical accretion onto BHs has been studied by means of 2D radiation and magneto-hydro simulations, that show the formation of an advection-dominated disc and an outflow region, with powerful clumpy winds driven by radiation pressure (e.g. \citealt{2009PASJ...61..783T,2011ApJ...736....2O,2013PASJ...65...88T}). In the following we study the evolution of ULXs binary systems and compute their optical emission assuming that they accrete onto a BH via a non standard, advection-dominated slim disc with an outflow. The plan of the paper is the following. In Section 2 we summarize the model of PZ for Eddington-limited accretion in ULX binaries, which is at the base of this work. In Section 3 we describe the implementation of our model for super-Eddington accretion in ULX binaries. In Section 4 we show the evolutionary tracks of our systems in the color-magnitude diagram and analyze the results obtained with and without an outflow. We then show a preliminary application of our model to NGC 1313 X-2 and NGC 4559 X-7. Finally, in Section 5 we discuss our results and further developments of this work. | In this work we modelled the optical emission of ULXs accreting super-Eddington. At first we considered a bimodal accretion disc formed by an inner advection-dominated slim disc and an outer standard disc. Then, we included the effects of an outflow produced by radiation pressure. As noted above, the case of a pure slim disc is useful to understand the effects of supercritical accretion on the emission properties of the disc and on self-irradiation. For $\dot{m} > 10^{3}$ the outflow can completely cover the accretion disc and the evolution can no longer be followed with the present model. Super-critical accretion has considerable effects on the optical emission. The disc self-irradiation is very different from that produced in the standard case. The innermost regions do not radiate the outer ones. Two competing effects influence self-irradiation. On one side, the irradiating flux grows with $\dot{m}$. On the other side, it decreases because the size of the irradiating region diminishes. Irradiation is considerably stronger than that produced by an Eddington-limited disc, but at very high $\dot m$ it is progressively less important than the intrinsic disc and donor emission. During MS, the evolutionary tracks on the CMD obtained with our model almost overlap with those of \cite{2008MNRAS.386..543P}. The residual difference depends on the treatment of photometry and to the fact that the accretion rate can be mildly super-Eddington. On the other hand, the post MS evolution is markedly different and is characterized by two phases. Initially, when the accretion disc is not very extended, the luminosity increases with $\dot m$ and the system becomes bluer ($B-V = -0.3-0.1$). As the orbital seperation increases, the accretion disc becomes bigger, the emission becomes progressively redder and the system moves to the right on the CMD. At super-Eddington rates, the disc flux typically overcomes that produced by the donor (apart from the case of small black holes and very massive donors) and the 'optical bump' that characterizes standard self-irradiated discs disappears. We compared the predictions of our model with the {\it HST} observations of NGC 1313 X-2 and NGC 4559 X-7. We constrain the donor and the BH mass of these objects, considering as a further constraint the age of the parent population and the observed bolometric luminosity. The position of NGC 1313 X-2 on the CMD is in agreement with a $20 M_{\odot}$ BH accreting above the Eddington limit from a post-MS donor with initial mass in the range $12-15 M_{\odot}$. The orbital period of the system is $\sim 5$ days, in fair agreement with the observed one. It should be emphasized that the $20 M_{\odot}$ BH and $12-15 M_{\odot}$ donor tracks intersect the observed photometric point of X-2 because accretion is highly super-critical and the optical emission, dominated by the outer standard portion of the disc, is significantly enhanced and blue in comparison with that for Eddington-limited accretion. We now compare the results of the dedicated analysis of NGC 1313 X-2 presented by \cite{2010MNRAS.403L..69P} (PZ2) for Eddington-limited accretion with those obtained here. PZ2 found that the photometric point representing X-2 is well reproduced by a system with a $\sim 50-100 M_\odot$ BH and a MS donor of $\sim 12-15 M_\odot$ or by a system with a $\sim 20 M_\odot$ BH undergoing mass transfer from a H-shell burning donor of $\sim 12-15 M_\odot$. The orbital period of the systems that intersect X-2 on the CMD is $\sim 6$ days in the first case and $\sim 12$ days in the second case. In both cases accretion is Eddington-limited. A similar conclusion for the $\sim 20 M_\odot$ BH case was reached by \cite{2014ApJ...794....7M} who calculated the magnitudes of simulated ULX binaries evolved in young star clusters and compared them with the available photometry of several ULXs. The adopted code is that of PZ and PZ2, while the input parameters at the beginning of the Roche-lobe overflow phase (radius, mass, optical luminosity, effective temperature, and age of the donor, mass of the BH, orbital period) were provided by $N$-body simulations, that did not produce matches with systems having BH masses larger than $\sim 25 M_\odot$. In fact, besides the accretion regime, there are two other aspects to consider when comparing the results of PZ2 with our ones. First, PZ2 considered the {\it HST} ACS observations performed in 2003 (taken from \citealt{2007ApJ...658..999M}), while here we considered a longer dataset, averaging over the variability induced by the orbital motion and X-ray irradiation. Second, the conversion from {\it HST} ACS/WFC F435W and F555W filters to the standard Johnson photometric system leads to some inaccuracy, especially for variable sources (see e. g. \citealt{2005PASP..117.1049S}). We note that also \cite{2014ApJ...794....7M} used the first 2003 {\it HST} ACS photometric epoch (taken from \citealt{2013ApJS..206...14G}). Using the two 2003 {\it HST} photometric measurements adopted in PZ2, we find agreement with the tracks of $20-25 M_\odot$ donors during MS for a $100 M_\odot$ BH and the track of a $20 M_\odot$ donor at terminal age MS for a $20 M_\odot$ BH, that do not have the correct age of the parent OB association. This would rule out both Eddington-limited accretion onto a $100 M_\odot$ BH and super-Eddington accretion onto a $20 M_\odot$ BH for X-2. On the other hand, comparison with the average photometry of the 2009 {\it HST} monitoring campaign still rules out the $100 M_\odot$ BH scenario, but allows for super-Eddington accretion onto a $20 M_\odot$ BH from a H-shell burning donor of $\sim 12-15 M_\odot$. Therefore, adopting the 2009 average photometry and performing the comparison with the new tracks in the original {\it HST} photometric system is crucial to rule out the Eddington-limited $100 M_\odot$ BH scenario of PZ2 and to pinpoint the matching $20 M_\odot$ BH super-Eddington system. Letting aside the details of the photometric comparison, we note that the orbital period of the $20 M_\odot$ BH matching binary system is $\sim 12$ days for Eddington-limited accretion, while it is $\sim 5$ days for super-Eddington accretion. In fact, in order to reach a comparable optical luminosity an Eddington-limited disc has to be more extended, and hence the system has to have a longer orbital period. This would provide a further means to distinguish between Eddington-limited and super-Eddington accretion in this sytem. Unfortunately, present measurements are not sufficiently accurate to discriminate between a $\sim 6$ days irradiation-modulated orbital periodicity and a $\sim 12$ days ellipsoidally-modulated one. Also the optical counterpart of NGC 4559 X-7 has been previously analysed by PZ. The same caveat concerning the photometric transformation to the Johnson system applies also here, but is less critical. The same {\it HST} measurement of \cite{2005MNRAS.356...12S} is considered. PZ found that X-7 is reproduced by a massive or a stellar-mass BH accreting from a $30-50 M_{\odot}$ donor during the H-shell burning phase. We did not consider donors more massive than $25 M_{\odot}$ for a 20 $M_{\odot}$ BH because, after the MS, the outflow starts to engulf the binary and the model is no longer self-consistent. For less massive donors, no agreement is found because the optical emission is not sufficiently luminous. For a 100 $M_{\odot}$ BH, agreement is found for evolved donors of $15-25 M_{\odot}$, smaller than in the Eddington-limited systems of PZ owing to the fact that super-Eddington accretion makes the tracks more luminous and bluer for a given donor mass. We note that our result for NGC 1313 X-2 is consistent with the findings of \cite{2013ApJ...778..163B}, who performed a detailed analysis of the \textit{NuSTAR} and \textit{XMM-Newton} spectra of the source using a slim disc plus Comptonization model and found that they are well described by a low mass BH ($M \sim 20-30 M_{\odot}$). The results for NGC 1313 X-2 and NGC 4559 X-7 are also in agreement with the BH masses estimated by \citealt{2017MNRAS.469L..99F} using the same wind model \citep{2007MNRAS.377.1187P}. From the properties of the outflow measured in the X-rays they constrain the masses and accretion rates of NGC 1313 X-1, NGC 55 ULX and NGC 5408 X-1, finding that the BH mass is likely to be in the range $10-100 M_{\odot}$. In the future we will explore in detail the properties of all the ULXs with avaiable optical observations. We will compare them with updated evolutionary tracks covering a wider parameter space in terms of BH and donor masses. The comparison will be performed in the same photometric system used for the observations, accounting for the variability of the sources and including the optical-through-X-ray spectral energy distribution. Moreover, the case of accreting NSs will be explored in order to asses whether optical emission can help distinguishing between ULXs hosting BHs and NSs. As detecting pulsation has proven to be very difficult, it would be important to have other methods to discriminate among them. Modelling accreting NSs is made more difficult by the dynamical and radiative effects of the magnetic fields, the structure and strength of which in pulsar ULXs are unknown. At present we are working at extending our super-Eddington accretion model to the case of a non-magnetized NS, which can be accomodated with relatively little effort within the present framework. Results will be presented in a forthcoming paper. | 18 | 8 | 1808.10640 |
1808 | 1808.00785_arXiv.txt | Seven different models are applied to the same problem of simulating the Sun's coronal magnetic field during the solar eclipse on 2015 March 20. All of the models are non-potential, allowing for free magnetic energy, but the associated electric currents are developed in significantly different ways. This is not a direct comparison of the coronal modelling techniques, in that the different models also use different photospheric boundary conditions, reflecting the range of approaches currently used in the community. Despite the significant differences, the results show broad agreement in the overall magnetic topology. Among those models with \edit{significant volume currents in much of the corona}, there is general agreement that the ratio of total to potential magnetic energy should be approximately 1.4. However, there are significant differences in the electric current distributions; while static extrapolations are best able to reproduce active regions, they are unable to recover sheared magnetic fields in filament channels using currently available vector magnetogram data. By contrast, time-evolving simulations can recover the filament channel fields at the expense of not matching the observed vector magnetic fields within active regions. We suggest that, at present, the best approach may be a hybrid model using static extrapolations but with additional energization informed by simplified evolution models. This is demonstrated by one of the models. | In recent years, a number of different approaches have been developed for modelling non-potential magnetic fields in the Sun's atmosphere, based on measurements of the magnetic field on the solar surface. Non-potential means that electric currents are allowed to be present within the coronal volume, in contrast to traditional potential-field extrapolations. However, different modellers use not only different approximations for the coronal magnetic field but also different input data and boundary conditions. To date, a direct comparison of these various approaches has been lacking in the literature. With this in mind, we convened a scientific team at the International Space Science Institute in Bern, Switzerland, and we report here on the results. In this paper, we present a number of non-potential models side-by-side in a way that enables a direct comparison. Since the problem of coronal modelling is very much an active area of research, there are inevitable disagreements between the models. By highlighting the similarities and differences between different modelling approaches, and why they occur, we hope to assist the community in moving toward a single non-potential modelling approach for the corona. We would like to highlight what factors should be taken into account, and what are the biggest uncertainties in existing models. \begin{figure} \includegraphics[width=\textwidth]{druck.eps} \caption{An extreme-ultraviolet and white-light composite of the corona on 2015 March 20. The white light image is a combination of 29 exposures made from Longyearbyen, Svalbard, and aligned with sub-pixel precision using the Phase Correlation technique \citep{2009ApJ...706.1605D}. This is overlaid with a combination of 171, 193 and 211 \AA{} (red, green, blue respectively) channels from the AIA instrument on the Solar Dynamics Observatory satellite. Each of the channels were processed using Multiscale Gaussian Normalization \citep[MGN,][]{2014SoPh..289.2945M} prior to combination.} \label{fig:druckcomp} \end{figure} We have fixed a single date and time, coinciding with the total solar eclipse of 2015 March 20. Fixing a single time allows us to compare both static and time-dependent models, and we chose an eclipse date during the Solar Dynamics Observatory (SDO) era so as to maximize the available observations of the real coronal structure. Figure \ref{fig:druckcomp} shows the structure of the observed corona on that day. There are no large active regions on the visible solar disk, although there is some activity on the far side and visible above both East and West limbs. The streamer structure is relatively complex, consistent with the fact that this eclipse occurred shortly after Solar Maximum. The streamers also show an asymmetry between the north and south poles, consistent with the formation of a polar coronal hole in the south but not in the north \citep{2017SoPh..292...13P}. In terms of non-potential structure, there is a clear polar crown prominence on the north-east limb, with suggestions of a coronal cavity surrounding it. Although this is not a time of particularly high solar activity, the coronal structure is nevertheless more complex than that typically found around Solar Minimum. It is therefore quite challenging to model all of the aspects of this observed corona within the context of a single global magnetic field model. The compared models are summarized in Section \ref{sec:models}. All cover the full global solar corona, except for the polar regions in some cases. The outer boundaries of the models vary; for the comparisons in this paper we will therefore focus on the region $R_\odot\leq r\leq 2.5R_\odot$ that is covered by all of the models. Grid resolution and boundary conditions were chosen by each individual modeller. In particular, different photospheric boundary conditions were used for each model, and these differences in input data are highlighted in Section \ref{sec:models}. All models used magnetic data from the same SDO/HMI instrument, but different methods were used to reconstruct boundary maps of the full solar surface, leading to quite different photospheric magnetic fields. Owing to these differences in input data, our study should not be viewed as a direct side-by-side comparison of numerical codes for modelling the coronal magnetic field, such as (for example) the active region exercises by \citet{2008ApJ...675.1637S} and \citet{2015ApJ...811..107D}. Rather, the approach is more qualitative: to compare and contrast the results from different non-potential modelling approaches, where these approaches include the different methods of processing magnetogram input data that are characteristic of present-day coronal modelling. Through this we can assess the strengths and weaknesses of each approach. Because we only observe (usually) one side of the Sun, it is difficult to make detailed comparisons with observations using only a single snapshot such as this. Moreover, the lack of direct magnetic measurements above the photosphere is a major driver for the development of these models in the first place. Nevertheless, we are able to compare with indirect observations of the coronal magnetic field, and do so qualitatively in this paper. It is hoped that by combining all available information, we can ultimately build a ``best guess'' picture of the coronal magnetic structure during the eclipse. Following our summary of the models in Section \ref{sec:models}, the resulting coronal magnetic fields are compared in Section \ref{sec:results}, both with each other and with the indirect observations. The overall findings are discussed in Section \ref{sec:discuss}. | \label{sec:discuss} Having analysed seven different non-potential models of the coronal magnetic field on 2015 March 20, we now draw some overall conclusions. The initial impression from Figure \ref{fig:fl}, for example, is one of significant disagreement between different models. This is true particularly in regard to the overall magnetic structure. This disagreement arises from several sources: the input data used by each modeller, the coronal modelling techniques themselves, and the outer boundary conditions. There are two fundamental limitations with currently available magnetogram input, not including the differences between magnetograms from different instruments and observatories \citep{2014SoPh..289..769R}, which we avoid here by focusing on SDO/HMI. One limitation is the lack of co-temporal full surface coverage, which necessitates the use of synoptic maps that combine observations taken at different times. The different models achieve this in different ways, as described in Section \ref{sec:models}, and this leads to different maps of the magnetic field across the whole solar surface (Figure \ref{fig:br1}), with corresponding differences in coronal magnetic topology. One consequence of the use of synoptic maps is that the majority of models (except for \mf{} and \mhdcese{}) use data taken after the eclipse time, meaning that this exercise is not equivalent to a prediction of the eclipse magnetic field which could have been made in advance. The $B_r$ distribution in the \mf{} model differs particularly from the others because it uses a surface flux transport model to evolve the photospheric magnetic field over a period of months, rather than inserting magnetogram data more directly. This has the advantage of allowing the build-up of free magnetic energy in weak-field regions, but does mean that there are resulting differences in the magnetic structure. \edit{The use of synoptic data also means that the magnetogram input near the limbs -- particularly the East limb -- is out-of-date, and this can particularly affect comparisons with eclipse images. The proposed space mission to the L5 Lagrange point would greatly improve the situation at the East limb, provided that a magnetograph were included on board.} The second limitation is with vector magnetograms. Firstly, the signal-to-noise ratio remains low in the transverse components of ${\bf B}$, so that the \nlfop{}, \nlfgr{} and \ffe{} models do not reproduce the sheared magnetic fields in filament channels. And the fact that the photospheric vector magnetograms do not satisfy ${\bf j}\times{\bf B}=0$ leads to problems in particular with the \ffe{} model, preventing it from reaching equilibrium. Further refinement will be needed before this model can be of practical use for the solar corona. In future, it is hoped that this issue will improve if and when upper-chromospheric magnetogram observations become available. In the coronal volume itself, we have shown that the different models vary in their degree of non-potentiality, as measured by either electric currents or free energy. The models with greater free energy achieve this with a variety of different current distributions: currents may be concentrated in active regions (\nlfgr{}), in filament channels (\mhdmas{} and \mf{}), or may be more distributed throughout the corona (\mf{} and \mhs{}). This aspect of the models is perhaps the most difficult to calibrate against observations, since no direct observations of coronal electric currents are available. The presence of filament channels, for example, illustrates the importance of the gradual build-up of coronal electric currents over time. Although these are not reproduced in the \nlfgr{}, \nlfop{}, \mhs{} and \mhdcese{} models, this is not due to a fundamental limitation of the equations used to model the magnetic field in the corona, but due to limitations in the available boundary data. In particular, we have shown with the \mhdmas{} model how static models can be further energized by the injection of electric currents in filament channels, and this could be applied in future with the other models. This hybrid approach of informing static models with the results either from simplified time-evolving models (like \mf{}) or from additional coronal observations could well be a useful one in the absence of improved magnetogram input data. The outer boundary conditions also have a significant impact, and deserve greater attention. With the exception of \mhdcese{}, none of the models presented here couples physically to a solar wind solution beyond $2.5\,R_\odot$. This is because the increasing plasma-$\beta$ in that region no longer allows for the use of a purely magnetic model. Several of the models impose an artificial source surface at $2.5\,R_\odot$, as in the common PFSS model, and this leads to inaccuracies in the streamer structure, and potentially also the open flux. The \mf{} model instead uses a radial outflow boundary condition to mimic the effect of the solar wind, but this seems to be inflating the field too much in this particular case, at least in terms of open field footpoints (though interestingly not in the height of the streamers). The corresponding currents higher in the corona change the open-closed magnetic topology significantly. Overall, this outer boundary is an important problem that requires more sophisticated MHD modelling that includes plasma thermodynamics. Such simulations have been performed with the full-MHD version of the \mhdmas{} model \citep[e.g.,][]{2009ApJ...690..902L, 2013Sci...340.1196D}, which can describe the solar wind. All of this being said, there are also areas of broad agreement between many of the models. For example, while they have very different input grid resolutions on $r=R_\odot$, this \edit{(in itself)} does not affect the estimated open flux and topology of the heliospheric current sheet on $r=2.5\,R_\odot$, \edit{which arises rather from the differences between the coronal modelling approaches}. On $r=R_\odot$, the footpoint regions of open magnetic field show similarities in all models, and there is agreement that the strongest currents are within the active regions. Among those models with significant free magnetic energy, there is general agreement on the ratio $\E/\Ep\approx 1.4$ to $1.5$. And the locations of closed field streamers are broadly in agreement, though not their height and shape. From this study it is clear that all of the models have positive aspects that agree with observations, but other aspects that do not match so well. Much of this can be related to the distribution of electric current both within and outside of active regions. At present, nonlinear force-free extrapolations such as \nlfop{} or \nlfgr{} are best at representing the structure of active regions where reliable vector magnetic field input data are available. But accounting for the free energy outside of active regions is currently possible only with time-evolving models such as \mf{}. Yet, in these models, it is too computationally expensive to account for the full plasma thermodynamics, something that has not been considered here but is already possible in state-of-the-art full-MHD models, albeit for static configurations. What is clear is that this is an exciting time for coronal magnetic field modelling, with progress on several fronts but much still to do. Rather than simply waiting for better magnetogram data, our comparisons with currently available observations -- though qualitative -- do suggest that these indirect observational constraints could be better used to optimize the models. The challenge is to do this systematically. The ideal model would match EUV observations of filament channels and coronal loops, the positions of white-light streamers, and the locations of observed coronal holes. A more sophisticated approach would involve forward modelling of actual observed emission, but we suggest that much can already be learned from morphological comparisons. | 18 | 8 | 1808.00785 |
1808 | 1808.10331_arXiv.txt | We present ALMA Band 9 observations of the \cii 158$\mu$m emission for a sample of 10 main-sequence galaxies at redshift $z$$\sim$2, with typical stellar masses ($\log$ M$_\star$/M$_\odot \sim$10.0--10.9) and star formation rates ($\sim$35--115 M$_\odot$ yr$^{-1}$). Given the strong and well understood evolution of the interstellar medium from the present to $z=2$, we investigate the behaviour of the \cii\ emission and empirically identify its primary driver. We detect \cii\ from six galaxies (four secure, two tentative) and estimate ensemble averages including non detections. The \cii -to-infrared luminosity ratio ($L_{\rm \cii}$/$L_{\rm IR}$) of our sample is similar to that of local main-sequence galaxies ($\sim2\times10^{-3}$), and $\sim$ 10 times higher than that of starbursts. The \cii\ emission has an average spatial extent of 4 -- 7~kpc, consistent with the optical size. Complementing our sample with literature data, we find that the \cii~ luminosity correlates with galaxies' molecular gas mass, with a mean absolute deviation of 0.2 dex and without evident systematics: the \cii -to-H$_2$ conversion factor ($\alpha_{\rm \cii} \sim 30$ M$_\odot$/L$_\odot$) is largely independent of galaxies' depletion time, metallicity, and redshift. \cii~ seems therefore a convenient tracer to estimate galaxies' molecular gas content regardless of their starburst or main-sequence nature, and extending to metal-poor galaxies at low- and high-redshifts. The dearth of \cii\ emission reported for $z>6$--7 galaxies might suggest either a high star formation efficiency or a small fraction of UV light from star formation reprocessed by dust. | \label{sec:introduction} A tight correlation between the star formation rates (SFR) and stellar masses (M$_\star$) in galaxies seems to be in place both in the local Universe and at high redshift (at least up to redshift $z \sim 7$, e.g. \citealt{Bouwens2012}, \citealt{Steinhardt2014}, \citealt{Salmon2015}): the so-called ``main-sequence'' (MS; e.g. \citealt{Noeske2007}, \citealt{Elbaz2007}, \citealt{Daddi2007}, \citealt{Stark2009}, followed by many others). The normalization of this relation increases with redshift. At fixed stellar mass ($\sim 10^{10}$ M$_\odot$), $z \sim 1$ galaxies have SFRs comparable to local Luminous Infrared Galaxies (LIRGs); at $z \sim 2$ their SFR is further enhanced and they form stars at rates comparable to local Ultra Luminous Infrared Galaxies (ULIRGs). However, the smooth dynamical disk structure of high-redshift main-sequence sources, together with the tightness of the SFR -- M$_\star$ relation, disfavour the hypothesis that the intense star formation activity of these galaxies is triggered by major mergers, as by contrast happens at $z = 0$ for ULIRGs (e.g., \citealt{Armus1987}, \citealt{Sanders1996}, \citealt{Bushouse2002}). The high SFRs in the distant Universe seem instead to be sustained by secular processes (e.g. cold gas inflows) producing more stable star formation histories (e.g., \citealt{Noeske2007}, \citealt{Dave2012}). Main sequence galaxies are responsible for $\sim 90$\% of the cosmic star formation rate density (e.g. \citealt{Rodighiero2011}, \citealt{Sargent2012}), whereas the remaining $\sim$ 10\% of the cosmic SFR density is due to sources strongly deviating from the main sequence, showing enhanced SFRs and extreme infrared luminosities. Similarly to local ULIRGs, star formation in these starburst (SB) galaxies is thought to be ignited by major merger episodes (e.g., \citealt{Elbaz2011}, \citealt{Nordon2012}, \citealt{Hung2013}, \citealt{Schreiber2015}, \citealt{Puglisi2017}). Throughout this paper we will consider as starbursts all the sources that fall $> 4$ times above the main sequence \citep{Rodighiero2011}. To understand the mechanisms triggering star formation, it is crucial to know the molecular gas reservoir in galaxies, which forms the main fuel for star formation (e.g. \citealt{Bigiel2008}), at the peak of the cosmic star formation history ($z \sim 2$). Due to their high luminosities, the starbursts have been the main sources studied for a long time, although they only represent a small fraction of the population of star-forming galaxies. Only recently it has been possible to gather large samples of $z \sim$ 1 -- 2 main-sequence sources and investigate their gas content thanks to their CO and dust emission (e.g. \citealt{Genzel2010}, \citealt{Carilli2013}, \citealt{Tacconi2013}, \citealt{Combes2013}, \citealt{Scoville2015}, \citealt{Daddi2015}, \citealt{Walter2016}, \citealt{Dunlop2017}). Observing the CO transitions at higher redshift, however, becomes challenging since the line luminosity dims with cosmological distance, the contrast against the CMB becomes lower (e.g. \citealt{DaCunha2013}), and it weakens as metallicity decreases (as expected at high $z$). Some authors describe the latter effect stating that a large fraction of molecular gas becomes ``CO dark'', meaning that the CO line no longer traces H$_2$ (e.g. \citealt{Wolfire2010}, \citealt{Shi2016}, \citealt{Madden2016}, \citealt{Amorin2016}, \citealt{Glover2016}) and therefore the CO luminosity per unit gas mass is much lower on average for these galaxies. Similarly, the dust content of galaxies decreases with metallicity and therefore it might not be a suitable tracer of molecular gas at high redshift. An alternative possibility is to use other rest-frame far-infrared (IR) lines instead. Recently \ci~ has been proposed as molecular gas tracer (e.g., \citealt{Papadopoulos2004}, \citealt{Walter2011}, \citealt{Bothwell2016}, \citealt{Popping2017}), although it is fainter than many CO transitions and this is still an open field of research. Alternatively the \cii~ $^2P_{3/2}$ -- $^2P_{1/2}$ transition at 158 $\mu$m might be a promising tool to investigate the gas physical conditions in the distant Universe (e.g. \citealt{Carilli2013}). \cii~ has been identified as one of the brightest fine structure lines emitted from star-forming galaxies. It has a lower ionization potential than \hi~ (11.3 eV instead of 13.6 eV) and therefore it can be produced in cold atomic interstellar medium (ISM), molecular, and ionized gas. However, several studies have argued that the bulk of galaxies' \cii~ emission originates in the external layers of molecular clouds heated by the far-UV radiation emitted from hot stars with $\gtrsim$ 60 -- 95\% of the total \cii~ luminosity arising from photodissociation regions (PDRs, e.g. \citealt{Stacey1991}, \citealt{Sargsyan2012}, \citealt{Rigopoulou2014}, \citealt{Cormier2015}, \citealt{Diaz-Santos2017}, \citealt{Croxall2017}). In particular, \cite{Pineda2013} and \cite{Velusamy2014} showed that $\sim$ 75\% of the \cii~ emission in the Milky Way is coming from the molecular gas; this is in good agreement with simulations showing that 60\% -- 85\% of the \cii~ luminosity emerges from the molecular phase (\citealt{Olsen2017}, \citealt{Accurso2017b}, \citealt{Vallini2015}). There are also observational and theoretical models suggesting that \cii~ is a good tracer of the putative ``CO dark'' gas. The main reason for this is the fact that in the outer regions of molecular clouds, where the bulk of the gas-phase carbon resides, H$_2$ is shielded either by dust or self-shielded from UV photodissociation, whereas CO is more easily photodissociated into C and C$^+$. This H$_2$ is therefore not traced by CO, but it mainly emits in \cii~ (e.g. \citealt{Maloney1988}, \citealt{Stacey1991}, \citealt{Madden1993}, \citealt{Poglitsch1995}, \citealt{Wolfire2010}, \citealt{Pineda2013}, \citealt{Nordon2016}, \citealt{Fahrion2017}, \citealt{Glover2016}). Another advantage of using the \cii~ emission line is the fact that it possibly traces also molecular gas with moderate density. In fact, the critical density needed to excite the \cii~ emitting level through electron impacts is $>$ 10 particle/cc ($\sim$ 5 - 50 cm$^{-3}$). For comparison, the critical density needed for CO excitation is higher ($\sim$ 1000 H/cc), so low-density molecular gas can emit \cii, but not CO (e.g. \citealt{Goldsmith2012}, \citealt{Narayanan2017}). This could be an important contribution given the fact that $\sim$ 30\% of the molecular gas in high-redshift galaxies has a density $<$ 50 H/cc \citep{Bournaud2017}, although detailed simulations of the \cii~ emission in turbulent disks are still missing and observational constraints are currently lacking. The link between the \cii~ emission and star-forming regions is further highlighted by the well known relation between the \cii~ and IR luminosities ($L_{\mathrm{\cii}}$ and $L_{\mathrm{IR}}$ respectively, e.g. \citealt{deLooze2010}, \citealt{deLooze2014}, \citealt{Popping2014}, \citealt{Herrera-Camus2015}, \citealt{Popping2016}, \citealt{Olsen2016}, \citealt{Vallini2016}), since the IR luminosity is considered a good indicator of the SFR \citep{Kennicutt1998}. However, this relation is not unique and different galaxies show distinct $L_{\mathrm{\cii}}/L_{\mathrm{IR}}$ ratios. In fact, \begin{landscape} \begin{figure} \includegraphics[width=1.35\textwidth]{figures/multi_panel_hst_radio.pdf} \caption{\textit{HST} and ALMA observations of our sample galaxies. For each source we show the \textit{HST}/WFC3 image taken with the F160W filter, the stellar mass map, the star formation rate map, and the radio observations taken with VLA. The overplotted black contours, when present, show the $> 3\sigma$ \cii~ emission. The green contours indicate the $> 3\sigma$ 850 $\mu$m continuum. The color scale in all panels is linear and it is chosen to show galaxies' features at best. The units of the color bars are the following: counts s$^{-1}$ for F160W, 10$^{9}$ M$_\odot$ for the stellar mass maps, M$_\odot$ yr$^{-1}$ for the SFR maps, and Jy for the radio.} \label{fig:hst_panels} \end{figure} \end{landscape} \noindent in the local Universe main-sequence sources show a constant $\langle L_{\mathrm{\cii}}/L_{\mathrm{IR}}\rangle \sim $ 0.002 -- 0.004, although with substantial scatter (e.g., \citealt{Stacey1991}, \citealt{Malhotra2001}, \citealt{Stacey2010}; \citealt{Cormier2015}, \citealt{Smith2017}, \citealt{Diaz-Santos2017}). Whereas when including also local starburst galaxies (LIRGs and ULIRGs) with $L_{\mathrm{IR}} > 10^{11}$ L$_\odot$, the \cii$/$IR luminosity ratio drops significantly by up to an order of magnitude (e.g. \citealt{Malhotra1997}, \citealt{Stacey2010}, \citealt{Diaz-Santos2013}, \citealt{Farrah2013}, \citealt{Magdis2014}). These sources are usually referred to as ``\cii~ deficient'' with respect to main-sequence galaxies. It has been shown that not only the \cii~ emission drops, but also other far-IR lines tracing both PDRs and \hii~ regions (e.g. \oi 145 $\mu$m, \nii 122 $\mu$m, \oiii 88 $\mu$m, \oi 63 $\mu$m, \niii 57 $\mu$m, \citealt{Gracia-Carpio2011}, \citealt{Zhao2013}, \citealt{Diaz-Santos2017}) show a deficit when starbursts are considered. This is likely related to the enhanced star formation efficiency (SFE = SFR/$M_{\mathrm{mol}}$) of starbursts with respect to local main-sequence galaxies, consistent with the results by \cite{Daddi2010} and \cite{Genzel2010}. This relation between the $L_{\mathrm{\cii}}/L_{\mathrm{IR}}$ and galaxies' SFE could be due to the fact that the average properties of the interstellar medium in main-sequence and starburst sources are significantly different: the highly compressed and more efficient star formation in starburst could enhance the ionization parameters and drive to lower line to continuum ratios \citep{Gracia-Carpio2011}. At high redshift, observations become more challenging, mainly due to the fainter fluxes of the targets: so far $z > 1$ studies have mainly targeted IR selected sources (e.g., the most luminous sub-millimeter galaxies and quasars), whereas measurements for IR fainter main-sequence targets are still limited (e.g., \citealt{Stacey2010}, \citealt{Hailey-Dunsheath2010}, \citealt{Ivison2010}, \citealt{Swinbank2012}, \citealt{Riechers2014}, \citealt{Magdis2014}, \citealt{Huynh2014}, \citealt{Brisbin2015}). Therefore it is not clear yet if high-$z$ main-sequence galaxies, which have similar SFRs as (U)LIRGs, are expected to be \cii~ deficient. With our sample we start to push the limit of current observations up to redshift $z \sim 2$. The goal of this paper is to understand whether main-sequence, $z \sim 2$ galaxies are \cii~ deficient and investigate what are the main physical parameters the \cii~ emission line is sensitive to. Interestingly we find that its luminosity traces galaxies' molecular gas mass and could therefore be used as an alternative to other proxies (e.g. CO, [CI], or dust emission). Given its brightness and the fact that it remains luminous at low metallicities where the CO largely fades, this emission line might become a valuable resource to explore the galaxies' gas content at very high redshift. Hence understanding the \cii~ behaviour in $z \sim 2$ main-sequence galaxies, whose physical properties are nowadays relatively well constrained, will lay the ground for future explorations of the ISM at higher redshift. The paper is structured as follows: in Section \ref{sec:data} we present our observations, sample selection, and data analysis; in Section \ref{sec:results} we discuss our results; in Section \ref{sec:summary} we conclude and summarize. Throughout the paper we use a flat $\Lambda$CDM cosmology with $\Omega_{\mathrm{m}} = 0.3$, $\Omega_{\mathrm{\Lambda}} = 0.7$, and $H_{0} = 70\, \mathrm{km\, s^{-1} Mpc^{-1}}$. We assumed a \cite{Chabrier2003} initial mass function (IMF) and, when necessary, we accordingly converted literature results obtained with different IMFs. | \label{sec:summary} In this paper we discuss the analysis of a sample of 10 main-sequence galaxies at redshift $z \sim 2$ in GOODS-S. We present new ALMA Band 7 850 $\mu$m observer frame continuum, and Band 9 \cii~ line together with 450 $\mu$m observer frame continuum observations, complemented by a suite of ancillary data, including \textit{HST}, \textit{Spitzer}, \textit{Herschel}, and VLA imaging, plus VLT and Keck longslit spectroscopy. The goal is to investigate whether $z \sim 2$, main-sequence galaxies are \cii~ deficient and understand what are the main physical parameters affecting the \cii~ luminosity. We summarize in the following the main conclusions we reached. \begin{itemize}[leftmargin=*] \item The ratio between the \cii~ and IR luminosity ($L_{\mathrm{[CII]}}/L_{\mathrm{IR}}$) of $z \sim 2$ main-sequence galaxies is $\sim 2 \times 10^{-3}$, comparable to that of local main-sequence sources and a factor of $\sim 10$ higher than local starbursts. This implies that there is not a unique correlation between $L_{\mathrm{\cii}}$ and L$_\mathrm{IR}$ and therefore we should be careful when using the \cii~ luminosity as a SFR indicator. Similarly, the \cii~ luminosity does not uniquely correlate with galaxies' specific star formation rate, intensity of the radiation field, and dust mass. \item The \cii\ emission is spatially extended, on average, on scales comparable to the stellar mass sizes (4 -- 7~kpc), as inferred from \textit{HST} imaging in the optical rest frame. This is in agreement with the results by \cite{Stacey2010}, \cite{Hailey-Dunsheath2010}, and \cite{Brisbin2015} who, for samples of $z \sim 1$ -- 2 galaxies, find similar \cii~ extensions. This also suggests that our sample of main sequence galaxies, with typical stellar masses and SFRs, is not made up of the ultra-compact (and more massive) sources selected and studied by \cite{Tadaki2015} and \cite{Barro2016}. \item The \cii~ luminosity linearly correlates with galaxies' molecular gas masses. By complementing our sample with those from the literature, we constrained the $L_{\mathrm{\cii}}$-to-H$_2$ conversion factor: it has a median $\alpha_{\mathrm{\cii}} = 31$ M$_\odot$/L$_\odot$ and a median absolute deviation of $\sim$ 0.2 dex. We find it mostly invariant with galaxies' redshift, depletion time, and gas phase metallicity. This makes \cii~ a convenient emission line to estimate the gas mass of starbursts, a notoriously hard property to constrain by using the CO and dust emission due to the large uncertainties in the conversion factors to be adopted. Furthermore, the invariance of $\alpha_{\mathrm{\cii}}$ with metallicity together with the remarkable brightness of \cii~ makes this emission line a useful tool to constrain gas masses at very high redshift, where galaxies' metallicity is expected to be low. \item Considering that \cii~ traces the molecular gas and the IR luminosity is a proxy for SFR, the $L_{\rm \cii}/L_{\rm IR}$ ratio seems to be mainly a tracer of galaxies' gas depletion time. The $L_{\rm \cii}/L_{\rm IR}$ ratio for our sample of $z\sim2$ main-sequence galaxies is $\sim$ 1.5 times lower than that of local main-sequence samples, as expected from the evolution of depletion time with redshift. \item The weak \cii\ signal from $z>6$ -- 7 galaxies and the many non-detections in the recent literature might be evidence of high star formation efficiency, but might be also due to the fact that the expected signal is computed from the total UV star formation rate, while local dwarfs suggest that \cii\ only reflects the portion of SFR reprocessed by dust in the IR. \item Although some caveats are present (e.g. \cii~ non-detections at very high redshift might also be due to the effects of a strong radiation field; \cii~ might be tracing different gas phases simultaneously; it is only emitted when the gas is illuminated by young stars, so it only traces molecular gas with ongoing star formation), the limitations that affect \cii~ are different with respect to those impacting more traditional gas tracers such as CO, \ci, and dust emission. This makes \cii~ an independent proxy, particularly suitable to push our current knowledge of galaxies' ISM to the highest redshifts. \end{itemize} | 18 | 8 | 1808.10331 |
1808 | 1808.02524_arXiv.txt | The site of Zn production remains an elusive and challenging problem in astrophysics. A large enhancement of the [Zn/Fe] ratios of very metal-poor stars in the Galactic halo suggests the death of short-lived massive stars, i.e., core-collapse supernovae (CCSNe), as one major site for Zn production. Previous studies have claimed that some specific CCSNe can produce Zn in sufficient quantities. However, it remains unclear which models can withstand the critical test of observations. Using a Zn abundance feature similar to that of r-process elements in faint satellite galaxies, we find evidence that Zn production took place through much rarer events than canonical CCSNe. This finding can be unified with the implied decrease in the rate of Zn production with an increasing metallicity for Galactic halo stars, which narrows down the major site of Zn production in the early galaxy to magneto-rotational SNe (MR-SNe). On the other hand, in the later phase of galactic evolution, we predict that the major Zn-production site switched from MR-SNe to thermonuclear SNe (SNe Ia). According to this scenario, an accumulation of the contributions from two types of SNe eventually led to the solar isotope composition of Zn which mainly owes $^{66,68}$Zn to MR-SNe and $^{64}$Zn to SNe Ia triggered by He-detonation. The requirement of Zn production in SNe Ia sheds a new light on the hot debate on the scenario for SN Ia progenitors, suggesting that a He-detonation model might be one major channel for SNe Ia. | The recent discovery of gravitational waves from the neutron star merger GW170817 and the subsequent discovery of multi-wavelength electromagnetic counterparts. i.e., kilonova, has remarkably improved our understanding of the origin of r-process elements \citep[e.g.,][]{Smartt_17, Pian_17, Cowperthwaite_17, Thielemann_17}. However, the periodic table is still incomplete in the astrophysical sense in that it includes elements without a clear explanation of their origins. A major example of such an element is a light trans-iron element, Zn. The remarkable feature of Zn abundance is represented by the high [Zn/Fe] abundance ratio, ranging from 0 to +0.6 for very metal-poor stars with [Fe/H]\ltsim $-2.5$ \citep{Cayrel_04}. This implies that Zn was efficiently produced with no time delay at a very early phase of galactic evolution. Therefore, core-collapse supernovae (CCSNe) occurring at the deaths of massive stars should be at least one major site for Zn production. However, Zn production through explosive burning in canonical CCSNe has been found insufficient to explain the observed [Zn/Fe] \citep[e.g.,][]{Woosley_95, Thielemann_96}. \citet{Umeda_02} thus proposed hypernova models, i.e., CCSNe with large explosion energies capable of increasing Zn production and lifting the predicted [Zn/Fe] ratios up to the value of +0.4 \citep[see also][]{Tominaga_07}. Another type of CCSNe that has been proposed as a major site of Zn production is electron-capture SNe (ECSNe), which are triggered by the collapse of O+Ne+Mg cores in stars with an initial mass of $\sim8-10$\ms \citep{Wanajo_11, Wanajo_18}. These Zn-production sites were discussed in terms of galactic chemical evolution \citep{Kobayashi_06, Hirai_18}. \citet{Kobayashi_06} found that a high frequency of hypernovae (as much as half of all CCSNe) would be required to achieve the observed broad constancy of [Zn/Fe]$\approx$0 in the range of $-2$\ltsim[Fe/H]\ltsim0 for Galactic stars. The deduced frequency of hypernovae seems extremely high. On the other hand, \citet{Hirai_18} reproduced the observed decreasing trend of [Zn/Fe] in the Sculptor dwarf spheroidal galaxy (dSph), assuming ECSNe to be the major source of Zn. It is, however, questionable whether their models are capable of predicting the non-decreasing feature of [Zn/Fe] in the Galaxy. Recently, a new channel for producing a large amount of Zn in CCSNe has been proposed. \citet{Nishimura_17} showed that magneto-rotational SNe (MR-SNe) triggered by fast rotations and high magnetic fields \citep[e.g.,][]{Takiwaki_09, Nishimura_15} produce light trans-iron elements including Zn as well as the first- to third-peak r-process isotopes. MR-SNe produce Zn more efficiently than the other two candidates, i.e., as high as $(5-6)\times10^{-3}$\ms for each MR-SN, which is about five times of that for an ECSN \citep{Wanajo_18} or more than ten times that for a hypernova from low-metallicity star \citep{Kobayashi_06}. Such a high Zn-production rate in MR-SNe might be reconciled with the low frequency expected for such events themselves to obtain a consistent view of the chemical enrichment of Zn in galaxies. Therefore, capturing an observational signature indicating whether Zn production is a rare event would be a major clue for understanding the connection of Zn sources to MR-SNe or other type of CCSNe. This issue is of growing significance if we consider the recent claims that canonical CCSNe driven by the neutrino heating are able to give a more important contribution of Zn production than previously thought \citep[e.g.,][]{Harris_17, Curtis_18, Eichler_18}. The small stellar masses in the Milky Way satellite galaxies offer an advantage for this test. The relatively small number of stars formed in these galaxies allows the detection of rare production events such as neutron star mergers in r-process abundances \citep[][Tsujimoto et al.~2015, 2017]{Tsujimoto_14}. Figure~1 demonstrates the observed [r-process/H] vs.~[Fe/H] results in the Draco dSph, which suggest that r-process events occurred sporadically around [Fe/H]=$-3$ and $-2.3$ with high r-process yields and did not happen afterwards until the end of metal enrichment. The revealed feature implies a level of rarity of r-process production which may be compatible with the frequency expected for neutron star mergers or MR-SNe \citep{TsujimotoN_15, Tsujimoto_17}. Similar assessment of the frequency of such production events using dSphs can be done for Zn. \begin{figure}[t] \vspace{0.4cm} \begin{center} \includegraphics[angle=0,width=8cm,clip=true]{f1.eps} \end{center} \caption{Observed r-process abundances vs.~Fe abundances for the Draco dSph. The [Ba/H] data for [Fe/H]$<-1.8$ and the [Eu/H] data for [Fe/H]$>-1.8$ are taken from \citet{Tsujimoto_17} and \citet{Tsujimoto_15}, respectively. The Ba abundances for these low-metallicity stars can be regarded as an r-process Ba abundance based on the pure r-process Ba/Eu ratios measured for several stars. The Eu abundances are shifted by $-0.64$ dex, which corresponds to the value of the solar r-process Ba/Eu ratio, and are thereby equivalent to the r-process Ba abundances for stars with [Fe/H]$>-1.8$.} \end{figure} Although such insights are hard to be gained from more massive galaxies such as our own, an assembly of the elemental abundances of solar neighborhood stars, tracing the whole history of Zn enrichment from the first generations of stars to the present, offers a treasure trove of clues as to the identity of the Zn source. In particular, if there is not a sole major site of Zn production (as is the case for many other elements), the evolution of Zn abundance with the stellar generation will be crucial information. In this Letter, we will begin by narrowing down the possible sites of Zn production based on the set of elemental abundances for dSphs and for the Galaxy. | We propose that MR-SNe are the major sites of Zn production during the early epoch of galactic evolution. However, this does not necessarily mean that MR-SNe simultaneously drive enrichment of heavy r-process elements such as Ba and Eu since models with high Zn production are associated with a low production efficiency of heavy r-process elements: CCSNe with stronger, but still intermediate magnetic fields produce Fe and Zn while ones with much stronger magnetic fields produce r-process elements \citep{Nishimura_17}. On the other hand, we see a similarity in the evolutionary paths of abundances between Zn and r-process elements in dSphs (compare Fig.~1 and the top panel of Fig.~2). More research on both the observational and theoretical sides will be needed to clarify this connection. Regular CCSNe driven by the neutrino heating are proposed to be capable of making Zn/Fe like a solar ratio \citep{Frohlich_06a, Curtis_18}. Their models yield a better fit to the Fe-group and also produce nuclei up to $A$=100 \citep{Frohlich_06b, Eichler_18}. These studies imply that regular CCSNe can be one major site of Zn production, at least in the range of $-2$\ltsim[Fe/H]\ltsim$-1$. However, we show that the observed abundance features of dSphs and the Galaxy argue against the continuous Zn production at the same rate over galactic evolution as predicted by their models. Our study poses an open question to the nucleosynthesis models for regular CCSNe. We suggest that the upturn of Zn/Fe (Zn/Mg) at very low metallicities could be related to less mass loss and thus less loss of angular momentum, leading to a higher fraction of fast-rotating objects which end with CCSNe with stronger magnetic fields, i.e., MR-SNe. In this view, a high fraction of MR-SNe at very low metallicities would make few stars with low Zn/Fe ratios ([Zn/Fe]$<$0), which leads to a relatively smaller scatter in [Zn/Fe] compared to that of [r-process/Fe], in spite of the presence of the rarity of Zn production event. On the other hand, there is a different argument that this trend reflects the abundance ratios predicted by hypernova models with different progenitor masses \citep{Tominaga_07}. However, in this case, a Zn contributor different from SNe Ia in the later phase is required to avoid an overproduction of $^{64}$Zn in the solar composition. This issue can be also discussed in terms of the upper side of scatter in [Zn/Fe]. The nucleosynthesis Zn/Fe ratios predicted by individual MR-SN models are distributed up to [Zn/Fe]$\sim +1.5$. This may promise that a large contribution to Zn enrichment from MR-SNe in the early Galaxy satisfactorily explains an observed scatter attaining above [Zn/Fe]$\sim +1$ among very low-metallicity stars, while hypernova models predict [Zn/Fe]$<+0.7$. Together with MR-SNe, SNe Ia triggered by He detonations are proposed as another site of Zn production in this study. The He-detonation model can be realized in both of two well-known scenarios for SNe Ia: a single degenerate scenario \citep[an accreting white dwarf from a non-degenerate companion star:][]{Woosley_11} and a double degenerate scenario \citep[a merger of double white dwarfs:][]{Pakmor_13}. Recently, this He-detonation mode of the explosion has been highlighted as a mechanism to explain the observed early emission feature for SNe Ia \citep{Jiang_17, Noebauer_17}. Other observational indications also ask strongly for a He-detonation contribution to SNe Ia's \citep{Shen_18}. In terms of nucleosynthesis, we claim that the presence of this pathway is important to SN Ia explosions. On the other hand, from Mn observations \citep[e.g.,][]{Mishenina_15}, we see an increase in [Mn/Fe] above [Fe/H]=$-1$. This argues for a single-degenerate deflagration/detonation contribution to SN Ia's, which have high central densities and electron captures reducing Y$_e$. Accordingly, combining the Mn observations arguing for deflagration/detonation type and the Zn observations arguing for He-detonation type, this gives a nice clue on the combination of both types, as recent observational surveys indicate \citep[e.g.,][]{Livio_18}. | 18 | 8 | 1808.02524 |
1808 | 1808.07906_arXiv.txt | We perform detailed spectroscopic analysis and numerical modelling of an H$_{2}$-bearing damped Lyman-$\alpha$ absorber (DLA) at $z_{abs}$ = 2.05 towards the quasar FBQS J2340-0053. Metal absorption features arise from fourteen components spread over $\Delta v_{90}$ = 114 km s$^{-1}$, seven of which harbour H$_{2}$. Column densities of atomic and molecular species are derived through Voigt profile analysis of their absorption lines. We measure total \textit{N}(\ion{H}{i}), \textit{N}(H$_{2}$) and \textit{N}(HD) to be 20.35$\pm$0.05, 17.99$\pm$0.05 and 14.28$\pm$0.08 (log cm$^{-2}$) respectively. H$_{2}$ is detected in the lowest six rotational levels of the ground vibrational state. The DLA has metallicity, Z = 0.3 $Z_{\sun}$ ([S/H] = -0.52$\pm$0.06) and dust-to-gas ratio, $\kappa$ = 0.34$\pm$0.07. Numerical models of the H$_{2}$ components are constrained individually to understand the physical structure of the DLA. We conclude that the DLA is subjected to the metagalactic background radiation and cosmic ray ionization rate of $\sim$ 10$^{-15.37}$ s$^{-1}$. Dust grains in this DLA are smaller than grains in the Galactic interstellar medium. The inner molecular regions of the H$_{2}$ components have density, temperature and gas pressure in the range 30--120 cm$^{-3}$, 140--360 K and 7,000--23,000 cm$^{-3}$ K respectively. Micro-turbulent pressure is a significant constituent of the total pressure, and can play an important role in these innermost regions. Our H$_{2}$ component models enable us to constrain component-wise \textit{N}(\ion{H}{i}), and elemental abundances of sulphur, silicon, iron and carbon. We deduce the line-of-sight thickness of the H$_2$-bearing parts of the DLA to be 7.2 pc. | \label{sec:intro} The spectra of luminous objects such as quasars and gamma ray bursts often indicate the presence of absorbing clouds along the line-of-sight. These absorbers are characterized by their content of neutral gas. Damped Lyman-$\alpha$ absorbers (DLAs) have the highest observed column densities of neutral hydrogen, \textit{N}(\ion{H}{i}) $\geq 10^{20.3}$ cm$^{-2}$ \citep* {Wolfe2005} and account for most of the neutral gas in the high-redshift Universe \citep {Noterdaeme2009, Noterdaeme2012}. Depending on the particular DLA sightline being probed, we may be able to observe the diffuse warm phase (n $\sim$ 0.6 cm$^{-3}$, T $\sim$ 5000 K), the dense cold phase (n $\sim$ 30 cm$^{-3}$ , T $\sim$ 100 K), or a combination of both \citep {Srianand2005b, Draine2011}. \par \setlength{\parindent}{2ex} The main sources of ionizing radiation in DLAs are the metagalactic background radiation from quasars and galaxies, and \textit{in situ} star formation. Studies indicate that the metagalactic background may be insufficient to account for the heating in DLAs \citep{Wolfe2003a, Wolfe2008, Srianand2005a, Dutta2014}. Emission lines have been detected in some high-redshift DLAs, indicating a local source of radiation; though the connection between DLAs and star formation remains open to further investigation \citep{Rahmani2010, Krogager2013, Fynbo2013, Fumagalli2015, Srianand2016}. \par \setlength{\parindent}{2ex} Various metal ions are observed in DLAs. The singly ionized state is usually the dominant form for most metals. Molecules are also detected in DLAs, but they can form only in the inner regions where there is sufficient H$_2$ self-shielding to protect them from being destroyed by incident ionizing radiation. In the context of this DLA, we find that dust shielding does not hold much significance. We thus, use the term `shielding' to refer to H$_2$ self-shielding throughout the paper, unless mentioned otherwise. H$_{2}$ is the most abundant molecule, and can be observed through the ultraviolet Lyman and Werner band transitions. These transitions occur when photons with energy 11.2--13.6 eV lead to excitation of the electronic states in the molecule. H$_{2}$ is detected in various rotational levels of the ground vibrational state. We use the notation H$_{2}$ (J), where J is the rotational level. As the first ionization potential of carbon is 11.2 eV, neutral carbon is also associated with the regions that harbour H$_{2}$. The ground state of carbon (\ion{C}{i}) has three fine structure levels $^3P_0$, $^3P_1$ and $^3P_2$. We denote these levels as \ion{C}{i*}, \ion{C}{i**} \& \ion{C}{i***}. Thus, observations of H$_{2}$ and \ion{C}{i} provide strong constraints for determining the physical state of cool gas in DLAs. Such studies to probe the physical environment prevalent in H$_{2}$-bearing DLAs (H$_{2}$-DLAs hereafter) have been attempted by \citet*{Ge2001}, \citet {Srianand2005a}, \citet{Jorgenson2010}, \citet{Noterdaeme2015a}, \citet{Klimenko2016}, \citet* {Shaw2016} and \citet{Noterdaeme2017}. \par \setlength{\parindent}{2ex} Most of the known H$_{2}$-DLAs are situated at $z_{abs} >$ 1.8, when the Lyman and Werner band transitions are redshifted into the optical region of the electromagnetic spectrum, and can be observed by ground-based telescopes. The atmospheric cut-off at 3000 {\AA} prevents observation of low-redshift H$_{2}$ from the ground. But recently, space-based missions have begun to be used to detect H$_{2}$ in low-redshift DLAs \citep {Crighton2013, Oliveira2014, Srianand2014, Muzahid2015}. It was earlier understood that 10--15 percent of DLAs at high redshift show the presence of H$_{2}$ absorption features \citep {Ledoux2003, Noterdaeme2008a}. However, recent surveys indicate that this number could be much lower, with the H$_2$ detection rate estimated to be less than 7 percent for \textit{N}(H$_2$) > 10$^{19}$ cm$^{-2}$ \citep {Balashev2014}, and less than 6 percent for \textit{N}(H$_2$) > 10$^{17.5}$ cm$^{-2}$ \citep {Jorgenson2014}. More recently, \citet* {Balashev2018} use composite absorption spectra to measure the H$_2$ detection rate to be 4 percent. So far, H$_{2}$ detections have been made in over 25 high-redshift DLAs \citep {Ledoux2003, Noterdaeme2008a, Bagdonaite2014, Balashev2015, Noterdaeme2015a, Krogager2016}. In addition to H$_2$, DLAs have been observed to harbour other molecules too. \citet {Varshalovich2001} reported the first high-redshift detection of HD. Subsequently, various other DLA systems have been found to contain HD molecules \citep {Noterdaeme2008b, Tumlinson2010, Ivanchik2010, Ivanchik2015, Balashev2010, Balashev2017, Albornoz2014, Klimenko2015a}. CO has also been observed along different high-redshift DLA sightlines \citep {Srianand2008, Noterdaeme2010, Noterdaeme2011, Noterdaeme2017, Noterdaeme2018}. \par \setlength{\parindent}{2ex} Absorption in a DLA may arise from either a single clump of gas, or multiple associated clumps. In the case of multiple clumps, only a few may satisfy the high density and low temperature conditions necessary for the formation of molecules. It is rare for DLAs to show molecular absorption features in multiple components spread over large velocity intervals. Some examples are the DLAs at $z_{abs}$ = 2.6265 towards FBQS J0812+3208 which shows the presence of H$_{2}$ in three components \citep {Jorgenson2009, Tumlinson2010, Jorgenson2010}, at $z_{abs}$ = 1.973 towards Q 0013-004 with H$_{2}$ in 4 components \citep {Petitjean2002}, and at $z_{abs}$ = 2.418 towards the quasar SDSS J143912.04+111740.5 which has H$_{2}$ in 6 components \citep {Noterdaeme2008b, Srianand2008}. Such multicomponent absorbers with many observed species provide us an excellent opportunity to probe the variation of physical properties within the DLA, and hence, to understand the internal structure of the absorbing region. \par \setlength{\parindent}{2ex} We present here spectroscopic analysis and detailed numerical modelling of a multicomponent H$_{2}$-DLA along the sightline to the QSO FBQS J2340-0053. There are two main absorption systems along this sightline -- an \ion{Mg}{ii} absorber at $z_{abs}$ = 1.36 \citep {Rahmani2012}, and a DLA at $z_{abs}$ = 2.05 \citep {Jorgenson2010}. \citet {Jorgenson2010} have detected H$_{2}$ absorption in the DLA and have extracted physical parameters through analysis of the spectrum obtained using the High Resolution Echelle Spectrometer (HIRES) on the Keck I Telescope. We study the DLA in greater detail in this paper using data obtained with the Ultraviolet and Visual Echelle Spectrograph (UVES) on the Very Large Telescope (VLT). The UVES spectrum has higher signal-to-noise ratio compared to the HIRES spectrum analysed by \citet {Jorgenson2010}. Voigt profile fitting of the H$_{2}$, \ion{C}{i} and metal absorption lines is performed to derive component-wise column densities. Numerical models are then constructed for each of the molecular components. By reproducing the observed column densities, we constrain the physical conditions in each molecular component. Such detailed modelling of a multicomponent H$_{2}$-absorber has as yet been unattempted. \par \setlength{\parindent}{2ex} This paper is organized as follows. In Section \ref{sec:reduction}, we mention details of the observations and data reduction techniques. The results of our Voigt profile fits can be found in Section \ref{sec:voigt}. In Section \ref{sec:phy_prop}, we obtain estimates of some physical properties of the DLA through the observed column densities of various species. Details of our numerical models are presented in Section \ref{sec:models}. In Section \ref{sec:result}, we combine the results of the observational analysis and the numerical models, to study the variation of different physical properties within the DLA. Section \ref{sec:conclude} provides a summary of our results. | \label{sec:conclude} We have performed detailed spectroscopic analysis and numerical modelling of the DLA at $z_{abs}$ = 2.05 towards the quasar FBQS J2340-0053. Metal absorption features associated with this system arise from fourteen distinct velocity components spread over an interval spanning $\Delta v_{90}$ = 114 km s$^{-1}$. Of these, seven components harbour H$_{2}$ and \ion{C}{i}. The multicomponent absorption features enable us to study the physical environment of the H$_{2}$ components individually. Here, we present a brief summary of the results of our study. \begin{itemize}[label=\textbullet] \item{We measure the total \textit{N}(\ion{H}{i}), \textit{N}(H$_{2}$) and \textit{N}(HD) to be 20.35$\pm$0.05, 17.99$\pm$0.05 and 14.28$\pm$0.08 (log cm$^{-2}$) respectively. H$_{2}$ is detected in the lowest six rotational levels of the ground vibrational state.} \item{The DLA has an average metallicity, Z = 0.3 $Z_{\sun}$ ([S/H] = -0.52$\pm$0.06) and dust-to-gas ratio, $\kappa$ = 0.34$\pm$0.07. The mean metallicity and dust-to-gas ratio from our models for the H$_{2}$ components are consistent with these values. } \item{The observed \ion{C}{ii*} column density indicates that the DLA is exposed to an intensity of ultraviolet radiation 0.35 times the intensity in the Milky Way. Our numerical models show that the physical environment of the DLA can be recreated by subjecting the DLA to solely the Khaire-Srianand metagalactic background radiation, along with mean cosmic ray ionization rate of $\sim$ 10$^{-15.37}$ s$^{-1}$ for the H$_2$ components.} \item{Our models indicate that the DLA harbours grains that are smaller than the grains in the Galactic ISM. We incorporate both silicate and graphite grains distributed as per the MRN distribution, but having sizes half those of the grains in the ISM (in the range 0.0025-0.125 $\umu$m).} \item{From the numerical models, we constrain neutral hydrogen density $n_\mathrm{H}$, in the different molecular regions of the DLA to be in the range 30--120 cm$^{-3}$. Gas temperature lies between 140 and 360 K for the different H$_{2}$ components, with five of the seven components having electron temperature greater than 200 K in the inner shielded regions. Hence, these components do not trace the cold phase, but are rather associated with a warmer phase of H$_{2}$. The gas pressure in the molecular regions of the H$_{2}$ components lies in the range 7,000--23,000 cm$^{-3}$ K, towards the higher end of the pressure range seen in H$_{2}$-DLAs. Our models also enable us to study various contributing factors to the total pressure in the DLA. We conclude that micro-turbulence plays a crucial role in the molecular region.} \item{Metal abundances vary across the DLA components. We constrain the abundances of sulphur, silicon, iron and carbon through the numerical models. The mean abundances of sulphur, silicon and iron across the seven H$_{2}$ components agree with the respective mean observed abundances obtained for the entire DLA. Though the carbon abundance cannot be constrained observationally, we are able to predict the mean carbon abundance from our models. We predict that [C/H] = -1.39. The abundances for phosphorus, chromium, nickel and zinc predicted by the average DLA model are similar to the observationally constrained values.} \item{We are able to determine the distribution of \ion{H}{i} across the H$_{2}$ and non-H$_{2}$ components through the {\tiny CLOUDY} models. The non-H$_{2}$ components give rise to log[\textit{N}(\ion{H}{i})(cm$^{-2}$)] = 19.86. This accounts for $\sim$ 32 percent of the total \ion{H}{i} in the DLA. These non-H$_{2}$ components have mean metallicity, Z = -0.54, which is slightly lower than the mean metallicity of -0.49 derived for the H$_2$ components, but agrees with the mean metallicity of 0.3 $Z_{\sun}$ derived for the entire DLA using the observed total column densities.} \item{The extent of the DLA along the line-of-sight is obtained from the numerical models. The average model of the DLA yields a size of 11.8 pc, while the total extent of the H$_{2}$ components is 7.2 pc. This is in agreement with previous studies which show that H$_{2}$ absorption arises in regions $\leq$ 15 pc across.} \item{We find that the H$_{2}$ component models trace the physical structure of the cloud better than the average model. Summing the species-wise column densities over all the H$_{2}$ components yields resultant column densities which are closer to the observed H$_{2}$ level population and \ion{C}{i} fine structure levels, as compared to the average model. The average model fails to trace the cold phase of H$_{2}$ seen in some of the components.} \end{itemize} | 18 | 8 | 1808.07906 |
1808 | 1808.05768_arXiv.txt | Fireball networks establish the trajectories of meteoritic material passing through Earth’s atmosphere, from which they can derive pre-entry orbits. Triangulated atmospheric trajectory data requires different orbit determination methods to those applied to observational data beyond the Earth’s sphere-of-influence, such as telescopic observations of asteroids. Currently, the vast majority of fireball networks determine and publish orbital data using an analytical approach, with little flexibility to include orbital perturbations. Here we present a novel numerical technique for determining meteoroid orbits from fireball network data and compare it to previously established methods. The re-entry of the Hayabusa spacecraft, with its known pre-Earth orbit, provides a unique opportunity to perform this comparison as it was observed by fireball network cameras. As initial sightings of the Hayabusa spacecraft and capsule were made at different altitudes, we are able to quantify the atmosphere’s influence on the determined pre-Earth orbit. Considering these trajectories independently, we found the orbits determined by the novel numerical approach to align closer to JAXA’s telemetry in both cases. Using simulations, we determine the atmospheric perturbation to become significant at $\sim$90 km; higher than the first observations of typical meteorite dropping events. Using further simulations, we find the most substantial differences between techniques to occur at both low entry velocities and Moon passing trajectories. These regions of comparative divergence demonstrate the need for perturbation inclusion within the chosen orbit determination algorithm. | Fireball networks track meteoritic material as it transits our atmosphere. Triangulated observations of fireballs provide precise trajectories for these objects. By propagating such trajectories back in time, we can acquire orbital data for meteoroids, be it of cometary or asteroidal origin. For objects $<$10\,m diameter - typically below the resolution of telescope observations - fireball networks are currently the only method capable of delivering bulk orbital datasets for this class of solar system material. Fireball networks have an additional value in providing trajectory data that can facilitate the physical recovery of meteorites with orbits. As of early 2018, only a mere 32 meteorites have been recovered where their observed atmospheric entry data allows an orbital trajectory to be determined with varying degrees of reliability and precision \citep{granvik_identification_2018}. The accurate knowledge of the origins of this material is vital to our understanding of Solar System formation. Differences in orbital characteristics, however slight, will be amplified with time as material is propagated back perhaps thousands, if not millions of years in order to find a match to a potential parent body or source region. Using probabilistic orbital evolution modelling techniques \citep{bottke_debiased_2002}, one can trace back a meteoroid’s determined pre-Earth orbit and probabilistically link the observed space rock to particular Near Earth Object (NEO) source regions. The mechanism triggering the migration of an object’s stable orbit, such as an unstable mean-motion orbital resonance or a close encounter with a planetary body, can be probabilistically identified. Understanding a meteoroid’s origin, and thereby uncovering a piece of recent dynamical history of the solar system, requires both accuracy and precision in the meteoroid’s initial orbit determination techniques. One such analytical technique is outlined in Section~11 of the work by Ceplecha (1987), hereafter referred to as “C-87”. It includes two corrections to the initial velocity vector based on simplifying assumptions to determine the meteoroid’s pre-Earth orbit. An alternative approach would be a numerical propagation method - an integration-based approach that iteratively propagates a meteoroid’s initial state vector, through the most significant perturbations, back in time until the Earth’s influence is considered negligible, at which point the pre-Earth orbit is produced. Historically, C-87 has long been used as the method of choice due to its computational ease and convenience. However, as computational power has increased, so has the viability of the numerical approach. There are at least 9 groups that publish orbital data from meteor and fireball observations, and C-87 is used by all but one of them [C-87: \citet{brown_development_2010}; \citet{colas_french_2015}; \citet{cooke_status_2012}; \citet{gural_california_2011}; \citet{madiedo_multi-station_2008}; \citet{rudawska_new_2014}; \citet{spurny_automation_2007}; \citet{wisniewski_current_2017}, Numerical: \citet{dmitriev_orbit_2015}]. The current numerical approach used by \citet{dmitriev_orbit_2015} is available as part of the standalone Meteor Toolkit package (hereafter referred to as “MT-15”) and will be compared alongside the novel numerical propagation method described in this work. This new numerical method will hereafter be referred to as “JS-19”. Some studies have been established in the past comparing the analytical and numerical approaches to orbit determination \citet{clark_numerical_2011}, however these comparisons were conducted using published meteor observations with no pre-Earth sightings. To compare the various orbit determination methods, a real world example with well recorded data both before and after it encounters Earth’s perturbing influence, namely the pre-Earth orbit and the triangulated atmospheric trajectory respectively, would be invaluable. In November 2005, Japan Aerospace Exploration Agency’s (JAXA’s) Hayabusa mission successfully retrieved samples from the near-Earth asteroid 25143 Itokawa \citep{nakamura_itokawa_2011}. On its scheduled return to Earth, the Hayabusa spacecraft made several trajectory correction manoeuvres, the last being about three days before predicted re-entry over the Woomera Prohibited Area (WPA), South Australia. Following this last correction burn, the orbit was calculated using precise positional telemetry by the Deep Space Network team at NASA’s Jet Propulsion Laboratory \citep{cassell_hayabusa_2011}. On 13 June, 2010, 13:52 UT, the Hayabusa spacecraft and its return capsule made a coordinated ballistic re-entry over WPA. This re-entry was recorded by two temporary stations set up by JAXA’s ground observation team \citep{fujita_overview_2011}, four autonomous observatories of Australia’s Desert Fireball Network (DFN) \citep{borovicka_photographic_2011}, and one optical imaging station within NASA’s DC-8 airborne laboratory \citep{cassell_hayabusa_2011}. Although it is not strictly a meteoroid, the Hayabusa mission is a fitting candidate for orbit determination analysis. Its re-entry mimicked real meteoroid entry phenomena in its ballistic nature and was observed in a similar fashion to fireballs, while also possessing a ‘ground truth’ orbit from DSN telemetry. | Ceplecha’s analytical method of orbit determination (C-87) is computationally easy, and historically the most widely used technique in determining the originating orbits of meteoroids. However, it does not allow for perturbations in orbit calculations such as third bodies (including the Moon) or Earth flattening effects. A numerical approach is able to incorporate such perturbations. With increasing computational power, such an approach is preferable. A new numerical method (JS-19) is presented in this study. To compare the results of this new orbital determination technique to the typical analytical method (C-87) and the numerical approach provided in the Meteor Toolkit package (MT-15), the re-entry observations of JAXA’s Hayabusa, with its known heliocentric orbit as a ‘ground truth’, was invaluable. As observations were made of both the spacecraft and the capsule re-entry separately, these data provide two excellent test cases with which models could be compared to heliocentric telemetry. The spacecraft was first observed at $\sim100\,km$ altitude while the capsule was not observed until $\sim65\,km$ altitude. The low observation altitude of the capsule tests the capability of models to incorporate atmospheric influences. In both cases, JS-19 determined the most similar orbit to JAXA’s recorded orbit than either C-87 or MT-15. This was especially evident in the second case due to the greater atmospheric influence that the capsule experienced before initial sighting. Further investigation of the atmospheric influence shows the need for atmospheric consideration in meteoroid orbit determination below $\sim90\,km$ altitude. This is therefore highly relevant for many meteorite dropping events which may not be initially observed above this height by fireball networks tuned to brighter events. We also stressed that C-87 alone does not account for atmospheric drag effects, requiring a pre-atmospheric initial velocity to be determined prior to its use. The calculation of this initial velocity by the majority of current fireball networks that use C-87 is unclear and may need to be revised. We made a detailed assessment on the accuracy and precision of orbital calculations. The numerical methods are shown to produce more realistic precision and deliver superior accuracy in estimating the Hayabusa spacecraft’s pre-Earth orbit from re-entry observations than the analytical method, verifying such claims of previous authors \citep{clark_numerical_2011, jenniskens_cams:_2011}. The resulting orbital element precision is primarily determined by the size of the initial velocity magnitude error, as all other foreseeable uncertainties combined correspond to orbital errors at least an order of magnitude smaller than the initial speed uncertainty, as discussed in Section~\ref{sssec:precision}. While the precision of the orbit determination methods were comparable, JS-19 demonstrated greater accuracy due to its complete detailed representation of Earth’s gravity and its inclusion of perturbations, as shown in Section~\ref{sssec:accuracy}. By generating a great variety of simulated re-entry trajectories, we were able to explore the effect of different perturbations by comparing orbits calculated by both C-87 and JS-19. Simulated trajectories with low entry velocities or which pass close to the Moon show the most drastic orbital divergences. This demonstrates the vital need for perturbation inclusion within the orbit determination method. The limitations of C-87 should be considered and discussed if used for meteoroid orbit determination. Previously determined orbits, especially those in regions of significant orbital divergence (as discussed in Section~\ref{sssec:accuracy}) should be re-analysed to avoid inaccurate orbital histories. The Hayabusa case used in this work has provided a unique opportunity to compare orbit determination techniques. Although this case assesses only a heliocentric orbit, it must be noted that JS-19 can compute an observed meteoroid’s orbit regardless of whether it originated around the Earth (geocentric), around the Sun (heliocentric), or from outside the solar system (hyperbolic), proving itself to be a more robust and real world approach than its analytical counterpart. | 18 | 8 | 1808.05768 |
1808 | 1808.07247_arXiv.txt | A number of giant cometary HII regions (cones) (GCH) sheathed inside molecular bow shocks (MBS) are found along spiral arms of the barred galaxy M83. The open cone structure is explained by a model of expanded HII front in a gaseous arm with steep density gradient, and the bow shock is shown to be formed by encounter of an HII region with the supersonic gas flow across the arm. It is suggested that dual-side compression of molecular gas at the bow head between the MBS and GCH enhances star formation along the spiral arms. | Astrophysical bow shock is a classical subject, and is observed around objects interacting with supersonic gas flows in a wide range of scales from planets to cosmic jets (Dyson et al. 1975; van Buren et al. 1990; Ogura et al. 1995; Wilkin 1996; Arce and Goodman 2002; Reipurth et al. 2002). Galactic-disk scale bow structure is observed in spiral arms, where a supersonic flow in galactic rotation encounters a stagnated gaseous arm in the density-wave potential (Martos and Cox 1998; G{\'o}mez and Cox 2004a, b). In scales of star-forming (SF) regions, a bow shock was observed at G30.5+00 associated with the SF region W43 in the tangential direction of the 4-kpc molecular arm (Scutum arm) in thermal radio continuum emission associated with a CO line molecular arc (Sofue 1985). The molecular bow at G30.5+00 has recently been studied in detail based on the Nobeyama 45-m CO line survey (Sofue et al. 2018), which we call the molecular bow shock (MBS) (figure \ref{G30}). \begin{figure} \begin{center} \includegraphics[width=7cm]{G30.ps} \end{center} \caption{\co intensity map (gray) of the molecular bow shock (MBS) G30.5 in the Galaxy overlaid on a 10-GHz continuum map (contours) (Sofue et al. 2018)), which compose concave arc with respect to W43. Thick lines indicate calculated bows for $\Rbow=25$, 50 and 75 pc.} \label{G30} \end{figure} MBS is a concave arc of molecular gas around an HII region (SF region) formed in the up-stream side of galactic rotation with respect to the SF region. An MBS is formed in such a way that the interstellar gas in galactic supersonic flow encounters a pre-existing HII region on the down stream side in the galactic-shock wave (figue \ref{illust}). \begin{figure} \begin{center} \includegraphics[width=7.5cm]{illust.ps} \end{center} \caption{Illustration of the molecular bow and GCH concave to the central OB star cluster proposed for the W43 SF complex in the 4-kpc arm in the Galaxy (Sofue et al. 2018). Inserted small is an illustration for a wavy sequential star formation discussed later. } \label{illust} \end{figure} A similar phenomenon is observed in star forming regions known as a cometary HII region tailing down stream, when a compact HII region is embedded in a flow of ambient interstellar gas (Arthur \& Hoare 2006; Reid \& Ho 1985; Steggles et al. 2017; van Buren et al. 1990; Fukuda and Hanawa 2000; Campbell-White et al. 2018; Deharveng et al. 2015). The current studies of cometary HII regions have been obtained of sub-parsec to parsec scale objects inside individual SF regions. However, our observations of the association of the spiral-arm scale MBS G30.5 and the SF complex around W43 suggests the existence of larger scale, spiral-arm scale cometary HII regions associated with MBS. Namely, MBS developed in the up-stream side of cometary HII regions may be a common phenemenon in spiral arms. On such premise, we have searched for bow-shock plus cometary structure in spiral arms of nearby galaxies. In the present paper, we report identification of a number of bow structures in the barred spiral galaxy M83 (NGC 5236). Assuming that dark clouds in optical images represent molecular clouds, we name them molecular bow shocks (MBS), We also show that MBS are generally associated with giant cometary HII regions (GCH) on their down-stream sides, which may alternatively be called giant HII cone (GHC). Therefore, an MBS and a GCH make one single set of objects. So, they may be often referred to either MBS or GCH. Morphology and energetics (luminosity) of individual HII regions and OB clusters have been studied by optical imaging of M83 using the Hubble Space Telescope (HST) (Chandar et al. 2010, 2014; Liu et al. 2013; Blair et al. 2014; Whitmore et al. 2011). High-resolution molecular gas distribution in M83 has been extensively observed in the CO line emissions, and detailed comparative study with HII regions are obtained using ALMA high resolution maps (Hirota et al. 2018; Egusa et al. 2018). Structural relation of HII regions and molecular clouds has been one of the major subjects of star formation mechanism in the Galaxy such as cloud-cloud collisions (McKee and Ostriker 2007). However, spatially-resolved relation between indiviidual HII regions and dark clouds in external galaxies seems to have not been studied yet. We here focus on individual HII regions and morphological relation with their associated dark clouds in M83. We will show that their morphology is similar to the cometary cone structure modeled for G30.5 in the Galaxy. In order to explain the morphology, we propose qualitative models based on theories of bow shocks and expanded HII regions. | Using optical images of nearby spiral galaxies taken with the HST (NASA APOD), we identified many sets of GCH and MBS in the barred spiral galaxy M83. We classified HII regions into Types I to III according to their degree of openness into the halo and disk. We argued that the GCH and MBS are general phenomena in galactic shock waves. The cone-shaped morphology of GCH is qualitatively explained by a model of an evolved HII sphere expanded in inhomogeneous ISM with steep density gradient, and the MBS is understood by the bow shock theory. Since in the actual galactic condition the GCH and MBS are coupled with each other, dual side compression of gas at the MBS/GCH heads makes the SFR more efficient by a factor of 10 than SFR by cloud-cloud collisions. We have further examined high-resolution images of other galaxies from HST and Subaru Telescope, and found that GCH and MBS are general phenomena in grand-designed spiral arms and/or bars. A full atlas of GCH/MBS in nearby galaxies will be presented in a separate paper. \vskip 5mm {\bf Aknowledgements} The optical images of M83 were reproduced from the web sites of STSci at http://www.stsci.edu/hst/wfc3/ and NASA at https://apod.nasa.gov/apod/. | 18 | 8 | 1808.07247 |
1808 | 1808.00467_arXiv.txt | The processes leading deformation and destruction of planets spiraling into the convective envelope of their host stars are described. The planet is compressed by the ram pressure, and deformed into a flattened shape for which a quantitative model is developed. Compression increases the planet's density contrast with the envelope and its gravitational binding energy. This increases the survivability especially of gas planets. An estimate is given for the depth of disruption by ram pressure, and for the subsequent fragmentation of the remnants. We show how the debris of rocky or iron planets, instead of mixing through the convection zone, sinks below the base of the convection zone. The time scale of the entire sequence of events is of the order of a few orbital times of the planet. If spiral-in of (partly) icy, rocky or iron planets has happened to the pre-main sequence Sun, it could account for the higher opacity below the base of the convection zone as inferred from helioseismology. | A correlation between the presence of a gas giant planet and its host stellar metallicity has been well established over the last two decades (e.g., Gonzalez 1997; Santos et al. 2004; Fischer \& Valenti 2005; Johnson et al. 2010), although there is still a debate for the planet-metallicity correlation of Neptune size and smaller planets (e.g., Wang \& Fischer 2015; Schuler et al. 2015, and references therein). Two main scenarios have been proposed to explain the planet-metallicity correlation. The primordial hypothesis (Pinsonneault et al. 2001) assumes that stars with planets are formed from metal-rich clouds. In the core accretion model of gas giant planet formation (Pollack et al. 1996), this hypothesis implies that the star forms metal-rich as a whole. The second scenario, the inhomogeneous accretion hypothesis, assumes that the higher metallicity of planet hosting stars derives from the accretion of material of enhanced metallicity during later stages of the star formation process (e.g., Gonzalez 1997; Laughlin \& Adams 1997; Murray et al. 2001). In this scenario, metal enhancement only occurs in the stellar convective envelope. The observed abundances should then decrease with increasing depth of the convective envelope. Such a correlation is not seen in the observations (e.g., Pinsonneault et al. 2001; Santos et al. 2001; Fischer \& Valenti 2005). The scenario also depends on the assumption that the enhancement remains confined to the convective envelope for much of the life of the star. This would not be happen if metal rich matter can settle into the radiative interior by thermohaline mixing (Vauclair 2004; Denissenkov \& Merryfield 2011; Th{\'e}ado \& Vauclair 2012). Depending on the (rather uncertain) efficiency of this process, it would even out metallicity differences between envelope and interior. The inhomogenous accretion scenario requires that material accreting later in the star formation process is enhanced in metals. This could be the case if this material derives from planets migrating to their host star by interaction with the accretion disk (e.g., Lin 1997; Laughlin \& Adams 1997; Sandquist et al. 1998, 2002). Whether this leads to enhanced abundances at the surface of the star depends on how mass transfer from the planet to the star takes place at the end of the migration (Sandquist et al. 1998, 2002; Th{\'e}ado \& Vauclair 2012). Depending on the mass and radius of planet and that of host and the equation of state of planet, transfer can be a slow process (in the case of stable Roche lobe overflow), rapid in the case of dynamically unstable Roche lobe overflow, or the planet can enter the star whole before Roche lobe overflow takes place (the `direct merger' case, see Jia \& Spruit 2017 for a recent analysis and references therein). An important issue is whether (much of) a planet can survive its travel through the convection zone (CZ), and dump its metal load on the radiation interior. The surface metallicity enhancement would then be negligible. Numerical simulations of direct merger by Sandquist et al.\ (1998, 2002) suggested that planets dissolve only gradually while spiraling in through the convective envelope of a sun-like star, but in some cases survive till the base of the CZ. Survival of planets spiraling in is made possible by their gravitational binding energy, as well as the high density of the planet's envelope relative to the star's CZ. These conditions also present obstacles to realistic numerical simulations, which are affected additionally by numerical diffusion (of momentum and of heat) due to finite spatial resolution. In the following we study the problem with a more analytical approach, addressing separately the processes of ablation of the outer layers of a planet, of the distortion of its shape under the ram pressure of a supersonic flow, and of its final disruption when the increasing ram pressure approaches its gravitational binding energy. The focus is on the depth the planet reaches before it is disrupted and on the fate of its debris. For a planet to enter its host star, it has to survive mass loss by Roche lobe overflow before it touches the surface of its host star. For main sequence stars this is the case only for iron-dominated or rather massive rocky or giant planets. Spiral-in is most likely to happen early in the evolution of the star, when its radius is larger and its mean density much lower than on the main sequence (Jia \& Spruit 2017). For the examples given below, we assume a $1 M_\odot$ star at a nominal age of 3.8 Myr, when its radius is $1.5 R_\odot$, its mean density $0.41 \ \mathrm{g \ {cm}^{-3}}$. | The goal of the calculations was to quantify the processes contributing to, or delaying, the destruction of planets spiraling into their host star. The high density of a planet, compared to conditions in the greater part of a stellar envelope allow it to survive to some depth into the envelope. The process of ablation (slow peeling of the surface) turns out to be ineffective because of the large density ratio between the planet's surface and the stellar envelope (Section \ref{ablat}). This is the case even for a gas planet, because external gas and ram pressure compress its (low entropy) atmosphere to a high density. We find that the actual disruption of the planet is likely to take place in the form of a global deformation (`splitting'), instead of by ablation. This happens when the ram pressure of the flow facing the planet is high enough to overcome the gravitational binding energy of the planet (Section \ref{disruption}). Before disruption, ram pressure deforms the planet into a flattened shape facing the flow; a model for this shape is developed in Section \ref{distortion}. The calculations were done for iron, rocky and gas planets entering a host star of 1 solar mass at different ages. Only planets dense enough to have avoided disruption in a previous Roche lobe overflow phase are considered. For a main sequence host, this limits the possibilities to iron-dominated or rather massive rocky or giant planets (cf. Jia \& Spruit 2017). The radii of pre-main sequence and post-main sequence hosts can be large enough (have low enough mean density) for such direct merger. For some combinations of mass and composition a planet can survive its path through the entire convective envelope, disrupting finally in the radiative interior. In this way, planets can increase the metallicity preferentially in the interior rather than the convective envelope (as usually assumed). It may not be necessary that the planet survives till the base of the convection zone, however, for such `interior pollution' to work. If a rocky, icy or iron planet instead disrupts already inside a star's convective envelope, the mean mass per particle of its debris is much higher than the surroundings. The debris is likely to settle in a layer near the base of the convection zone, instead of mixing through the convective envelope (Section \ref{debris}). It can then descend into the stable interior by a `saltfingering' process as discussed in Vauclair (2004), again yielding a higher metallicity below the base of the convection zone. A sufficient mass of rocky and or iron planet(s) polluting the interior of the Sun could explain the current discrepancy between helioseismic evidence and models of the solar interior (e.g., Asplund et al. 2009; Serenelli et al. 2009; Bergemann \& Serenelli 2014; Christensen-Dalsgaard et al. 2018). | 18 | 8 | 1808.00467 |
1808 | 1808.04843_arXiv.txt | We present a new distance estimation for the Milky Way dwarf spheroidal satellite Sculptor obtained from multi-epoch mid-infrared observations of RR Lyrae stars. The 3.6 $\mu$m observations have been acquired with the Infrared Array Camera on board the {\it Spitzer} Space Telescope as part of the SMHASH Program. Mid-infrared light curves for 42 RRL were obtained, from which we measured Sculptor's distance modulus to be $\mu$ = 19.60 $\pm$ 0.02 (statistical) $\pm$ 0.04 (photometric) mag (with $\sigma_{sys}=$ 0.09 mag), using the 3.6~$\mu$m empirical period-luminosity relations derived from the Galactic globular cluster M4, or $\mu$ = 19.57 $\pm$ 0.02 (statistical) $\pm$ 0.04 (photometric) mag (with $\sigma_{sys}=$ 0.11 mag) using empirical relations in the same passband recently derived from the Large Magellanic Cloud globular cluster Reticulum. Both these measurements are in good agreement with values presented in previous works with Sculptor RR Lyrae stars in optical bands, and are also consistent with recent near-infrared RR Lyrae results. Best agreement with the literature is found for the latter modulus which is equivalent to a distance of d = 82 $\pm$ 1 (statistical) $\pm$ 2 (photometric) kpc (with $\sigma_{sys}=$ 4 kpc). Finally, using a subsample of RR Lyrae stars with spectroscopic metallicities, we demonstrate that these distance estimates are not affected by metallicity effects. \\ | The processes driving the formation and evolution of dwarf spheroidal (dSph) satellite galaxies around the Milky Way (MW) are still open problems. These systems are precious laboratories, contributing to our understanding of the Universe on both small and large scales -- from the formation of the MW stellar halo at the smallest scale, to constraints on cosmological parameters at the largest. % The importance of dSphs is based on the assumption that, under the current $\Lambda$CDM paradigm, if hierarchical galaxy formation theory holds, then these old satellites could be witnesses of the accretion events that led to the formation of the Milky Way's stellar halo \citep{sal07,sti17}. The MW satellites are close enough that their stellar populations can be resolved. This offers a unique means to understand the building up of the MW halo by exploiting the information derived from the stars belonging to its satellites. The different types of pulsating variable stars can help us to distinguish different stellar generations and their radial distributions, particularly when crowding is significant in the host galaxy. It is well known that the dSphs located in the Local Group are characterized by the presence of a significant old stellar component (t$\sim10-13$ Gyr) that is dominant in dSphs surrounding the MW \citep{tol09}. % RR Lyrae stars (RRL), besides being the most numerous pulsating variable type, are ever-present, excellent tracers of the old stellar component in dSphs (for a detailed compilation of the RRLs located in dSphs see table 3 from \citealt{cle10} and table 6 from \citealt{mar17}). With the distance-gauging precision they afford, these variable stars can also be used to map the 3D structures of nearby galaxies \citep [and references therein]{cle10,dra13,gra16,jac16,bel16,mur18a}. The association between dSphs and RRL is so strong that recently these variable stars, as efficient stellar structure indicators, have been used to reveal previously unknown low luminosity dSphs. Indeed RRL are employed both as luminous guides for nearby, faint MW dwarf galaxies (d$<$50 kpc, L$<$1000 $L_{\odot}$; \citealt{ses14}) and as lighthouses marking more distant dwarfs (d$>$50 kpc, L$>$1000 $L_{\odot}$) using current and future deep wide field surveys such as the Large Synoptic Survey Telescope (LSST, \citealt{bak15}). Furthermore, RRL are the primary standard candles for Population II stellar systems widely used to determine distances within our own Galaxy and its nearest neighbours. In fact, thanks to the relation linking the metallicity with the absolute visual magnitude of RRL ($M_V$(RR) - [Fe/H]), their use as Population II primary distance indicators at optical wavelengths is widespread in nearby galaxies like the MW dSph satellites (see \citealt{gar13} and references therein). After \citet{lon86,lon90} showed empirically that the RRL follow a well-defined Period-Luminosity (PL) relation in the $K$-band, several theoretical and empirical studies came in quick succession \citep{bon01,bon03,cat04,dal04,sol06,cop11,mad13,bra15,mar15,mur15,mur18a,mur18b}, to turn the optical--only luminosity--metallicity relation into an extensive, multi-wavelength period--luminosity relation. In particular, the Carnegie RR Lyrae Program (CRRP; \citealt{frd12}) has shown that it is possible with IRAC-{\it Spitzer} \citep{faz04} to measure distances down to 2\% accuracy per individual RRL as far as $\sim 60$ kpc. Moreover, in their recent work on the RRL populations of M4, based on the Galactic calibrator sample (5 RR Lyrae stars with {\it HST} trigonometric parallaxes measured by \citealt{ben11}), \citet{nee17} demonstrated that the dispersion of RRL PL and period-luminosity-metallicity (PLZ) relations decreased to 0.02 mag at \textit{Spitzer} wavelengths. To make everything more compelling, the recently occurred \textit{Gaia} data release 2 (DR2; \citealt{gai18}), next releases to come and their exploitation will provide a powerful help for the scientific community even in this field. Indeed thanks to \textit{Gaia}, parallax measurements for hundreds of local RRL will serve as calibrators to reshape the fundamental relations followed by these stars with unprecedented precision. A taste of \textit{Gaia}'s potential relative to RRL calibration has been shown after the first \textit{Gaia} data release \citep{gai17} where the parallaxes published are a joint astrometric solution of Tycho and \textit{Gaia} measurements, Tycho-Gaia Astrometric Solution (TGAS; \citealt{lin16}), specific for the first release not adopted for DR2 and next Gaia data releases that all contain Gaia-only astrometry (see e.g. \citealt{lin18}, \citealt{mur18c}). The SMHASH program ({\it Spitzer} Merger History And Shape of the Galactic Halo; \citealt{joh13}) moves the study of RR Lyrae stars in the MW dSphs to mid-infrared (mid-IR) bands where the RRL treatment is advantageous compared with optical bands for the following reasons: (i) the RRL PL intrinsic dispersion at mid-infrared bands is narrower, (ii) the RRL light curves are generally more symmetrical and their amplitudes smaller, hence the measurement of the mean magnitudes is more precise, (iii) the extinction effects are weaker and (iv) the mid-infrared bands are less dependent on metallicity effects. SMHASH % intends to use high-precision mid-IR distances from RRL in the MW halo, its debris streams (e.g., the Sagittarius and Orphan streams; \citealt{hen17}), and its dSph satellites, to build an accurate 3-dimensional map of our Galaxy. These satellites and streams are the residuals of the disruption events that formed the halo; they can be considered `fossils' of the halo formation. Because they are systems at different stages of dynamical evolution (i.e., different disruption levels) they are the ideal tools to study the processes that occur during the hierarchical build-up of the dark matter (DM) halos \citep{bul01,bul05}. SMHASH targeted four MW dSphs: Ursa Minor, Bootes, Sculptor and Carina. Multiple studies of these four dSphs and their variable star populations have revealed a diversity in their morphological properties. The consistent study of these dSphs - containing from a few tens of RRL in Bootes \citep{dal06, sie06}, that also has a distinctly elongated structure, to over 500 RRL in Sculptor \citep{vaz15} - using {\it Spitzer}-IRAC, will allows us to more tightly constrain their evolutionary history. Sculptor was the first MW dSph satellite discovered (\citealt{sha38}) and, consequently, is among the best studied ones. \citet{van78} identified 602 variables associated with the galaxy, deriving and publishing periods for 64 of these. \citet[hereafter, K95]{kal95}, as a part of the Optical Gravitational Lensing Experiment (OGLE) project, has published a catalogue of 229 variables (226 RRL and 3 Anomalous Cepheids) located in the inner part of Sculptor. Using the period distribution of RRab stars, these authors estimated that the bulk of Sculptor RRL has metallicity $\text{[Fe/H]}_{\text{ZW}} \leq -1.7$ dex\footnote{ZW denotes \citet{zew84} metallicity scale. This scale is widely used in the literature and is based on the average of integrated-light and spectroscopic indices calibrated on a small number of photographic high resolution spectra. However, different metallicity scales were later developed based on abundance analysis of high resolution spectra of red giant branch stars in MW globular clusters. A widely used one is the \citet{car97} scale, that is now superseded by the \citet{car09} metallicity scale. On average ZW and \citet{car09} scales differ by only 0.01 dex. Detailed transformation relations between the two scales are provided by \citet{car09}.}. However, they also note that the colour range spanned by RGB stars is suggestive of a metallicity spread as large as $-2.2\lesssim\text{[Fe/H]}_{\text{ZW}}\lesssim-1.6$ dex. Indeed, \citet{maj99}, from an analysis of RGB and HB stars based on optical photometry, found that Sculptor has a bimodal metallicity distribution with a metal-poor stellar component having $\text{[Fe/H]}\sim$ $-2.3$ dex and a more metal-rich component at $\text{[Fe/H]}\sim$ $-1.5$ dex. Combining photometric and high resolution spectroscopic data \citet{tol04} confirmed the presence of two stellar populations in Sculptor, one metal-rich, $-0.9<\text{[Fe/H]}< -1.7$ dex, and one metal-poor, $-1.7<\text{[Fe/H]}<-2.8$ dex, that are kinematically and spatially separate from each other. Independently, \citet[][using the velocity dispersion gradient from the calcium triplet lines in spectra of the galaxy's red giant stars]{bat08} and \citet[][by measuring the age gradient from the outer to inner galaxy regions with wide-field photometry]{deb11} confirmed the existence of multiple components in this dSph. \citet[hereafter, C05]{cle05} obtained low resolution spectra for 107 RRL in Sculptor (about half the sample of RRL in \citetalias{kal95}) and measured individual metallicities in the range $-0.85<\text{[Fe/H]}<-2.40$ dex, with an average value of $\text{[Fe/H]}_{\text{ZW}} =-1.83 \pm 0.03$ dex ($rms=0.26$). \citetalias{cle05} remains so far the only spectroscopic measurement study of Sculptor RRL metal abundances. It confirms the existence of a real metallicity spread in this dSph, wider than that found by \citetalias{kal95} and consistent with the spread obtained by \citet{gei05} based on high resolution spectra of four RGB stars ($-2.1\lesssim\text{[Fe/H]}_{\text{ZW}}\lesssim-0.97$ dex). The distance modulus of Sculptor has been measured using several different distance indicators and independent techniques. Over 30 measurements exist in the literature, the majority using RR Lyrae stars. \citetalias{kal95} derived % a distance modulus of $19.71$ mag based on the average V magnitude of more than 100 RRab stars in their catalogue. Recently, \citet{vaz15,vez16a} used archival data spanning 24 years to redouble the known RRL population in Sculptor. They discovered more than 300 new variables spread over $\sim$6 deg$^{2}$ from the galaxy's centre. They used the RRL Period-Luminosity (PL) relation in the $I$-band to pin the Sculptor distance modulus down to $19.62 \pm 0.04$ mag\footnote{These authors also inferred (semi-theoretical) metallicities for their RRL sample, exploiting the dependence of the $I$-band PL relation on metallicity \citep{mar15}. Their average metallicity is consistent with the majority of previous spectroscopic measurements.}. A detailed comparison of values in the literature for the distance to Sculptor is presented in Section~\ref{sec:distances}. This paper is the first in a series dedicated to the results obtained for the four dSph galaxies % observed in the SMHASH program. As Sculptor is the dSph with the largest number of previously known RRL in our sample, we have chosen this galaxy to demonstrate the observational and data reduction methodologies adopted throughout the dwarf satellites section component of this program. This paper serves as a fiducial work for the rest of the SMHASH program on dSphs. The paper is organised as follows: observations, data reduction and the IRAC-{\it Spitzer} photometry calibration are presented in Section~\ref{sec:obs_data}. Section~\ref{sec:lc} describes the analysis of the RR Lyrae mid-infrared light curves and presents the catalogue (atlas). The determination of the distance to Sculptor derived from the RR Lyrae stars is presented in Section~\ref{sec:pl_dist} along with a discussion of potential metallicity effects and a comparison with previous distance determinations in the literature. % Finally, Section \ref{summary} summarises the paper main results and conclusions. | \label{summary} As part of the SMHASH program, using IRAC-\textit{Spitzer} data we have determined a new distance modulus of the Sculptor dSph using RR Lyrae stars located in the inner region of the galaxy. We obtained time series photometry for 49 RR Lyrae stars, (36 RRab and 13 RRc) at 3.6 $\mu$m. Seven stars were discarded from the initial sample due mainly to photometric contamination effects. Adopting periods from \citet{kal95} and \citet{cle05} we built light curves for the remaining 42 highest quality stars, delineating their mid-infrared pulsation properties. In order to investigate the photometric properties of the sample, and to choose the highest quality subsample of stars, we created four datasets (D1, D2, D3 and D4) by removing various problematical stars (see Section~\ref{sec:lc} for details). PL relations were derived for each RRab-only and RRab+RRc ({\it fundamentalised}) dataset, and were found to be in reasonable agreement (i.e., within $1\sigma$) with the empirical relations published in \citet{mad13}, \citet{nee15}, as well as the revised relations from \citet{nee17} and the recent PL relations derived by \citet{mur18b} (Table~\ref{tab:slo}). We adopt for Sculptor the distance modulus derived from the D4 sample, as this has the cleanest RRL selection and the best-fit slopes are the closest to the published empirical relations that we have considered as a reference in this work. We are aware that mid-infrared studies of the RRL PL are increasing \citep{mad13,dam14,kle14,nee15,nee17,mur18b}, but choose the \citet{mad13}, ~\citet{nee15}, ~\citet{nee17} and ~\citet{mur18b} PLs as fiducial as they are built using the sample of RRL calibrators whose trigonometric parallaxes were measured by \citet{ben11} with the FGS@HST and, more recently, by \textit{Gaia}. Furthermore, because \citet{nee15} and \citet{mur18b} derived PL relations using Warm IRAC-\textit{Spitzer} data, the same instrument and passband used for the work here, we consider them the most reliable reference for our study. Due to the significant metallicity spread observed in the Sculptor's RRL and the presence of two separate stellar populations (\citealt{maj99,tol04}), we also investigated the potential for metallicity effects on the mid-IR RRL PL relation and our subsequent Sculptor distance determination. We considered a sample (DZ) containing 20 RRL for which \citet{cle05} provided spectroscopic metallicity measurements. In addition, we split the DZ sample into two further sub-samples -- \textit{metal-poor} ($\text{[Fe/H]}_{\text{ZW}} <-1.7$) and \textit{metal-rich} ($\text{[Fe/H]}_{\text{ZW}} >-1.7$) -- reflecting the two populations found by \citet{tol04}. Using these sub-samples to remeasure the PL slope, and making comparisons both between the different PLs and distance moduli measured in our work and adopting the slopes from \citet{mad13}, \citet{nee15}, \citet{nee17} and \citet{mur18b}, we do not find any evidence for a significant metallicity effect on our result. We measure the distance modulus of Sculptor as ${\mu = 19.60 \pm0.02}$~(statistical) $\pm 0.04$~(photometric) mag (with $\sigma_{sys}=$0.09 mag), corresponding to $83 \pm 1$~(statistical) $\pm 2$ ~(photometric) kpc (with $\sigma_{sys}=$4 kpc), using the 17 RRab stars of the D4 sample and adopting as fiducial the 3.6~$\mu$m empirical period--luminosity relation for only RRab stars in the Galactic globular cluster M4 derived by \citet{nee17}, or $\mu$ = 19.57 $\pm$ 0.02 (statistical) $\pm$ 0.04 (photometric) mag (with $\sigma_{sys}=$0.11 mag) using the whole D4 sample (19 RRL) and the empirical period--luminosity relation at 3.6~$\mu$m for RRab+RRc+RRd stars in the Large Magellanic Cloud globular cluster Reticulum recently derived by \citet{mur18b} calibrated on \textit{Gaia} parallaxes. We find consistent results for the distance modulus using also the \citet{mad13,nee15} relations (Table~\ref{tab:mod}). These distances are also in good agreement with the estimates by \citet{tam08}, \cite{pie08} and \citet{vaz15}. \\We have also tried to quantify the depth effect set by our data and whether it can affect our distance estimation. The line of sight depth can be measured by subtracting in quadrature the distance scatter we found for Sculptor adopting the D4 sample and the distance scatter that \citet{mur18b} provide for Reticulum: $[(0.08)^{2}-(0.06)^{2}]^{1/2} \simeq 0.05$ mag, corresponding to $\pm2$ kpc, which is completely within our photometric error. \\ A significant advantage of our study is that we are able to obtain a precise distance estimate of comparable accuracy to the larger studies using an RRL sample that is less than 10$\%$ of the size analysed by \citet{vaz15} and less than 4$\%$ of the total number of Sculptor RRL stars discovered to date. The Sculptor RRL catalogue may not yet be complete, despite having 536 variables identified so far \citep{vez16b}. The key feature of our study that has enabled this significant leap forward has been moving to the mid-IR to observe RRL, where (i) the intrinsic dispersion of the RRL PL relation is narrower compared to that at shorter wavelengths; (ii) RRL light curves at 3.6 $\mu$m have more symmetrical shapes and smaller amplitudes, providing more precise mean magnitudes, and (iii) the effects of reddening/extinction are dramatically reduced. Combined with our confirmation here that any metallicity effect on the 3.6~$\mu$m PL must be small, if it exists at all, our study of Sculptor sets the stage for our future work on the other dSphs observed in the SMHASH project. % It is undeniable that the error budget of our results is dominated by the systematic error affecting the absolute zero-point calibration of the RRL mid-infrared PL relations. Indeed testing the quality of our mid-infrared photometry using different RRL subsamples we found very similar distance moduli, even identical in many cases, for given fiducial PL relation, proving that the accuracy of the final distance is not limited by the quality of mid-infrared data but rather by the choice of the adopted fiducial PL relation. In this SMHASH project great contribution is expected from exploitation of Gaia DR2 and future data released of this mission. Gaia DR2 contains a first mapping of full-sky RRL (\citealt{holl18}, \citealt{cle18}) and parallaxes based on Gaia-only measurements for about 1.3 billion sources (\citealt{gai18}; \citealt{lin18}). Among them is a much larger number of Galactic RRL than the 5 calibrators with HST parallaxes of \citet{ben11}. \citet{mur18c} have recently derived a new RRL PLZ relation whose slope and zero point are based on the Gaia DR2 parallaxes of about 400 Galactic RRL. \citet{mur18c} manuscript is not yet published therefore we decide to not include results based on the new PLZ in our paper. % | 18 | 8 | 1808.04843 |
1808 | 1808.03652_arXiv.txt | We present moderate resolution near-infrared spectra in $H, J$ and $K$ band of M dwarf hosts to candidate transiting exoplanets discovered by NASA's K2 mission. We employ known empirical relationships between spectral features and physical stellar properties to measure the effective temperature, radius, metallicity, and luminosity of our sample. Out of an initial sample of 56 late-type stars in K2, we identify 35 objects as M dwarfs. For that sub-sample, we derive temperatures ranging from 2,870 to 4,187 K, radii of $0.09-0.83$ $R_{\odot}$, luminosities of $-2.67<log L/L_{\odot}<-0.67$ and [Fe/H] metallicities between $-0.49$ and $0.83$ dex. We then employ the stellar properties derived from spectra, in tandem with the K2 lightcurves, to characterize their planets. We report 33 exoplanet candidates with orbital periods ranging from 0.19 to 21.16 days, and median radii and equilibrium temperatures of 2.3 $R_{\oplus}$ and 986 K, respectively. Using planet mass-radius relationships from the literature, we identify 7 exoplanets as potentially rocky, although we conclude that probably none reside in the habitable zone of their parent stars. | Since its launch in 2009, the NASA $Kepler$ spacecraft has gathered exquisite photometry of over 150,000 stars and has uncovered thousands of exoplanets in our galaxy via the transit photometry method \citep{2010Sci...327..977B,2011ApJ...728..117B,2013ApJS..204...24B,2014yCat..22100019B}. $Kepler$ continuously monitored the same part of the sky for four years, until reaction wheel failure compromised the pointing stability of the spacecraft. However, engineers soon found a way to balance the spacecraft using solar pressure and repurposed it for a new mission, K2 \citep{2014PASP..126..398H}. In this new mode of operation, K2 observes different regions along the ecliptic, targeting between 10 and 30 thousand stars for approximately 80 days. K2 is therefore particularly suited for searches of transiting exoplanets in short-period orbits. The motivations for targeting M dwarfs for both exoplanet searches and follow-up observations are manifold. First, M dwarfs are the most common type of star, comprising nearly 70\% of all stars in the Milky Way \citep{2010AJ....139.2679B}. Second, although they were initially thought to host planets infrequently for their dearth of Jupiter-size planets, the $Kepler$ and K2 missions revealed that M dwarfs form smaller (potentially rocky) planets in greatest abundance \citep{2012ApJS..201...15H}. Studies have shown that for planets with periods of less than 50 days, planets between $2-4R_{\oplus}$ are twice as abundant around M dwarfs than around sunlike stars \citep{2012ApJS..201...15H,2015ApJ...814..130M}. This fact, combined with the ubiquity of M dwarfs, establish them as the majority of hosts to small planets in the Milky Way. \citet{2015ApJ...807...45D} found that the mean number of small planets $(0.5-4R_{\oplus})$ per late K dwarf or early M dwarf is $2.5\pm0.2$ for orbital periods shorter than 200 days, comparable to the $2.0 \pm 0.45$ determined by \citet{2014DPS....4630109M}. Additionally, the smaller radii and masses of M dwarfs translate to larger transit depths, larger radial velocity semi-amplitudes, and larger transmission spectroscopy signals for exoplanet study (for a detailed summary of the advantages and complications of M dwarfs as planet host stars, see \cite{2016PhR...663....1S}). The recent discoveries of small, temperate exoplanets circling M dwarfs, such as Proxima b \citep{2016Natur.536..437A}, the TRAPPIST-1 system \citep{2017Natur.542..456G} and LHS1140 b \citep{2017Natur.544..333D} have further demonstrated the feasibility of targeting cool, small stars in the search for potentially life-bearing worlds. Despite these facts, there is a relative paucity of detected planets orbiting M dwarfs. They number several hundred, as compared to the several thousand of their FGK counterparts \footnote[1]{https://exoplanetarchive.ipac.caltech.edu/}. They are challenging to characterize from spectra (\citet{2011ESS.....2.1903T}, with summary in \citet{2016PhR...663....1S}) and also comprised a small fraction in the $Kepler$ Input Catalogue \citep{2011AJ....142..112B}. However, recent studies have made critical inroads linking spectral features to physical properties of M dwarfs \citep{2012ApJ...757..112B, 2012ApJ...748...93R, 2012ApJ...747L..38T, 2012ApJ...753...90M, 2013ApJ...779..188M, 2015ApJ...800...85N}. Moreover, stars cooler than 4000 K make up 25\% of the TESS Input Catalog \citep{2015ApJ...809...77S,2018AJ....155..180M}, as opposed to 5\% of the $Kepler$ Input Catalog \citep{2011AJ....142..112B}. Precise stellar characterization is ultimately crucial to understand the planet sample. The characteristics of these new worlds are so closely tied to the physical properties of their host stars, that we must understand the stars first if we aim to understand the planets in detail. Eking out the mass-radius relationship of exoplanets, for example, relies on large spectroscopic or asteroseismic surveys to characterize the host stars to better than $10\%$ \citep{2013AAS...22140705W,2013giec.conf30103H,2014AJ....148...78D,2016ApJ...825...19W,2017AJ....154..109F,2018MNRAS.479.4786V}. Furthermore, the deluge of exoplanet discoveries and our limited resources make it impossible to follow-up every single planet candidate. Reliably identifying the most promising candidates for follow-up characterization, demands that we know the characteristics of the candidates. For K2, in contrast to $Kepler$, the target-selection has been proposal-driven. Likewise, stellar characterization of large samples of K2 planet host stars has been an ongoing community effort \citep{2016ApJS..224....2H,2017ApJ...836..167D}. To contribute to this endeavor, we present in this study the stellar characterization of 35 candidate exoplanet host stars from K2 with near-infrared spectra. We infer the temperatures, radii, luminosities, mass and metallicities of the stellar sample using empirial relationships. We subsequently estimate the radii and equilibrium temperatures of the planet candidates. The paper is organized as follows: in Section 2, we describe the observation techniques and the reduction pipeline of our spectra. In Section 3, we present an analysis of the data, the derivation of the equivalent widths (EWs) of different metals and a comparison of our derived equivalent widths of the aluminum feature at 1.67 microns to those previously published. In Section 4, we summarize the results of our analysis for the cool dwarf sample. In Sections 5 and 6, we explain the derivation of the planet parameters and discuss the potential habitability of the planets. We identify two systems suitable for follow-up Doppler and atmospheric characterization, and we highlight several false positives from the K2 photometry pipeline. In Section 7, we conclude and summarize our findings and recommendations for follow-up observations. | In this study, we employ NIR spectra to derive the physical properties of a subset of M dwarf exoplanets and their host stars, uncovered by K2. We adopted a number of empirical calibrations for low-mass stars that relate the EWs of spectral features in the NIR to the stars' physical properties. We compared our EWs of a line sensitive to both radius and temperature, to those from other publications and find that they are in good agreement. Our original sample of K2 stars was contaminated by red giants or dwarfs of hotter classifications, and we discarded those from the characterization presented here. Additionally, we characterized the associated exoplanet candidates of the stellar sample using the inferred updated properties of their hosts. We specifically estimated the candidate planets' radius and temperature. Our planet sample is largely comprised of small planets, with 11 exoplanet candidates with $R_{p} < 2 R_{\oplus}$, and 22 exoplanets (66\%) with $2 R_{\oplus}< R_{p} <6 R_{\oplus}$. We assessed the habitability of these planets and determined that although some of them might be consistent with a rocky bulk composition, they are too highly radiated by their host stars to be in the habitable zone. Nevertheless, because the stars studied here are relatively bright targets $(\overline{K_{s}} = 11.5)$, some of them could be suitable for follow-up characterization with JWST. In particular, we highlight two systems that are good for atmospheric characterization with HST, $Spitzer$ or JWST: EPIC 211509553 (with R= 9.65 $R_{\oplus}$ and $R_{p}/R_{\star}= 0.18$) which has been statistically validated in other publications as a cool giant; and EPIC 211995398 (R= 10.5 $R_{\oplus}$ and $R_{p}/R_{\star}= 0.15$), which remains a candidate at present. Of our final sample of 35 M dwarfs, 24 possess published characterization \citet{2017ApJ...836..167D}, while 11 are new to the literature. These 11 bring the total number of validated exoplanets to 318 from NASA's K2 mission to date. | 18 | 8 | 1808.03652 |
1808 | 1808.04628_arXiv.txt | { Cosmic dust is a key tracer of structure formation and evolution in the universe. In active galactic nuclei (AGN) the origin and role of dust are uncertain. Here, we have studied dust in the X-ray bright and reddened type-1 quasar \ic, which exhibits an ionised AGN wind. We incorporated high-resolution X-ray and mid-IR spectroscopy, combined with broad-band continuum modelling, to investigate the properties of dust in this AGN. We used new \chandra HETGS observations taken in June 2017, as well as archival data from \xmm, \swift, \hst, \spitzer, IRAS, and \herschel for our IR-optical-UV-X-ray modelling. Two distinct components of dust in \ic are found. One component is in the interstellar medium (ISM) of the host galaxy, and the other is a nuclear component in the AGN torus and its associated wind. The emitting dust in the torus is evident in mid-IR emission (9.7 and 18 \micron features), while dust in the wind is present through both reddening and X-ray absorption (O, Si, and Fe edge features). The gas depletion factors into dust for O, Si, and Fe are measured. We derive an intrinsic reddening $\ebv \approx 1.0$, which is most consistent with a grey (flat) extinction law. The AGN wind consists of three ionisation components. From analysis of long-term changes in the wind, we determine limits on the location of the wind components. The two lowest ionisation components are likely carriers of dust from the AGN torus. We find that the dust in the nuclear component of \ic is different from dust in the Milky Way. The dust grains in the AGN torus and wind are likely larger than the standard Galactic dust, and are in a porous composite form (containing amorphous silicate with iron and oxygen). This can be a consequence of grain coagulation in the dense nuclear environment of the AGN. } | Cosmic dust is widespread in the universe. It can be used to trace the evolutionary paths of planets, stars, and even black holes. Dust grains in the ISM of galaxies alter the appearance of the observable universe through absorption and scattering of photons. Thus, determining the effects of dust is needed for studying a wide range of astrophysical phenomena. Indeed a significant fraction of ISM is locked up in dust grains (e.g. \citealt{Jenk09}). However, many aspects of cosmic dust remain poorly understood, such as: their chemical composition and origin; their physical properties and spectral signatures; their formation and evolution, and destruction mechanisms; and their role and impact on their environment. In AGN the properties of dust are particularly uncertain (see e.g. the review by \citealt{Li07}). Also, dust in AGN can be associated to different possible origins, such as: dust lanes of recent galaxy merger remnants, or dusty winds from the AGN (see e.g. \citealt{Komo97,Reyn97,Lee01,Cren01b}). Dust is an essential player in the unification theory of AGN, where the supermassive black hole (SMBH) and the accretion disk are surrounded by an optically-thick dusty torus. The observational properties of AGN are hence strongly influenced by our viewing angle relative to the orientation of this obscuring torus (\citealt{Anto85,Anto93,Urry95}). Yet, our knowledge of dust properties in the AGN torus and its environment is limited. Accretion onto SMBHs at the core of AGN is accompanied by winds of gas, which couple the SMBHs to their environment. The observed relations between SMBHs and their host galaxies, such as the M--$\sigma$ relation \citep{Ferr00}, indicate that SMBHs and their host galaxies are likely co-evolved through a feedback mechanism. The AGN winds can play a key role in this co-evolution as they can significantly impact star formation (e.g. \citealt{Silk98}) and chemical enrichment of the surrounding intergalactic medium (e.g. \citealt{Oppen06}). However, there are significant gaps in our understanding of the outflow phenomenon in AGN, which cause major uncertainties in determining their role and impact in galaxy evolution. The origin and physical structure of AGN winds are generally poorly understood. Different mechanisms have been postulated for the launch and driving of winds from either the accretion disk or the AGN torus (e.g. \citealt{Krol01,Prog04,Fuku10}). However, their association to the different kinds of winds found from observations is uncertain. AGN winds can originate as either thermally-driven \citep{Krol01} or radiatively-driven \citep{Doro08} winds from the dusty torus. Indeed the warm-absorber winds, which are commonly detected in the UV and X-ray spectra of bright AGN, are most consistent with being torus winds (e.g. \citealt{Kaas12,Meh18}); thus dust could be mixed with such winds. Importantly, the infrared (IR) radiation pressure on dust grains can boost winds from the torus \citep{Doro11}. Therefore, establishing the existence of dust in AGN winds is important for understanding the driving mechanism of AGN winds, and defining their impact on their environment. This is needed for assessing the contribution of such winds to AGN feedback. There are observational evidence, which indicate that AGN winds are likely carriers of dust into the ISM. For example, in the case of \object{ESO~113-G010} \citep{Meh12}, presence of dust embedded in the AGN wind was inferred based on the altering of the AGN emission, dust-to-gas ratio arguments, and the properties of the wind. In order to advance our understanding of cosmic dust in the universe we need to utilise all available tools at our disposal. The X-ray energy band, which is invaluable for exploring both the cold and hot gas, is a relatively new scientific window for dust studies. The X-ray absorption fine structures (XAFS) at the K edge of O, Mg, Si, Fe, and the LII and LIII edges of Fe provide distinct and unblended signatures of dust grains in X-rays (e.g. \citealt{Lee09,Cost12,Zeeg17,Roga18}). Therefore, in addition to the traditional low-energy domain observations, like in the IR, the X-ray band enables us to directly access the chemical composition of dust in the diffuse ISM of galaxies. Thus, high-resolution X-ray spectroscopy provides a powerful and sensitive diagnostic tool to probe the properties of both gas and dust. This is invaluable for understanding the formation and evolution history of galaxies, including the host galaxies of AGN. Indeed X-ray spectroscopy can help in studying the chemistry of dust in AGN (e.g. \citealt{Lee13}), which is an important indicator of the evolutionary phase of AGN. \object{IC~4329A} is bright nearby AGN at redshift ${z = 0.016054}$ \citep{Will91}. It has been described as `an extreme Seyfert galaxy' \citep{Disn73} and `the nearest quasar' \citep{Wils79}, based on the spectroscopy of its broad optical emission lines. However, it is technically classified as a Seyfert 1.2 by \citet{Vero06}. The host galaxy of the AGN is highly inclined (i.e. edge-on), with the observed ratio of minor to major axis ${b/a = 0.28}$ \citep{deVa91}. A prominent dust lane bisects the nucleus of \ic, which can be seen in the HST image of Fig. \ref{dustlane_fig}. The dust lane is indicative of the past merger history of this galaxy. \ic is a member of a group of seven galaxies \citep{Koll89}. It is displaced by a projected distance of 59 kpc from the giant lenticular galaxy \object{IC 4329} \citep{Wols95}. The relative orientations of the axes of the AGN and the disk of the host galaxy may have been influenced by interaction between \ic and its massive neighbour IC~4329 \citep{Wols95}. The mass of the supermassive black hole (\MBH) in \ic is not accurately determined. The \MBH from reverberation study is poorly constrained due to low quality lightcurves, and hence unreliable lag measurements, from which \citet{Pet04} estimate an upper limit of $\sim 3 \times 10^{7}$~$M_{\odot}$. However, measurements using other methods find higher \MBH. Using the empirical relation derived by \citet{McHa06} between the bolometric luminosity $L_{\rm bol}$, \MBH, and the break frequency in the X-ray power spectral density function (PSD), \citet{Mark09} calculate $M_{\rm BH} = 1.3_{-0.3}^{+1.0} \times 10^{8}$~$M_{\odot}$. Also, using relations between \MBH and the stellar velocity dispersion $\sigma_*$, \citet{Mark09} find $\MBH \approx 2_{-1}^{+2} \times 10^{8}$~$M_{\odot}$. Furthermore, \citet{deLa10} report $\MBH \sim 1.2 \times 10^{8}$~$M_{\odot}$. From the AGN sample study of \citet{Vasu10}, the black hole mass is estimated from the $K$-band luminosity of the host galaxy bulge, which in the case of \ic is found to be about $2 \times 10^{8}$~$M_{\odot}$. Therefore, in our calculations we assume \MBH is $\sim$1--2~$\times 10^{8}$~$M_{\odot}$. \citet{Stee05} studied the X-ray absorption in \ic with \xmm RGS spectroscopy. They found absorption by neutral gas in the host galaxy of the AGN, as well as warm absorption by an AGN wind. Despite significant absorption, \ic is bright enough for high-resolution X-ray spectroscopy, which is often not the case for many reddened and absorbed AGN, making \ic a valuable target. The column density \NH of the neutral gas was measured to be about ${1.7 \times 10^{21}}$~\cm \citep{Stee05}. The warm absorber was found to have four ionisation components, with a total \NH of about ${1.0 \times 10^{22}}$~\cm. The velocity of the warm absorber components ranges from ${-200 \pm 100}$ to ${+20 \pm 160}$~\kms. Possible X-ray spectral features of dust were not investigated in \citet{Stee05}. Dust reddened and absorbed AGN are often too faint for dust X-ray spectroscopy because of strong absorption. Therefore, finding a suitable target is key. For our X-ray spectroscopic investigation of dust in winds, the AGN target must meet these required selection criteria: (1) bright enough in X-rays; (2) displays significant intrinsic reddening; (3) exhibits evidence of dust features in both X-rays and IR; (4) shows the presence of an AGN wind; (5) minimum amount of reddening and absorption contamination by the Milky Way in our of sight. Among many candidates that we systematically searched, \ic is one of the most suitable AGN that meets all these criteria. Our newly acquired \chandra-HETGS observations of \ic are presented for the first time in this paper. The structure of the paper is as follows. The observations and the reduction of data are described in Sect. \ref{data_sect}. The modelling of the spectral energy distribution (SED) is presented in Sect. \ref{sed_sect}. The modelling of the X-ray absorption by the ISM gas and the AGN wind are explained in Sect. \ref{wind_sect}. The multi-wavelength analysis of dust in \ic based on reddening, IR emission features, and X-ray absorption features, is presented in Sect. \ref{dust_sect}. We discuss all our findings in Sect. \ref{discussion}, and give concluding remarks in Sect. \ref{conclusions}. The spectral analysis and modelling presented in this paper were done using the {\tt SPEX} package \citep{Kaa96} v3.04.00. The spectra shown in this paper are background-subtracted and are displayed in the observed frame. We use C-statistics for spectral fitting and give errors at the $1\sigma$ confidence level. We adopt a luminosity distance of 69.61 Mpc in our calculations with the cosmological parameters ${H_{0}=70\ \mathrm{km\ s^{-1}\ Mpc^{-1}}}$, $\Omega_{\Lambda}=0.70$, and $\Omega_{m}=0.30$. We assume proto-solar abundances of \citet{Lod09} in all our computations in this paper. \begin{figure}[!tbp] \centering \hspace{-0.8cm}\resizebox{0.95\hsize}{!}{\includegraphics[angle=0]{IC4329A_hst_image_final.ps}\hspace{-2.8cm}} \caption{Nuclear region of \ic as observed by the HST, showing the presence of a dust lane covering the nucleus. The image is obtained from an observation taken with the ACS/HRC F550M filter on 22 February 2006, and is displayed with a logarithmic intensity scale.} \label{dustlane_fig} \end{figure} | \label{conclusions} In this paper we have carried out broad-band continuum modelling spanning far-IR to hard X-rays, combined with high-resolution X-ray and IR spectroscopy, to investigate the nature and origin of dust in \ic. From the findings of our investigation we conclude the following. \begin{enumerate} \item There are two distinct components of dust in \ic: an ISM dust lane component, and a nuclear component. The nuclear dust component originates from the AGN torus and its associated wind. Dust in the AGN torus is seen through IR emission, while the dust in the torus wind is detected through reddening and X-ray absorption in our line of sight. \medskip \item The AGN wind in \ic consists of three ionisation components. They have moderate outflow velocities: $-340$ to $-440$ \kms for two of the components, while the other is consistent with zero outflow velocity. \medskip \item According to our variability analysis, the two lowest ionisation components of the AGN wind show no long-term changes between historical and new observations (${\sim 14}$ years apart), while the highest component shows changes in \NH and ionisation parameter $\xi$. From the recombination timescale analysis, we derive limits on the distance of the wind components from the central engine. The two lowest ionisation components are at ${r > 350}$~pc, and ${r > 83}$~pc, while the highest ionisation component is at ${r < 93}$~pc. \medskip \item The total internal reddening in \ic is $\ebv \approx 1.0$. The reddening is most consistent with a grey (flat) extinction law. \medskip \item From high-resolution X-ray spectroscopy of dust in \ic we derive the total depletion factors from gas into dust for O, Si, and Fe. They correspond to 17--23\% for O, 70--100\% for Si, and 77--98\% for Fe. \medskip \item The dust grains associated to the AGN torus and its wind in \ic are likely larger than the Milky Way ISM dust, and are in a porous composite form, containing amorphous silicate with iron and oxygen. \medskip \item From on our modelling of the continuum from far-infrared to X-rays, we derive a bolometric luminosity of about ${2.5 \times 10^{45}}$~\ergs for \ic, which corresponds to 10--20\% of the Eddington luminosity. \end{enumerate} | 18 | 8 | 1808.04628 |
1808 | 1808.02304_arXiv.txt | Differing reaction rates of long-lived nuclear states can force the level occupations out of thermal equilibrium, causing calculations of overall rates which rely on thermal equilibrium to be inaccurate. Therefore, nucleosynthesis calculations which include nuclei with isomers must use techniques that do not assume thermal equilibrium, and it is imperative that such techniques appropriately account for transitions between the ground and isomeric states via higher-lying levels. We develop a formalism to compute the steady state occupations of nuclear levels and apply it to the examples {\Al}, {\Cl}, and {\Kr}. We show that this approach is useful both for assessing the required number of nuclear levels and for determining the temperature above which thermal equilibrium rates are appropriate. | Introduction} In astrophysical nuclear reaction calculations, nuclear isomers present a particular challenge. An isomer is an excited nuclear state with a lifetime much longer than typical excited states. Known isomers in nuclei span the range of lifetimes from $10^{15}$ years in $^{180}$Ta -- much longer than the accepted age of the universe -- to an informal rule of thumb on the lower side of approximately 1 ns. Isomers arise from nuclear structure effects (spin-trap, shape change, K quantum number, etc.) that inhibit $\gamma$-decay to lower energy levels \citep{wd:1999}. In most isotopes, thermally-driven electromagnetic transitions are fast and keep the nuclear state occupations in thermal equilibrium. Indeed, thermal $\beta$-decay rates and neutrino spectra are typically computed under the assumption of a Boltzmann distribution of level occupations \citep{ffn:1982b,oda-etal:1994,lm:2001,msf:2018}, with the total $\beta$-decay rate of the nucleus given by a thermal weighting of the decay rates of the individual states. \begin{equation} \lambda^{\beta} = \sum\limits_i \lambda_{i}^{\beta}n_i \label{eq:beta_inst} \end{equation} The sum is over all nuclear states $i$, $\lambda_{i}^{\beta}$ is the $\beta$-decay rate of state $i$, and $n_i$ is the occupation fraction of state $i$. \begin{equation} n_i = \frac{g_i}{G(T)}e^{-E_i/T} \label{eq:ni_therm} \end{equation} Here $g_i=2J_i+1$ is the degeneracy of state $i$, $J_i$ is the state's spin, $G(T)$ is the nuclear partition function at temperature $T$, and $E_i$ is the energy of nuclear state $i$. The suppressed $\gamma$ transitions between an isomer and lower-lying levels, however, can cause these long-lived states to fall out of thermal equilibrium, particularly if the isomer's destruction rate is vastly different from the ground state (GS). Essentially, if one destruction rate proceeds faster than the long-lived states can equilibrate, the rapidly-detroyed state will be depopulated relative to its thermal equilibrium occupation. This in turn results in a deviation of the total destruction rate from its thermal equilibrium value. Hence, when an isotope has a long-lived isomer sufficiently low in energy that it will have an appreciable thermal equilibrium occupation, it must be handled carefully in nucleosynthesis calculations. One of the best-known examples of this situation is the $\beta$-decay of {\Al}, a radioisotope used as a cosmochronometer for early solar system studies and $\gamma$-ray astronomy. The GS of {\Al} has a half-life against $\beta$-decay of $0.717$ Myr, but it also has a long-lived isomer at 228 keV. This isomer has a super-allowed $\beta$-decay to the GS of {\Mg}, giving it a half-life of 6.35 s. Thermal processes at low temperature populate this isomer slowly compared to its $\beta$-decay rate, so its occupation in medium will be significantly lower than the thermal Boltzmann value. This results in a lower $\lambda^\beta$ than that computed from a Boltzmann distribution. Because of its observational importance, the $\beta$-decay rates of {\Al} in a thermal bath have been studied extensively, including numerous approaches to computing an effective $\lambda^\beta$ \citep{wf:1980,coc2000,runkle2001,gupta2001,iliadis2011,reifarth}. The techniques from previous studies consider differing numbers of nuclear levels in their calculations. It is generally agreed that the number of included states can impact the results, as higher-lying levels act as intermediate states that facilitate ``communication'' between the GS and the isomer. At sufficiently high temperature, however, thermal processes are fast enough to keep the nuclear levels in thermal equilibrium. Above this equilibration temperature, effective treatments should in principle converge, and thermal destruction rates are appropriate. This paper provides a method for determining an appropriate number of nuclear levels to include in nucleosynthesis calculations. This technique also provides the equilibration temperature. After some brief general comments on isomers in section \ref{sec:isomers}, we show how to express the long term ($t\rightarrow\infty$) steady state nuclear level occupations from which to compute total destruction rates. This formulation, detailed in section \ref{sec:evolution}, includes the effects of producing nuclei in any configuration of initial states and uses generalized destruction rates. We give example results for {\Al}, {\Kr}, and {\Cl} in section \ref{sec:results}, and we discuss the results with some concluding remarks in section \ref{sec:concl}. | } We have described a method for estimating destruction rates of nuclei with long-lived isomers by computing their steady state behavior, and we have provided examples using $\beta$ decay. While the time dependence of astrophysical environments will generally render the steady state approach inapplicable directly in nucleosynthesis network codes, it is nonetheless useful for evaluating other techniques, determining the minimum number of states other techniques must include (whether directly or indirectly), and the temperature above which thermal equilibrium rates apply (the equilibration temperature). We emphasize that TE rates eventually become necessary. Higher-lying states may contribute significantly to the total $\beta$-decay rate $\lambda^\beta$, and in such cases, any technique which treats $\beta$ decay as proceeding principally from the long-lived states must be abandoned at high temperature. In {\Al}, for example, at $T\gtrsim 800$ keV, the thermal population of the 1058 keV level is similar to the isomer, owing to its greater spin degeneracy (see equation \ref{eq:ni_therm}). The higher level has isospin $\tau =1$, and its corresponding superallowed $\beta$ decay dominates the isomer's contribution to $\lambda^\beta$. Therefore, we recommend using TE rates above the equilibration temperature. Below the equilibration temperature, our steady state results show that nucleosynthesis calculations should include four states in {\Al}, while three states are sufficient for {\Cl}. As previous authors have found, the ground state of {\Al} electromagnetically couples most strongly to the 417 keV state, while the isomer couples to the 1058 keV state. Transitions between the two higher levels then effect communication between the ground and isomeric states. From table \ref{tab:kr_nuc_data}, the {\Kr} isomer couples to the $3/2^-$ 1107 keV level, with the 1141 keV level linking $3/2^-$ 1107 keV and ground. While our calculations include all five lowest states, the inefficient transitions between $1/2^-$ 1107 keV and 1141 keV suggest that the former can be excluded. In {\Cl}, the spontaneous $\gamma$-decay rate $\lambda_{42}$ of the 666 keV state (state 4) to the isomer (state 2) is approximately one order of magnitude faster than the experimental limit on the rate $\lambda_{32}$ from 461 keV (state 3) to the isomer; the calculations in this work used the shell model transition rate $\lambda_{32}$ reported in the appendix of \cite{banerjee-etal:2018}, which is more than two orders of magnitude slower than $\lambda_{42}$. Furthermore, both the experimental limits and the shell model calculation of $\lambda_{32}$ indicate that it is a generically slow transition. This qualitative analysis suggests that four states should be included. However, the lower transition energy from the isomer to 461 keV renders it thermodynamically favorable which, coupled with the strong transition from 461 keV to ground, gives the result that three states are sufficient for {\Cl}. Below the equilibration temperature, the total $\beta$-decay rates $\lambda^\beta$ are impacted significantly by which state a nuclide is produced in. Therefore, we caution against using the bare no-production steady state $\lambda^\beta$ in nucleosynthesis network calculations. While this is understood within the nucleosynthesis community, it bears repeating that network calculations should incorporate production channel branching into multiple long-lived states. Our technique of solving for steady state occupations of energy levels in nuclei with isomers uses no theoretical approximation methods apart from estimates of experimentally unverified nuclear rates (internal transition and $\beta$-decay). From the occupations, the overall rates of destruction processes such as $\beta$ decay can be computed for hot environments. Comparing these occupations with thermal equilibrium calculations yields the equilibration temperature above which TE rates should be used. We have shown (as previous authors have) that excited states facilitate transitions between the GS and isomer, and furthermore, more than one other excited state may be involved in the most efficient communication channels. It is therefore prudent to ensure that the chosen technique employs sufficient states, whether they are included explicitly or implicitly; steady state calculations can confidently determine that number, since the occupations are sensitive to the efficiency of communication between the long-lived states. Finally, we remark that the influence of long-lived isomers in astrophysics is likely insufficiently explored. There are of course the issues with the nuclei discussed here, as well as with the cosmochronometer $^{182}$Hf \citep{lugaro-etal:2014} and others. Furthermore, most nuclei in the nuclear chart are deformed, and K-isomers are common in well-deformed, heavy mass regions \citep{chen-etal:2012,kdk:2015,dwk:2016,wu-etal:2017}. Thus, many nuclides in the r-process path have K-isomers, and there may be others in the s- and rp-process paths. The structure issues of isomers and their consequences in astrophysics remain to be fully understood. | 18 | 8 | 1808.02304 |
1808 | 1808.07651_arXiv.txt | Dual active galactic nuclei (DAGN) and supermassive black hole binaries (SMBHBs) at kpc and pc-scale separations, respectively, are expected during stages of galaxy merger and evolution. Their observational identification can address a range of areas of current astrophysics frontiers including the final parsec problem and their contribution towards the emission of low-frequency gravitational waves. This has however been difficult to achieve with current spectroscopy and time domain strategies. Very long baseline interferometry (VLBI) as a method of directly imaging radio structures with milli-arcsecond (mas) and sub-mas resolutions is introduced as a possible means of detecting DAGN and SMBHBs. We motivate its usage with expected observational signatures and cite some studies from literature to illustrate its current status, and present an updated list of candidates imaged with high-resolution radio observations. We then recall some shortcomings of the method with possible solutions and discuss future directions, relevant to large surveys with the upcoming Square Kilometer Array and future space VLBI missions.\\ {\bf Key points} \begin{itemize} \item Dual active galactic nuclei (DAGN) and supermassive black hole binaries (SMBHBs): observational status. \item Very long baseline interferometry (VLBI): a promising tool to detect dual AGN and SMBHBs. \item Observation strategies for the future. \end{itemize} | Hierarchical models of cosmological structure formation \citep[e.g.][]{2005Natur.435..629S} expect major mergers shaping galaxy evolution. Binary evolution upto kpc scales are governed by dynamical friction \citep{1943ApJ....97..255C} which here involves a decreasing binary separation through the extraction of their effective angular momentum and energy through stellar encounters \cite[e.g.][]{2001ApJ...563...34M,2005LRR.....8....8M} over $<$ 10 Myr timescales, which can be sped up by gravitational encounters with intervening gas \cite[e.g.][]{2007Sci...316.1874M,2007MNRAS.379..956D,2017MNRAS.469.4258T}; the kpc-separated central objects appear as a dual AGN (DAGN) \cite[e.g.][]{2003ApJ...596..860M,2005LRR.....8....8M}, possibly owing to rapid accretion. A continued merger aided by stellar gravitational interactions leads to a pc-scale separation Keplerian bound supermassive black hole binary (SMBHB) \citep[e.g.][]{1980Natur.287..307B}. The SMBHB is expected to be strongly gravitationally bound when its specific binding energy exceeds the nuclear stellar velocity dispersion based energy with a fiducial separation of $\sim 2.7$ pc marking this transition assuming a SMBH mass (smaller mass binary companion) of $10^8 M_\odot$ and a stellar bulge velocity dispersion of 200 km s$^{-1}$ \citep{2005LRR.....8....8M}. The central core is now depleted of stars and gas rendering dynamic friction ineffective in enabling further merger, the `final parsec problem' \cite[e.g.][]{1980Natur.287..307B}. This could be overcome through three-body interactions involving a companion massive black hole \cite[e.g.][]{2016MNRAS.461.4419B}, if the initial extraction of angular momentum and energy proceeds through episodes of stellar and gas interactions \cite[e.g.][]{2017MNRAS.472..514G}, or if the stellar loss cone can be re-populated efficiently thus enabling a continuity in stellar encounters \cite[e.g.][]{2017MNRAS.464.2301G}. These cause the bound SMBHB to enter the gravitational wave regime and tend towards coalescence rapidly. Alternatively, simulations of mergers in triaxial rotating galaxies indicate that the binary hardening rates are sufficient to enable efficient coalescence, avoiding stalling of the merger at pc-scales \citep{2006ApJ...642L..21B}. Observational identification of DAGN and SMBHBs, however, has mostly been indirect and serendipitous so far, mainly owing to the small separation and associated physical processes involved in both being distinct, thus requiring different search strategies in these classes of objects. Employed strategies have mainly involved spectroscopy and timing based on the double-peaked line profiles and continuum light curves from candidate sources. A range of multi-wavelength searches % have been met with varying levels of success \citep[e.g.][]{2003ApJ...582L..15K,2006MmSAI..77..733K,2012ApJ...746L..22K,2013ApJ...777...64C}. Double peaked spectral emission lines (e.g. H$\beta$, [O III]) separated in radial velocity by $\sim$ few hundred -- thousand km s$^{-1}$ are expected in a merging system hosting narrow- and broad-line regions (at larger and smaller physical distances from the central engine, respectively) \cite[e.g.][]{2007ApJ...660L..23G,2009ApJ...705L..20X}. Double peaked narrow lines are expected to indicate a DAGN while broader peaked lines could indicate a SMBHB. Though, these lines could originate from the superposition of unrelated overlapping AGN, peculiar geometry of the narrow line region (NLR) and kinematics within a single cloud (e.g. clumpy structure), powerful biconical outflows, jet--NLR interaction \citep[e.g.][]{2009ApJ...705L..20X,2012ApJ...753...42C} or as equal strength peaks from a rotating disk or ring ionized by a single underlying source \cite[e.g.][]{2012ApJ...752...63S}. % In fact, only a tiny fraction of AGN showing double-peaked emission line profiles have been identified as DAGN \citep[e.g.][]{2011ApJ...735...48S,2012ApJ...745...67F,2015ApJ...813..103M}. Updated lists of inferred DAGN compiled from the literature are presented in \citet{2018JApA...39....8R} and \citet{2018BSRSL..87..299D}. The continuum or line-based optical light curves may indicate quasi-periodicity over timescales of a few to tens of years, possibly related to the orbital period of a Keplerian SMBHB \citep[e.g.][]{% 2015MNRAS.453.1562G,% 2016MNRAS.463.2145C,2016MNRAS.463.1812M}. The well studied AGN OJ 287 putatively hosts a SMBHB, inferred through a pair of periodic optical outbursts every $\sim$ 12 yr \cite[e.g.][]{1988ApJ...325..628S,2011ApJ...729...33V} resulting from the impinging of the accretion disk of the primary by the secondary SMBH at these intervals during its orbital motion \cite[e.g.][]{1996ApJ...460..207L}. However, the recent study of \cite{2018MNRAS.478.3199B} notes that jet precession can explain the periodic variability though the driver of precession may still be a SMBBH. As spectroscopic and timing searches are indirect, they require ruling out competing models and need independent confirmation. % High resolution X-ray imaging spectroscopy observations with Chandra have resulted in the discovery of DAGNs \citep[e.g. NGC 6240:][]{2003ApJ...582L..15K}, \citep[Mrk 463:][]{2008MNRAS.386..105B}, \citep[Mrk 739:][]{2011ApJ...735L..42K}, \citep[Mrk 266:][]{2012AJ....144..125M}, and others from studies of candidate samples \citep[e.g.][]{2012ApJ...746L..22K,2013ApJ...777...64C}. Similar targeted X-ray and optical imaging observations are often hampered by obscuration and scattering of the central kpc-scale region by interstellar gas in the host galaxy or unsuitable orientation of the galaxy. Further, there is not sufficient resolution to clearly separate the two nuclei in these images, especially in objects at cosmological distances (well beyond the local Universe). Very long baseline interferometry (VLBI) was developed during the 1960s to resolve fine structures of compact bright radio sources, and is the highest-resolution imaging technique \citep{2001ARA&A..39..457K}; VLBI observations with baselines $\sim$ few thousand kilometers can resolve milli-arcsecond (mas) structures (physical sizes of pc to kpc) and directly image even closely-separated nuclei, thus offering a promising method of spatially identifying DAGN and SMBHBs. In comparison, the angular resolutions achievable in other wavebands are $\sim$ 0.5 arcsec with the {\em Chandra} X-ray Observatory, and $\sim$ 0.1 arcsec with the {\em Hubble Space Telescope} in the optical and ultraviolet and with the {\em W. M. Keck Observatory} adaptive optics system in the near infrared. The VLBI radio observations are then indispensable in studying binary evolution from kpc to pc scales \citep[e.g.][]{2017MNRAS.471.3646P} and constructing a statistically viable sample through direct imaging observations, clarifying mechanisms enabling coalescence of a binary before gravitational wave emission becomes dominant (to avoid or overcome the final parsec problem), and helping to understand the nano-Hz gravitational wave background emission \citep[e.g.][]{2017NatAs...1..886M} using pulsar timing arrays \cite[e.g.][]{2008MNRAS.390..192S,2010CQGra..27h4013H}. % The method and observational signatures relevant to it are discussed in Section \ref{obs}. % Future directions relevant to VLBI observation of DAGN and SMBHBs are then discussed in Section \ref{future}. | \label{future} The expected number of binary SMBH hosts can be inferred from the AGN luminosity function by accounting for the rate of mergers, the timescale of existence of the AGN phase, the SMBH mass function, and the spatial distribution of AGN in the redshift volume being probed \citep[e.g.][]{2009ApJ...700.1952H}; though, estimates are model dependent and hence could result in large uncertainties. Modeling SMBHBs during the inspiral phase driven by gas and gravitational wave emission, \cite{2018ApJ...863..185D} estimate $\sim$ 100 SMBHBs at $z \leq 0.5$ which can show periodic variability $<$ 10 yr that can be resolved using mm-wavelength VLBI, relevant to facilities such as the Event Horizon Telescope. The study of \cite{2015MNRAS.453.1562G} predicts 450 candidates showing optical periodic variability (assuming $R \leq 0.01$ pc, limiting $V$ magnitude of 20 and $z \leq 4.5$) but find only 111 candidates from a sample of 243500 quasars, indicating a conservative agreement. A similar $\geq$ 100 candidate DAGN ($R \sim$ kpc) in high frequency radio (e.g. 1.6 and 5 GHz) surveys with either medium sensitivity $\sim$ 0.1 mJy and sky area of $\sim$ thousand square degree or high sensitivity $\sim$ 10 $\mu$Jy and sky area of $\sim$ few hundred square degree is predicted by \cite{2014arXiv1402.0548B}. The study of \cite{2016MNRAS.463.2145C} finds a similarly conservative estimate of 33 candidates indicating periodic optical variability from a sample of 35383 quasars. SMBHBs indicate a transition to the gravitational wave emitting regime and the study of \cite{2018ApJ...856...42S} characterizes the expected gravitational wave background limits from pulsar timing arrays and finds a moderate tension with the above observational estimates, suggesting that the inferred candidate samples are contaminated with false detections. The above estimates based on periodic variability indicate an efficiency of 0.05 -- 0.09 \% which may only be upper limits, but are likely to improve with continued monitoring which will enable a more robust statistical identification. With the Square Kilometre Array (SKA) phase 1 Mid configuration in the 4 cm band ($\sim$ 8.4 GHz; applicable to possible SKA-VLBI observation) and a maximum baseline of $\sim$ 10000 km (between SKA 1-Mid and European VLBI stations), the resolution is about 0.15 mas. The expected image sensitivity is 3 $\mu$Jy/beam for an integration time of 1 hour with the full SKA1-Mid in the global VLBI network \citep{2015aska.confE.143P} so that the combination of high resolution and high sensitivity with reasonable integration time can resolve sub-mas structures in DAGN and SMBHB candidates \citep{2015aska.confE.151D}. The major shortcoming of the current VLBI technique is the small field of view at a given time, limiting its applicability for blind surveys. Further issue in the observation itself may arise from a combination of selection criteria and biases (methodology), instrumental properties and limitations (detection sensitivity) and intrinsic source-based properties (accretion and jet production mechanisms, radio quietness and non-active galaxies) \citep[e.g.][]{% 2018arXiv180302831S}. Further, as only $\sim$ 10\% AGN are typically radio loud, fainter sources should be sufficiently radio bright (and compact) to be VLBI detected; more DAGN are expected to be detected with an increasing VLBI sensitivity. Continuing efforts towards addressing these include the upgrading of equipment with higher data recording rate and updated software correlators, developing robust and time optimal algorithms for data handling and reduction, and their deployment and testing on smaller arrays and scaling up \citep[e.g.][]{2018NatAs...2..118A}. % For faint and un-beamed AGN hosting SMBHBs (non-existent or weak large-scale jet), the multi-beam, wide-field SKA can offer fast surveys, and its high sensitivity allows for discovering even weak radio loud/quiet pairs. It is essential to thus address why a larger number of DAGN and SMBHBs are yet to be observed using current strategies. An alternate means to resolve pc and sub-pc separation SMBHBs is by resorting to space VLBI observations with two or three space-based telescopes, operational in the 1.5 - 8.4 GHz frequency range and offering few tens of $\mu$as-mas resolutions. The space VLBI is expected to resolve the central regions of nearby bright AGN \citep[e.g. 3C 84, ][]{2018NatAs...2..472G} and revealing the precession of the jet nozzle, and to search for sub-pc-separation SMBHBs in elliptical galaxies which have likely experienced multiple mergers. Such space VLBI telescopes can be connected with large ground-based telescopes, such as SKA1-Mid, FAST 500m, Arecibo 300m, Effelsberg 100m and Green Bank 110m, pushing detection limits down to sub-mJy levels. Additionally, one can use ground based mm-wavelength facilities to achieve sub-mas resolutions \cite[e.g.][]{2011ApJ...735...57B} and even approach mJy sensitivity in the near future. | 18 | 8 | 1808.07651 |
1808 | 1808.09961_arXiv.txt | In a recent paper \citep{fumagalli17} we reported on the detection of a diffuse H$\alpha$ glow in the outskirts of the nearby, edge-on disc galaxy UGC 7321 observed with the Multi Unit Spectroscopic Explorer (MUSE) at the ESO Very Large Telescope. By interpreting the H$\alpha$ emission as fluorescence arising from hydrogen ionised by an external (i.e., extragalactic) radiation field, we estimated the UV background (UVB) intensity in terms of \HI ionisation rate (per ion) at $z\simeq 0$ to be in the range $\Gamma_\nHI\sim 6-8\times 10^{-14}$ s$^{-1}$. In the present work, by performing radiative transfer calculations over a large set of models of the gaseous disc of UGC 7321, we refine our estimate and through an MCMC analysis derive a value for the photoionisaton rate of $\Gamma_\nHI=7.27^{+2.93}_{-2.90}\times 10^{-14}$ s$^{-1}$. In particular, our analysis demonstrates that this value is robust against large variations in the galaxy model and that the uncertainties are mainly driven by the errors associated with the observed \ha\ surface brightness. Our measurement is consistent with several recent determinations of the same quantity by a completely independent technique (i.e., flux decrement analysis of the Ly$\alpha$-forest), and support the notion that the low redshift UVB is largely dominated by active galactic nuclei (AGNs), possibly with no need of further contribution from star forming galaxies. | \label{sec:introduction} The reionisation of the all-pervading intergalactic medium (IGM), the repository of most of the baryons across the history of the Universe, is a landmark event in the cosmic history of structure formation. Modern observations of the IGM have provided several tests of the $\Lambda$CDM paradigm, including a measurement of the power spectrum, upper limits to the neutrino masses, and a measure of baryonic acoustic oscillations \citep[e.g.,][]{mcdonald05,viel10,slosar13}. Most of our understanding of IGM physics, and its implication for galaxy formation and metal enrichment, depends critically on the properties of the cosmic ionising UV background (UVB), the integrated UV emission from all possible emitting sources in the Universe. Massive stars in young star forming galaxies and accreting supermassive black holes in active galactic nuclei (AGNs) are the most obvious sources of ionising UV radiation \citep[e.g.,][]{miralda90,HM96}, still their relative importance across the cosmic time is not firmly established \citep[see, e.g.,][and references therein]{kulkarni18}. Recent observational and theoretical progress are forging a coherent description of the thermal state and ionisation degree of the IGM. The UVB reionised the hydrogen component of the IGM by $z\simeq 6$ \citep[e.g.,][]{davies18,planck18}, while the double reionisation of helium occurred later, at $z\gta 3$ \citep[e.g.,][]{worseck16}, because of the reduced cross section and higher ionisation potential. In the post reionisation Universe, the UVB keeps the bulk of the IGM ionised \citep[e.g.,][]{gunn65,bolton07}, regulates its temperature \citep[e.g.,][]{theuns02}, and sets a characteristic mass below which haloes fail to form galaxies \citep[e.g.][]{okamoto08}. In the absence of firm observational constraints on $\Gamma_\nHI$ the current parametrisation of the UVB relies mostly on 1D radiative transfer calculations that follow the build-up of the UVB accounting for sources and sinks of radiation. These models have input parameters that are difficult to measure, such as the emissivity and escape fraction of ionising photons from galaxies and AGNs, and the distribution of \HI\ absorbers \citep[e.g.,][]{HM96,shull99,faucher09,HM12}. Therefore, different models predict values of $\Gamma_{\rm HI}$ that differ by factors of a few, primarily because the observational data that enter the modelling are not well known. As an example, the most recent models of the low-redshift UVB \citep{khaire15,MH15,onorbe17,puchwein18}, adopting an updated AGN emissivity predict a value of $\Gamma_\nHI$ at $z\simeq 0$ which lies a factor $\simeq 2$ above the value predicted by \citet{HM12}. However, independently upon details, all recently proposed models agree with a UVB which is largely dominated by AGNs at low resdhifts. The amplitude of the UVB can be measured by three different methods. Firstly, the hydrogen ionsation rate per ion, $\Gamma_\nHI$, can be inferred using the so called "proximity effect" \citep[e.g.,][]{murdoch86,bajtlik88}, i.e., by determining out to which distance the local ionisation front of a single QSO outshines the UVB. Secondly, constraints on $\Gamma_\nHI$ can be derived from the statistical comparison of the observed Ly$\alpha$ forest to numerical simulation predictions \cite[e.g.,][]{rauch97,calverley11}. This method, albeit affected by systematic uncertainties, offers the primary constraints on $\Gamma_\nHI$ both at low \citep[e.g.,][for $z\lta 1$]{khaire15,shull15,viel17,gaikwad17} and high \citep[e.g.,][for $2\lta z \lta 6$]{bolton05,kirkman05,faucher08a,wyithe11,becker13,davies18} redshifts. Note however that observing the Ly$\alpha$ forest at $z\lta 1$ requires UV spectroscopy from space. A third method, the detection of fluorescence Ly$\alpha$ from the recombining IGM overdensities in ionisation equilibrium with the UVB, proved to be extremely challenging because of the very low surface brightness (SB) involved \citep[see, e.g.,][]{gould96,cantalupo05,rauch08,gallego18}. However, fluorescence could also be detected in H$\alpha$ in the local Universe, hence without the redshift SB dimming effect as in the case of Ly$\alpha$, by observing the ionisation front in clouds photoionised by the UVB \citep[][]{vogel95,donahue95,weymann01}, or in the outskirts of the \HI discs of galaxies \citep[e.g.][]{maloney93,dove94,bland97,cirkovic99,madsen01,bland17}. Using this technique, \citet{adams11} targeted the nearby edge-on galaxy UGC 7321, obtaining an upper limit for $\Gamma_\nHI$. In a recent paper \citep{fumagalli17} we described the results from a pilot MUSE \citep{bacon10} observation at the VLT, following the line proposed by \citet{adams11}, in the attempt to measure the UVB intensity by searching for the \ha\ recombination line at the edge of the \HI\ disk in the nearby, edge-on disc galaxy UGC 7321. We described how an emission line was detected in a deep 5.7-hour exposure at $\lambda \simeq 6574~$\AA, which is the wavelength where H$\alpha$ is expected given the \HI\ radial velocity of UGC 7321. Despite the presence of a skyline at similar wavelengths, we consistently recovered the \ha\ signal within data cubes reduced with different pipelines, and within data cubes containing two independent sets of exposures. We concluded that we indeed detected \ha\ recombination radiation at a level of $(1.2 \pm 0.5) \times 10^{-19}~$\sbline. Assuming photoionisation from the the UVB as origin of the observed signal, through 1-D radiative transfer calculations and the joint analysis of spatially-resolved \HI\ column density and \ha\ SB maps, we translated the observed SB into a value for $\Gamma_\nHI$ of order of $(6-8)\times 10^{-14}~\rm s^{-1}$, consistent with the values inferred from the statistics of the low-redshift Ly$\alpha$ forest. In this paper we present a more refined statistical analysis of our data based on a Monte Carlo Markov's Chain (MCMC) procedure, leading to a more precise and robust determination of the UVB in terms of $\Gamma_\nHI$ and its associated error. | Thanks to pilot MUSE observations \citep{fumagalli17}, we detected \ha\ emission in the outskirts of the nearby edge-on spiral UGC 7321, at the spatial location, wavelength position, and intensity expected for \HI in ionisation equilibrium with the cosmic extragalactic UVB. By means of a large set of radiative transfer galaxy models, and MCMC statistical analysis, we translated our detection into a value of the UVB at $z\simeq 0$, which is consistent with several other independent measurements obtained with different techniques. When compared to empirical synthetic models of the UVB, our result strengthens the notion that the low-redshift ionising photon budget is largely dominated by AGNs, with star forming galaxies giving a marginal contribution. This is consistent with the low fraction of ionising photons leaking into the IGM generally measured in bright galaxies \citep[see, e.g.,][and references therein]{kakiichi18}. Incidentally, the decline of the AGN number density at $z\gta 2$ \citep[but see][]{giallongo15} requires that such escape fraction has to be on average much larger, $\gta 15$\%, in high-redshift galaxies if they are responsible for the reionisation of the IGM at $z\gta6$ \citep[e.g.,][]{khaire16}. It is interesting to note that, in such picture, the declining population of AGNs and the rising escape fraction from star forming galaxies must concur to produce an almost constant ionisation rate, $\Gamma_\nHI \simeq 10^{-12}$ s$^{-1}$, in the redshift range $2\lta z\lta 6$ \citep[e.g.,][]{becker13}. Further observations are required to confirm our measurements and track with new techniques the amplitude of the UVB with resdhift. Our MCMC analysis demonstrates that the derived value of $\Gamma_\nHI$ is robust against large variations in the galaxy model, and that the uncertainties are mainly driven by the errors associated with the observed \ha\ SB. This implies that future, deeper observations using a similar technique would be able to put much more stringent constraints on the value of the UVB. As we have shown, a reduction of the uncertainties on the measured \ha\ SB would lead to a proportional reduction in the $\Gamma_\nHI$ error estimate. In this respect, we anticipate that new MUSE observations of the same target (but in two different galaxy's regions) are currently scheduled at VLT (PID 101.A-0042, PI Fumagalli). These will test more robustly the origin of the detected signal and are expected to yield a more precise and accurate determination of the \HI photoionisation rate at $z\simeq 0$. | 18 | 8 | 1808.09961 |
1808 | 1808.05462_arXiv.txt | The algorithms used in the construction of a semi-analytical propagator for the long-term propagation of High\-ly Elliptical Orbits (HEO) are described. The software propagates mean elements and include the main gravitational and non-grav\-i\-ta\-tion\-al effects that may affect common HEO orbits, as, for instance, geostationary transfer orbits or Molniya orbits. Comparisons with numerical integration show that it provides good results even in extreme orbital configurations, as the case of SymbolX. | \label{sec:intro} The subject of analytical or semi-analytical propagation is very old. Since the first analytical orbit propagators based on intermediary solutions to the $J_2$ problem \cite{Sterne1958,Garfinkel1958}, the continuous increase in the accuracy of observations demanded the use of more complex dynamical models to achieve a similar precision in the orbit predictions. In particular higher degrees in the Legendre polynomials expansion of the third-body disturbing function are commonly required (see \cite{Kaufman1981,LaraSanJuanLopezCefola2012}, for instance). Useful analytical theories needed to deal with a growing number of effects, a fact that made that the trigonometric series evaluated by the theory comprised tens of thousands of terms \cite{CoffeyNealSegermanTravisano1995}. \par In an epoch of computational plenty, the vast possibilities offered by special perturbation methods clearly surpass those of general perturbation methods in their traditional application to orbit propagation. Apparently by this reason analytical perturbations have these days been cornered to a downgraded role of providing some insight into the problem under investigation, a task for which a first order averaging is usually considered to be enough, yet the computations of higher orders may provide important details on the dynamics \cite{SanJuanLaraFerrer2006,Lara2008}. However, analytical theories like the popular SGP4 \cite{HootsRoehrich1980} still enjoy a wide number of users mainly involved in catalog propagation duties, a role in which other tools like the Draper Semi-Analytic Satellite Theory \cite{McClain1977,DanielsonNetaEarly1994} or the numeric-analytic theory THEONA \cite{Golikov2012} can compete to numerical integration up to a limited accuracy.\footnote{A partial list of orbit propagators can be found in \href{http://faculty.nps.edu/bneta/papers/list.pdf}{http://fac\-ul\-ty.nps.edu/bneta/papers/list.pdf}, accessed Sep\-tem\-ber 29, 2016.} \par On the other hand, new needs in satellite propagation, like the challenges derived of compliance with Space Law, motivate the development of software tools based on analytical or semi-analytical methods, as, for instance, STELA\footnote{\href{https://logiciels.cnes.fr/content/stela?language=en}{https://logiciels.cnes.fr/content/stela}}. In addition, design of end of life disposal strategies may require the long term propagation of thousands of trajectories to find an optimal solution; accurate ephemeris are not needed in the preliminary design and using semi-analytic propagation makes the approach quite feasible \cite{ArmellinSanJuanLara2015}. \par Current needs for long-term propagation at the Centre National d'\'Etudes Spatiales motivate the present research. HEOSAT, a semi-analytical orbit propagator to study the long-term evolution of spacecraft in Highly Elliptical Orbits (HEO) is presented. The perturbation model used includes the gravitational effects produced by the more relevant zonal harmonics as well as the main tes\-se\-ral harmonics affecting to the 2:1 resonance of earth's gravitational potential, which has an impact on Molniya-type orbits; the third body perturbations in the mass-point approximation, which only include the Legendre polynomial of second order for the sun and the polynomials from second order to sixth order in the case of the moon; solar radiation pressure, in the cannonball approximation, and atmospheric drag. \par The forces of gravitational origin are modeled taking advantage of the Hamiltonian formalism. Besides, the problem is formulated in the extended phase space in order to avoid time-dependence issues. The solar radiation pressure and the atmospheric drag are added as generalized forces. The semi-analytical theory is developed using perturbation techniques based on Lie transforms. Deprit's perturbation algorithm \cite{Deprit1969} is applied up to the second order of the second zonal harmonics, $J_2$. In order to avoid as far as possible the lost of long-period effects from the mean elements Hamiltonian, the theory is corrected by the inclusion of long-period terms of the Kozai-type \cite{Kozai1962,ExertierThesis1988}. The transformation is developed in closed-form of the eccentricity except for tesseral resonances, and the coupling between $J_2$ and the moon's disturbing effects are neglected. \par This paper describes the semi-analytical theory and pres\-ents relevant examples of the numerical validation. An extensive description of the tests performed in the validation of the HEOSAT software is given in \cite{LaraSanJuanHautesserresCNES2016}. \par | HEO propagation is a challenging problem due to the different perturbations that have an effect in highly elliptical orbits, the relative influence of which may notably vary along the orbit. However, modern tools and methods allow to approach the problem by means of analytical methods. Indeed, using perturbation theory we succeeded in the implementation of a fast and efficient semi-analytical propagator which is able to capture the main frequencies of the HEO motion over long time spans, even in extreme cases, as corroborated with the tests performed on the SymbolX orbit. In particular, we used the Lie transforms method, which is standard these days in the construction of perturbation theories. This method is specifically designed for automatic computation by machine, and is easily implemented with modern, commercial, general purpose software. \par Future evolutions of the semi-analytical theory should incorporate the transformation from osculating to mean elements, in this way enhancing the precision of the mean elements predictions based on it. Also, in spite of common HEO orbits are not affected by singularities, a reformulation in non-singular variables will make the orbit propagator software more versatile, widening its scope to the propagation of the majority of objects in a catalogue of earth satellite and debris orbits. | 18 | 8 | 1808.05462 |
1808 | 1808.01846_arXiv.txt | {Of all the distance and temporal measures in cosmology, the angular-diameter distance, $d_A(z)$, uniquely reaches a maximum value at some finite redshift $z_{\rm max}$ and then decreases to zero towards the big bang. This effect has been difficult to observe due to a lack of reliable, standard rulers, though refinements to the identification of the compact structure in radio quasars may have overcome this deficiency. In this {\it Letter}, we assemble a catalog of 140 such sources with $0\lesssim z\lesssim 3$ for model selection and the measurement of $z_{\rm max}$. In flat $\Lambda$CDM, we find that $\Omega_{\rm m}= 0.24^{+0.1}_{-0.09}$, fully consistent with {\it Planck}, with $z_{\rm max}=1.69$. Both of these values are associated with a $d_A(z)$ indistinguishable from that predicted by the zero active mass condition, $\rho+3p=0$, in terms of the total pressure $p$ and total energy density $\rho$ of the cosmic fluid. An expansion driven by this constraint, known as the $R_{\rm h}=ct$ universe, has $z_{\rm max}=1.718$, which differs from the measured value by less than $\sim 1.6\%$. Indeed, the Bayes Information Criterion favours $R_{\rm h}=ct$ over flat $\Lambda$CDM with a likelihood of $\sim 81\%$ versus $19\%$, suggesting that the optimized parameters in {\it Planck} $\Lambda$CDM mimic the constraint $p=-\rho/3$.} \begin{document} | The luminosity distance is used often in cosmology for measurements involving standard candles, such as Type Ia SNe \cite{Kowalski:2008} and gamma ray bursts \cite{Wei:2013}. By comparison, the angular-diameter distance, $d_A(z)$, applicable to objects whose diameter (preferably a `standard ruler') is known, is used only sparingly, given the relative paucity of such sources and complications arising from size evolution with redshift. More typically, sources used to measure $d_A(z)$ have been restricted to narrow ranges in redshift, mitigating their possible impact on revealing the geometric structure of the Universe over large distances. The cases where some progress has been made with the use of $d_A(z)$ include (1) the use of baryon acoustic oscillations seen in large-scale structure \cite{MeliaLopez:2017,Alcock:1979}; (2) the Sachs-Wolfe induced $\sim 10^\circ$ fluctuations seen in the cosmic microwave background \cite{Bennett:2003,Spergel:2003,MeliaLopez:2018}; (3) strong lensing systems, with and without time delays \cite{Refsdal:1964,Treu:2006,Biesiada:2010,Wei:2014a,MeliaWei:2015a}; and (4) galaxy clusters \cite{Sasaki:1996,Pen:1997,Melia:2016a}. But several developments in our understanding of the compact structure in radio quasars have presented us with what appears to be a more reliable measuring rod, whose negligible evolution in the redshift range $0\lesssim z\lesssim 3$ permits precision cosmological testing over a larger fraction of the Universe's age than is feasible with these other methods, or even through the measurement of the luminosity distance using Type Ia SNe. As we shall see below, these developments follow primarily from our improved understanding of synchrotron self-absorption processes near the central engine of active galactic nuclei (see, e.g., refs.~\cite{Blandford:1979,Melia:2009} and references cited therein) and the identification of critical constraints on the observed characteristics of these sources---principally their spectral index and luminosity---that permit the selection of an appropriate sample with a more or less fixed size of the emission region for cosmological testing \cite{Gurvits:1999,Cao:2015,Cao:2017a,Cao:2017b}. Measuring the geometry of the Universe with standard rulers was first proposed by Hoyle \cite{Hoyle:1959} over half a century ago, though it took several decades before attempts were made to actually implement this proposal using actual sources. And the earliest tests of cosmological models based on the observed redshift dependence of the angular size of kpc-scale radio sources and galaxies were not successful due to the lack of a reliable, well-defined standard ruler \cite{Sandage:1988,Kapahi:1987,Barthel:1988,Neeser:1995,Singal:1993,Nilsson:1993}. Some motivation to continue pursuing this quest finally came with a study of double-lobed quasars within the redshift range $1.0\lesssim z\lesssim 2.7$, which showed no change in apparent angular size with angular-diameter distance, somewhat consistent with Friedmann-Robertson-Walker cosmology without any significant evolution (see fig.~1 below) \cite{Buchalter:1998}. It eventually became apparent that ultracompact radio sources are more likely to produce standard measuring rods than the large-scale jets in quasars and radio galaxies. The emission from these compact regions is dominated by self-absorbed synchrotron emission \cite{Blandford:1979}, forming at least partially opaque features with angular diameters in the milliarcsecond (mas) range, and linear sizes of the order of $10$ parsecs \cite{Kellerman:1981,Melia:2009}. Their significant advantage over larger structures, such as galaxies and kpc-scale jets, is that these central cores are much smaller than their parent active galactic nuclei (AGN), so their ambient physical environment should be similar from source to source and be reasonably stable, unlike the variations one expects in the intergalactic medium over large distances and times \cite{Kellermann:1993,Jackson:2008}. The compact structures in these sources therefore evolve principally under the influence of the central engine itself, which is typically characterized by only a few physical parameters, such as the mass of the black hole and its spin. Dynamical timescales in such environments are only tens of years, much shorter than the age of the Universe. The compact structures in radio quasars should therefore be free of long-term evolutionary effects \cite{Gurvits:1999}. In one of the more significant studies involving the compact structure of radio quasars, Gurvits, Kellermann \& Frey \cite{Gurvits:1999} showed that a large sample of images taken with Very Large Baseline Interferometry (VLBI) may be used to establish some general constraints on cosmological parameters. This work has formed the basis of many subsequent investigations \cite{Lima:2002,Zhu:2002,Chen:2003}, leading to a second significant advancement with the use of these sources that we shall discuss shortly \cite{Cao:2017a}. A persistent complication with compact radio jets has been that they are found in a mixed population of radio galaxies and AGNs---quasars, BL Lacs, OVVs, etc.---so systematic differences are not always easy to disentangle from true cosmological variations. Recent work by Cao et al. \cite{Cao:2015}, however, has included the analysis of different AGN sub-samples based on different source optical counterparts and lying in different redshift ranges, leading to the conclusion that radio galaxies and quasars need to be handled with distinct strategies. This result is the basis for the current study of such sources, focusing only on compact structures in radio quasars \cite{Cao:2017a,Cao:2017b}. The net outcome of this effort has been a significant reduction in scatter to produce a reliable sample of compact structures in radio quasars for use as standard rulers, allowing us to carry out the study reported in this {\it Letter}, which compares models in ways not previously feasible with other measures of cosmological distance. | Needless to say, the identification of the compact structure in radio quasars as standard rulers has opened up an entirely new chapter in cosmology. With them, we may now map the geometry of the Universe well beyond the reach of Type Ia SNe, sampling even the epoch during which the apparent size of sources increases with redshift, an effect not seen with any other kind of measurement probe. The results thus far point to the zero active mass condition in general relativity as the influence guiding the Universe's expansion. Developing this notion further, and testing it with even higher precision measurements, promises a very exciting future in observational cosmology. | 18 | 8 | 1808.01846 |
1808 | 1808.08967_arXiv.txt | {De Sitter solutions have been recently conjectured to be incompatible with quantum gravity. In this paper we critically assess the progress and challenges of different mechanisms to obtain de Sitter vacua in string compactifications and compare them to quintessence models. We argue that, despite recent criticisms, de Sitter models reached a level of concreteness and calculational control which has been improving over time. On the other hand, building string models of quintessence appears to be more challenging and requires additional fine-tuning. We discuss the tension between the swampland conjecture and the Higgs potential and find examples which can evade fifth-force bounds even if they seem very hard to realise in string theory. We also comment on the tension with low-redshift data and explore ultra-light axions from string theory as dark energy candidates.} \begin{document} | Ever since the first superstring revolution, there has been constant progress in the area of string phenomenology~\cite{Ibanez:2012zz, Quevedo:2016tbh}. Based on our current understanding of string theory, the picture of the string landscape with a large number of vacua that can accommodate our universe (with a positive cosmological constant) has emerged~\cite{Douglas:2006es}. As our understanding of string theory improves and new computational techniques are developed, we should be able to establish the existence of these vacua more and more rigorously and make contact with phenomenology. At the same time, a number of criteria to determine which effective field theories can be consistently embedded into a theory of quantum gravity have been proposed and are called the \textit{swampland conjectures}~\cite{Vafa:2005ui, Ooguri:2006in, Ooguri:2016pdq, Brennan:2017rbf}. Effective field theories that can be consistently embedded in string theory are part of the string landscape, as opposed to those in the swampland which are not consistent with quantum gravity. The typical example is the swampland conjecture about the boundary of moduli spaces: any effective field theory is valid only within an $\mc{O}(M_{\rm p})$ field range in field space, since new light states appear in the spectrum of the theory as one moves farther away \cite{Ooguri:2006in}. Recently, a new swampland criterion has been proposed \cite{Obied:2018sgi} which is in contradiction with the picture of a large number of (possibly dS) vacua in the string landscape and inflationary models. The conjecture states that everywhere in field space the full quantum scalar potential $V$ obeys the relation: \be M_{\rm p}\,\frac{\left|\nabla V\right|}{V} \gtrsim c \,, \label{eq:SwamplandConjecture} \ee where $c$ is an $\mc{O}(1)$ positive constant. It is important to examine whether such a criterion can be consistent with phenomenology. The criterion (\ref{eq:SwamplandConjecture}) has many strong implications for cosmology \cite{Agrawal:2018own, Andriot:2018wzk, Colgain:2018wgk}. In particular it implies that at present we are necessarily in an epoch of quintessence. The tight bounds on fifth-forces \cite{Adelberger:2003zx} and the time variation of fundamental constants \cite{Martins:2017yxk}, provide strong constraints on the couplings of the quintessence field. Furthermore, in the context of $N=1$ supergravity it seems very hard to be able to decouple a quintessence field from the Standard Model. Finally, depending on the model, naturalness considerations require fine-tuning of the quintessence potential at the functional level\footnote{A similar problem has been discussed in the context of attempts to explain time variation of coupling constants in terms of a time varying field \cite{Banks:2001qc}.}, or at least one additional tuning compared to dS models. This makes explicit constructions of quintessence models from string compactifications very challenging. This conjecture is the most recent of a series of articles claiming potential problems with the standard approach to obtain a landscape of metastable dS string vacua as initiated by the KKLT seminal paper \cite{Kachru:2003aw} and followed-up by many other developments that have improved the robustness of the original and other related scenarios. The challenges vary from points of principle (e.g. how to properly define an S-matrix and a quantum theory in general in dS space \cite{Witten:2001kn, Banks:2012hx, Maltz:2016iaw}) to details about each of the different steps of the KKLT scenario \cite{Sethi:2017phn, Bena:2009xk, Moritz:2017xto} which seem to make it natural to explore alternatives to dS. The main purpose of the first part of this article is to assess the pros and cons of the different approaches to dS compactifications. This is important in order to have a clear idea of the assumptions used and the continuous progress but also the open challenges. We will argue that dS models reached a good level of concreteness and calculational control which has been improving over time and provide interesting phenomenological applications to cosmology and particle physics. Moreover we shall stress that some of the computational challenges apply also to 4D $N=1$ supersymmetric vacua which, above all, do not seem to be promising starting points for phenomenology. We will also point out that, even if dS string models are not characterised by expansion parameters which can be made parametrically small, these parameters can still be small enough to trust the phenomenological implications of these constructions. In the second part of the paper we first discuss the theoretical consistency of quintessence models pointing out that in general, in the absence of a symmetry principle, their construction is more challenging that dS models since one needs to perform two fine-tunings to get the correct energy scale and mass of the quintessence field. We then use a more phenomenological approach to assess to which extent quintessence is a viable alternative to dS from observations. In particular, we found (as recently shown also in \cite{Denef:2018etk}), that if the quintessence picture is valid, and there is no other scalar field around other than the Higgs, in order to satisfy the swampland conjecture \eqref{eq:SwamplandConjecture}, the Higgs field has to couple directly to the quintessence field. This would be particularly challenging in any string theory/supergravity scenario, as a quintessence field that couples directly to the Higgs would also couple to the SM fermions, violating fifth-force constraints. We explore these issues, providing examples that avoid the direct coupling of the Higgs to quintessence even if they seem very hard to realise in a supergravity setup. The paper is organised as follows. Sec. \ref{sec:dSstrings} is devoted to the discussion of dS models from string theory. After briefly recalling the need for dS in Sec. \ref{WhydS}, we provide a review of pros and cons of type IIB string models to achieve dS vacua in Sec. \ref{sec:ProsCons}. We then turn to a more detailed analysis of various advantages and criticisms of dS vacua from anti-branes in Sec. \ref{Dbar} and from T-branes in Sec. \ref{T}, while Sec. \ref{OtherdS} contains short comments on other existing string mechanisms to achieve dS vacua. After that, we turn to quintessence in Sec. \ref{sec:QuintessenceStrings}. In particular we discuss various general challenges for quintessence model building in Sec. \ref{sec:QuintessenceChallenges} and the constraints on the coupling between the Higgs and the quintessence field due to the swampland conjecture in Sec. \ref{sec:SwampandHiggs}. We then review the quintessence models already present in the literature in Sec. \ref{sec:StringQuintessenceModels} and finally we study the r\^ole that ultra-light axions can play to explain dark energy data in Sec. \ref{sec:LowRedshift}. | In this paper we have analysed general aspects regarding dS and quintessence scenarios to have a concrete realisation in effective field theories derived from string compactifications. We have seen that even though in order to have full control of dS moduli stabilisation a non-perturbative formulation of string theory is needed, there has been substantial progress in the past decades to be confident that these solutions do exist and that the string theory landscape is a generic outcome of string theory. It is actually remarkable that, without having a full non-perturbative formulation of the theory and not knowing even the metric of the extra dimensional manifolds, there is a coherent picture in which all moduli are stabilised and dS space in 4D can appear as a solution. It is worth emphasising that this procedure uses explicit string theory features with solid mathematical structures such as the topological properties of the compact space, warping induced by fluxes, tadpole cancellation conditions, brane and anti-brane dynamics, explicit computations of leading order perturbative and non-perturbative corrections to the effective field theory, etc. It is fair to say that a full control is difficult to achieve with our current understanding of string compactifications which are not maximally supersymmetric but not having full control on the calculations should not be confused with having no control at all. The results are based on well defined approximations which are justified as long as the couplings are weak and the volumes are large enough. Luckily this is the regime that is also interesting for phenomenological applications\footnote{Notice that the challenge to obtain proper inflationary models from string theory with large tensor modes is mostly due to the fact that, if these modes were observable, the corresponding EFT would be at the edge of its validity.}. We have also seen that the natural alternative to dS space, quintessence, can also be accommodated in string compactifications albeit in a more complicated way. Having a rolling direction which is flat enough to give rise to the observed dark energy requires all other moduli to be stabilised in a similar way as in dS compactifications or rolling even more slowly, something which is more challenging than getting dS. Typical candidates for the quintessence field such as the overall volume and the dilaton are not appropriate to be the quintessence field since they couple to all matter in hidden and observable sectors, and so would be subject to stringent fifth-force constraints \cite{Adelberger:2003zx}. On the other hand, moduli associated with cycles hosting only hidden sector fields \cite{Cicoli:2012tz} may still be allowed by observational constraints although that may require a very small string scale. A low string scale has also appeared in efforts to construct quintessence models in warped throats \cite{Panda:2010uq}. We also studied the nature of the Higgs couplings to various fields in light of the swampland conjectures. We have found that a direct coupling between the Higgs and the quintessence field can be avoided if there are other fields which give non-trivial contributions to $\nabla V$ at the symmetric point of the Higgs potential. However such realisations seem difficult to realise from the point of view of string theory. We have also analysed the possibility of quintessence in the context of supergravity and illustrated the presence of generic couplings (including one loop effects) between all fermions and the quintessence field, which are in tension with the observational bounds. Moreover, analysis of renormalisation group effects showed the requirement of functional fine-tuning of the tree-level potential of the quintessence field or at least additional fine-tuning compared to dS models. The best candidates of quintessence fields are the multiple axions that abound in string compactifications. Considering them just as rolling quintessence fields is a very limited option. However since they correspond to periodic fields with a compact support, their scalar potential has to have a minimum. A natural possibility is that these fields may be oscillating around a dS minimum giving rise to a small modification of the standard $\Lambda$CDM scenario. It is important to notice that in general some of the K\"ahler moduli obtain mass via perturbative effects. This implies that the corresponding axions, which get lifted only by non-perturbative effects, are much lighter yielding a large mass hierarchy among the two components of the same complex scalar field. This is precisely the case for the overall volume modulus and fibration moduli in LVS models. It is worth emphasising that having an extremely light axion is the most model-independent prediction of LVS constructions. Having fibre moduli is also very generic. It is then possible to have one of the axions to correspond to ultra light dark matter with a mass of order $10^{-22}$ eV and another to provide dark energy with a mass of order $10^{-32}$ eV. Furthermore both can be candidates to be part of dark radiation for which there are strong constraints. This justifies a more detailed study of the cosmological implications of these light axions. It would be highly desirable to count on a non-perturbative formulation of string theory that could hopefully determine once and for all that there are or not dS or quintessence solutions of string theory (as it would also be good to have a full proof of the AdS/CFT correspondence or the finiteness of string theory or any potential alternative). As usual in science we have to content ourselves to extract information based on limited experimental input and theoretical control. In the Standard Model we have experimental data which we can confront whereas string constructions cannot at the moment be discriminated on the basis of observations. In the case of dS vs quintessence we hope we have argued that the theoretical progress made over the years, although not $100\%$ satisfactory, is encouraging and present a coherent picture. Furthermore, experimentally, the fact that the equation of state $w$ has been converging over the years towards $w=-1$ is tantalising to bend the preference in favour of dS, following standard Bayesian criteria. However, the recent tension among values of the Hubble parameter determined from high and low redshift may hint at a variable equation of state that could be at odds with both dS and quintessence (see for instance \cite{Wang:2018fng, Capozziello:2018jya, Dutta:2018vmq}). Even though it is too early to judge the robustness of this analysis we have to keep an open mind. Low redshift measurements have surprised us already once, against our theoretical prejudices, and may do it again. Finally we would like to remark that it is healthy to challenge the different approaches to obtain dS space in a fundamental theory. Having criticism and skepticism to a concrete scientific development helps to sharpen the arguments and clarify the achievements and open questions. In view of the lack of further experimental input, this is the best avenue to address theoretical questions and converge towards the best possible explanations. In the case of dS vacua, the question is of utmost importance and having an open debate helps to streamline all the arguments and eventually improve the existing constructions to make them more explicit and coherent or even rule them out. Given the importance of the question being addressed, a high level of scrutiny of the solutions is important -- in fact no bar is too high a bar. We hope to come back and address some of the open questions highlighted in this article. | 18 | 8 | 1808.08967 |
1808 | 1808.04378_arXiv.txt | I present a graphical-user interface for performing several image operations on segmentation maps. The package is written entirely in IDL, and is provided as source code (for those who may want to develop, link to existing packages, or reappropriate the code base) and eventually as a stand-alone, run-time executable upon request (for those without an IDL license). The software facilitates a number of operations, which are generally tedious without a graphical interface, such as deleting, merging, ungrouping, and drawing regions; erasing and painting individual pixels; and compression, dilation, and erosion of a segmentation image. The segmentation image is displayed with random RGB triplets to ensure adjacent regions are readily discernible, whereas the direct image is shown as an inverted greyscale with controls for brightness range, bias, and contrast with several scaling functions (as similar to \texttt{ds9}). The opacity between the segmentation and direct image is tunable, which gives full control to the image display. | \label{sec:intro} Image segmentation refers to the process of uniquely identifying a given pixel or set of pixels in a digital image as a member of a region. In astronomy, this notion led to the development of segmentation images (or maps) that define astrophysical sources in pixelated images. Such images are often used used to define apertures through which various measurements are made (for example brightness or center-of-mass). Therefore, it is imperative to ensure that the segmentation maps are free of pathological defects and false positives are judiciously removed. One common tool for algorithmically creating segmentation maps is \texttt{Source Extractor} \citep[\sex;][]{sex}, which has a host of parameters that govern the properties of the deblending of nearby sources. Although \sex\ is extremely efficient, it can often segment an image in a way far different than a human might expect or desire (notably regions near extended sources or bright point sources). But also, it is challenging to force a segmentation region without inadvertently creating many false sources. To remedy these issues, several schemes have proposed to remove extraneous sources \citep[such as hot/cold running;][]{bard12}. Here, I propose an alternative paradigm: a graphical-user interface (GUI) that allows the user to directly interact with the segmentation image pixels. Although there are distinct advantages with an algorithmic approach (such as repeatability), a properly cleaned segmentation map avoids erroneous sources corrupting the aggregate properties of the sample and/or biasing measurements of other sources in the field. With these tradeoffs in mind, I expect the ideal approach is to begin with a segmentation map derived by some algorithmic means then sensibly polishing the map for clear mistakes, but \textit{primum non nocere}. This document is organized as follows: I introduce the package, including installation and functionality in \Sect{sec:editor}, I present several examples in \Sect{sec:examples}, I describe the User preferences in \Sect{sec:pref}, I present additional improvements and limitations of the current implementation in \Sect{sec:add}, and close with a few closing remarks and waivers in \Sect{sec:coda}. | 18 | 8 | 1808.04378 |
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1808 | 1808.08226_arXiv.txt | A large scientific community depends on the precise modelling of complex processes in particle cascades in various types of matter. These models are used most prevalently in cosmic-ray physics, astrophysical-neutrino physics, and gamma-ray astronomy. In this white paper, we summarize the necessary steps to ensure the evolution and future availability of optimal simulation tools. The purpose of this document is not to act as a strict blueprint for next-generation software, but to provide guidance for the vital aspects of its design. The topics considered here are driven by physics and scientific applications. Furthermore, the main consequences of implementation decisions on performance are outlined. We highlight the computational performance as an important aspect guiding the design since future scientific applications will heavily depend on an efficient use of computational resources. | Simulations of air showers are an essential instrument for successful analysis of cosmic-ray data. The air-shower simulation program CORSIKA~\cite{Heck:1998vt} is the leading tool for the research in this field. It has found use in many applications, from calculating inclusive particle fluxes to simulating ultra-high energy extensive air showers, and has been in the last decades employed by most of the experiments (see e.g.~\cite{Horandel:2005at} and references therein). It has supported and helped shape the research during the last 25\,years with great success. Originally designed as a FORTRAN\,77 program and as a part of the detector simulation for the KASCADE experiment (the name itself comes from ``COsmic Ray SImulations for KAscade''), it was soon adapted by other collaborations to their uses. The first were the MACRO~\cite{Ambrosio:2002mb} and HEGRA~\cite{Daum:1997fp} experiments in 1993. As a consequence, over the time it has evolved enormously and is nowadays used by essentially all cosmic-ray, gamma-ray, and neutrino astronomy experiments. Furthermore, it helped to create a universal common reference for the worldwide interpretation and comparison of cosmic-ray air-shower data. Before CORSIKA, it was very difficult for many types of experiments to assess the physics content of their data, and almost impossible to qualify the compatibility with different measurements. In general, the simulation of extensive air showers was recognized as one of the fundamental prerequisites for successful research in astroparticle physics~\cite{Knapp:2002vs}. In the past, some other tools have also been developed for these purposes, of which the most well known are MOCCA~\cite{Hillas:1997tf}, AIRES~\cite{Sciutto:1999jh} (with the extension TIERRAS~\cite{Tueros:2010zz} for simulations of showers below ground), and SENECA~\cite{Drescher:2002cr}. Over all the years CORSIKA evolved into a large and hard to maintain example of highly complex software, mostly due to the language features and restrictions inherent to FORTRAN\,77. While the performance is still excellent and the mainstream use-cases are frequently tested as well as verified, it is increasingly difficult to keep the development up-to-date with requests and requirements. It is becoming obvious that the limited features of the FORTRAN language and the evident complexity of the new developments are getting into a conflict. Furthermore, in the future, the expertise needed to maintain such a large FORTRAN codebase will be more-and-more difficult to provide. Therefore, it is important to make CORSIKA competitive for the challenges we are facing in the future, requiring us to make a major step in terms of used software technology. This will ensure that CORSIKA will evolve further and become the most comprehensive and useful tool for simulating extensive particle cascades in all required environments. | The steps towards creation of \ngc outlined here are optimized to best support scientific research in fields where the simulation involves particle transport and particle cascades with stochastic and continuous processes. The targeted goals of the resulting framework will be far beyond the capabilities of the original CORSIKA program. It is up to the scientific community to decide in which concrete applications \ngc will be used in the future. It is our aim to offer long-term support for the \ngc program over a period of more than 20\,years. The modularity of the proposed code and the magnitude of the project offers the opportunity for the scientific community to participate in a collaborative manner. Specific functionality and modules can be provided and maintained by different groups. The core of the project, the integration, and the steering are provided by KIT. This can be also a suitable model for a scenario where different communities have different requirements, but the overall collaborative approach is the one we want to promote and foster. This will require dedicated and strict commitment to the project from all the participating parties in order to assure the stability and functionality with no compromises needed. A better access to the air-shower physics-simulation process will be one of the keys to address the main open questions of cosmic-ray physics, the universe at the highest energies, and related scientific problems. | 18 | 8 | 1808.08226 |
1808 | 1808.08232_arXiv.txt | We show that the Deep Underground Neutrino Experiment (DUNE), with significant but feasible new efforts, has the potential to deliver world-leading results in solar neutrinos. With a 100~kton-year exposure, DUNE could detect $\gtrsim 10^5$ signal events above 5~MeV electron energy. Separate precision measurements of neutrino-mixing parameters and the $^8$B flux could be made using two detection channels ($\nu_e + \, ^{40}$Ar and $\nu_{e,\mu,\tau} + e^-$) and the day-night effect ($> 10 \sigma$). New particle physics may be revealed through the comparison of solar neutrinos (with matter effects) and reactor neutrinos (without), which is discrepant by $\sim 2 \sigma$ (and could become $5.6 \sigma$). New astrophysics may be revealed through the most precise measurement of the $^8$B flux (to 2.5\%) and the first detection of the {\it hep} flux (to 11\%). {\it DUNE is required:} No other experiment, even proposed, has been shown capable of fully realizing these discovery opportunities. | \label{sec:CC_sigma} To exploit the full potential of a solar-neutrino program in DUNE, the total cross section for \begin{equation} \nu_e + \, ^{40}{\rm Ar} \rightarrow e^- + \, ^{40}{\rm K}^*, \end{equation} when convolved with the $^8$B spectrum and a detector threshold of $T_e = 5$~MeV, should be known to $\sim 1\%$. With a larger uncertainty, DUNE alone can still precisely measure $\Delta m^2_{21}$ and $\phi(hep)$; DUNE in combination with other experiments can also still precisely measure $\sin^2\theta_{12}$ and $\phi(^8\text{B})$. See Sec.~\ref{sec:detector}. A cross-section uncertainty of $\lesssim 2.4\%$ has been claimed based on indirect measurements, though our assessment below suggests that $\lesssim 10\%$ is more realistic. Importantly, the uncertainty is unlikely to be worse than that. Although this may be surprising, based on the larger uncertainties for neutrino-nucleus interactions at GeV energies, the physics at these low energies is much simpler. Our conclusions are robust to possible changes in the central value of the cross section. For example, a 10\% change in the cross section and thus signal counts would change significances of measured parameters by $\simeq 5\%$. Only the scale of its uncertainty is important. A precise determination of the cross section is challenging but realistic. There are ways to reduce the uncertainty on the cross section, including through a first direct measurement. \subsection{Details of Calculations} \label{sec:CC_sigma.1} We first state the form of the cross section we use, which follows Ref.~\cite{Bhattacharya:2009zz}, which presents the most recent indirect measurements. At leading order, the total cross section is \begin{equation} \sigma(E_\nu) = \sum_i \frac{G_{F, \beta}^2 \left| V_{ud} \right|^2}{\pi} \left| \mathcal{M}_{o \rightarrow i} \right|^2 E_e^i \, p_e^i \, F(Z,E_e^i), \label{eq:CC_cross_section} \end{equation} where $i$ indexes transitions from the ground state of $^{40}$Ar to distinct relevant nuclear excited states in $^{40}{\rm K}$, collectively denoted with a * (transitions to its ground state are forbidden by selection rules). The $i$-dependent terms are the amplitude squared, phase space ($E_e$ is the electron's total energy and $p_e = v_e E_e \simeq E_e$ its momentum), and Fermi function $F$ (to account for Coulomb effects). $G_{F, \beta}$ is the Fermi constant for beta decay (see below) and $V_{ud}$ is the quark mixing matrix element. For each nuclear transition, which could, in principle, be identified by the total gamma-ray energy, the neutrino spectrum is sampled faithfully, weighted by cross section and shifted by the nuclear threshold. For the final states we consider, the transition amplitudes squared can be expressed as \begin{equation} \left|\mathcal{M}_{o\rightarrow i}\right|^2 = B_i(\text{F})+ B_i(\text{GT}), \end{equation} where the transitions are of the Fermi or Gamow-Teller type, or mixed~\cite{Konopinski1950}. For allowed Fermi transitions, which correspond to the vector part of the weak current, the leptons have total spin zero and the change in the nuclear total angular momentum is zero. For allowed Gamow-Teller transitions, which correspond to the axial-vector part of the weak current, the leptons have total spin one and the change in the nuclear total angular momentum is one or zero (but not $0 \rightarrow 0$). For $\nu_e + \, ^{40}$Ar, the transitions are seemingly not mixed and the only relevant Fermi transition is super-allowed, with its strength given by a sum rule, $B(\text{F}) = N - Z = 4$ (defined for the parent nucleus)~\cite{Ormand:1994js, Bhattacharya:2009zz}. For the Gamow-Teller strengths, we use those based on measurements of $^{40}\text{Ar}(p, n)^{40}\text{K}^*$ in forward-angle kinematics~\cite{Bhattacharya:2009zz}. See Table~\ref{table:CC_cross_section}. \begin{table}[t] \centering \vspace{0.8em} \begin{tabular}{||C{1.0cm}|C{2.0cm}|C{1.4cm}|C{1.4cm}||} \hline\hline i & $\Delta E_i$ [MeV] & $B_i({\rm F})$ & $B_i({\rm GT})$\\[-1pt] \hline \hline 1 & 2.333 & & 1.64 \\[-1pt] \hline 2 & 2.775 & & 1.49 \\[-1pt] \hline 3 & 3.204 & & 0.06 \\[-1pt] \hline 4 & 3.503 & & 0.16 \\[-1pt] \hline 5 & 3.870 & & 0.44 \\[-1pt] \hline 6 & 4.384 & 4.00 & \\[-1pt] \hline 7 & 4.421 & & 0.86 \\[-1pt] \hline 8 & 4.763 & & 0.48 \\[-1pt] \hline 9 & 5.162 & & 0.59 \\[-1pt] \hline 10 & 5.681 & & 0.21 \\[-1pt] \hline 11 & 6.118 & & 0.48 \\[-1pt] \hline 12 & 6.790 & & 0.71 \\[-1pt] \hline 13 & 7.468 & & 0.06 \\[-1pt] \hline 14 & 7.795 & & 0.14 \\[-1pt] \hline 15 & 7.952 & & 0.97 \\[-1pt] \hline\hline total & & 4.00 & 8.29 \\[-1pt] \hline\hline \end{tabular} \vspace{1em} \caption{Transition strengths for $\nu_e + \, ^{40}{\rm Ar} \rightarrow e^- + \, ^{40}{\rm K}^*$~\cite{Bhattacharya:2009zz}. Here we have multiplied the $B_i({\rm GT})$ values by the axial coupling constant squared (with $g_A = -1.26$), so that they have the same normalization as $B_i({\rm F})$, as appropriate for Ref.~\cite{Bhattacharya:2009zz}. In the literature, it is not always clearly noted if $B_i({\rm GT})$ values are normalized with or without this factor. The energy of the Fermi state is taken from Ref.~\cite{Bhattacharya:1998hc}.} \label{table:CC_cross_section} \end{table} Because the interaction is a 2-to-2 process and the nuclear transitions are between discrete states, the kinematics and the phase-space factor are simple. (Recoil-order corrections are $\lesssim 5$ keV, and can be neglected.) The electron kinetic energy is $T_e = E_\nu - Q_i$, where $Q_i = Q_\text{gs} + \Delta E_i$, with $Q_\text{gs} = 1.504$~MeV the reaction threshold to reach the ground state of $^{40}$K (including creation of the electron) and $\Delta E_i$ the excitation energy above that~\cite{NNDC, Bhattacharya:2009zz}. We assume a detection threshold of $T_e = 5$~MeV, conservatively neglecting the detectability of nuclear de-excitation gamma rays (of total energy $\Delta E_i$), which primarily undergo Compton scattering, and may be detectable in coincidence, improving particle and reaction identification. For a neutrino interaction to register, its energy must exceed $E_\nu^{thr,i} = (Q_\text{gs} + \Delta E_i) + 5 {\rm \ MeV}$, which is 8.837~MeV for the lowest allowed transition and higher for others. The electron angular distribution, $d\sigma/d\cos\theta$, is $\propto 1 + \cos\theta$ for Fermi transitions and $\propto 1 - \frac{1}{3} \cos\theta$ for Gamow-Teller transitions~\cite{Beacom:1998fj, Vogel:1999zy}. For an isotropic angular distribution, the fraction of $\nu_e + \, ^{40}{\rm Ar}$ events outside the forward cone is 88\%. Taking into account the weighting of different transitions does not change this number appreciably. \begin{figure}[t] \begin{center} \includegraphics[width=\columnwidth]{fermi_function.pdf} \caption{Fermi function for $\nu_e + \, ^{40}{\rm Ar} \rightarrow e^- + \, ^{40}{\rm K}^*$ in terms of electron momentum, interpolated from data in Ref.~\cite{Behrens1969, Bhattacharya:2009zz}. The shaded region indicates the approximate range of interest.} \label{fig:fermi_function} \end{center} \end{figure} The Fermi function $F$ accounts for the distortion of the outgoing electron wave function due to its Coulomb interaction with the nuclear charge $Z$ (defined for the daughter nucleus)~\cite{Schenter1983, Behrens1969, Hayes:2016qnu}. For an outgoing electron, the interaction is attractive, making $F > 1$, and, in this case, the correction is substantial, a factor $\simeq 1.6$. A commonly used analytic estimate, $F \simeq 2\pi \nu / [1 - \exp(- 2 \pi \nu)]$, with $\nu = Z \alpha /v_e$, based on the solution to the Schr\"{o}edinger equation for an electron in the potential of a point-like nucleus, is only suitable for small Z~\cite{Schenter1983}. At high momentum, this is a constant; at low momentum, it varies as $1/v_e$. A detailed calculation of $F$, based on the solution of the Dirac equation for an electron in the potential of a finite-sized nucleus, is tabulated in Table II of Ref.~\cite{Behrens1969, Bhattacharya:2009zz}. Figure~\ref{fig:fermi_function} shows our interpolated result, which differs from the simple analytic expression~\cite{Schenter1983} by being $\sim 10\%$ larger and by varying at large momenta, both of which are important. Figure~\ref{fig:CC_cross_section} shows the total cross section for $\nu_e + \, ^{40}{\rm Ar}$, combining the factors above, including the detector threshold of $T_e = 5$ MeV. At $E_\nu = 10 $~MeV, a typical energy, the relevant cross section is $\sigma \approx 3 \times 10^{-42}$ cm$^2$, a factor $\sim 30$ larger than that for $\nu_e + e^-$, though the latter's density of targets is 18 times higher. The $\nu_e + \, ^{40}{\rm Ar}$ cross section grows rapidly, faster than $\sigma \propto E_e^2 \propto (E_\nu - E_\nu^{thr,i} + 5 {\rm\ MeV} + m_e)^2$, because with increasing neutrino energy, more nuclear thresholds are surpassed, and because of the strong effect of the detector threshold. In our calculations, we do not use this total cross section; instead, we sum the partial cross sections for each independent transition. Figure~\ref{fig:CC_components} shows how different transitions contribute to the total cross section, now showing only the case where the detector threshold of $T_e = 5$~MeV is applied to each transition separately. The relative contributions vary depending on their strengths compared to those of all other kinematically accessible transitions. Below $E_\nu = 10.888$ MeV, corresponding to the threshold for the super-allowed Fermi transition, the cross section is dominated by the two lowest-energy Gamow-Teller transitions. For higher $E_\nu$, there are four comparable contributions: each of the two lowest-energy Gamow-Teller transitions, the Fermi transition, and the sum of all other kinematically accessible Gamow-Teller transitions. (Though we do not exploit the angular distribution, doing so~\cite{Beacom:1998fj, Vogel:1999zy} would increase sensitivity.) \begin{figure}[t] \begin{center} \includegraphics[width=\columnwidth]{CC_cross_section.pdf} \caption{Total cross section for $\nu_e + \, ^{40}{\rm Ar} \rightarrow e^- + \, ^{40}{\rm K}^*$. The solid line takes into account the 5-MeV threshold of DUNE, while the dotted line neglects it.} \label{fig:CC_cross_section} \end{center} \end{figure} \begin{figure}[t] \begin{center} \includegraphics[width=\columnwidth]{Fig_A3_norm.pdf} \caption{Relative contributions to the total cross section for $\nu_e + \, ^{40}{\rm Ar} \rightarrow e^- + \, ^{40}{\rm K}^*$, with the minor transitions smoothed. The detector threshold is taken into account.} \label{fig:CC_components} \end{center} \end{figure} In principle, there are additional contributions to the $\nu_e + \, ^{40}$Ar total cross section from particle-unbound final states, e.g., $e^- + \, ^{39}{\rm Ar} + p$ and $e^- + \, ^{39}{\rm K} + n$. However, even if the transition strengths are appreciable, the nuclear thresholds are above 9~MeV~\cite{NNDC}, making the neutrino thresholds above 14~MeV, and even higher if we account for the energy of the outgoing nucleons. For a given neutrino energy, $T_e$ will be substantially lower than for the particle-bound transitions, burying any additional contributions in the falling total spectra of Fig.~3. \subsection{Assessment of Uncertainties} \label{sec:CC_sigma.2} To assess the uncertainty on the cross section, we first consider two data-based evaluations. The $B_i({\rm GT})$ values we use are from the $^{40}\text{Ar}(p,n)^{40}$K$^*$ data of Ref.~\cite{Bhattacharya:2009zz}. For the uncertainties, we focus on the strengths themselves, though there may also be uncertainties in the excitation energies (through identification of the relevant transitions). Though the uncertainties on individual $B_i$ are $\sim$ 5--20\%, the uncertainty on the summed strength is 2.4\%. This reduction in uncertainty is because the strength for the super-allowed Fermi transition is considered known from the sum rule and because the uncertainties of independent Gamow-Teller transitions combine in a central-limit fashion for the total strength. The uncertainty on the total cross section (convolved with the $^8$B spectrum and with a detector threshold of $T_e = 5$~MeV) is comparable to that on the summed strength. In a paper preceding Ref.~\cite{Bhattacharya:2009zz}, a related group of authors obtained $B_i({\rm F + GT})$ values based on measurements of $^{40}$Ti $\beta^+$ decay to $^{40}$Sc$^*$, the isospin mirror process for $\nu_e + \, ^{40}{\rm Ar} \rightarrow e^- + \, ^{40}{\rm K}^*$, with an uncertainty of 2.1\% on the summed strength~\cite{Bhattacharya:1998hc}. However, there are discrepancies between the two techniques, with the convolved cross sections at the most important energies differing at the $\sim 10\%$ level. It is difficult to assess the systematics, as the two techniques access somewhat different transitions, and both rely on some assumptions: for the $(p,n)$ data, that the weak transitions are in the same proportions as the strong transitions; for the beta-decay data, that isospin symmetry holds. A shell-model study~\cite{Karakoc:2014awa} suggests that the $(p,n)$ data are preferred over the beta-decay data, which is one of the reasons we adopted the strengths from Ref.~\cite{Bhattacharya:2009zz}. Further work is needed to resolve differences between the two techniques. The cross section can also be evaluated using $B_i$ values calculated with nuclear theory~\cite{Ormand:1994js, GilBotella:2003sz, Kolbe:2003ys, Cheoun:2011zza, Suzuki2014}. For the low energies of solar neutrinos, the preferred technique is the nuclear shell model, treating most of the nucleons as belonging to a closed core, and treating the remaining valence nucleons as subject to an effective potential from the core as well as to a residual nucleon-nucleon interaction. For the higher energies of supernova neutrinos, the preferred technique is the random phase approximation (RPA), which describes collective states of nuclei in a basis of particle-hole excitations. A hybrid approach is also possible, with RPA used to calculate transitions not well described by the shell model. Compared to our calculation, the hybrid calculation of Ref.~\cite{Suzuki2014}, which we consider to be the most reliable, is $\simeq 10\%$ smaller. However, its $B_i$ values for known important low-lying transitions fall well below the data of Ref.~\cite{Bhattacharya:2009zz}, allowing its cross section to be smaller, despite the additional contributions of RPA-calculated transitions ($\lesssim 10\%$ at solar-neutrino energies). We neglect the results of some other calculations: the early shell-model calculation of Ref.~\cite{Ormand:1994js} ($\simeq 30\%$ smaller than ours, but it omits relevant nuclear operators) and the RPA calculations of Refs.~\cite{GilBotella:2003sz, Kolbe:2003ys, Cheoun:2011zza} (a factor of a few difference, but they are not suited for the solar-neutrino energy range). New work is needed on all of these techniques. Thus, based on both experimental and theoretical evaluations of the cross section, its uncertainty (for $^8$B neutrinos in DUNE) is likely $\lesssim 10\%$. This is small enough that our conclusions are robust, but large enough that new efforts to reduce uncertainties are needed. \subsection{Towards Reducing Uncertainties} \label{sec:CC_sigma.3} Even without new experimental data, it seems likely that the cross-section uncertainty can be reduced through new theoretical work: calculations of the $B_i$, calculations to help reconcile differences in experimental inputs, and the development of a framework to consistently include all known effects. These effects include corrections that, while not all uncertainties per se, cause discrepancies between different results if they are not applied uniformly, of which we give several examples, following e.g., Refs.~\cite{Vogel:1999zy, Beacom:2001hr, Kurylov:2002vj, Hardy:2014qxa, Hayes:2016qnu}. The inner radiative corrections for charged-current semi-leptonic processes with nucleons increase the cross section by $\simeq 2.4\%$, which can be absorbed into a change in the Fermi constant for beta decay ($G_{F, \beta}$) relative to that measured from muon decay ($G_F$). The outer radiative corrections can also increase the cross section by $\sim$ 1--2\%, depending on the nucleus and how the energy deposition by bremsstrahlung affects the detectability of the electron. In principle, updating the value of the axial coupling constant from $g_A = -1.26$ to the contemporary $-1.27$ would also increase the cross section by $\simeq 2\%$, but $g_A$ may be quenched in nuclei. In addition, the effects of the following should also be considered: isospin-violation corrections, subdominant argon isotopes (0.4\%), particle-unbound transitions, forbidden transitions, more accurate identifications of the energies of the relevant nuclear transitions, and so on. To reduce the uncertainty to $< 1\%$, new data are needed, starting with comprehensive new measurements of auxiliary data to evaluate $B_i$, e.g., from $^{40}\text{Ar}(p, n)^{40}\text{K}^*$ and $^{40}$Ti $\beta^+$ decay. It seems likely that new measurements, supported by theoretical efforts, could ensure that these techniques reach their intended precision. Ultimately, the $\nu_e + \, ^{40}$Ar cross section must be directly measured with a laboratory source of neutrinos, which has never been done. Achieving an uncertainty $< 1\%$ will require the statistics of $\gtrsim 10^4$ events and commensurate control of systematics. The neutrino source could be accelerator-produced $\mu^+$ decay at rest, for which the $\nu_e$ spectrum, before weighting with the rising cross section, peaks at $\simeq 35$~MeV. At this energy, the total charged-current cross section is $\simeq 300 \times 10^{-42}$ cm$^2$, taking into account only the nuclear transitions noted above; the true cross section will be larger. At the location of the suite of COHERENT neutrino detectors at the Spallation Neutron Source at Oak Ridge, the time-averaged $\nu_e$ flux is $\simeq 10^7$ cm$^{-2}$ s$^{-1}$~\cite{Akimov:2017ade}. We thus estimate that an exposure of $\sim 10$ ton-year is needed. With a low detection threshold and good collection of scintillation light, the nuclear transition of each interaction could be identified by the total energy of its de-excitation gamma rays, which would reduce backgrounds. If systematics are more challenging than statistics, then identifying specific nuclear transitions by their gamma rays could be used to measure relative strengths (including compared to the super-allowed Fermi transition) instead of the absolute cross section. There would be numerous technical challenges, but the importance of the problem encourages significant investments. | 18 | 8 | 1808.08232 |
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1808 | 1808.03316_arXiv.txt | We study infrared emission of 17 isolated, diffuse clouds with masses of order $10^2 M_\odot$, to test the hypothesis that grain property variations cause the apparently low gas-to-dust ratios that have been measured in those clouds. Maps of the clouds were constructed from {\it WISE} data and directly compared to the maps of dust optical depth from {\it Planck}. The mid-infrared emission per unit dust optical depth has a significant trend toward lower values at higher optical depths. The trend can be quantitatively explained by extinction of starlight within the clouds. The relative amounts of PAH and very small grains traced by {\it WISE}, compared to large grains tracked by {\it Planck}, are consistent with being constant. The temperature of the large grains significantly decreases for clouds with larger dust optical depth; this trend is partially due to dust property variations but is primarily due to extinction of starlight. We updated the prediction for molecular hydrogen column density, taking into account variations in dust properties, and find it can explain the observed dust optical depth per unit gas column density. Thus the low gas-to-dust ratios in the clouds are most likely due to `dark gas' that is molecular hydrogen. | The nature and content of interstellar clouds can be measured through various tracers including the 21-cm line of atomic hydrogen, far-infrared emission of dust, microwave emission lines of CO, ultraviolet and optical absorption lines, extinction by dust, and $\gamma$-rays. These diverse tracers reveal material with the range of physical conditions and geometrical observing conditions in which they apply, leading to an overall understanding of the transition in the interstellar medium between low-density ionized gas, diffuse atomic gas, translucent clouds, dark clouds, and giant molecular clouds \citep{snow06}. The relative amount of atomic and molecular material in the diffuse and translucent clouds, where H$_2$ molecules form on dust grain surfaces with column density limited by destruction from ultraviolet photons in the interstellar radiation field \citep{hollenbach71}, remains uncertain at the factor of 2 level because H$_2$ is not readily directly observed \citep{xfactorreview}. We initiated a study of isolated, approximately degree-sized, approximately $10^2 M_\odot$, interstellar clouds that allow clear separation between the cloud and the unrelated diffuse interstellar medium and that have a range of brightnesses and locations across the sky. We showed in Paper 1 \citep{reach15} that such clouds have a wide range of gas-to-dust ratios. To explain them, we asserted three hypotheses: \begin{enumerate} \item[(1)] The amount of gas was underestimated due to the presence of extensive molecular hydrogen not accounted for by the 21-cm observations of $N_{\rm H}$. \item[(2)] The amount of gas was underestimated due to the 21-cm line being optically thick. \item[(3)] The amount of dust was overestimated by the submm opacity because of variations in the dust properties. \end{enumerate} In all cases we retain the ansatz that the {\it actual} gas-to-dust mass ratio remains constant, which is quite likely because there are no evident local sources of dust in the clouds nor mechanisms to separate the gas from dust. Recent theoretical work supports that interstellar grains remain closely coupled to the gas even in molecular clouds (and even neglecting magnetic fields), with only rare grains larger than 1 $\mu$m sized grains experiencing significant segregation \citep{tricco17}. We fully expect that all three hypotheses are active, and our goal is to measure the relative importance of each. Paper 1 showed a simple analytical calculation \citep[from][]{reach94} for the formation of molecular hydrogen and showed that hypothesis (1) could match the observations with no free parameters. In Paper 2 \citep{reach17}, we showed, from 21-cm absorption observations toward radio continuum sources behind the clouds, that an apparently low gas-to-dust ratio could not be fully explained by cold atomic gas, because there is not enough opacity measured in the 21-cm line. While there is clearly some cold, atomic gas that explains a small part of the high specific opacity, Paper 2 effectively ruled out hypothesis (2). In this paper, we test hypothesis (3). The initial sample for comparison between far-infrared dust and \ion{H}{1} gas distribution defined in Paper 1; that sample was restricted to the Arecibo declination range. We maintained that sample for Paper 2, which again used Arecibo 21-cm observations (of absorption this time). For this paper, we expand the sample to have a more diverse set of clouds for studying potential dust property variations. The supplemental clouds are from \citet{hrk88}, where isolated, degree-sized clouds were identified from inspection of the {\it IRAS} 100 $\mu$m images and the all-sky \ion{H}{1} images at half-degree resolution. To further diversify the sample, we added DIR015+54, which has a distinctively warmer dust temperature than other high-latitude clouds, despite having no internal heating source \citep{reach98}. For all clouds, we used maps of the dust opacities at $5'$ resolution from the {\it Planck} \citep{tauber2010a} survey, specifically the `thermal dust' foreground separation \citep{planck2013viii}, to compare to mid-infrared emission maps from the {\it Wide Field Infrared Survey Explorer (WISE)} all-sky survey \citep{wright10}, specifically the {\it WISE} Image Atlas served through the Infrared Science Archive. | {\bfc Dust grain properties vary in diffuse interstellar clouds, but that variation is insufficient to explain the observed range of dust emission per unit atomic gas column density. Within our sample of isolated, diffuse clouds the relative amounts of PAH, Very Small Grains, and Big Grains remain approximately constant to within a factor of 2. The trends in the relative amount of emission from different types of grain, and he large grain temperature differences, can be explained by a decrease of the radiation field from due to extinction of the starlight that heats the grains. In the core of a high-latitude dark cloud, there is no evidence for any PAH at all, likely due to the absence of heating photons but also consistent with absence of PAH themselves. In Paper 1, we showed significant variations in the gas-to-dust ratio, when the gas is traced by the 21-cm line of \ion{H}{1}. In Paper 2, we showed the H~I was not significantly underestimating the atomic column density, because there is little column density of 21-cm-optically-thick, cold atomic gas. In this Paper, we find no evidence that changes in dust properties that can explain the apparently high gas-to-dust ratio (equivalently, higher specific opacity) of diffuse clouds. While there is evidence for a modest increase in the far-infrared opacity in the diffuse interstellar medium, the total range of observed gas-to-dust ratios is too large to be explained by this effect alone. An updated empirical model for H$_2$ formation on large grain surfaces falls far short of the atomic gas-to-dust ratio, with extrapolation to low radiation fields yielding predictions consistent with a high-latitude dark cloud known to contain significant molecular gas. In terms of the hypotheses posed in the Introduction, we show that while there is a small amount of cold atomic gas (hypothesis 2) and there are modest dust property variations (hypothesis 3), the results support that diffuse clouds contain `dark gas' (hypothesis 1), presumably H$_2$, not traced by the \ion{H}{1}, even in places with little CO emission. Where there is CO emission, the dust optical depth per unit total gas is consistent with the trend of dust optical depth per unit atomic gas in diffuse clouds. In dark clouds with extinction $A_{\rm V}>2$, where there is bright CO emission and the dust grains are cold ($T_{\rm d}<16$ K), dust property variations may be more extreme than in diffuse clouds. } | 18 | 8 | 1808.03316 |
1808 | 1808.04536_arXiv.txt | Black holes at the centers of the galaxies grow mainly by the processes of accretion, mergers, and consumption of stars. In the case of gas accretion with cooling sources, the flow is momentum driven, after which the black hole reaches a saturated mass, and subsequently, it grows only by consumption of stars. In addition, we include the effect of mergers on the growth of black hole spin and mass and study its evolution as a function of redshift in a $\Lambda$CDM cosmology using an initial seed mass and spin distribution functions that we have derived. For the stellar ingestion, we have assumed a power-law density profile for the galaxy in our framework of a new relativistic loss cone theory that includes the effect of the black hole spin. We predict the impact of the evolution on the $M_{\bullet} - \sigma$ relation and compare it with available observations. | The $M_{\bullet} - \sigma$ relation, $M_{\bullet} \propto \sigma^{p}$, is a very astonishing relation and its origin is still a topic of debate. \cite[Bhattacharyya \& Mangalam (2018)]{Bhattacharyya_Mangalam2018} [BM18 hereafter] have constructed a static model of deriving the $M_{\bullet} - \sigma $ relation and $M_{\bullet} - M_{b}$ relation together from intensity profiles of 12 elliptical galaxies. Here we discuss the dynamical aspect of the $M_{\bullet} - \sigma$ relation, i. e., the evolution of the relation with redshift and time in $\Lambda$CDM cosmology. From the basic equations of mass and spin evolution of the black hole [\cite[c. f. Mangalam (2015)]{Mangalam_2015}] we have derived the evolution of this relation. For the rate of growth of mass, $\dot{M}_{\bullet}$, we have considered the accretion process, stellar ingestion process and mergers, where, the accretion rate is considered to be a fraction of the Eddington accretion rate, the mass growth by stellar consumption is calculated by using both full and steady loss cone theory [\cite[Mageshwaran \& Mangalam (2015)]{Mageshwaran_Mangalam_2015}] for a galaxy cusp following power law mass density (power law index is $\gamma$) and in case of mergers we have considered both major and minor mergers [\cite[Stewart et al., (2009)]{Stewart_2009}]. We have also considered the BZ torque which contributes to spinning down the black hole while the accretion process spins it up. For spin evolution we have considered only the effect of minor mergers which also contributes in spinning the hole down [\cite[Gammie et al., (2004)]{Gammie_2004}], while we neglect major mergers because the accretion process is the dominant one for spinning up the black hole. We have also incorporated the prescription of saturated mass, $M_{sat}$, given by \cite[King (2003)]{King_2003} which is the critical mass after which the accretion stops and the black hole grows only by stellar ingestion and mergers. We have considered the mergers to be effective from $z \leq 4$ considering the peak of merger activity. Starting from an initial spin, $j_{s}$, an initial mass, $M_{\bullet s}$ we have derived the evolution of the mass and spin of the black hole and its effect on the $M_{\bullet} - \sigma$ relation. % \begin{figure} \begin{center} \subfigure[]{\includegraphics[scale=0.21]{m_t_z_sd.pdf}}\label{figa}\hspace{0.15 in} \subfigure[]{\includegraphics[scale=0.21]{slope_z_sat_sd.pdf}}\label{figb}\vspace{0.1 in} \subfigure[]{\includegraphics[scale=0.19]{j_t_z_sd.pdf}}\label{figc}\hspace{0.15 in} \subfigure[]{\includegraphics[scale=0.17]{mbh_sigma_obs.pdf}}\label{figd} \caption{Comic evolution of the mass and the spin of the black hole and the $M_{\bullet} - \sigma$ relation. \textit{(1a, 1c)} Evolution of the mass of the black hole in units of $M_{\bullet s}$ and spin of the black hole as function of time and redshift with merger mass ratio, $q$ = 0.1, $j_{s}$ = 0.2, magnetic field of BZ torque, $B_{4} = B / (10^{4}$ Gauss) = 5, formation redshift, $z_{f}$ = 4 and $\gamma$ = 1.5 and $M_{\bullet s}$ = $10^{5} M_{\odot}$. \textit{(1b)} Evolution of the index $p$ of the $M_{\bullet} \propto \sigma^{p}$ relation. \textit{(1d)} shows $\log(M_{\bullet {7}})$ vs $\log(\sigma_{100})$ for two different redshifts ($z = 0.003$, red and $z = 0.23$, green) along with the data obtained from our calculation in BM18 for 12 elliptical galaxies (their redshift lies in the range 0.004 - 0.002).} \end{center} \end{figure} For a few examples, the resulting mass and spin evolution of the black hole is shown in Figures [\ref{figa}(a), \ref{figc} (c)] and the impact on the index of the $M_{\bullet} - \sigma$ relation which is obtained from the slope of $\log{M_{\bullet}}$ vs $\log{\sigma}$ plot is shown in Figure \ref{figb}(b). We show how our results matches with observations in Figure \ref{figd} (d), where the data of $M_{\bullet}$ and $\sigma$ of 12 elliptical galaxies was obtained from their observed intensity profile in BM18. A more detailed study of the models is discussed in the paper by Bhattacharyya \& Mangalam (2018b) (in preparation). \vspace{-0.24 in} | We have obtained the relativistic as well as the non-relativistic evolution of black hole mass and spin as a function of redshift using cosmological $\Lambda CDM$ model for different values of the spin parameter, seed masses and different formation redshifts. For calculation of stellar consumption rate, we use the steady loss cone model. We have compared our model with the available observations of $z$, $M_{\bullet}$ and $\sigma_{||}$ of 12 elliptical galaxies which follow the $M_{\bullet} - \sigma$ relation and we are able to explain the observations from our model. We have computed the evolution of the $M_{\bullet} - \sigma$ relation with redshift by deriving the evolution of the slope and intercept of $\log[M_{\bullet 7}]$ vs $\log[\sigma_{100}]$ plot. Using formula given by \cite[Shankar \etal (2009)]{Shankar_2009}, for renormalization, $p \propto (1 + z)^{-\alpha}$, we show that the $M_{\bullet} - \sigma$ relation holds with $\alpha \simeq $ 0.24 - 0.34 upto $z \simeq 1$ for the index, $p$ lying between 4 - 5. The data from future surveys at high redshift, for example from TMT, can be used to probe the $M_{\bullet} - \sigma$ evolution. \vspace{-0.24 in} | 18 | 8 | 1808.04536 |
1808 | 1808.06643_arXiv.txt | Current single dish, low-frequency radio pulsar surveys provide efficient sky coverage, but poor localization of new discoveries. Here, we describe a practical technique for rapidly localizing pulsars discovered in these surveys with on-the-fly mapping and provide code to facilitate and formalize its implementation. As a proof of concept, we alter the positions of four test sources and use the Green Bank Telescope (GBT) 350\,MHz receiver to recover source positions within $\approx1-3\,\arcmin$ of their true values, compared to an $18\arcmin$ error radius for new discoveries. Achieving similar precision with a traditional gridding strategy using the GBT requires $2-3$ times as much telescope time (including overhead), multiple receivers and relies on assumptions about the pulsars' spectral indices. For one of our test sources (PSR J1400$-$1431), this method revealed a discrepancy with the initial, published position, prompting additional follow-up and an improved timing solution. Rapid localization is important for improving data quality and providing flexibility in choice of center frequency for future timing observations -- both of which facilitate evaluating new millisecond pulsars for potential inclusion in pulsar timing arrays. | The choice of center frequency for single dish radio pulsar surveys is critical. Low frequencies maximize survey speed in covering large areas of the sky and help take advantage of pulsars’ steep spectral energy distributions, while high frequencies minimize the adverse effects of sky temperature, scattering, and dispersive smearing. Since a telescope's angular beam size is inversely proportional to observing frequency ($f$) and its diameter ($D$), the time required to conduct all-sky surveys with the most sensitive (largest diameter) telescopes at frequencies $>1$\,GHz becomes prohibitive. For this reason, recent all-sky pulsar surveys with the Green Bank Telescope (GBT) and Arecibo Observatory (AO) -- two of the largest radio telescopes in the world, both with $D>100$\,m -- have been carried out at center frequencies, $f\approx350$\,MHz \citep{slr+14,dsm+13}. Although low-frequency surveys are more efficient in survey speed, discoveries are poorly localized. For example, the Green Bank North Celestial Cap \citep[GBNCC;][]{slr+14} survey and the 350\,MHz Drift Scan Survey before it \citep{blr+13,lbr+13,rsm+13} used the GBT's 350\,MHz receiver, which is sensitive to an angular region on the sky $36\arcmin$ wide. With an initial error circle that large, conducting follow-up observations at higher frequencies without further refinement is unreliable given that the GBT beam sizes at 820\,MHz and 1.5\,GHz are $15\arcmin$ and $9\arcmin$ wide respectively. This can delay multi-frequency follow-up, which is important for high-precision timing -- particularly for millisecond pulsars (MSPs) in pulsar timing array (PTA) experiments \citep{abb+15,dcl+16,rhc+16,vlh+16}. These experiments require MSPs to be monitored at multiple frequencies in order to precisely measure and correct for dispersive delays and other interstellar medium effects, which change over time \citep{jml+17}. Multi-frequency timing precision must be assessed before adding new MSPs to PTAs. In order to do this properly with the GBT, an MSP position must be known to $\lesssim3\arcmin$ (i.e. within a 1.5\,GHz beam radius from the true position). Pulsar timing provides sub-arcsecond position measurements, but it requires $\simeq1$\,year of monthly observing and a high-cadence session to achieve phase connection and yield results. Conducting multi-frequency follow-up on shorter timescales requires other methods. \subsection{Gridding} A commonly-used approach to incrementally improve pulsar localization is called {\it gridding} and involves tiling the discovery error region with multiple scans to refine a pulsar's position in stages \citep{mhl+02}. Oftentimes gridding observations are carried out at higher observing frequencies (smaller wavelengths, $\lambda$) to more significantly improve localization \citep[e.g.][]{lbr+13} since beam size is proportional to $\lambda$ (see Equation \ref{eq:hpbw}). Considering a pulsar discovered with the GBT at 350\,MHz, for example, gridding typically involves tiling the $36\arcmin$-wide beam with seven 820\,MHz pointings. Then, one or more detections at the higher frequency are used to determine a central position for a second round of seven grid pointings carried out at 1.5\,GHz to further refine the position. At each stage, if multiple grid points produce detections, an average position is calculated, weighted by detection signal-to-noise ratios. In the best case scenario, progressive stages of this process improve the pulsar's error radius to $\lesssim5\arcmin$, then $\lesssim2\arcmin$ respectively. This can be logistically complicated due to the overhead time required for receiver switches (10$-$15\,minutes). Also, gaining access to these receivers may require dedicated proposals. Furthermore, pulsars are steep-spectrum objects \citep{blv+13}; increasing the observing frequency by a factor of $\approx2$ decreases the expected pulsar flux by a factor of $\approx3$. Even after considering the additional bandwidth and improved system temperatures at higher observing frequencies, pulsars' steep spectral indices require increased observing time for individual grid points to ensure detections. For a two-minute discovery scan at 350\,MHz, grid point scans at 820\,MHz and 1.5\,GHz are typically $\approx5$\,minutes to be safe. Including overhead time spent switching receivers and slewing, the entire process can take $1.5-2$\,hours per source, resulting in source localization of $\lesssim2\arcmin$. In this paper, we outline \--- in some cases \--- a more effective approach for rapid localization of new pulsars using on-the-fly (OTF) mapping. OTF mapping is not a novel technique (commonly used to measure positions for continuum sources with single dish telescopes), but one that is under-utilized in the pulsar community and is especially convenient for localizing pulsars discovered in drift scan surveys and with telescopes that do not have multi-beam capabilities. This study is a proof of concept, motivated by the need for rapid assessment of new MSPs for inclusion in PTAs, and meant to facilitate the process. In \S\ref{sec:method}, we describe the method, observations of four test sources, and our procedure for measuring position offsets; \S\ref{sec:results} describes the precision of recovered positions resulting from our test observations and a notable result for millisecond pulsar J1400$-$1431 -- its measured coordinates were discrepant with the previously published values, prompting additional follow-up and an improved timing solution. Finally, we discuss systematic errors that should be considered and conclude in \S\ref{sec:conclusion}. | \label{sec:conclusion} Current single dish, low-frequency radio pulsar surveys sacrifice precise localization of discoveries for efficient sky coverage. Since the telescope's beam size is inversely proportional to the observing frequency, poor localization hampers high-frequency follow-up and degrades the signal-to-noise ratio in future detections. Positions acquired through pulsar timing are extremely precise (often known to a fraction of an arcsecond), but measuring positions this way requires $\simeq1$\,year of dedicated pulsar timing efforts. Therefore, rapid $\approx1\arcmin$ localization is useful for improving the quality (signal-to-noise) of future observations, aids in establishing phase connection, and provides flexibility in follow-up observing frequency, which is useful for evaluating MSP suitability for PTAs. In the current regime, PTA sensitivity is most significantly improved by adding new pulsars to the array \citep{sej+13,tve+16}. The sooner MSPs can be added to PTAs, the more their timing baselines can be extended, maximizing PTA sensitivity to gravitational waves. Although gridding works well for incremental improvements in pulsar localization, OTF mapping simplifies the procedure when higher precision is required (e.g. improving localization from an $18\arcmin$ error radius to $\approx1-3\arcmin$) for several reasons. First, the observing set-up is nearly identical to that of the discovery scan with more time spent effectively on-source, making follow-up detections more likely (gridding requires assumptions be made about a pulsar's spectral index to ensure detection at higher frequencies). Unlike with gridding, OTF mapping only involves use of a single receiver, eliminating the need for proposing time at multiple frequencies and overhead time for switching between corresponding receivers. Finally, OTF mapping can be used directly on data from drift scan surveys, providing immediate localization in right ascension for free. This is immediately applicable to new discoveries in the 327\,MHz Arecibo drift scan survey \citep{dsm+13} and may also prove useful for current and future drift scan surveys with the Five hundred meter Aperture Spherical Telescope \citep[FAST; e.g.][]{slk+09,zhl+16,lp+16,yln+13}. This study demonstrates that on-the-fly (OTF) mapping has the capability of localizing pulsars to within $\approx1-3\arcmin$ precision in 30\,mins, with fewer complications and requiring $2-3$ times less telescope time than a traditional gridding method. We also provide code (described in \S\ref{sec:reduction}) to measure position offsets for general purpose use, given standard folded output files from {\tt PRESTO}. The majority of test scans showed reliable position recovery to within measurement uncertainties. For PSR J1400$-$1431, position improvements from OTF mapping facilitated establishing a coherent timing solution, now spanning $>5$\,years \citep{skm+17}. | 18 | 8 | 1808.06643 |
1808 | 1808.09975_arXiv.txt | We present simulations of isolated disc galaxies in a realistic environment performed with the Tree-SPMHD-Code \textsc{Gadget-3}. Our simulations include a spherical circum-galactic medium (CGM) surrounding the galactic disc, motivated by observations and the results of cosmological simulations. We present three galactic models with different halo masses between $10^{10} M_\odot$ and $10^{12} M_\odot$, and for each we use two different approaches to seed the magnetic field, as well as a control simulation without a magnetic field. We find that the amplification of the magnetic field in the centre of the disc leads to a biconical magnetic outflow of gas that magnetizes the CGM. This biconical magnetic outflow reduces the star formation rate (SFR) of the galaxy by roughly $40 \%$ compared to the simulations without magnetic fields. As the key aspect of our simulations, we find that small scale turbulent motion of the gas in the disc leads to the amplification of the magnetic field up to tens of $\mu G$, as long as the magnetic field strength is low. For stronger magnetic fields turbulent motion does not lead to significant amplification but is replaced by an $\alpha$ - $\omega$ dynamo. The occurance of a small scale turbulent dynamo becomes apparent through the magnetic power spectrum and analysis of the field lines' curvature. In accordance with recent observations we find an anti-correlation between the spiral structure in the gas density and in the magnetic field due to a diffusion term added to the induction equation. | Magnetic fields are a fundamental aspect in astrophysics and cosmology. They are essential for describing many processes in theoretical astrophysics properly. The relevance of magnetic fields ranges from the small scales in star formation and in the ISM over galactic scales up to galaxy-clusters and the large scale structure of the Universe. While there is a large amount of observational data on magnetic fields, especially in the area of galaxy formation and evolution \citep[i.e.][]{Hummel1986, Chyzy2003, Chyzy2007, Beck2007} the situation is different for numerical studies that investigate the behaviour of magnetic fields in detail \citep{Kotarba2011, Pakmor2013, Mbeck2016, Rieder2016, Pakmor2017}. In the case of galaxies the magnetic field becomes important for several reasons. It acts as an additional pressure component, and thus is needed as a correction of the equations of hydrodynamics, resulting in the well known equations of magnetohydrodynamics. Moreover, the magnetic pressure in galaxies can reach the same order of magnitude as the turbulent pressure of the ISM, and thus it can completely dominate the thermal pressure of the disc. Hence, it should be taken into account in simulations of galaxy formation and evolution. However, this is often not the case and pure hydrodynamical simulations are used to study the formation and evolution of galactic discs. On the other hand magnetic fields can be very important for star formation and the regularization of cosmic rays and should not be excluded when these processes are taken into account. Still, the origin of magnetic fields in the Universe is unclear. It is possible to generate magnetic seed fields below $10^{-20}$ G by either battery processes in the early Universe \citep[e.g.][]{Biermann1950, Mishustin1972, Zeldovich1983} or the phase transitions that appear in the standard model, shortly after the Big Bang \citep[e.g.][]{Hogan1983, Ruzmaikin1988a, Ruzmaikin1988b, Widrow2002}. Those initial magnetic fields can then be amplified by various dynamo processes, namely the $\alpha$-$\omega$-dynamo \citep{Ruzmaikin1979}, the cosmic ray driven dynamo \citep{Lesch2003, Hanasz2009} or the small scale turbulent dynamo \citep{Kazantsev1968, Kraichnan1968}. While, the first and the second dynamo process operate on $10^{8}$ yr-scales, the third process has typical timescales in the Myr-regime \citep{Biermann1951}. The magnetic energy is exponentially amplified on the small scales and random motion regulates it on the largest turbulent scales \citep{Zeldovich1983, Kulsrud1992, Kulsrud1997, Malyshkin2002, Schekochihin2002, Schekochihin2004, Schleicher2010}. Observationally, there are several methods to measure the magnetic field strengths in galaxies. \citet{Brown2007} investigated the magnetic field of the inner Milky Way by using rotation measurements of $148$ objects behind the galactic disc. Further, magnetic fields of nearby galaxies can be determined using their radio synchrotron emission. In this case the unpolarized component of the synchrotron emission is important because it is needed to explain galactic dynamics and magnetic driven outflows \citep{Beck2007}. Radio synchrotron emission is also used to calculate the magnetic field strengths in nearby galaxies which leads to values between $20$ and $30$ $\mu$G in the spiral arms and to $50$ to $100$ $\mu$G in the galactic centre, as described in \citet{Beck2007} or \citet{Beck2009}. \citet{Robishaw2008} presented measurements of magnetic fields due to Zeeman-splitting emission in OH megamasers of five ultra luminous infrared galaxies leading to magnetic field strengths along the line of sight between $0.5$ and $18$ mG. Beyond the observations of the magnetic fields in galactic discs there are also those of their CGM. \citet{Carretti2013} present measurements of magnetized outflows towards the CGM of the Milky Way in two giant lobes located in the north and south of the galactic centre with a magnetic field strength of around $15$ $\mu$G, known as the 'Fermi-bubbles'. Simulations of galactic magnetic fields are often done with hydrodynamical grid codes. \citet{Wang2009} investigated the magnetic field in isolated disc galaxies without star formation using the grid code \textsc{enzo} \citep{Bryan1997, Oshea2004, Bryan2014}. \citet{Dubois2010} studied the magnetic field of dwarf galaxies with a closer look on winds driven by stars using the grid code \textsc{ramses} \citep{Teyssier2002}. \citet{Pakmor2013} and \citet{Rieder2016} present studies of magnetic fields for isolated galaxy formation by collapsing a giant gaseous halo in a dark matter potential using the moving mesh code \textsc{arepo} \citep{Springel2010} and the grid code \textsc{ramses}, respectively. While \citet{Pakmor2013} investigate general properties of the magnetic field, \citet{Rieder2016} point out the importance of supernova feedback on the structure of the ISM and its magnetic field. Another detailed study of magnetic fields in isolated discs is presented in \citet{Butsky2017} where they find a small scale turbulent dynamo of the magnetic field. The same behaviour can be found in \citet{Rieder2017a} for an isolated disc galaxy as well as in \citet{Pakmor2017} and \citet{Rieder2017b} for cosmological zoom-in simulations. The evolution of magnetic fields has been extensively studied with particle-based methods for magnetohydrodynamics as well. \citet{Kotarba2009} investigate the magnetic field in an isolated disc galaxy using the SPH-code \textsc{vine} \citep{Wetzstein2009}. In \citet{Kotarba2010} \textsc{vine} is used for studies of the magnetic field in the Antennae-galaxies. In \citet{Kotarba2011}, \citet{Ageng2012a}, and in \citet{Ageng2012b}, \textsc{gadget-3} is used to study the magnetic field in other galaxy mergers. \citet{Mbeck2016} is investigating the magnetic field structure of the Milky Way in more detail, by calculating its synchrotron-emission. Many of these simulations study the evolution of galaxies in isolation by sampling a dark matter halo, a stellar bulge, and a stellar and gaseous disc to create the initial conditions. The hot CGM is typically neglected to save computational effort and as it is mainly irrelevant for galactic dynamics. However, cosmological simulations show that galaxies are constantly accreting gas from their hot haloes, such that this component is essential to model realistic galactic systems. Moreover, a hot gaseous halo around the Milky Way can now be detected observationally \citep{miller13}. These observations indicate that the density profile of the CGM can be described with a $\beta$-power law \citep{cavaliere78}, which is common in studies of globular clusters \citep{Plummer1911} and cosmological simulations of galaxy-clusters \citep[e.g.][]{donnert14}. Consequently, it may be critical to include the hot gaseous component in simulations of isolated galaxies. In SPMHD simulations the presence of the CGM has a further advantage. In the SPMHD formalism the magnetic field is a property of the gas particles. Therefore, a carrier for the magnetic field is needed which gives further justification for the presence of the CGM in magnetohydrodynamic simulations. In this work we present a set of nine high-resolution simulations that include a spherical hot CGM for each galaxy. The paper is structured as follows. We give a short summary of our simulation method in section \ref{sec:simulation_method}, where we point out recent improvements of our numerical methods and the physical models that are considered. In section \ref{sec:initial_conditions} we present the methods that we use to build our numerical model for an isolated disc galaxy that includes an observationally constrained CGM. We then examine the general properties of each galactic system and investigate the interaction between the galactic disc and the CGM in section \ref{sec:results}. Our conclusions are presented in section \ref{sec:conclusions}. | \label{sec:conclusions} We present a modified model for isolated disc galaxies including a realistic CGM. Using this model we simulate a set of galaxies with different halo masses ranging from $10^{10} M_{\odot}$ over $10^{11} M_{\odot}$ to $10^{12} M_{\odot}$ and study the general properties (like the morphological structure and the SFR) of these systems. We focus on the Milky Way-like system, and present a detailed study of the morphological structure of the gas density, as well as the magnetic field. We observe a mean magnetic field strength of a few $\mu$G in the galactic disc, which is in good agreement with observations. In the galactic centre we find higher field strengths up to a few $100 \mu$G. In the spiral arms the magnetic field strength is about an order of magnitude lower compared to the galactic centre. We find that the structure of the magnetic field strength does not follow exactly the spiral arms in the gas density, but is strongest between two neighbouring spiral arms. This result differs from those reported by other groups \citep{Pakmor2013, Butsky2017}. The reason for that is that we include a magnetic diffusion term in our simulations, which makes it possible to follow the magnetic field evolution in the non-linear regime. Furthermore, this effect is in agreement with many observations (see \citet{Beck2015} for and references therein). The amplification of the magnetic field in our simulations is mainly driven by small scale turbulence. We show clear evidence for this in the magnetic power spectra (figure \ref{fig:power}), in agreement with simulations by other groups \citep{Pakmor2013, Rieder2016, Butsky2017}. Moreover, we find further evidence for a small scale dynamo by examining the curvature of the magnetic field lines, which can be used to distinguish between amplification by adiabatic compression and by a small scale dynamo (figure \ref{fig:curvature}). Our simulations indicate that at later times the slope of the magnetic power spectra turns around. This shows that the galaxies are entering a new regime that is dominated by strong magnetic fields instead of small scale turbulence. Thus, the dominating amplification process in this regime is either driven by the $\alpha-\omega$-dynamo or completely saturated and thus switched off. In the simulations with $M_\mathrm{h}=10^{12} M_{\odot}$ and $M_\mathrm{h}=10^{11} M_{\odot}$, we find galactic outflows that are driven by the magnetic field. In this regime the magnetic pressure is several orders of magnitude higher than the thermal pressure. In our simulations with $M_\mathrm{h}=10^{10} M_{\odot}$ this is not the case, so that we do not observe a dominating magnetic outflow in haloes below $M_\mathrm{h}=10^{11} M_{\odot}$. A more detailed study of the interaction between galactic disc and CGM shows that a certain amount of magnetic energy is released in the outer regions of the CGM having its origin in the centre of the galactic disc. Studying the turbulence in the magnetic field, we find that the highly magnetized outflows are mainly driven by the turbulent magnetic field in the centre of the galactic disc. The structural analysis of the magnetic field indicates that it follows a complex structure besides the obvious spiral patterns and does not necessarily follow the spiral structure of the gas density because of magnetic diffusion. Finally, we summarize the three most important findings of this study. \begin{itemize} \item Amplification of the magnetic field strength is driven by small scale turbulence until the magnetic field in the disc is strong enough so that the dynamo saturates. We provide evidence for this \citet{Kazantsev1968} dynamo in the magnetic power spectra as well as the anti-correlation of the magnetic field strength and the curvature of the magnetic field lines for a small scale dynamo \citep[e.g.][]{Schekochihin2004, Vazza2018}.\\ \item Galaxies in which the magnetic pressure dominates the thermal pressure show magnetic-driven outflows that can lead to a significant mass loss of the baryonic disc. The outflows appear as low density bubbles reaching a several $100$ km/s before they mix with the CGM and fall back to the disc.\\ \item Diffusive terms in the inducution equation can lead to an anti-correlation between the spiral structure of the gas disc and the spiral structure within the magnetic field strength that can be seen in observations. \end{itemize} Future work will need to focus on detailed resolution studies to determine the spatial and the mass resolution that is needed to actually resolve the small scale turbulent dynamo, which may be crucial in the framework of cosmological zoom-in simulations of Milky Way-like galaxies. Furthermore, none of the current models for star formation in hydrodynamical simulations includes the pressure given by the magnetic field directly. Only indirect effects on the SFR can be captured by the current simulations. In future studies the magnetic pressure may be directly included by using pressure-based star formation models. | 18 | 8 | 1808.09975 |
1808 | 1808.02851_arXiv.txt | The multifractal geometry remains an under-exploited approach to describe and quantify the large-scale structure of interstellar clouds. In this paper, the typical tools of multifractal analysis are applied to \textit{Herschel} far-infrared (70-500~$\mu$m) dust continuum maps, which represent an ideal case of study. This dust component is a relatively optically thin tracer at these wavelengths and the size in pixel of the maps is well suitable for this statistical analysis. We investigate the so-called multifractal spectrum and generalised fractal dimension of six Hi-GAL regions in the third Galactic quadrant. We measure systematic variations of the spectrum at increasing wavelength, which generally correspond to an increasing complexity of the image, and we observe peculiar behaviours of the investigated fields, strictly related to the presence of high-emission regions, which in turn are connected to star formation activity. The same analysis is applied to synthetic column density maps, generated from numerical turbulent molecular cloud models and from fractal Brownian motion (fBm), allowing for the confrontation of the observations with models with well controlled physical parameters. This comparison shows that, in terms of multifractal descriptors of the structure, fBm images exhibit a very different, quite unrealistic behaviour when compared with Hi-GAL observations, whereas the numerical simulations appear in some cases (depending on the specific model) more similar to the observations. Finally, the link between mono-fractal parameters (commonly found in the literature) and multifractal indicators is investigated: the former appear to be only partially connected with the latter, with the multifractal analysis offering a more extended and complete characterization of the cloud structure. | \defcitealias{eli14}{Paper~I} The complex morphology of Galactic interstellar clouds generally eludes a description simply based on the typical shapes of Euclidean geometry \citep[e.g.,][]{sca93,elm96,pfe96}. The mostly self-similar appearance of the interstellar medium (ISM), especially at scales $L \gtrsim 1$~pc is generally thought to be the result of turbulence \citep{elm95,elm04,dib05,kru14}, because of the intrinsic self-similarity of this phenomenon, triggered by the very high value of the Reynolds number in these environments. The fractal geometry is largely invoked to provide a quantitative characterization of the ISM morphology, as it can be deduced from far-infrared (FIR) or sub-millimetre maps, through fractal descriptors \citep[][hereafter \citetalias{eli14}]{stu98,ben01,sch11,sun18,eli14} and comparing these quantities with theoretical expectations has two important advantages. On the one hand, a comparison between models and observations gives indications about the kind of turbulence that is prevalent in the observed cloud and, on the other hand, the obtained fractal parameters can be used as further constraints for future simulations. In this respect, fractal or, in a broad sense, statistical analysis techniques are applied also to numerical simulations of turbulent clouds, to make possible a comparison between model and ISM morphological properties. Three-dimensional magneto-hydrodynamic simulations have been characterised in terms of probability density function, structure function and power spectrum \citep{kow07,kri07}, fractal dimension \citep{fed09}, or dendrograms \citep{burk13}. It should also be emphasised that natural fractal structures, such as ISM, are self-similar only in a statistical sense (\textit{stochastic fractals}) and show complexity only over a finite range of scales. Identifying such a range, which should correspond to the scales actually involved by the turbulent energy cascade, can give important information on the injection and dissipation scale of turbulence \citepalias[see][and references therein]{eli14}. Interestingly, the latter is expected to correspond to the characteristic size of gravity-dominated structures (filaments and cores) relevant for star formation, as highlighted, e.g., by \citet{fal04} and \citet{sch11} \citep[for more recent analysis of the turbulence-regulated star formation, see also][]{bur17,moc17}. This (mono-)fractal approach, however, still underlies a certain degree of degeneracy: as said above, a large number of natural objects exhibit properties of self-similarity, but can not be described as perfect fractals, especially because such a description is based on a sole parameter, namely the fractal dimension. In contrast, \textit{Multifractal geometry} provides a more suited mathematical framework for detecting and identifying complex local structure, and for describing local singularities. It is invoked in the fields of economy, medicine, hydrography, environmental sciences, and physics (e.g. in studying turbulent flows). In astrophysics, it has been used, for example, in the study of the distribution of galaxies \citep{man89,bor93,pan00,del06}, gamma-ray burst time series \citep{mer95}, and solar activity \citep{wu15,cad16,mar17}. The first application of the multifractal approach to characterize the ISM structure was carried out by \citet{cha01}, who analyzed 13 \emph{IRAS} maps (at 60 and 100~$\mu$m) taken from Chamaeleon-Musca, R~Corona Australis and Scorpius-Ophiucus star forming regions, all located at distance $d<160$~pc from the Sun, but spanning a relatively wide range of different conditions of star formation. A multifractal behaviour of the investigated clouds was revealed over the range 0.4-4~pc, and a possible relation with underlying turbulent cascades and hierarchical structure was found. While the multifractal properties of a cloud can be directly related to its geometry, a direct relation with the properties of the star formation is not found by these authors; this link has been established indirectly for the first time by \citet{tas07} using global parameters of external galaxies. Finally, \citet{kha06} studied the multifractal structure of Galactic atomic hydrogen through wavelet transform techniques, discussing arm vs inter-arm differences. As already pointed out in \citetalias{eli14}, the advent of \textit{Herschel} \citep{pil10} offered an extraordinary chance for studying the morphology of the cold Galactic ISM, thanks to the combination of several favourable conditions and features: $i$) the spectral coverage of \textit{Herschel} photometric surveys ($70-500~\mu$m) encompasses the peak of the continuum emission of cold dust ($T \leq 50$~K), with the dust getting optically thinner at increasing wavelengths, which helps revealing the structure of dense clouds with unprecedented accuracy; $ii$) the angular resolution of \textit{Herschel} photometric observations ($6\arcsec-36\arcsec$) is better or comparable with that of the most recent CO surveys of the ISM \citep[e.g.,][]{jac06,bur13,sch17}, and their dynamic range is so large \citep[more than two orders of magnitude, e.g.,][]{mol16} that the obtained 2-D picture of the ISM structure generally turns out to be highly detailed and reliable; $iii$) large \textit{Herschel} photometric surveys produced a huge amount of data, corresponding to a wide variety of Galactic locations, physical conditions, and star formation modes to be compared; $iv$) thanks to good angular resolution and excellent mapping capabilities, single \textit{Herschel} maps represent highly suitable data sets for pixel statistical analysis, namely techniques aimed at deriving fractal properties of maps starting from intensity values in single pixels. This improvement can be appreciated, for instance, by comparing how much the size in pixels of the analysed maps increased from the pioneering work of, e.g., \citet{stu98} (several tens or a few hundred pixels) to that of \citetalias{eli14} (up to a few thousands of pixels). Despite this potential, the promising approach of \citet{cha01} for describing the structure of the ISM through multifractal parameters has not been yet applied to \textit{Herschel} maps. With this paper we intend to fill this gap. Furthermore, choosing the same fields already analysed through mono-fractal descriptors in \citetalias{eli14}, we explore possible relations between mono- and multifractal parameters for any investigated field. Finally, analysing with the same techniques also column density maps obtained from numerical simulations of insterstellar turbulence, we search for possible recipes connecting the quantitative description provided by multifractal tools and the underlying physics of the analysed regions. The paper is organized as follows: in Section~\ref{fields} the analysed maps, both observational and synthetic, are presented. In Section~\ref{multi} basics of multifractal geometry are introduced, together with a description of the tools used in the rest of the paper. In Section~\ref{results} the results of the multifractal analysis of the aforementioned data sets are reported and discussed by means of specific diagnostics, while our conclusions are given in Section~\ref{conclusions}. Additional details and discussion of the method are reported in the Appendices~\ref{fbmappend}, \ref{simevol}, and \ref{dvarapp}. | The need of extending the multifractal description of the ISM, so far attempted only by \citet{cha01}, to more recent, high-quality, and statistically meaningful data motivated this work. We carried out the multifractal analysis of six Hi-GAL fields in a region of the third Galactic quadrant already described by \citet{eli13}, and characterised by a conveniently low degree of velocity component overlap along the line of sight. These fields are interesting by themselves, thanks to the variety of morphologies and physical conditions displayed by the ISM in this region. For comparison, the same analysis was extended to 30 synthetic maps: 12 column density maps of simulated clouds extracted from the STARFORMAT data base and obtained from four different numerical models, at two projections and two evolutionary epochs, and 18 fBm sets spanning a variety of power spectrum slopes and initial phase distributions. A number of results emerged from this analysis. The most important ones are summarised as follows: \begin{enumerate} \item All the investigated fields exhibit a multifractal rather than a simple monofractal structure. The variety of the obtained MFS shapes permits a further differentiation among them. \item Strong differences are found between the left and the right tail of the MFS. Most of the analysed Hi-GAL maps exhibit a broader left tail of the MFS with respect to the right one, with the extreme case of the 70~$\mu$m maps, presenting a right tail almost collapsed to a single point against a pronounced left one, signature of the presence of several bright spots on a very low-signal background, as the maps at this wavelength typically appear in this portion of the Galaxy. \item The roughly linear relation between the strength of the brightest singularities and dimensional diversity in the ISM maps found by \citet{cha01} is confirmed by our analysis of Hi-GAL fields at various wavelengths. \item The peak position and the total width of the MFS appear to systematically drift, for a given tile, with wavelength, denoting an increase of image complexity at increasing wavelength due to the progressive appearance of a network of filaments and of cold structures in general. Moreover, global behaviours are recognisable from tile to tile, from star formation-rich to more quiescent ones (more and less ``complex'', respectively). \item The MFS of the Hi-GAL fields is generally left-skewed, with the exception of the $\ell215$ tile. This is mostly associated to a lower $f$ initial value for the predominant tail with respect to the opposite extreme of the MFS, so that the ``vertical'' versus ``horizontal balance'' of the MFS appear to follow a direct power law with exponent close to 1. \item Comparing the generalised fractal dimensions of the Hi-GAL maps with the mono-fractal ones, a clear correlation is seen at positive orders (nearly linear at $q=10$), suggesting that the estimates of the fractal dimension are strongly influenced by the strongest brightness peaks present in the maps. \item The cloud models partly exhibit different behaviours, depending on the underlying physics. The ``compressive forcing'' maps show a different MFS compared to observations. The ``solenoidal forcing'', ``quasi-hydrodynamical'', and ``high-magnetization'' show relatively similar spectra at the earliest of the two considered epochs (with small differences among different projections), but with the last two presenting a systematic broadening of the left tail of the MFS as their star formation content increases under gravity action, in agreement with the behaviour recognised for observational maps. The presence of a magnetic support of the cloud, instead, is seen to contrast this effect \item Despite qualitative similarities between the MFS derived for observed maps and numerical simulations, using quantitative descriptors of the MFS shape (such as peak position, spectrum width and skewness, etc.) a segregation between the two image classes is found. This is also emphasized by the analysis of the generalised fractal dimension, suggesting that, at least for the analysed set of maps, simulations do not completely fulfill the constraints on the structure suggested by the multifractal analysis of observational maps. \item The multifractal analysis of fBm images reveals that they show a remarkably different behaviour compared with our observed maps, suggesting that, despite analogies between power spectra, the Fourier phase distributions for these two classes can be quite different and responsible of the observed discrepancies. All the used indicators advise against the use of the fBm images as a surrogate for the observations. \end{enumerate} Moreover, this study has produced some interesting results about fBm images by themselves, of interdisciplinary relevance independently from the comparison with observations: \begin{enumerate} \setcounter{enumi}{9} \item The increase of the power spectrum exponent $\beta$ generally produces a rise of the last point of the left part of the MFS and a strong systematic enlargement of the right tail of the MFS. The peak position increases as well at increasing $\beta$. \item On the other hand, the MFSs of two fBm generated with the same $\beta$ and a different random phase distribution, are not identical although they have the same fractal dimension. This represents a further evidence of the general importance of analysing the Fourier phases together with the simple power spectrum. \end{enumerate} Possible extension of this work will consist in enlarging the sample of analysed \textit{Herschel} fields, provided that they are associated to a predominant gas velocity component, as well as the number of the considered models, searching for possible points of contact of the two classes that could have been missed in the present analysis. | 18 | 8 | 1808.02851 |
1808 | 1808.09002_arXiv.txt | {} {The optical emission of black hole transients increases by several magnitudes during the X-ray outbursts. Whether the extra light arises from the X-ray heated outer disc, from the inner hot accretion flow, or from the jet is currently debated. Optical polarisation measurements are able to distinguish the relative contributions of these components.} {We present the results of {\it BVR} polarisation measurements of the black hole X-ray binary MAXI~J1820+070 during the period of March-April 2018.} {We detect small, $\sim$0.7\%, but statistically significant polarisation, part of which is of interstellar origin. Depending on the interstellar polarisation estimate, the intrinsic polarisation degree of the source is between $\sim$0.3\% and 0.7\%, and the polarisation position angle is between $\sim$$10\degr-30$$\degr$. We show that the polarisation increases after MJD~58222 (2018 April 14). The change is of the order of 0.1\% and is most pronounced in the {\it R} band. The change of the source Stokes parameters occurs simultaneously with the drop of the observed {\it V}-band flux and a slow softening of the X-ray spectrum. The Stokes vectors of intrinsic polarisation before and after the drop are parallel, at least in the {\it V} and {\it R} filters. } {We suggest that the increased polarisation is due to the decreasing contribution of the non-polarized component, which we associate with the the hot flow or jet emission. The low polarisation can result from the tangled geometry of the magnetic field or from the Faraday rotation in the dense, ionised, and magnetised medium close to the black hole. The polarized optical emission is likely produced by the irradiated disc or by scattering of its radiation in the optically thin outflow.} | The black hole X-ray binaries play a key role in understanding the processes of accretion onto and ejection from the compact objects in the presence of a strong gravitational field. These sources evolve through the cycle of the bright outbursts that proceed on timescales of weeks to months, separated by long periods of quiescence of years to decades \citep[see][for reviews]{RM06,DGK07}. Their typical X-ray luminosities at the outburst peak are $\sim$$10^{37}-10^{39}$~erg~s$^{-1}$, and typical distances are a few kpc. A few exceptional sources have reached or exceeded fluxes of 1~Crab in the X-rays: A~0620--00 \citep{Kuulkers98}, V404~Cyg \citep{Makino1989,Rodriguez15,Motta17} and V4641~Sgr \citep{Hjellming00,Revnivtsev02}. The X-ray transient MAXI~J1820+070 was first detected on 2018 March 11 \citep{ATel11399} by the Monitor of All-sky X-ray Image \citep[MAXI,][]{MAXI09} and was associated with the optical transient ASASSN-18ey \citep{ATel11400,Tucker18}. In the X-rays, the source flux exceeded 3~Crabs \citep{ATel11478,ATel11488}, and in the optical, the source reached a magnitude of $m_{V}=12-13$ \citep{ATel11421,ATel11533}. The parallax of the source $\pi=0.3\pm0.1$~mas was presented in the {\it Gaia} DR2 catalogue \citep{GaiaDR2}. This corresponds to a distance of $3.9^{+3.3}_{-1.3}$~kpc \citep{GRJ18}. This unusually bright event allows a detailed investigation of multi-wavelength spectral and timing properties. The course of the outburst was monitored in radio \citep{ATel11539,ATel11540}, sub-millimeter \citep{ATel11440}, optical \citep{ATel11418}, X-rays \citep{ATel11423}, and $\gamma$-rays \citep{ATel11478,ATel11490}. Because the object was sufficiently bright even for small telescopes, the target was almost continuously monitored, and a rich variety of phenomena was observed. Fast variability and powerful flares in the optical and infrared \citep{ATel11421,ATel11426,ATel11437,ATel11451}, optical, and X-ray quasi-periodic oscillations \citep{ATel11488,ATel11510,ATel11578,ATel11591,ATel11723} as well as low linear polarisation \citep{ATel11445} were detected in the source. A 17~h photometric period was recently reported \citep{ATel11756} and was tentatively associated with the orbital or superhump period (previously, the source showed a 3.4~h periodicity, \citealt{ATel11596}). The X-ray spectral and timing properties as well as the optical-to-X-ray flux ratio suggests that the source is a black hole binary \citep{ATel11418,ATel11488}. The origin of the optical emission of black hole transients in the outburst is still debated \citep[see][]{PV14}. The optical flux can be produced in the outer disc that is irradiated by the central X-ray source, in the jet, and in the inner hot accretion flow. Accurate measurements of optical polarisation at different outburst stages with simultaneous studies of optical and X-ray spectral and timing properties are expected to help separate the relative contributions of these components. In this work, we present the results of our polarisation campaign with the highly sensitive Dipol-2 instrument \citep{PBB14}, which was conducted at the initial stages of the outburst. We show that the source demonstrates small but statistically significant intrinsic polarisation, and we study its spectral and temporal properties. We describe the data in Sect.~\ref{sect:data}, present the results in Sect.~\ref{sect:results}, discuss them within the accretion-ejection framework in Sect.~\ref{sect:discuss}, and summarise our findings in Sect.~\ref{sect:conclus}. \begin{figure} \center{\includegraphics[width=0.8\columnwidth]{fig_1}} \caption{Evolution of the polarisation degree and polarisation angle of MAXI~J1820+070 in different filters: $B$ (blue triangles), $V$ (green diamonds), and $R$ (red crosses). For clarity, 0.5~d was added to MJD of the $B$ filter and subtracted from MJD of the $V$ filter. The vertical dashed line marks MJD~58222. } \label{fig:lc_scale} \end{figure} \begin{table*} \centering \caption{Polarimetric data for MAXI~J1820+070. } \begin{tabular}{ccccccc} \hline & \multicolumn{2}{c}{$B$} & \multicolumn{2}{c}{$V$} & \multicolumn{2}{c}{$R$} \\ MJD & $P$ (\%) & PA ($\degr$) & $P$ (\%) & PA ($\degr$) & $P$ (\%) & PA ($\degr$)\\ \hline 58195.61983 & $0.78 \pm 0.02$ & $53.9 \pm 0.8$ & $0.70 \pm 0.03$ & $53.9 \pm 1.2$ & $0.77 \pm 0.02$ & $54.7 \pm 0.8$ \\ 58199.61832 & $0.71 \pm 0.03$ & $55.5 \pm 1.4$ & $0.86 \pm 0.05$ & $51.1 \pm 1.8$ & $0.74 \pm 0.03$ & $51.8 \pm 1.3$ \\ 58206.61784 & $0.75 \pm 0.02$ & $54.0 \pm 0.6$ & $0.77 \pm 0.02$ & $55.8 \pm 0.8$ & $0.75 \pm 0.02$ & $54.8 \pm 0.6$ \\ 58208.61502 & $0.79 \pm 0.02$ & $53.3 \pm 0.7$ & $0.80 \pm 0.03$ & $57.6 \pm 1.0$ & $0.76 \pm 0.02$ & $54.8 \pm 0.8$ \\ 58220.61279 & $0.79 \pm 0.02$ & $51.5 \pm 0.9$ & $0.83 \pm 0.04$ & $53.0 \pm 1.3$ & $0.77 \pm 0.03$ & $49.9 \pm 1.0$ \\ 58221.59912 & $0.75 \pm 0.02$ & $54.8 \pm 0.8$ & $0.84 \pm 0.02$ & $54.3 \pm 0.8$ & $0.78 \pm 0.02$ & $51.7 \pm 0.8$ \\ 58222.58917 & $0.81 \pm 0.06$ & $57.4 \pm 2.0$ & $0.86 \pm 0.08$ & $53.3 \pm 2.8$ & $0.76 \pm 0.11$ & $40.4 \pm 4.0$ \\ 58225.59632 & $0.62 \pm 0.08$ & $57.5 \pm 3.6$ & $0.68 \pm 0.11$ & $54.5 \pm 4.6$ & $0.76 \pm 0.13$ & $50.3 \pm 4.9$ \\ 58227.57404 & $0.76 \pm 0.04$ & $53.0 \pm 1.7$ & $0.87 \pm 0.08$ & $47.2 \pm 2.6$ & $0.84 \pm 0.06$ & $47.9 \pm 2.0$ \\ 58231.60084 & $0.74 \pm 0.03$ & $50.8 \pm 1.2$ & $0.83 \pm 0.04$ & $52.0 \pm 1.5$ & $0.88 \pm 0.03$ & $45.1 \pm 1.0$ \\ 58232.60051 & $0.76 \pm 0.02$ & $51.4 \pm 0.9$ & $0.91 \pm 0.04$ & $50.1 \pm 1.2$ & $0.90 \pm 0.03$ & $45.7 \pm 1.0$ \\ 58234.60428 & $0.86 \pm 0.08$ & $46.5 \pm 2.6$ & $0.9 \pm 0.14$ & $54.5 \pm 4.4$ & $0.87 \pm 0.10$ & $42.5 \pm 3.7$ \\ \hline $<$58222 & $0.76 \pm 0.01$ & $53.9 \pm 0.3$ & $0.79 \pm 0.01$ & $54.7 \pm 0.4$ & $0.76 \pm 0.01$ & $53.3 \pm 0.3$ \\ $>$58222 & $0.76 \pm 0.02$ & $51.4 \pm 0.6$ & $0.87 \pm 0.02$ & $50.5 \pm 0.8$ & $0.86 \pm 0.02$ & $45.8 \pm 0.6$ \\ \hline \end{tabular} \label{tab:maxi_ppa} \end{table*} | \label{sect:conclus} We presented the results of the observational campaign studying {\it BVR} polarisation properties of the black hole X-ray binary candidate MAXI~J1820+070. We found evidence for a low, but statistically significant polarisation, about 0.7\%--0.9\%, in the source direction, at PA$\approx$$50\degr$ in all three filters. This high accuracy is possible owing to the original design of the Dipol-2 instrument. We found that the observed polarisation degree increases by about 0.1\% after MJD~58222 in the $V$ and $R$ filters with an additional change in PA by 4$\degr$ and 7.5$\degr$. In $B$, an enhancement of the polarisation at a $3\sigma$ level is seen. The moment when the polarisation started to significantly evolve coincides in time with the drop in the $V$ flux, suggesting that an increase in polarisation is associated with the decreasing flux of the non-polarized component. We noted that at about the same date, the X-ray spectral index started to increase, suggesting a start of the transition to the soft state. To determine the interstellar component of polarisation, we performed a polarimetric study of the field stars and found the ISM polarisation degree of $\sim$0.6\%--0.8\% at PA$\approx$$65\degr-80\degr$, depending on the way we estimate it. The resulting intrinsic source polarisation degree is at a level of $\sim$0.3\% to 0.7\% at PA$\approx$$10\degr-30\degr$. We suggest that the jet or the hot flow contribute to the optical flux, but either of these components have to be unpolarized, implying a rather tangled magnetic field or a large role of the Faraday rotation that destroys polarisation in the ionised magnetized medium close to the black hole. The likely source of the intrinsic polarized emission is the outer irradiated accretion disc or the disc radiation that is scattered by the optically thin wind. | 18 | 8 | 1808.09002 |
1808 | 1808.09833_arXiv.txt | \noindent Gravitational waves and electromagnetic radiations from a neutron star merger were discovered on 17 August 2017. Multiband observations of the optical transient have identified brightness and spectrum features broadly consistent with theoretical predictions. According to the theoretical model, the optical radiation from a neutron star merger originates from the radioactive decay of unstable nuclides freshly synthesized in the merger ejecta. In about a day the ejecta transits from an optically thick state to an optically thin state due to its subrelativistic expansion. Hence, we expect that about a day after the merger, the gamma-ray photons produced by radioactive decays start to escape from the ejecta and make it bright in the MeV band. In this paper, we study the features of the radioactive gamma-ray emission from a neutron star merger, including the brightness and the spectrum, and discuss the observability of the gamma-ray emission. We find that more than $95\%$ of the radiated gamma-ray energy is carried by photons of $0.2$--$4\,\MeV$, with a spectrum shaped by the nucleosynthesis process and the subrelativistic expansion of the ejecta. Under favorable conditions, a prominent pair annihilation line can be present in the gamma-ray spectrum with the energy flux about $3$--$5\%$ of the total. For a merger event similar to GW170817, the gamma-ray emission attains a peak luminosity $\approx 2\times 10^{41}\,\erg\,\s^{-1}$ at $\approx 1.2\,\oday$ after the merger, and fades by a factor of two in about two days. Such a source will be detectable by Satellite-ETCC if it occurs at a distance $\la 12\,\Mpc$. \vspace{0.3cm} \noindent\textit{Keywords:} binaries: close -- gamma-ray burst: general -- gravitational waves -- nuclear reactions, nucleosynthesis, abundances -- stars: neutron -- supernovae: general | \label{intro} Mergers of double neutron stars, or a neutron star and a stellar mass black hole, have long been expected to occur in the universe with a rate estimated to be several orders of magnitude lower than the supernova rate \citep{nar91,phi91,van96,blo99}. Three major transient observable phenomena have been predicted to arise from a neutron star merger (a neutron star-neutron star merger, or a neutron star-black hole merger): a gravitational wave signal \citep{cla77,tho87}, a short gamma-ray burst \citep[][and references therein]{goo86,pac86,pac91,eic89,pop99,ber14}, and a UV-optical-NIR (hereafter UVOIR) transient powered by the radioactive decay of unstable heavy elements freshly synthesized in the merger ejecta \citep[][and references therein]{li98,kul05,ros05,met10,rob11,bar13,kas13,tan13,gro14,kas15,met17,ros17,tan18,wol17}. In addition, mergers of neutron stars have been proposed to be a major site for nucleosynthesis of heavy and rare elements in the universe like gold and platinum \citep[][and references therein]{lat74,lat76,lat77,fre99,kor12,baus13,wan14,kas17,thi17,hot18}. Although the above mentioned three observable phenomena have been firmly predicted for decades and gamma-ray bursts (GRBs) have been observed for more than half a century, mergers of neutron stars have not been directly detected until 17 August 2017 after the joint detection of GW170817 and GRB170817A, and the identification of an optical counterpart SSS17a/AT2017gfo \citep{abb17a,abb17b,cou17,gol17,sav17,sie17,val17}. The gravitational wave signal was consistent with being produced by binary stars with component masses between $0.86$ and $2.26\,M_\odot$, in agreement with the masses of known neutron stars. In the region of GW170817 on the sky ($28\,\deg^2$ jointly determined by Advanced LIGO and Advanced Virgo), a short gamma-ray burst of duration $\approx 2\,\s$, GRB170817A, was detected by {\it Fermi}/GBM and {\it INTEGRAL}/SPI-ACS at $1.7\,\s$ after the coalescence time. About $10.87\,\hr$ later, an optical transient SSS17a/AT2017gfo was detected in the region of GW170817/GRB170817A, which occurred in the outskirts of NGC4993 at about $40\,\Mpc$. This distance agrees with the distance of GW170817 determined by the gravitational wave signal alone, which is $40_{-14}^{+8}\Mpc$. The possibility of being a supernova or the GRB afterglow for the optical transient was quickly excluded. The UVOIR spectra of SSS17a/AT2017gfo do not have any typical supernova feature. Attempts to spectrally classify the source using the Supernova Identification Code failed to get a good match, even using an expanded template set \citep{tro17}. The luminosity and spectra evolved much faster than those of a supernova. For instance, the $r$-band brightness of the source declined by 1.1\,mag from the peak in one day \citep{val17}. The X-ray and radio emissions were not detected until nine days and two weeks, respectively, after the burst of gravitational waves and are consistent with the GRB afterglow emissions from an off-axis jet \citep{hal17,tro17,ale18,mar18}. The afterglow emissions in the UVOIR range interpolated from the observed X-ray and radio emissions are much fainter than the observed emissions \citep{pia17,sha17,tro17}. The spectra of the transient in the early epoch ($\la 3.5\,\oday$) can be well fitted by blackbodies, while the afterglow spectra of GRBs are usually highly nonthermal. On the other hand, the observed optical transient has all the features predicted for neutron star mergers: (1)~The emissions are in the UVOIR range, and are characterized by blackbody radiations in the early time; (2)~The peak luminosity is in the supernova range (although in the faint end) and occurs at a time $\sim 1\,\oday$ after the merger; (3)~Both the luminosity and spectra evolve rapidly with time, fading and reddening on a timescale of days. Hence, the optical transit SSS17a/AT2017gfo is clearly identified as the radioactive glow of a neutron star merger, i.e., a kilonova or macronova as often called in the literature. In the early epoch ($\la 2\,\oday$ after the merger), the observed spectra are dominated by strong thermal UV-Optical emissions, with the brightness declining on a timescale of 1--2 days, and the colour reddening on a similar timescale \citep{eva17,mcc17,pia17,buc18}. After a couple of days, the bulk emissions of SSS17a/AT2017gfo shift to the near-infrared range, causing the spectra to redden quickly. This can be interpreted by the variation in the opacity of the merger ejecta, at least in principle. As pointed out by \citet{kas13} and \citet{tan13}, the opacity of a merger ejecta is very sensitive to the abundance of lanthanide elements. If the mass fraction of lanthanides is $>10^{-2}$, the opacity can be as high as $10\,\cm^2\,\g^{-1}$, due to the bound-bound transition of the $f$-shell electrons of lanthanides. To account for the fact that the spectra of SSS17a/AT2017gfo are dominated by a blue component in the early time and by a red component in the late time, multi-component models of kilonovae have been used to fit the data \citep{cow17,dro17,kil17,pia17,tan17,vil17,wax17}. The presence of multiple components in a merger seems plausible: a dynamical ejecta generated by the tidal and hydrodynamic forces produced by the violent merger process, and a disk-wind ejecta driven by neutrino-antineutrino annihilation following the merger \citep{tho01,pac02}. It is natural to expect that these distinct components have different compositions of heavy elements hence different opacities, and different values of other parameters such as the expansion velocity and mass. However, the later red emissions may also arise from delayed energy injection from a long-lived remnant neutron star at the center \citep{yu17}. Before the discovery of GW170817, some clues for the existence of kilonovae/macronovae had been found in GRBs 050709, 060614, and 130603B. The very faint near-infrared rebrightening found in their late afterglows was interpreted as the emergence of kilonova/macronova emissions \citep{ber13,tanv13,jin15,jin16,yan15}. GRBs 050709 and 130603B are short bursts with a duration $<2\,\s$. GRB060614 has a duration of $102\,\s$ but is more like a short burst in many other aspects \citep{zha07}. However, all these previous evidences are not strong cases, because of the limit in available data with good qualities. The case of GW170817/GRB170817A and SSS17a/AT2017gfo is a very strong case for the GW-GRB-Kilonova/macronova connection. Without any doubt, GW170717, GRB170817A, and SSS17a/AT2017gfo are different representations at different evolution stages of one physical event: the merger of two neutron stars. In spite of the successful identification of a kilonova/macronova associated with the GW170817/GRB170817A, a proof of the energy source for powering the UVOIR emission as arising from the decay of radioactive elements in a neutron star merger is not easy. Presumably, the violent merger produces copious radioactive nuclides with different lifetimes and quantum states, whose decay releases energies in the form of neutrinos, gamma-ray photons, and the kinetic energy of electrons, positrons, and other particles. Because the merger ejecta is initially opaque to photons and particles but transparent to neutrinos, only neutrinos can escape freely and the energies carried by photons and particles will be thermalized and eventually escape from the surface of the ejecta in the form of blackbody radiation. Because of the subrelativistic expansion of the ejecta, all emission and absorption lines from the surface of the ejecta are broadened and merged smoothly. As a result, a smooth and almost featureless thermal spectrum is generated \citep[with superposition of smooth undulations that might arise from broad absorptions,][]{tan18}, which is verified by the observations of SSS17a/AT2017gfo \citep{pia17}. The intense near-infrared emissions have sometimes been used to argue for the presence of lanthanides in the merger---presumably produced by the r-process (rapid neutron capture process) in the merger ejecta---but this is very indirect and not conclusive. The most direct approach for identification of nuclear elements produced during the nucleosynthesis process, and hence the energy mechanism for powering the optical transient from a neutron star merger, would be the direct observation of the gamma-ray photons emitted by the radioactive decay in the merger ejecta. However, this can only be possible after the ejecta becomes transparent to the gamma-ray photons. According to theoretical estimates, for reasonable parameters the ejecta will become optically thin after a day to a few days since the moment of merger. This seems having been confirmed by the optical observations of SSS17a/AT2017gfo. According to the analysis of \citet{pia17}, starting from about three days after the GW170817, the merger ejecta was becoming increasingly transparent to photons and more absorption lines become visible. The analysis by \citet{dro17} also shows that the spectra between 0.5--8.5 days after the merger are broadly consistent with a thermal distribution, then become nonthermal. These conclusions are broadly consistent with the results in other analyses \citep[e.g.,][]{kil17,sha17,tro17,wax17}. If we accept the two-component model for the merger (a blue component plus a red component), we expect that the gamma-ray photons produced by the radioactive decay will start to emerge from about one day after the merger, since the blue component cools very fast. The emerging photons will be in the energy range of $\MeV$ with a peak luminosity of $\sim 10^{41}\,\erg\,\s^{-1}$ (the same order of the optical peak luminosity of SSS17a/AT2017gfo). Since this luminosity is lower than that of the faintest observed GRB by about five orders of magnitude, to observe it requires a very sensitive gamma-ray detector given its distance of $40\,\Mpc$. The importance of observations of the gamma-ray emission from Type Ia supernovae (thought to be powered by the decay chain of $\prescript{56}{}{\rm Ni}\rightarrow\prescript{56}{}{\rm Co}\rightarrow\prescript{56}{}{\rm Fe}$) for diagnosing their progenitor and explosion mechanism has been noticed and studied for many decades \citep[][and references therein]{clay69,clay74,sum13,the14}. However, so far only for two supernovae have the gamma-ray emissions produced by radioactive decays been detected. The first detection of gamma-ray emission lines caused by the radioactive decay in a Type Ia supernova was in SN2014J in M82, for which two gamma-ray emission lines of $\prescript{56}{}{\rm Co}$ ($847$ and $1,238\,\keV$, respectively) were detected by {\it INTEGRAL}. From the observed luminosity of the emission lines ($4.7$ and $8.1\times 10^{41}\,\erg\,\s^{-1}$, respectively), it is successfully derived that about $0.6\,M_\odot$ radioactive $\prescript{56}{}{\rm Ni}$ were synthesized during the explosion \citep{chu14}. Before that, the same gamma-ray emission lines were also detected in type II SN1987A (thought to be powered by both radioactive decays and shock waves) with the Solar Max satellite \citep{mat88}. However, the derived mass of $\prescript{56}{}{\rm Co}$ was only a very small fraction ($\approx 1.3\%$) of the total mass of $\prescript{56}{}{\rm Co}$ inferred from the bolometric light curve at a similar time. The rare detection of radioactive gamma-ray lines in supernovae is mainly caused by the fact that we are lacking of gamma-ray detectors with a high enough sensitivity in the $\MeV$ energy range \citep[][and references therein]{tan15}. Both SN1987A and SN2014J are among the nearest supernovae that have ever been observed, with a distance of $51\,\kpc$ and $3.5\,\Mpc$, respectively. Since the occurrence frequency of neutron star mergers is about 1,000 times smaller than that of supernovae, in principle the closest merger that we have a fair chance to discover would be farther way than the closest supernova by a factor of $\sim 10$. So, for a similar luminosity, we expect that the radioactive gamma-ray emission from neutron star mergers would be more difficult to detect than that from supernovae, since its flux density would be weaker by about two orders of magnitude. However, this does not reduce the importance of observations of the radioactive gamma-ray emission from neutron star mergers. In addition, given the fact that we have discovered SN 1987A although the local rate of type II supernovae is only $\approx 2.5\times 10^{-8}\,\yr^{-1}$ in a spherical volume with a radius of $51\,\kpc$ \citep{li11}, detection of a neutron star merger at a distance $\la 1\,\Mpc$ may not be impossible. In this paper, we study the gamma-ray emissions due to the radioactive decay of unstable nuclides produced in a neutron star merger. After the merger ejecta becomes transparent a few days after the merger, the gamma-ray photons will escape from the ejecta and become visible. Unlike in the case of supernovae where the dominant gamma-ray emissions come from the decay of a single radioactive nuclear isotope $\prescript{56}{}{\rm Co}$ after the supernova envelope becomes transparent (about 100 days after the explosion), in the case of neutron star mergers the merger ejecta are expected to contain hundreds to thousands of unstable nuclides with a wide distribution in lifetimes. Hence, the gamma-ray emissions from a neutron star merger are expected to contain tons of emission lines with a distribution over the photon energy. The subrelativistic expansion of the ejecta will broaden the emission lines and merge them, resulting in a smooth gamma-ray spectrum in contrast to the case of supernovae where we can see distinct emission lines from one unstable nuclide. In this paper we will calculate the magnitude and the shape of the radioactive gamma-ray spectra of a neutron star merger in its optically thin stage, identify the features in the emission spectrum associated with specific nucleosynthesis processes, and study their dependence on model parameters (expansion velocity, opacity, etc) as well as the observability of the gamma-ray emission. \citet{hot16} studied the gamma-ray emission resulting from the radioactive decay of r-process elements outside the photosphere in an ejecta of a neutron star merger. They concluded that to observe the emissions, new detectors with a sensitivity higher than current ones by at least a factor of ten are required. Their research was based on a dynamical r-process network. Since in the r-process the dominant nuclear reaction consists of neutron captures, $\beta$-decay, $\alpha$-decay and fissions \citep{mar08}, in the calculation of \citet{hot16} the dominant contribution to the gamma-ray emission comes from the $\beta$-decay of r-nuclides. In our work, without using an r-process network, we assume at some initial time a power-law distribution in the number of radioactive nuclides over their lifetimes, then calculate the energy generation by tracing the decay process of nuclides. The sample of radioactive nuclides is constructed from the NuDat\,2 database at the National Nuclear Data Center according to some selection criteria. For the calculation of the energy generation and the nonthermal gamma-ray spectrum, we make use of the gamma-ray radiation data for each nuclide provided by the NuDat\,2 website. We note that the original work of \citet{li98} was also based on an assumption of power-law distribution of the number of unstable nuclides over their lifetimes, and the luminosity and temperature of blackbody radiations were correctly derived. So, in this work we also take this simple approach. Since our data sample is uniformly extracted from a nuclear database, it includes not only r-nuclides. The sample also includes p-nuclides---proton-rich nuclides, which cannot be produced by the r-process, but the r-nuclides produced during the r-process can serve as the seed for production of p-nuclides if the thermodynamic conditions in the ejecta are appropriate. Inclusion of both r- and p-nuclides in the sample will allow us to identify the specific feature of the gamma-ray emissions produced by each type of nuclides, which is necessary for diagnosing the nucleosynthesis process in the ejecta by observing its gamma-ray emissions. Later in the paper we will also argue that the possibility for the occurrence of p-process---a process for the production of p-nuclides---in a merger ejecta cannot be excluded in principle. In our model the gamma-ray emission comes from the following five decay processes: $\beta^-$-decay, $\beta^+$-decay, electron capture, $\alpha$-decay, and isomeric transition. The electron capture is a process where a proton-rich nucleus of a neutral or partially-ionized atom absorbs an electron from the K or L shell. It is a process that competes with the $\beta^+$-decay, and has the same effect on the atomic number. The $\beta^-$-decay is a major feature of r-nuclides, through which the unstable and neutron-rich nuclides decay toward the bottom of the valley of nuclear stability in the nuclear chart. The isomeric transition is a process where a long-lived excited nuclear level decays by gamma-ray emissions or internal conversion. We find that $\beta^\pm$-decays and electron captures make the dominant contribution to the gamma-ray energy generation in the merger ejecta. The isomeric transition contributes to the total gamma-ray energy generation with a fraction smaller than that contributed by the electron capture and the $\beta^\pm$-decay, but larger than that contributed by the $\alpha$-decay. We also find that the $\beta^+$-decay and the electron capture produce a gamma-ray spectrum with a feature very different from that generated by the $\beta^-$-decay, including the presence of electron-positron annihilation lines. The $\beta^-$-decay alone cannot produce annihilation lines. This feature, and other differences between the gamma-ray spectrum produced by r-nuclides and that produced by p-nuclides which will be discussed in detail later in the paper, will allow us to distinguish the r-process from the p-process in the merger ejecta through observations of the gamma-ray emissions from a neutron star merger. In our model we do not include the fission process, since the NuDat\,2 website contains very few radiation data for fissions. However, other works have claimed that the contribution of fissions to the total energy generation is small relative to the $\beta$-decay, though they may make a nonignorable contribution at very late time \citep{met10,hot16}. The paper is organized as follows. In Section~\ref{outline}, we apply the model of \citet[][with minor modifications]{li98} to fit the UVOIR bolometric luminosity data of SSS17a/AT2017gfo. We derive some critical quantities that will be used as a reference for normalizing the parameters of the model for calculation of the gamma-ray emission. In Section~\ref{model}, we derive the mathematical formulae for calculation of the energy generation by radioactive decays in a merger ejecta, and describe how to calculate the luminosity and spectrum of the gamma-ray emission. In Section~\ref{data}, we construct a sample of radioactive nuclides that will be used in our model, and generate the abundance of each nuclide according to a power-law distribution over their lifetime with a Monte Carlo approach. In Sections~\ref{lum} and \ref{spectra} we present results for the calculation of the energy generation rate, the luminosity and spectrum of the gamma-ray emission, and the efficiency in converting the nuclide mass into nuclear energy by radioactive decays. Section~\ref{dec_chains} contains a discussion on the effect of decay chains on the gamma-ray energy generation. In Section~\ref{detect}, we take the merger model for GW170817 as an example to calculate the spectra of its gamma-ray emissions, and discuss their observability by comparing the result to the sensitivity of some modern gamma-ray detectors. We argue that the gamma-ray emission from a merger event like GW170817 will be detectable by Satellite-ETCC if it occurs at a distance $\la 12\,\Mpc$. In Section~\ref{sum}, we summarize the result of this work and draw our conclusions. Appendix~\ref{sphere} contains some details not included in Section~\ref{model} on derivation of the formulae for calculation of the energy generation rate and the spectrum of the gamma-ray emission produced by radioactive nuclides in an expanding sphere. Appendix~\ref{tdc} contains the mathematical formulae for the treatment of decay chains. | \label{sum} A neutron star merger is expected to produce a subrelativistic ejecta with heavy and unstable nuclei arising from the complex nucleosynthesis process in the rapidly decompressed nuclear density matter. The radioactive decay of the unstable nuclei provides a long-term energy source for the expanding ejecta. During the initial optically thick stage, an optical transient is produced with a fast evolving brightness and spectrum. The existence of such a transient was solidly verified on 17 August 2017 by the discovery of the optical source SSS17a/AT2017gfo associated with GW170817/GRB170817A. The comprehensive multiband observation of SSS17a/AT2017gfo revealed that the dominant radiation covers the UV, optical, and near-IR bands, with a peak bolometric luminosity $\approx 8\times 10^{41}\,\erg\,\s^{-1}$ at $t\approx 0.6\,\oday$ after the merger. All the observed features agree nicely with theoretical predictions, including the fast evolution with time of the luminosity and the spectrum, and the thermal feature in the early emission. Due to the subrelativistic expansion, the optical depth of the merger ejecta decreases quickly with time. After about a day to a few days from the time of merger, the ejecta is expected to become optically thin to MeV photons. Then the gamma-ray photons generated inside the ejecta by the continuing radioactive decay process will start to escape without interaction with the ejecta material. Detection and observation of these radioactive gamma-ray photons would be the best approach for directly probing the physical conditions and the nuclear reaction process inside the merger ejecta, understanding the physics of the merger process, and be the most robust test for the hypothesis of neutron star mergers as a major site for the formation of heavy and rare elements in the universe. In this work we have calculated the luminosity and the spectrum of the gamma-ray emission produced by the radioactive decay of the unstable nuclides freshly synthesized in a neutron star merger ejecta. The calculation is based on a model constructed as follows: we extract from the NuDat\,2 database at the National Nuclear Data Center a sample of radioactive nuclides which have their half-lives in the range of $0.05$--$50,000\,\oday$ and satisfy some other conditions related to data completeness. We get in total 494 isotopes in 537 energy states that satisfy the conditions. An isotope in a given energy state (determined by a given {\jpi} value) is treated as an independent nuclide species. Then we have a sample of 537 nuclide species, each of which has available gamma-ray radiation data. We assume that the nuclides are uniformly distributed in the ejecta, with their relative abundances at time $t=0$ determined by a distribution over the mean lifetime according to a power-law with a Gaussian deviation. Then, by tracing the decay process of the nuclides, we can calculate the gamma-ray energy generation rate in the ejecta, the luminosity, and the spectrum of the emerging gamma-ray emission. Assuming that the number of nuclide species in a given interval of lifetime $\tau$ is $\propto\tau^{-1.1}$, we get a gamma-ray energy generation rate that is approximately $\propto t^{-1.2}$ (Figure~\ref{power}). This result agrees with that obtained by numerical simulations based on the r-process network \citep{met10,kor12}, and is consistent with the result of model fitting to the UVOIR data of SSS17a/AT2017gfo obtained in Section~\ref{outline}. Therefore, the model that we have constructed is suitable for calculation of the luminosity and spectrum of the radioactive gamma-ray emission produced by a neutron star merger. In our calculations, we determine the absolute magnitude of the abundance of each nuclide species by normalizing the calculated gamma-ray energy generation rate at $t=1\,\oday$ to a reference value obtained by the model fitting to SSS17a/AT2017gfo (Table~\ref{parameter}), with the fraction of the gamma-ray energy generation in the total heating rate being properly taken into account. Then the luminosity and the spectrum of the gamma-ray emission are calculated, with the result displayed in Figures~\ref{power}--\ref{eff_g_dc} and \ref{spec_lp}--\ref{spec_ener}. After fixing the power-law index in the distribution of nuclide abundances over their lifetime, the model contains three independent parameters: the expansion velocity of the ejecta $V$; the critical time $t_c$, corresponding to the time when the ejecta becomes optically thin; and the normalization of the gamma-ray energy generation rate, $\dot{E}_{\gamma,1}=\dot{E}_\gamma(t=1\,\oday)$. The $\dot{E}_{\gamma,1}$ simply affects the amplitudes of the luminosity and the spectrum of the gamma-ray emission. If the value of $\dot{E}_{\gamma,1}$ is boosted by a factor of three but the values of $V$ and $t_c$ are fixed, for instance, the amplitudes of the luminosity and the spectrum are also boosted by a factor of three. The expansion velocity $V$ has a very small effect on the luminosity, only to the order of $V^2/c^2$ if the other two parameters are fixed. However, the value of $V$ can significantly affect the shape of the gamma-ray spectrum through the line broadening effect, which can be clearly seen by comparing Figure~\ref{spec1} to Figure~\ref{spec2}. For instance, when $V\la 0.2c$, a pair annihilation line of $511\,\keV$ superposed on the continuous spectrum is clearly seen (Figure~\ref{spec2}). When $V\ga 0.3c$, the annihilation line is significantly smeared by the line broadening effect and hence becomes hard to identify, resulting in a more smoother spectrum (Figure~\ref{spec1}). In a realistic model the opacity in the ejecta can be a function of the photon energy. For photon energy $\varepsilon\la 300\,\keV$, the opacity increases quickly with decreasing photon energy, caused by the strong photoelectric absorption of photons by the heavy elements inside the ejecta. For $\varepsilon\ga 300\,\keV$, the opacity varies very slowly with the photon energy and is dominantly contributed by the Compton scattering and the pair production in the nuclear field. As a result, the critical time $t_c$ is also a function of the photon energy, implying that low energy photons emerge from the ejecta later than high energy photons. This effect causes the observed spectrum of the gamma-ray emission to have a ``width'' broadening toward the low energy end as time goes on (Figures~\ref{spec_lp}--\ref{spec_ener}). In our calculations, we require that the energy flux averaged critical time, $\langle t_c\rangle$, is equal to the value obtained by fitting the UVOIR data of SSS17a/AT2017gfo where a constant opacity has been assumed. For the gamma-ray emission produced by radioactive decays, about $90\%$ of the total emitted energy is carried by photons with $\varepsilon\ga 300\,\keV$ which are not affected by the photoelectric absorption (Figure~\ref{specInt}). Hence, the absorption of low energy photons has little effect on the calculation of the energy generation in the merger ejecta and the luminosity of the gamma-ray emission. However, as we have stated, the photon absorption can have important effects on the observed spectrum of the gamma-ray emission, causing that the low energy part of the gamma-ray spectrum is seriously cut off in the early epoch. From the calculated intrinsic photon spectra, i.e., the spectra without consideration of the effect of optical depth (Figures~\ref{spec1} and \ref{spec2}), we see that the emitted photons are clustered in three distinct energy groups: a group with the strongest emission in the range of $150$--$3,000\,\keV$, a group with the intermediate strong emission in the range of $20$--$150\,\keV$, and a group with the weakest emission in the range of $3$--$20\,\keV$. This is a feature of the emission produced by $\beta^\pm$-decays and electron captures, which make the dominant contribution to the gamma-ray emission in the ejecta. Calculations of the radiation spectrum in each decay mode (Figure~\ref{spec_mode}) reveal that in our model, the electron capture and the $\beta^+$-decay contribute about $65\%$ to the total energy of the gamma-ray emission, and the $\beta^-$-decay contributes about $32\%$ (see Table~\ref{chain3}). The remaining $3\%$ radiation comes from the contribution of the $\alpha$-decay and the isomeric transition. The spectra of the radiation generated by different decay modes have some subtle differences in their shapes. Since $\beta^\pm$-decays and electron captures make the dominant contribution to the gamma-ray energy generation, the shape of the emerging gamma-ray spectrum of the ejecta is dominantly determined by the radiation produced by the $\beta^\pm$-decay and the electron capture. The nuclide species with dominant contribution to the spectral peaks evolve with time, as indicated by Tables~\ref{ele_bpec} and \ref{ele_bm}. After taking into account the effect of decay chains, we get an averaged gamma-ray radiation efficiency for the dadioactive decay: $\eta\approx 6.23\times 10^{-6}$. This number may have been somewhat underestimated considering the fact that the radiation data in the sample may not be complete. However, the possible incompleteness in the radiation data should not have affected the calculation of the luminosity and the spectrum seriously. The profile and shape of the luminosity and the spectrum are determined by the collective and statistical properties of the gamma-ray radiation by all radioactive nuclides in the sample, which are not seriously affected by the slight data incompleteness. The magnitudes of the luminosity and the spectrum, on the other hand, are normalized by referencing to the corresponding values obtained by fitting the UVOIR data of SSS17a/AT2017gfo. Inclusion of the $\beta^+$-decay and the electron capture in the calculation of the gamma-ray energy generation in a merger ejecta is a major feature distinguishing our model from other existing models based on the r-process network. The $\beta^+$-decay and the electron capture can arise from proton-rich nuclides in the ejecta. The p-nuclides can, under favorable conditions, be synthesized from the abundant r-nuclides produced by the r-process. As we have argued in Section~\ref{data}, these favorable conditions can be satisfied in a merger ejecta, at least in principle. Hence, it appears that the presence of p-nuclides in a merger ejecta cannot be excluded {\it a priori}. In our model, the contribution of the $\beta^+$-decay and the electron capture to the total gamma-ray energy generation is about twice the contribution by the $\beta^-$-decay. As a result, a prominent electron-positron annihilation line at $511\,\keV$ can be created in the observed gamma-ray spectrum, which is a critical feature that other models do not have. Detection of strong pair annihilation lines in a neutron star merger will be a solid proof of our model. The results obtained in this work are generally consistent with that obtained by \citet{hot16}, except that proton-rich nuclides are not included in their model based on an r-process network and hence pair annihilation lines are not present in their spectra. In particular, our calculations give rise to a specific gamma-ray energy generation rate $\epsilon_\gamma\approx 7.7\times 10^9\,\erg\,\s^{-1}\,\g^{-1}(t/1\,\oday)^{-1.2}$, which is in agreement with their $\epsilon_\gamma\approx 8\times 10^9\,\erg\,\s^{-1}\,\g^{-1}(t/1\,\oday)^{-1.3}$. Although observed spectra are not presented by \citet{hot16}, their intrinsic gamma-ray spectra are broadly consistent with what we have got, in particular if only r-nuclides are included in our data sample. This is not surprising, since all r-nuclides produce gamma-ray emissions with similar spectra. Inclusion of p-nuclides in our model allows us to compare the gamma-ray spectra produced by r-nuclides to that produced by p-nuclides, and to identify the presence of pair annihilation lines in a p-nuclide dominant ejecta. Since we have treated the opacity in the merger ejecta in a similar way to that taken by \citet{hot16}, the gamma-ray luminosity and the observed spectra calculated in both works should agree in principle, except for some specific features for the gamma-ray emission by p-nuclides. To study the detectability of the gamma-ray emission from neutron star mergers, we have calculated the gamma-ray radiation for a two-component model corresponding to the case of GW170817/GRB170817A. The model contains an ejecta component A and an ejecta component B, with the parameters for each component given in Table~\ref{parameter} where the $t_c$ is understood as the energy flux averaged critical time. The calculated gamma-ray luminosity curve for this model is shown in Figure~\ref{power2}. The peak of the gamma-ray luminosity, where the major contribution to the emission comes from component A, occurs at $t\approx 1.2\,\oday$ after the merger. The peak gamma-ray luminosity is $\approx 2\times 10^{41}\,\erg\,\s^{-1}$. The contribution of the component B to the luminosity starts to be seen at $t\approx 5\,\oday$ and dominates in later times. The observable spectra of the gamma-ray emission are calculated and shown in Figures~\ref{spec_lp}--\ref{spec_ener}. More than $95\%$ of the radiated gamma-ray energy is carried by photons in the energy range of $0.2$--$4\,\MeV$. The cut-off arising from the photoelectric absorption for photons of energy $\la 300\,\keV$ is clearly seen in the very early spectra. To detect such a ``typical'' merger event at $D=40\,\Mpc$, we need a detector with an energy flux threshold $\la 4\times 10^{-13}\,\erg\,\cm^{-2}\,\s^{-1}$ in the photon energy range of $0.2$--$4\,\MeV$, with an exposure time of $10^{6}\,\s$. The modern advanced gamma-ray detectors, such as Satellite-ETCC and e-ASTROGAM, cover this photon energy range but have sensitivities above the required energy flux threshold by a factor of 10 and 40, respectively. The proposed AMEGO also covers this photon energy range, but has an energy flux sensitivity above the required threshold by a factor of 20. However, if the merger event occurs at a distance $\la 12\,\Mpc$, it would be detectable with Satellite-ETCC. If the merger event occurs at a distance $\la 6\,\Mpc$, it would also be detectable with e-ASTROGAM. The probability for detection of a neutron star merger event at such a near distance is very small, but it may not be completely impossible. Of course, the detection probability can be significantly larger for a much brighter merger event (e.g., brighter than SSS17a/AT2017gfo by a factor of 10), whose existence in nature cannot be excluded. Finally, we remark that the major results in this paper regarding the gamma-ray emission from a neutron star merger do not depend on the details of the nuclear ingredients contained in the nuclear data sample. These results include the brightness and the peak time of the gamma-ray emission, the rate of the brightness declining with time, and the energy range of the radiated gamma-ray photons. From the UVOIR light curve of SSS17a/AT2017gfo we can derive the heating rate during the optically thick phase, from which we can get the gamma-ray energy generation rate as a function of time with an assumption about the fraction of the gamma-ray energy rate in the total heating rate. Then, with the theoretically estimated and observationally determined critical time for the transition from the optically thick stage to the optically thin stage, we can get the gamma-ray luminosity and its peak time. From nuclear physics it is well known that the gamma-rays emitted by the decay of radioactive nuclei are typically in the MeV range. Hence, the results mentioned above are general and robust, no matter whether the merger ejecta is p-nuclide dominated or r-nuclide dominated. The only critical difference between the gamma-ray spectrum generated by a p-nuclide dominated ejecta and that by an r-nuclide dominated ejecta is in the presence and absence of pair annihilation lines at $511\,\keV$. Observations of the annihilation line and other subtle spectral features as discussed in Section~\ref{detect} can be used to determine the element composition of the merger ejecta and diagnose the relevant nucleosynthesis process. | 18 | 8 | 1808.09833 |
1808 | 1808.10505_arXiv.txt | Applying the seminal work of Bose in 1924 on what was later known as Bose-Einstein statistics, Einstein predicted in 1925 that at sufficiently low temperatures, a macroscopic fraction of constituents of a gas of bosons will drop down to the lowest available energy state, forming a `giant molecule' or a Bose-Einstein condensate (BEC), described by a `macroscopic wavefunction'. In this article we show that when the BEC of ultralight bosons extends over cosmological length scales, it can potentially explain the origins of both dark matter and dark energy. We speculate on the nature of these bosons. {}\\ {}\\ {\bf Invited review written for the special issue of {\it Physics News} on the occasion of 125${}^{th}$ birthday anniversary of S. N. Bose. } | Two of the enduring mysteries in cosmology are dark matter (DM) and dark energy (DE). Whereas DM holds the rotating galaxies together, DE makes the expanding universe accelerate. In accounting for the distribution of mass/energy in the universe, visible hadronic matter and radiation contribute only about five percent, DM about twenty five percent, while the rest, a whopping seventy percent, comes from DE \footnote{For alternative theories to DM and DE which also try to explain cosmological observations, see \cite{mond1,mond2,altdm,altde}.}. To start with, the constituents of DE are not known, despite viable candidates such as the cosmological constant and a dynamical scalar field \cite{dereview1,dereview2}. The constituents of DM are not known either. There has been many studies invoking weakly interacting massive particles (WIMPs) that may form cold DM. Not only does it have shortcomings in reproducing the DM density profiles within a galaxy, no such particle has been experimentally found. Other DM candidates include solitons, massive compact (halo) objects, primordial black holes, gravitons etc. They have similar shortcomings \cite{dmreview1,dmreview2}. Given that DM is all-pervading, cold and dark, and clumped near galaxies, we pose the following question: can it be a giant BEC, of cosmological length scales? Following the paper by Bose which laid the foundations of Bose-Einstein statistics \cite{bose}, Einstein predicted that a gas of bosons will form a BEC at sufficiently low temperatures \cite{einstein}. Here we show that following an earlier proposal by the current authors \cite{db1}, \\ (i) a sea of weakly interacting light bosons can form a BEC, preserving large scale homogeneity and isotropy, and be a viable DM candidate, as long as the mass of each constituent does not exceed a few $eV/c^2$ \footnote{$1$ kg = $5.6\times 10^{35}~eV/c^2$, where $c=3\times 10^8~m/s$ is the speed of light in vacuum.}, and \\ (ii) the quantum potential associated with the above BEC can also explain DE. Note that in a BEC, the bosons are in the lowest energy state that is nearly at zero energy, even if outside the condensate the bosons are highly relativistic due to its low mass. We should point out that BEC model for DM has been studied by many authors in the past. For example, one can consider a scalar field dark matter (SFDM) that invokes spin zero ultralight bosons whose Compton wave length spans cosmic distances \cite{Hu2000,Lopez,Bohua}. For previous studies of superfluids and BEC in cosmology see \cite{sudarshan,khlo1,khlo2,morikawa,moffat,wang,boehmer,sikivie,chavanis,dvali,houri,kain,suarez,ebadi,laszlo1,bettoni,gielen,schive,davidson,casadio1,casadio2}. But as mentioned earlier, the novel aspect of our model is that it also provides us with a viable source of DE. In this semi-technical article, we present the bulk of our work in an elementary fashion using Newtonian dynamics, after staging the backdrop of the cosmological model. A more rigorous derivation of essentially the same results using general relativity will be presented in the Appendix. | 18 | 8 | 1808.10505 |
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1808 | 1808.01369_arXiv.txt | The Probe of Inflation and Cosmic Origins (PICO) is a probe-class mission concept currently under study by NASA. PICO will probe the physics of the Big Bang and the energy scale of inflation, constrain the sum of neutrino masses, measure the growth of structures in the universe, and constrain its reionization history by making full sky maps of the cosmic microwave background with sensitivity 80 times higher than the {\it Planck} space mission. With bands at 21-799~GHz and arcmin resolution at the highest frequencies, PICO will make polarization maps of Galactic synchrotron and dust emission to observe the role of magnetic fields in Milky Way's evolution and star formation. We discuss PICO's optical system, focal plane, and give current best case noise estimates. The optical design is a two-reflector optimized open-Dragone design with a cold aperture stop. It gives a diffraction limited field of view (DLFOV) with throughput of 910 cm$^{2}$sr at 21 GHz. The large 82 square degree DLFOV hosts 12,996 transition edge sensor bolometers distributed in 21 frequency bands and maintained at 0.1~K. We use focal plane technologies that are currently implemented on operating CMB instruments including three-color multi-chroic pixels and multiplexed readouts. To our knowledge, this is the first use of an open-Dragone design for mm-wave astrophysical observations, and the only monolithic CMB instrument to have such a broad frequency coverage. With current best case estimate polarization depth of 0.65~$\mu$K$_{\rm CMB}$-arcmin over the entire sky, PICO is the most sensitive CMB instrument designed to date. | \label{sec:intro} Over the last decade NASA's astrophysics division has funded design and construction of space missions that are either Explorer-class, with cost cap of up to \$250M or Flagship-class that cost above \$1B. To study the science opportunities available at intermediate costs, NASA initiated studies of Probe-class missions with cost window between \$400M and \$1B. We are conducting one these studies for a mission called the Probe of Inflation and Cosmic Origins (PICO). A paper by Sutin et al.\cite{brian_spie}\ in these proceedings gives an overall review of PICO and the scientific motivation. This paper describes the design of the telescope and focal plane and gives our current best estimates for the sensitivity of the instrument. The mission study is not complete; the final report is due in December 2018. Therefore, the quantitative assessments we provide for component temperatures and detector noise levels are temporary in nature and subject to revision. Even so, the design is fairly mature and we do not expect significant changes. Values in this paper are current best estimates and don't represent finalized mission requirements. | The PICO optical system is a two reflector open-Dragone design. It gives a large DLFOV and a total throughput larger than 900 cm$^{2}$sr without lenses. The use of a system with only reflectors, as opposed to a combination of reflectors and refractors, gives the system high transmission efficiency across a wide frequency band and obviates the need to provide broad band anti-reflection coatings. Using only two reflectors reduces the volume, mass, and complexity of the system compared to designs with more reflectors. The optical system has a cold aperture stop between the primary and secondary reflectors. The stop reduces sidelobes while maintaining the other reflectors compact. The native Dragone system has been numerically optimized using Zernike polynomials to give a significantly larger DLFOV. The focal plane takes advantage of the large DLFOV and MCP technology using TES bolometers to implement 12996 polarization sensitive detectors in 21 bands from 21-799~GHz. This is the first monolithic CMB instrument to have sensitivity to such a broad frequency range and to baseline a single detector technology across this entire band. Under the current set of assumptions, PICO is predicted to have an unprecedented full sky polarization map depth of 0.65~$\mu$K$_{\rm CMB}$-arcmin, which is $\sim$80 times the depth {\it Planck} had achieved. | 18 | 8 | 1808.01369 |
1808 | 1808.08886_arXiv.txt | Standard 1D stellar evolution models do not correctly reproduce the structure of the outermost layers of stars with convective envelopes. This has been a long-standing problem in stellar modelling affecting both the predicted evolutionary paths and the attributed oscillation frequencies, and indirectly biasing numerous quantities derived from stellar evolution calculations. We present a novel method that mostly eliminates these structural defects by appending mean 3D simulations of stellar envelopes. In contrast to previous attempts we impose the complete structure derived from 3D simulations at each time step during the entire evolution. For this purpose, we interpolate in grids of pre-computed 3D simulations and use the resulting structure as boundary conditions, in order to solve the stellar structure equations for the 1D interior at each time step. Our method provides a continuous transition in many quantities from the interior to the imposed interpolated 3D surface layers. We present a solar calibration model and show that the obtained structure of the surface layers reliably mimics that of the underlying 3D simulations for the present Sun. Moreover, we perform a helioseismic analysis, showing that our method mostly eliminates the structural contribution to the discrepancy between model frequencies and observed p-mode frequencies. | \label{sec:intro} Stellar evolution codes do not yield the correct outermost structure of stars with convective envelopes. Instead, 1D stellar models employ {\color{black}1D model atmospheres, such as plane-parallel Eddington grey atmospheres, and parametrizations of superadiabatic convection, such the mixing length theory by \cite{Bohm-Vitense1958} (MLT). This treatment of convection necessitates the calibration of a free parameter, the mixing length ($\alpha_\textsc{mlt}$), which is usually done based on the present Sun. This is a well-known weakness of MLT, since the extent to which the calibrated value is applicable for other evolutionary stages is disputed.} Furthermore, the inadequate modelling of the surface layers results in a systematic offset between observations and the predicted p-mode frequencies, the so-called surface effect \citep{Brown1984,Christensen-Dalsgaard1988}. When interpreting asteroseismic data from, e.g., the CoRoT \citep{Baglin2009} and the \textit{Kepler} \citep{Borucki2010x} space missions, most authors account for this discrepancy by using empirical corrections based on the Sun \citep{Kjeldsen2008,Ball2014}. \cite{Schlattl1997} and \cite{Rosenthal1999} were among the first to include data from 2D and 3D hydrodynamic simulations of stellar envelopes, in order to improve the structure of the surface layers. Recently, several authors have addressed the problem similarly by substituting the outermost envelope with mean structures from 3D hydrodynamic simulations \citep{Piau2014, Sonoi2015, Ball2016, Magic2016,Joergensen2017, Trampedach2017}. In all mentioned cases, this substitution has been performed for a given final structure, i.e. the 3D simulations have not been included throughout the evolution. This substitution is known as patching. As elaborated upon by \cite{Joergensen2017} --- hereafter J17 ---, the fact that patching is performed after a traditional 1D evolutionary calculation {\color{black} has been performed} can lead to inconsistencies and discontinuities in the patched models. Nevertheless, as shown by \cite{Houdek2017}, this approach does mend the structural inadequacies of stellar models and results in model frequencies that are in good agreement with observations once so-called modal effects including non-adiabatic energetics have been taken into account. In order to include information from 3D simulations during the entire evolution, \cite{Trampedach2014a,Trampedach2014b} have computed $T(\tau$) relations and calibrated mixing lengths for a grid of 3D models. Here $T(\tau)$ denotes the temperature as a function of optical depth. While this is a step forward, an implementation by \cite{Mosumgaard2018a} shows that this parametrization does not account for the structural surface effect. The reason for this inability to mimic the correct structure is that the calibrated mixing length only reproduces the mean temperature gradient of the envelope and not the actual temperature gradient as a function of depth. {\color{black}Furthermore, these 1D models neither account properly for turbulent pressure nor for so-called convective back-warming \cite[e.g.][]{Trampedach2017}.} In this paper, we present the solar calibration model for which we have substituted the outermost layers with a mean 3D structure, throughout the entire evolution of the star, adjusting the interior model accordingly in each iteration at every time step. This solar model has been obtained using the usual solar calibration procedure, i.e. a first-order Newton iteration scheme \citep[cf.][]{Weiss2008}. We compare the obtained structure with the employed 3D simulations and present p-mode frequencies. | \label{sec:conclusion} We have presented a novel method for including the mean pressure and temperature stratifications from 3D simulations directly in 1D stellar evolution codes and exploit this to adjust the structure at every time step. This has been achieved without the need of parametrizations or post-evolutionary patching. It is the first computation of a solar model, for which the structure from 3D simulations has been fully accounted for on the fly. The structure of the resulting 1D models is in very good agreement with the underlying 3D simulations, despite the neglect of turbulent pressure, and despite the fact that only a limited amount of information is taken from the 3D models. We find that our new method is largely able to eliminate the structural surface effect, leading to very promising p-mode frequencies. Modal effects have not been accounted for. A direct comparison with post-evolutionarily patched models show only small frequency differences. We largely attribute the remaining differences to the neglect of turbulent pressure. In the case of the present Sun, our analysis confirms that post-evolutionary patching provides an adequate structural correction. A disadvantage of patching, however, is that it relies on the assumption that the evolutionary tracks are unaltered by the use of crude outer boundary conditions and mixing length theory. Our method, on the other hand, overcomes this deficiency by adjusting the structure of stellar models on the fly based on 3D simulations. We address the impact of our new method on the evolutionary tracks in detail in Paper-II. In the companion paper, we will go beyond the present Sun. This includes the first asteroseismic analysis of stars in the \textit{Kepler} field and an investigation of how well our method reproduces the correct structures of 3D-envelopes throughout $(T_\mathrm{eff},\log g)$-plane. In future work, we also plan to alter the presented method: we intend to include turbulent pressure and take composition changes into account by interpolation in $\mathrm{[Fe/H]}$. | 18 | 8 | 1808.08886 |
1808 | 1808.00473_arXiv.txt | We present ALMA and MUSE observations of the Brightest Cluster Galaxy in Abell 2597, a nearby ($z=0.0821$) cool core cluster of galaxies. The data map the kinematics of a three billion solar mass filamentary nebula that spans the innermost 30 kpc of the galaxy's core. Its warm ionized and cold molecular components are both cospatial and comoving, consistent with the hypothesis that the optical nebula traces the warm envelopes of many cold molecular clouds that drift in the velocity field of the hot X-ray atmosphere. The clouds are not in dynamical equilibrium, and instead show evidence for inflow toward the central supermassive black hole, outflow along the jets it launches, and uplift by the buoyant hot bubbles those jets inflate. The entire scenario is therefore consistent with a galaxy-spanning ``fountain'', wherein cold gas clouds drain into the black hole accretion reservoir, powering jets and bubbles that uplift a cooling plume of low-entropy multiphase gas, which may stimulate additional cooling and accretion as part of a self-regulating feedback loop. All velocities are below the escape speed from the galaxy, and so these clouds should rain back toward the galaxy center from which they came, keeping the fountain long-lived. The data are consistent with major predictions of chaotic cold accretion, precipitation, and stimulated feedback models, and may trace processes fundamental to galaxy evolution at effectively all mass scales. | \label{sec:intro} Abell 2597 is a cool core cluster of galaxies at redshift $z=0.0821$ (\autoref{fig:overview}). The galaxies inhabit a megaparsec-scale bath of X-ray bright, $\sim 10^{7-8}$ K plasma whose central particle density is sharply peaked about a giant elliptical brightest cluster galaxy (BCG) in the cluster core. Under the right conditions (e.g., \citealt{fabian94, peterson06}), the dense halo of plasma that surrounds this galaxy can act like a reservoir from which hot gas rapidly cools, driving a long-lived rain of thermally unstable multiphase gas that collapses toward the galaxy's center (e.g., \citealt{gaspari17b}), powering black hole accretion and $\sim 5$ \Msol\ yr\mone\ of star formation \citep{tremblay12a,tremblay16}. The rate at which these cooling flow mass sinks accumulate would likely be higher were the hot atmosphere not permeated by a $\sim30$ kpc-scale network of buoyantly rising bubbles (\autoref{fig:overview}\textit{a}), inflated by the propagating jet launched by the BCG's central accreting supermassive black hole \citep{taylor99,mcnamara01,clarke05,tremblay12b}. Those clouds that have managed to cool now form a multiphase filamentary nebula, replete with young stars, that spans the inner $\sim30$ kpc of the galaxy. Its fractal tendrils, likely made of many cold molecular clouds with warmer ionized envelopes (e.g., \citealt{jaffe05}), wrap around both the radio jet and the the X-ray cavities the jet has inflated (\autoref{fig:overview}\textit{b}/\textit{c}, \citealt{mcnamara93, voit97, koekemoer99, mcnamara99, odea04,oonk10,tremblay12a, tremblay15, mittal15}). \begin{figure*} \begin{center} \includegraphics[width=\textwidth]{Fig_overview.pdf} \end{center} \vspace*{-5mm} \caption{ A multiwavelength view of the Abell 2597 Brightest Cluster Galaxy. (\textit{Left}) \textit{ Chandra} X-ray, \textit{HST} and DSS optical, and Magellan H$\alpha$+[N~\textsc{ ii}] emission is shown in blue, yellow, and red, respectively {\small (Credit: X-ray: NASA/CXC/Michigan State Univ/G.Voit et al; Optical: NASA/STScI \& DSS; H$\alpha$: Carnegie Obs./Magellan/W.Baade Telescope/U.Maryland/M.McDonald)}. (\textit{Top right}) \textit{HST}/STIS MAMA image of Ly$\alpha$ emission associated with the ionized gas nebula. Very Large Array (VLA) radio contours of the 8.4 GHz source are overlaid in black. (\textit{Bottom right}) Unsharp mask of the \textit{HST}/ACS SBC far-ultraviolet continuum image of the central regions of the nebula. 8.4 GHz contours are once again overlaid. In projection, sharp-edged rims of FUV continuum to the north and south wrap around the edges of the radio lobes. Dashed lines indicate relative fields of view between each panel. The centroids of all panels are aligned, with East left and North up. This figure has been partially adapted from \citealt{tremblay16}. } \label{fig:overview} \end{figure*} These X-ray cavities act as a calorimeter for the efficient coupling between the kinetic energy of the jet and the hot intracluster medium through which it propagates (e.g., \citealt{churazov01,churazov02}). Given their ubiquity in effectively all cool core clusters, systems like Abell 2597 are canonical examples of mechanical black hole feedback, a model now routinely invoked to reconcile observations with a theory that would otherwise over-predict the size of galaxies and the star formation history of the Universe (see, e.g., reviews by \citealt{veilleux05,mcnamara07,mcnamara12,fabian12,alexander12,kormendy13,gaspari13,bykov15}). Yet, just as for quasar-driven radiative feedback invoked at earlier epochs (e.g., \citealt{croton06,bower06}), the degree to which the mechanical luminosity of jets might quench (or even trigger) star formation depends on how it might couple to the origin and fate of cold molecular gas, from which all stars are born. Observational evidence for this coupling grows even in the absence of a consensus explanation for it. The density contrast between hot ($\sim10^7$ K) plasma and cold ($\sim10$ K) molecular gas is nearly a million times greater than that between air and granite. So while one might naturally expect that the working surface of a jet can drive sound waves and shocks into the tenuous X-ray atmosphere, it is more difficult to explain the growing literature reporting observations of massive atomic and molecular outflows apparently entrained by jets (e.g., \citealt{morganti05,morganti13,rupke11,alatalo11,alatalo15, dasyra15, cicone14, cicone18}), or uplifted in the wakes of the buoyant hot bubbles they inflate (e.g., \citealt{mcnamara14,mcnamara16,russell14,russell16a,russell16b,russell17}). One might instead expect molecular nebulae to act like seawalls, damping turbulence, breaking waves in the hotter phases of the ISM, and redirecting jets. Recent single-dish and Atacama Large Millimeter/submillimeter Array (ALMA) observations of cool core clusters nevertheless reveal billions of solar masses of cold gas in kpc-scale filaments draped around the rims of radio lobes or X-ray cavities (e.g., Perseus: \citealt{salome08,lim08}, Phoenix: \citealt{russell16b}, Abell 1795: \citealt{russell17}, M87: \citealt{simionescu18}), or trailing behind them as if drawn upward by their buoyant ascent (e.g., Abell 1835: \citealt{mcnamara14}; 2A 0335+096: \citealt{vantyghem16}; PKS 0745-191: \citealt{russell16a}). Such a coupling would be easier to understand were it the manifestation of a top-down multiphase condensation cascade, wherein both the warm ionized and cold molecular nebulae are pools of cooling gas clouds that rain from the ambient hot halo. The disruption of this halo into a multiphase medium is regulated by the survivability of thermal instabilities, which lose entropy over a cooling time $t_\mathrm{cool}$, descend on a free-fall time $t_\mathrm{ff}$, and remain long-lived only if their local density contrast increases as they sink (e.g., \citealt{voit17a}). This implies that there is an entropy threshold for the onset of nebular emission in BCGs, long known to exist observationally \citep{rafferty08,cavagnolo08}, set wherever the cooling time becomes short compared to the effective gas dynamical timescale. This underlying principle is not new (e.g., \citealt{hoyle53,rees77,binney77,cowie80,nulsen86,balbus89}), but has found renewed importance in light of recent papers arguing that it may be fundamental to all of galaxy evolution \citep{pizzolato05,pizzolato10,marinacci10,mccourt12, sharma12,gaspari12,gaspari13,gaspari15,gaspari17b,gaspari18,voit15,voit15d,voit15b,voit15c,voit17a,voit18,li15,prasad15, prasad17, prasad18, singh15, mcnamara16, yang16, meece17, hogan17, main17,pulido18}. Amid minor disagreement over the importance of the free-fall time, (compare, e.g., \citealt{voit15d}, \citealt{mcnamara16} and \citealt{gaspari17b}), these works suggest that the existence of this threshold establishes a stochastically oscillating but tightly self-regulated feedback loop between ICM cooling and AGN heating. The entire process would be mediated by chaotic cold accretion (CCA) onto the central supermassive black hole \citep{gaspari13}, a prediction that has recently found observational support with the detection of cold clouds falling toward black hole fuel reservoirs (e.g., \citealt{tremblay16}; Edge et al.~in prep.). The radio jets that the black hole launches, and the buoyant hot bubbles it inflates, inject sound waves, shocks, and turbulence into the X-ray bright halo, lowering the cooling rate and acting as a thermostat for the heating-cooling feedback loop (e.g., \citealt{birzan04,birzan12,zhuravleva14,hlavacek12,hlavacek15,gaspari17a}). Those same outflows can adiabatically uplift low entropy gas to an altitude that crosses the thermal instability threshold, explaining their close spatial assocation with molecular filaments and star formation \citep{tremblay15,russell17}. In this scenario, a supermassive black hole acts much like a mechanical pump in a water fountain\footnote{The supermassive black hole, in this case, is akin to the ``pump-like'' action of supernova feedback driving similar fountains in less massive galaxies \citep{fraternali08,marinacci11,marasco13,marasco15}.} (e.g.~\citealt{lim08,salome06,salome11}), wherein cold gas drains into the black hole accretion reservoir, powering jets, cavity inflation, and therefore a plume of low-entropy gas uplifted as they rise. The velocity of this cold plume is often well below both the escape speed from the galaxy and the Kepler speed at any given radius (e.g., \citealt{mcnamara16}), and so those clouds that do not evaporate or form stars should then rain back toward the galaxy center from which they were lifted. This, along with merger-induced gas motions \citep{lau17} and the feedback-regulated precipitation of thermal instabilities from the hot atmosphere, keeps the fountain long-lived and oscillatory. The apparently violent and bursty cluster core must nevertheless be the engine of a process that is smooth over long timescales, as the remarkably fine-tuned thermostatic control of the heating-cooling feedback loop now appears to persist across at least ten billion years of cosmic time (e.g., \citealt{birzan04,birzan08,rafferty06,dunn06,best06,best07,mittal09,dong10,hlavacek12,hlavacek15,webb15,simpson13,mcdonald13b,mcdonald16,mcdonald17,mcdonald18, bonaventura17}). These hypotheses are testable. Whether it is called ``chaotic cold accretion'' \citep{gaspari13}, ``precipitation'' \citep{voit15d}, or ``stimulated feedback'' \citep{mcnamara16}, the threshold criterion predicts that the kinematics of the hot, warm, and cold phases of the ISM should retain memory of their shared journey along what is ultimately the same thermodynamic pathway \citep{gaspari18}. Observational tests for the onset of nebular emission, star formation, and AGN activity, and how these may be coupled to this threshold, have been underway for many years (e.g., \citealt{cavagnolo08,rafferty08,sanderson09,tremblay12b,tremblay14,tremblay15,mcnamara16,voit18,hogan17,main17,pulido18}). The multiphase uplift hypothesis, motivated by theory and simulations \citep{pope10,gaspari12,wagner12,li14a,li14b,li15}, is corroborated by observations of kpc-scale metal-enriched outflows along the radio axis (e.g., \citealt{simionescu09,kirkpatrick11}), and an increasing number of ionized and molecular filaments spatially associated with jets or cavities (e.g, \citealt{salome08,mcnamara14,tremblay15,vantyghem16,russell17}). More complete tests of these supposed kpc-scale molecular fountains will require mapping the kinematics of \textit{all} gas phases in galaxies. As we await a replacement for the \textit{Hitomi} mission to reveal the velocity structure of the hot phase \citep{hitomi16,hitomi18, fabian17}, combined ALMA and optical integral field unit (IFU) spectrograph observations of cool core BCGs can at least begin to further our joint understanding of the cold molecular and warm ionized gas motions, respectively. To that end, in this paper we present new ALMA observations that map the kinematics of cold gas in the Abell 2597 BCG. We compare these with new Multi-Unit Spectroscopic Explorer (MUSE, \citealt{bacon10}) IFU data that do the same for the warm ionized phase, as well as a new deep \textit{Chandra} X-ray image revealing what is likely filament uplift by A2597's buoyant hot bubbles. These data are described in \autoref{sec:observations}, presented in \autoref{sec:results}, and discussed in \autoref{sec:discussion}. Throughout this paper we assume $H_0 = 70$ km s$^{-1}$ Mpc$^{-1}$, $\Omega_M = 0.27$, and $\Omega_{\Lambda} = 0.73$. In this cosmology, 1\arcsec\ corresponds to 1.549 kpc at the redshift of the A2597 BCG ($z=0.0821$), where the associated luminosity and angular size distances are 374.0 and 319.4 Mpc, respectively, and the age of the Universe is 12.78 Gyr. Unless otherwise noted, all images are centered on the nucleus of the A2597 BCG at Right Ascension (R.A.) 23$^{\mathrm{h}}$ 25$^{\mathrm{m}}$ 19.7$^{\mathrm{s}}$ and Declination $-12$\arcdeg\ 07\arcmin\ 27\arcsec\ (J2000), with East left and North up. \begin{deluxetable*}{cccccc} \tabletypesize{\footnotesize} \tablecaption{\textsc{Summary of Abell 2597 Observations}} \tablehead{ \colhead{Waveband / Line} & \colhead{Facility} & \colhead{Instrument / Mode} & \colhead{Exp. Time} & \colhead{Prog. / Obs. ID (Date)} & \colhead{Reference} } \colnumbers \startdata \label{tab:observation_summary} X-ray (0.2-10 keV) & \textit{Chandra} & ACIS-S & 39.80 ksec & 922 (2000 Jul 28) & \citet{mcnamara01, clarke05} \cr \nodata & \nodata & \nodata & 52.20 ksec & 6934 (2006 May 1) & \citet{tremblay12a,tremblay12b} \cr \nodata & \nodata & \nodata & 60.10 ksec & 7329 (2006 May 4) & \citet{tremblay12a,tremblay12b} \cr \nodata & \nodata & \nodata & 69.39 ksec & 19596 (2017 Oct 8) & Tremblay et al.~(in prep) \cr \nodata & \nodata & \nodata & 44.52 ksec & 19597 (2017 Oct 16) & (Large Program 18800649) \cr \nodata & \nodata & \nodata & 14.34 ksec & 19598 (2017 Aug 15) & \nodata \cr \nodata & \nodata & \nodata & 24.73 ksec & 20626 (2017 Aug 15) & \nodata \cr \nodata & \nodata & \nodata & 20.85 ksec & 20627 (2017 Aug 17) & \nodata \cr \nodata & \nodata & \nodata & 10.92 ksec & 20628 (2017 Aug 19) & \nodata \cr \nodata & \nodata & \nodata & 56.36 ksec & 20629 (2017 Oct 3) & \nodata \cr \nodata & \nodata & \nodata & 53.40 ksec & 20805 (2017 Oct 5) & \nodata \cr \nodata & \nodata & \nodata & 37.62 ksec & 20806 (2017 Oct 7) & \nodata \cr \nodata & \nodata & \nodata & 79.85 ksec & 20811 (2017 Oct 21) & \nodata \cr \nodata & \nodata & \nodata & 62.29 ksec & 20817 (2017 Oct 19) & \nodata \cr \hline Ly$\alpha$ $\lambda$1216 \AA & \textit{HST} & STIS F25SRF2 & 1000 sec & 8107 (2000 Jul 27) & \citet{odea04,tremblay15} \cr FUV Continuum & \nodata & ACS/SBC F150LP & 8141 sec & 11131 (2008 Jul 21) & \citet{oonk10,tremblay15} \cr [\ion{O}{2}]$\lambda$3727 \AA & \nodata & WFPC2 F410M & 2200 sec & 6717 (1996 Jul 27) & \citet{koekemoer99} \cr $B$-band \& [\ion{O}{2}]$\lambda$3727 \AA & \nodata & WFPC2 F450W & 2100 sec & 6228 (1995 May 07) & \citet{koekemoer99} \cr $R$-band \& H$\alpha$+[\ion{N}{2}] & \nodata & WFPC2 F702W & 2100 sec & 6228 (1995 May 07) & \citet{holtzman96} \cr H$_2 1-0$ S(3) $\lambda1.9576 \mu$m & \nodata & NICMOS F212N & 12032 sec & 7457 (1997 Oct 19) & \citet{donahue00} \cr $H$-band & \nodata & NICMOS F160W & 384 sec & 7457 (1997 Dec 03) & \citet{donahue00} \cr H$\alpha$ (Narrowband) & Baade 6.5m & IMACS / MMTF & 1200 sec & (2010 Nov 30) & \citet{mcdonald11b, mcdonald11a} \cr $i$-band & VLT / UT1 & FORS & 330 sec & 67.A-0597(A) & \citet{oonk11} \cr Optical Lines \& Continuum & VLT / UT4 & MUSE & 2700 sec & 094.A-0859(A) & Hamer et al.~(in prep) \cr \hline NIR (3.6, 4.5, 5.8, 8 $\mu$m) & \textit{Spitzer} & IRAC & 3600 sec (each) & 3506 (2005 Nov 24) & \citet{donahue07} \cr MIR (24, 70, 160 $\mu$m) & \nodata & MIPS & 2160 sec (each) & 3506 (2005 Jun 18) & \citet{donahue07} \cr MIR (70, 100, 160 $\mu$m) & \textit{Herschel} & PACS & 722 sec (each) & 13421871(18-20) & \citet{edge10phot} \cr FIR (250, 350, 500 $\mu$m) & \nodata & SPIRE & 3336 sec (each) & (2009 Nov 30) & \citet{edge10phot} \cr \hline CO(2-1) & ALMA & Band 6 / 213 GHz & 3 hrs & 2012.1.00988.S & \citet{tremblay16} \& this paper \cr \hline Radio (8.44 GHz) & VLA & A array & 15 min & AR279 (1992 Nov 30) & \citet{sarazin95} \cr 4.99 GHz & \nodata & A array & 95 min & BT024 (1996 Dec 7) & \citet{taylor99, clarke05} \cr 1.3 GHz & \nodata & A array & 323 min & BT024 (1996 Dec 7) & \citet{taylor99,clarke05} \cr 330 MHz & \nodata & A array & 180 min & AC647 (2003 Aug 18) & \citet{clarke05} \cr 330 MHz & \nodata & B array & 138 min & AC647 (2003 Jun 10) & \citet{clarke05} \cr \enddata \tablecomments{A summary of all Abell 2597 observations used (either directly or indirectly) in this analysis, in decending order from short to long wavelength (i.e. from X-ray through radio). (1) Waveband or emission line targeted by the listed observation; (2) telescope used; (3) instrument, receiver setup, or array configuration used; (4) on-source integration time; (5) facility-specific program or proposal ID (or observation ID in the case of \textit{Chandra}) associated with the listed dataset; (6) reference to publication(s) where the listed data first appeared, or were otherwise discussed in detail. Further details for most of these observations, including Principal Investigators, can be found in Table 1 of \citet{tremblay12b}. } \end{deluxetable*} | X-ray (0.2-10 keV) & \textit{Chandra} & ACIS-S & 39.80 ksec & 922 (2000 Jul 28) & \citet{mcnamara01, clarke05} \cr \nodata & \nodata & \nodata & 52.20 ksec & 6934 (2006 May 1) & \citet{tremblay12a,tremblay12b} \cr \nodata & \nodata & \nodata & 60.10 ksec & 7329 (2006 May 4) & \citet{tremblay12a,tremblay12b} \cr \nodata & \nodata & \nodata & 69.39 ksec & 19596 (2017 Oct 8) & Tremblay et al.~(in prep) \cr \nodata & \nodata & \nodata & 44.52 ksec & 19597 (2017 Oct 16) & (Large Program 18800649) \cr \nodata & \nodata & \nodata & 14.34 ksec & 19598 (2017 Aug 15) & \nodata \cr \nodata & \nodata & \nodata & 24.73 ksec & 20626 (2017 Aug 15) & \nodata \cr \nodata & \nodata & \nodata & 20.85 ksec & 20627 (2017 Aug 17) & \nodata \cr \nodata & \nodata & \nodata & 10.92 ksec & 20628 (2017 Aug 19) & \nodata \cr \nodata & \nodata & \nodata & 56.36 ksec & 20629 (2017 Oct 3) & \nodata \cr \nodata & \nodata & \nodata & 53.40 ksec & 20805 (2017 Oct 5) & \nodata \cr \nodata & \nodata & \nodata & 37.62 ksec & 20806 (2017 Oct 7) & \nodata \cr \nodata & \nodata & \nodata & 79.85 ksec & 20811 (2017 Oct 21) & \nodata \cr \nodata & \nodata & \nodata & 62.29 ksec & 20817 (2017 Oct 19) & \nodata \cr \hline Ly$\alpha$ $\lambda$1216 \AA & \textit{HST} & STIS F25SRF2 & 1000 sec & 8107 (2000 Jul 27) & \citet{odea04,tremblay15} \cr FUV Continuum & \nodata & ACS/SBC F150LP & 8141 sec & 11131 (2008 Jul 21) & \citet{oonk10,tremblay15} \cr [\ion{O}{2}]$\lambda$3727 \AA & \nodata & WFPC2 F410M & 2200 sec & 6717 (1996 Jul 27) & \citet{koekemoer99} \cr $B$-band \& [\ion{O}{2}]$\lambda$3727 \AA & \nodata & WFPC2 F450W & 2100 sec & 6228 (1995 May 07) & \citet{koekemoer99} \cr $R$-band \& H$\alpha$+[\ion{N}{2}] & \nodata & WFPC2 F702W & 2100 sec & 6228 (1995 May 07) & \citet{holtzman96} \cr H$_2 1-0$ S(3) $\lambda1.9576 \mu$m & \nodata & NICMOS F212N & 12032 sec & 7457 (1997 Oct 19) & \citet{donahue00} \cr $H$-band & \nodata & NICMOS F160W & 384 sec & 7457 (1997 Dec 03) & \citet{donahue00} \cr H$\alpha$ (Narrowband) & Baade 6.5m & IMACS / MMTF & 1200 sec & (2010 Nov 30) & \citet{mcdonald11b, mcdonald11a} \cr $i$-band & VLT / UT1 & FORS & 330 sec & 67.A-0597(A) & \citet{oonk11} \cr Optical Lines \& Continuum & VLT / UT4 & MUSE & 2700 sec & 094.A-0859(A) & Hamer et al.~(in prep) \cr \hline NIR (3.6, 4.5, 5.8, 8 $\mu$m) & \textit{Spitzer} & IRAC & 3600 sec (each) & 3506 (2005 Nov 24) & \citet{donahue07} \cr MIR (24, 70, 160 $\mu$m) & \nodata & MIPS & 2160 sec (each) & 3506 (2005 Jun 18) & \citet{donahue07} \cr MIR (70, 100, 160 $\mu$m) & \textit{Herschel} & PACS & 722 sec (each) & 13421871(18-20) & \citet{edge10phot} \cr FIR (250, 350, 500 $\mu$m) & \nodata & SPIRE & 3336 sec (each) & (2009 Nov 30) & \citet{edge10phot} \cr \hline CO(2-1) & ALMA & Band 6 / 213 GHz & 3 hrs & 2012.1.00988.S & \citet{tremblay16} \& this paper \cr \hline Radio (8.44 GHz) & VLA & A array & 15 min & AR279 (1992 Nov 30) & \citet{sarazin95} \cr 4.99 GHz & \nodata & A array & 95 min & BT024 (1996 Dec 7) & \citet{taylor99, clarke05} \cr 1.3 GHz & \nodata & A array & 323 min & BT024 (1996 Dec 7) & \citet{taylor99,clarke05} \cr 330 MHz & \nodata & A array & 180 min & AC647 (2003 Aug 18) & \citet{clarke05} \cr 330 MHz & \nodata & B array & 138 min & AC647 (2003 Jun 10) & \citet{clarke05} \cr \enddata \tablecomments{A summary of all Abell 2597 observations used (either directly or indirectly) in this analysis, in decending order from short to long wavelength (i.e. from X-ray through radio). (1) Waveband or emission line targeted by the listed observation; (2) telescope used; (3) instrument, receiver setup, or array configuration used; (4) on-source integration time; (5) facility-specific program or proposal ID (or observation ID in the case of \textit{Chandra}) associated with the listed dataset; (6) reference to publication(s) where the listed data first appeared, or were otherwise discussed in detail. Further details for most of these observations, including Principal Investigators, can be found in Table 1 of \citet{tremblay12b}. } \end{deluxetable*} \label{sec:discussion} This paper presents three results: \begin{enumerate} \item \textbf{Cold gas is cospatial and comoving with warm gas}. A three billion solar mass filamentary molecular nebula is found to span the inner 30 kpc of the galaxy. Limited by the critical density of CO(2-1), its volume filling factor must be low, and so the nebula must be more like a ``mist'' than a monolithic slab of cold gas (e.g., \citealt{mccourt18}). These cold clouds are likely wrapped in warm envelopes that shine with Balmer and forbidden line emission at the cloud's interface with the hot X-ray atmosphere, explaining why the H$\alpha$ and CO(2-1) nebulae are largely cospatial and comoving. This hypothesis is now supported by a large and growing number of ALMA observations of CC BCGs (e.g., papers by Russell, McNamara and collaborators). \item \textbf{Cold gas is moving inward, and perhaps feeding the black hole}. Clouds are directly observed to fall inward toward the galaxy nucleus, probably within close proximity ($\lae 100$ pc) to the central supermassive black hole. These clouds may therefore provide a substantial (even dominant) component of the mass flux toward the black hole accretion reservoir. This result, discussed in \citealt{tremblay16} and considered in a broader context here, is consistent with a major prediction of the chaotic cold accretion (CCA) model \citep{gaspari13}. \item \textbf{Cold gas is dynamically coupled to mechanical black hole feedback}. In projection, a bright rim of blueshifted molecular gas appears to encase the radio lobes (see e.g., \autoref{fig:channel_maps}), perhaps suggestive of dynamical coupling between the cold molecular gas and the powerful radio jet plowing through it. The broadest distribution of cold gas velocities is found copatial with the southern jet (\autoref{fig:jet_detail_expand}, right panel). Just south of the radio core, this jet deflects in position angle, perhaps because it has exchanged momentum with a dense ensemble of cold clouds. Nearly all cloud velocities, save for the most extreme wings of the distribution, are nevertheless below the circular speed at any given radius, and so the clouds should be falling inward unless tethered to the hot medium. $\sim1$ billion \Msol\ of cold gas is found in dynamically short-lived filaments spanning altitudes greater than 10 kpc from the galaxy center, and may be draped around the rims of buoyant X-ray cavities. We argue that effectively all of these non-equilibrium cold gas structures are directly or indirectly due to mechanical black hole feedback, as mediated either by jets, buoyant hot cavities, or turbulence in the velocity field of the hot atmosphere. \end{enumerate} It is possible that the molecular and ionized nebula at the heart of Abell 2597 is effectively a galaxy-scale ``fountain'', wherein cold gas drains into the black hole accretion reservoir, powering a jet- or cavity-driven plume of uplifted low-entropy gas that ultimately rains back toward the galaxy center from which it came. This scenario might establish a long-lived heating-cooling feedback loop, mediated by the supermassive black hole, which would act much like a mechanical ``pump'' for this fountain. \subsection{The Fountain's ``Drain''} We directly observe at least three cold molecular clouds moving toward what would be the fountain's drain (see \autoref{sec:natureresult} and \citealt{tremblay16}). If this line-of-sight observation is at all representative of a (much) larger three-dimensional distribution of inward-moving clouds, and if indeed they are as close to the black hole as corroborating evidence suggests they are, they could supply on the order of $\sim0.1$ to a few \Msol\ yr\mone\ of cold gas to the black hole's fuel reservoir. The observation would then be consistent with a major prediction of \citet{gaspari13,gaspari15,gaspari17b}, who argue that that nonlinear condensation from a turbulent, stratified hot halo induces a cascade of multiphase gas that condenses from the $\sim10^7$ K to the $\sim20$ K regime. This cooling ``rain'' manifests as chaotic motions that dominate over coherent rotation (with turbulent Taylor number $<1$; e.g., \citealt{gaspari15}). Warm filaments condense along large-scale turbulent eddies (generated, for example, by AGN feedback), naturally creating extended and elongated structures like the H$\alpha$ filaments ubiquitously observed in CC BCGs, and possibly explaining their apparent close spatial association with radio jets and X-ray cavities (e.g., \citealt{tremblay15}). Warm overdensity peaks further condense into many cold molecular clouds\footnote{Though the need for dust grains to act as a catalyst for the formation of molecular gas remains a persistent issue, e.g., \citealt{fabian94,voit11}.}, hosting most of the total mass, that form giant associations. The thermodynamics and kinematics of the cooler gas phases should then retain ``memory'' of the hot plasma from which they have condensed \citep{gaspari17b,gaspari18,voit18b}. Despite important differences (reviewed in part by \citealt{hogan17,gaspari18,voit18b,pulido18}), the chaotic cold accretion model of \citealt{gaspari13} succeeds alongside the ``circumgalactic precipitation'' and ``stimulated feedback'' models of \citet{voit15b} and \citet{mcnamara16} (respectively) in predicting many of the major observational results we find in Abell 2597. Were we to (roughly) attempt to unify these models within the same ``fountain'' analogy, all would effectively include a ``drain'' into which cold clouds fall, providing a substantial (even dominant) mass flux toward the black hole fuel reservoir. That we have strong observational evidence for exactly such a drain in Abell 2597 enables us to place at least broad constraints on how the drain might operate. For example, whether they condense in the turbulent eddies of cavity wakes or not, a cascade of gas cooling from hot plasma will still require roughly a cooling time $t_\mathrm{cool}$ to reach the molecular phase. Using the buoyant rise time as a rough age estimate, the oldest X-ray cavities in A2597 are $\sim2\times10^8$ yr \citep{tremblay12b}, which is roughly comparable to the cooling time at the same $20-30$ kpc radius \citep{tremblay12a}. The time it takes for clouds to descend from any given altitude to the center of the galaxy is a more complicated issue. Following \citealt{lim08}, a thermal instability, precipitating at rest with respect to the local ICM velocity, will freefall in response to the gravitational potential and accelerate to a velocity $v$ given roughly by \begin{equation} v = \sqrt{v(r_0)^2 + 2GM \left( \frac{1}{r + a} - \frac{1}{r_0 - a} \right)}, \end{equation} where $v(r_0)$ is its initial velocity (assumed to be zero if the ICM and BCG velocities are roughly matched), $r_0$ is its starting radius relative to the BCG core, $G$ is the gravitational constant, $M$ is the total gravitating mass of the BCG, and $a$ is its scale radius (which is roughly half the effective radius $R_e$, as $a\approx R_e / 1.815$). For a scale radius of $a\sim20$ kpc and a gravitating mass of $M\approx10^{12}$ \Msol\ \citep{tremblay12a}, the cooling cloud would attain a rough velocity of $\sim470$ km s\mone, $\sim380$ km s\mone, or $\sim300$ km s\mone\ if it fell from a height of 20, 10 or 5 kpc, respectively. Observed line-of-sight cloud velocities in Abell 2597 are significantly lower than these freefall values, just as they are for effectively all other CC BCGs thus far observed with ALMA (see e.g. \citealt{vantyghem18}, for the latest example). The clouds might still be ballistic if most of their motion is contained in the plane of the sky, but this argument weakens with every new observation showing the same result. It is therefore now clear that the velocity of cold clouds in the hot atmospheres of CC BCGs cannot be governed by gravity alone. Simulations and arguments by (e.g.) \citet{gaspari18} and \citet{li18} indeed suggest that the clouds must have sub-virial velocities, consistent with those observed in CC BCGs including Abell 2597 (\autoref{sec:velocitystructure}). If a cooling cloud's terminal speed is smaller than typical infall speeds \citep{mcnamara16}, it can drift in the macro-scale turbulent velocity field of the hot X-ray atmosphere \citep{gaspari18}, whose dynamical structure is sculpted by jets, sound waves, and bubbles. The terminal velocity of cold clouds is set by the balance of their weight against the ram pressure of the medium through which they move (e.g., \citealt{li18}). That the clouds in Abell 2597 are apparently not in freefall may simply mean that their terminal velocity is the lower of the two speeds. While the extreme density contrast between molecular gas and hot plasma remains an issue, one simple explanation is that the clouds' velocity in the hot atmosphere has been arrested by more efficient coupling mediated by their warm ionized skins, which would effectively lower their average density (and therefore their terminal speed) and increase the strength of any magnetic interaction (e.g., \citealt{fabian08}). Given the apparent lack of coherent velocity gradients along the molecular and ionized filaments, it is also likely that the multiphase nebula is dynamically young. Such a result is unsurprising in the context of chaotic cold accretion, precipitation, and stimulated feedback models. In essence, all suggest that the cold clouds are just one manifestation of what is ultimately the same hydrodynamical flow, drifting in the velocity field of the hot plasma. That velocity field, in turn, is continually stirred by subsonic turbulence induced by buoyant bubbles, jets, and merger-driven sloshing \citep{gaspari18}. This omni-present dynamical mixing may inhibit virialization, preventing the formation of smooth gradients over kpc scales. At the very least, the recent \textit{Hitomi} observation of Perseus confirms that bulk shear in the hot plasma is similar to molecular gas speeds observed with ALMA, supporting the idea that they move together \citep{hitomi16}. At sub-kpc scales, inelastic collisions and tidal stress between clouds can funnel cold gas toward the nucleus, which we observe directly in Abell 2597 (\autoref{sec:natureresult} and \citealt{tremblay16}). Chaotic cold accretion can then boost black hole feeding far in excess of the Bondi rate, powering the ``pump'' at the fountain's center. \begin{figure*} \begin{center} \includegraphics[scale=0.17]{Fig_chandra.pdf} \end{center} \vspace*{-4mm} \caption{ A new, deeper look at the X-ray cool core cospatial with the A2597 BCG. (\textit{a}) 626 ksec \textit{Chandra} X-ray observation of $0.2 - 10$ keV emission in the innermost $\sim250\times250$ kpc$^2$ of the cluster. The X-ray data have been convolved with a Gaussian gradient magnitude (GGM) filter (e.g., \citealt{sanders16b}) to better show ripples and cavities. The optical Petrosian radius of the BCG's stellar component is (roughly) marked by the gray dashed ellipse. Brackets indicate the relative fields of view shown in the surrounding panels. (\textit{b}), (\textit{c}), and (\textit{d}) the same data, slightly zoomed in, with MUSE H$\alpha$, ALMA CO(2-1), and 8.4 GHz radio contours overlaid in green, blue, and gray, respectively. Moving inward, the ALMA contours in panel \textit{d} show emission that is $3\sigma$, $5\sigma$, $10\sigma$, and $20\sigma$ over the background RMS noise level. With the caveat that projection effects complicate interpretation, the H$\alpha$ nebula shows strong circumstantial evidence that at least some of the filaments are draped around the edges of the buoyant X-ray cavities marked by arrows. } \label{fig:deepchandra} \end{figure*} \begin{figure} \begin{center} \includegraphics[width=0.47\textwidth]{Fig_musealmavel.pdf} \end{center} \vspace*{-3mm} \caption{A side-by-side comparison of the MUSE H$\alpha$ and ALMA CO(2-1) LOS velocity maps, shown on the same spatial and velocity scales. Insets show a zoom-in on the nuclear region for both maps. Black contours again show the 8.4 GHz radio source. Where they overlap, the MUSE and ALMA velocity maps look very similar to one another. These maps are more quantitatively compared in \autoref{fig:MuseALMARatios}. } \label{fig:MuseALMAVelocity} \end{figure} \subsection{The Fountain's ``Plume''} There is little doubt that this pump injects an enormous amount of kinetic energy into the hot $\sim10^{7}-10^{8}$ K phase. In \autoref{fig:deepchandra} we present a new, deep \textit{Chandra} X-ray map of the A2597 BCG and its outskirts, made by combining the new observations from our recent Cycle 18 Large Program with the archival exposures previously published by \citet{mcnamara01,clarke05} and \citet{tremblay12a}. The new map contains 1.54 million source counts collected over 626 ksec of total integration time, enabling an exquisitely deep look at the X-ray cavity network that permeates the innermost 30 kpc of the cool core. The figure makes use of a Gaussian Gradient Magnitude (GGM) filter as an edge-detector \citep{sanders16b,walker17}, revealing the X-ray cavities in sharp relief. A discussion of detailed X-ray morphology along with deep spectral maps, etc., will be discussed in a forthcoming paper (Tremblay et al.~in prep). We preview the map here because it makes obvious the need to consider uplift by buoyant hot cavities as a primary sculptor of morphology in the cold and warm nebulae. To the north and south, H$\alpha$ filaments (green contours on \autoref{fig:deepchandra}) appear draped over the edges of the inner X-ray cavities, as if they have either been uplifted as they buoyantly rise, or have formed \textit{in situ} along their wakes and rims (e.g., \citealt{brighenti15,mcnamara16}). The nothernmost H$\alpha$ filament has a morphology and X-ray cavity correspondence that is reminiscent of the Northwestern ``horseshoe'' filament in Perseus (e.g., \citealt{hatch06,fabian08,gendron-marsolais18}). In projection, the southern H$\alpha$ filaments reach a terminus at the rim of the southern cavity, forking like a snake's tongue into two thinner filaments. As seen in the H$\alpha$ velocity map (\autoref{fig:MuseShowcase}), one filament approaches and the other recedes, yet both have a coherent bulk line of sight velocity that is similar to the expected terminal velocity of the buoyantly rising hot bubble with which it is cospatial (roughly half the sound speed in the hot gas, or $\sim375$ km s\mone, \citealt{tremblay12a}). A similar ``snakes tongue'' split is seen in the redshifted northern filaments, whose $\gae15$ kpc outskirts at the edges of cavities show the fastest LOS velocities of any optical emission line in the galaxy ($+400$ km s\mone). The cospatial and comoving components of the warm and cold nebulae likely trace the same population of clouds, as we have argued repeatedly throughout this paper, and as has been suggested by many authors over many years (e.g., \citealt{odea94,jaffe97,jaffe05,wilman06,emonts13,anderson17}). In \autoref{fig:MuseALMAVelocity} we compare the H$\alpha$ and CO(2-1) line of sight velocity maps side-by-side. Where they overlap, the projected velocity of the molecular gas matches that of the warm gas, consistent with the hypothesis that much of the Balmer emission stems from warm ionized envelopes of cold molecular cores, tracing their interface with the ambient hot gas. As projected on the sky, the H$\alpha$ nebula only shows line of sight velocities consistently in excess of mean CO(2-1) velocities at galaxy-centric radii that are greater than the outermost extent of the detected CO(2-1) emission. Were we able to detect CO(2-1) at these large radii, we would likely find it at similar LOS velocities as the H$\alpha$. The fact that the latter shows a factor of two broader linewidth, then, is not necessarily surprising. Perhaps simply because of a sensitivity floor, cold molecular gas is confined to smaller radii. Any given line of sight therefore intersects a smaller volume occupied by CO(2-1)-bright clouds -- and therefore smaller-scale turbulent eddies -- which in turn have smaller velocity dispersions. H$\alpha$ is both vastly brighter (i.e. easier to detect at large radii) than CO(2-1) relative to the sensitivity limits of our optical and mm observations, respectively. Moreover, CO(2-1)-bright molecular clouds can dissociate easily, absent sufficient shielding, and so may be more vulnerable to destruction at larger galaxy-centric radii. \ion{H}{1} in A2597, as mapped in detail by \citet{odea94}, shows broader linewidths more consistent with those found in H$\alpha$, supporting this notion. In any case, if a substantial component of the H$\alpha$ filaments have been buoyantly uplifted in the rise of the X-ray cavities, then so too must be the molecular filaments. Assuming (hypothetically) that coupling efficiency is not an issue, simple energetics arguments suggest that the cavity network in Abell 2597 is powerful enough to uplift the entirety of the cold molecular nebula. Archimedes' principle dictates that the bubbles cannot lift more mass than they displace (e.g., \citealt{mcnamara14,russell17,vantyghem16}). The mass of hot gas displaced in the inflation of the cavity network is at least $\sim7\times10^9$ \Msol\ (using X-ray gas density and cavity size measurements from \citealt{tremblay12b}, assuming spherical cavity geometry, and adopting the arguments in \citealt{gitti11}), while the total cold gas mass in the molecular nebula is less than this ($\sim3.2\times10^9$ \Msol). Moreover, the cavity system has an estimated $4pV$ mechanical energy of $\sim4\times10^{58}$ ergs \citep{tremblay12b}, while the total kinetic energy in the cold molecular nebula (e.g., $\frac{1}{2} M_\mathrm{mol} v^2$) is about an order of magnitude lower, at roughly $\sim2\times10^{57}$ ergs. Therefore, if we ignore coupling efficiency, uplift of the entire mass of the molecular nebula would be safely within the kinetic energy budget of the system. Any such uplift would be temporary. The escape speed from the galaxy, which is roughly twice the circular speed at any given radius, is far in excess of any observed line of sight velocity in the system. After decoupling from either the cavity wake or jet entrainment layer that has lifted them to higher altitudes, cold clouds should fall back inward at their terminal speed, drifting in the hot gas velocity field as they descend. These infalling clouds may join the population we observe in absorption, powering black hole activity once again, and keeping the fountain long-lived. | 18 | 8 | 1808.00473 |
1808 | 1808.07065_arXiv.txt | We present a detailed census of galaxies in and around PC217.96+32.3, a spectroscopically confirmed Coma analog at $z=3.78$. Diverse galaxy types identified in the field include Ly$\alpha$ emitters (LAEs), massive star-forming galaxies, and ultra-massive galaxies ($\gtrsim 10^{11}M_\odot$) which may have already halted their star formation. The sky distribution of the star-forming galaxies suggests the presence of a significant overdensity ($\delta_{\rm SFG}\approx 8\pm2$), which is spatially offset from the previously confirmed members by 3--4~Mpc to the west. Candidate quiescent and post-starburst galaxies are also found in large excess (a factor of $\sim$8--15 higher surface density than the field) although their redshifts are less certain. We estimate that the total enclosed mass traced by candidate star-forming galaxies is roughly comparable to that of PC217.96+32.3 traced by the LAEs. We speculate that the true extent of P217.96+32.3 may be larger than previously known, a half of which is missed by our LAE selection. Alternatively, the newly discovered overdensity may belong to another Coma progenitor not associated with PC217.96+32.3. Expectations from theory suggest that both scenarios are equally unlikely ($<1$\%), in the cosmic volume probed in our survey. If confirmed as a single structure, its total mass will be well in excess of Coma, making this an exceptionally large cosmic structure rarely seen even in large cosmological simulations. Finally, we find that the protocluster galaxies follow the same SFR-$M_{*}$ scaling relation as the field galaxies, suggesting that the environmental effect at $z\sim4$ is a subtle one at best for normal star-forming galaxies. | \label{sec:intro} Local environment has a profound influence on the formation and evolution of galaxies. At low redshift, galaxies in dense cluster environments tend to be more massive, contain older stellar populations, have lower star formation rates and dust content, and a higher fraction have elliptical morphologies than their average field counterparts \citep[][]{stanford98, blakeslee03,vandokkum07,eisenhardt08}. The redshift evolution of the cluster red sequence and the properties of cluster ellipticals strongly support a scenario in which cluster galaxies underwent early accelerated formation followed by swift quenching \citep[e.g.,][]{thomas05,Bolzonella10,mancone10,Fritz14}. While this general picture is accepted, the mechanisms responsible for the formation, evolution and quenching processes are still not well understood \citep[e.g.,][]{snyder12}. In high-density environments, the accretion rates of infalling gas and the frequency of galaxy interactions are expected to be higher, fostering enhanced star formation activities. A merger of gas-rich galaxies may include an ultra-luminous infrared galaxy \citep[ULIRG;][]{Aaronson84,sanders96} phase which efficiently converts the majority of their gas into stars over a short timescale. Dissipative gas-rich mergers may help the efficient feeding of gas into the central blackholes, triggering nuclear activity, which may quench star formation and create old, massive cluster ellipticals. \citep{hopkins08}. High-density environments are therefore expected to consist of diverse galaxy constituents, including normal star-forming galaxies, ULIRGs, X-ray sources, AGN, and massive quiescent galaxies. A detailed census of diverse galaxy `types' and their spatial distribution within the large-scale structure are essential to obtain a more comprehensive understanding of how the high density environment drives the evolution. To directly witness the key epoch of cluster galaxy formation, one needs to identify the galaxy populations residing in young `protoclusters'. In recent years, substantial progress has been made in the search for high-z protoclusters \citep[see review by][and references therein]{overzier16}. Searches around powerful radio sources at high redshift have identified significant galaxy overdensities \citep[e.g.,][]{venemans05, miley06, kajisawa06, venemans07,hatch11a,Noirot18}. A population of extremely dusty starburst systems, optically or X-ray-luminous AGN, and large Ly$\alpha$ nebulae are reported in some of the known protoclusters \citep{matsuda04,dey05, prescott08, lehmer09, capak11,casey16,hung16,cai17,badescu17}, in support of the theoretical expectations \citep[but see][]{rigby14,kato16}. The existence of massive `red and dead' galaxy candidates at $z\sim3$ offers tantalizing evidence that the formation of massive cluster ellipticals may have been well underway as early as 2 Gyr after the Big Bang \citep{kubo13}. The number of confirmed protoclusters and protocluster candidates has been increasing rapidly \citep[e.g.,][]{lemaux14, cucciati14, toshikawa16, planck_overdensity,lemaux17,cucciati18}, offering a promising outlook for future protocluster studies; such as the impact of environment on the galaxy inhabitants, as well as the evolutionary link between unvirialized proto-structures and present-day clusters. Despite this progress, a clear and coherent physical picture of how cluster environment influences galaxy formation has yet to emerge. We do not yet know how dense protocluster environments influence the galaxy therein: e.g., are rare systems such as radio galaxies, quasars, Ly$\alpha$ nebulae ubiquitous enough to be used as beacons of the highest density peaks of the universe? Do dense protocluster environments produce a different `zoo' of galaxy constituents, or simply a scaled-up version of the average field? Addressing such questions may have an important cosmological implication: given their large pre-virialization volume and high galaxy overdensities, star formation in protoclusters can account for up to 30\% of the cosmic star formation rate density at $z=4$ \citep{chiang17}. Observationally, one of the main limitations has been the lack of our knowledge of the density structure of protoclusters. The angular size of the cosmic volume that will end up virialized by the present-day epoch is expected to be as large as 20\arcmin\ -- 30\arcmin\ in the sky \citep[e.g.,][]{chiang13,muldrew15}, making it expensive to rely on blind spectroscopic programs to map out their structures with reasonable precision. To date, only a few systems exist with a detailed characterization of their sizes and density structures \citep[][]{matsuda05,lee14,badescu17}. Another critical element in making progress is to obtain a detailed census of protocluster constituents. Understanding how different types of galaxy constituents are distributed within the large-scale structure is necessary to make a fair assessment of how the formation of galaxies is impacted by the environment in which they reside. For example, luminous Ly$\alpha$ nebulae are often found located at the outskirts or an intersection of the densest regions of a protocluster \citep{matsuda05,badescu17}. Several studies reported that powerful AGN may suppress low-level star formation activity and produce a deficit of Ly$\alpha$-emitting galaxies \citep[e.g.,][]{kashikawa07,goto17} although claims to the contrary also exist \citep[e.g.,][]{cai18}. In this paper, we present a multi-wavelength study of galaxies along the sightline to the PC217.96+32.3 protocluster at $z=3.78$, one of the most massive protoclusters discovered to date \citep{lee14}. Existing spectroscopy has confirmed 48 members at $z$=3.76--3.81 \citep[of which 34 lie at $z$=3.77--3.79;][]{dey16}. The locations of these members are indicated in Figure~\ref{field_layout}. The three-dimensional `map' of the spectroscopic members suggests that the structure is mainly composed of two large groups with a small velocity offset and of additional smaller groups falling in toward the center \citep{dey16}. Given the level and angular extent of the galaxy overdensity, PC217.96+32.3 will likely collapse into a system with a present-day mass of $M_{\rm total}\gtrsim 10^{15}{\rm M}_{\odot}$, making it one of the few spectroscopically confirmed Coma progenitors. \begin{figure}[h!] \epsscale{1.2} \plotone{pcf_field_layout.eps} \caption{ The layout of our protocluster survey field is shown for the Mosaic ($B_WRI$: green), NEWFIRM ($HK_S$: red), and SDWFS data (blue to the north). The Subaru $y$-band data covers the field shown here in its entirety. Open circles denote the positions of photometrically selected LAEs, while filled circles show the spectroscopic sources in the range $z$=3.76--3.82, color coded by the redshift indicated by bar on top. PC217.96+32.3 is situated in the middle of our Mosaic field. } \label{field_layout} \end{figure} Having established the significance of the structure, we are motivated to take a broader view of the constituents of PC217.96+32.3; in particular, we are interested in identifying more evolved galaxies which may be more closely linked to massive cluster ellipticals in the present-day universe. To this end, we have conducted a deep near-infrared imaging survey of the region, sampling the continuum emission at rest-frame visible wavelengths. In this paper, we present new near-infrared $H$ and $K_S$-band imaging on the central portion of the protocluster field (\S2). Combining this with existing optical data from the NOAO Deep Wide-Field survey \citep[NDWFS:][]{ndwfs} and mid-infrared data from the {\it Spitzer Space Telescope} \citep{ashby09}, we identify a large overdensity of luminous galaxies in the region (\S3). Population synthesis modeling of these galaxies suggests that they are likely to lie close to the redshift of the protocluster traced by the Lyman Alpha emitters (LAEs), although they have a somewhat different spatial distribution (\S4). We discuss the masses, star-formation rates, and estimate the size of the overdensity in \S4, and discuss the implications of finding such an overdense region in \S5. Throughout this paper, we use the WMAP7 cosmology $(\Omega_m, \Omega_\Lambda, \sigma_8, h)=(0.27, 0.73, 0.8, 0.7)$ from \citet{wmap7}. Distance scales are given in comoving units unless noted otherwise. Magnitudes are given in the AB system \citep{oke83} unless noted otherwise. In the adopted cosmology, PC217.96+32.3 at $z=3.78$ is observed when the universe was 1.7~Gyr old; 1\arcmin\ corresponds to the physical scale of 2.1~Mpc at this redshift. | \subsection{The prevalence of massive quiescent galaxies in protocluster environment}\label{bbg_discussion} We evaluate how the number of massive quiescent galaxies ($\geq 10^{11}M_\odot$) in our field compares with that expected in an average field. Based on $K_S$-selected galaxies in the 1.6~deg$^2$ COSMOS/UltraVISTA field, \citet{muzzin13} estimated that at $z=3-4$, the cumulative number density of galaxies with $M_{\rm star}\geq 10^{11}M_\odot$ is $(1.4^{+2.2}_{-0.5})\times 10^{-6}$~Mpc$^{-3}$. In our survey field (28\arcmin$\times$35\arcmin), one expects to find $2.5^{+3.9}_{-0.8}$ BBG-selected quiescent galaxies. Similarly, \citet{spitler14} identified 6 quiescent galaxies above $M\geq 10^{11}M_\odot$ in the ZFOURGE survey corresponding to the surface density of $0.015\pm0.006$~arcmin$^{-2}$, such that $3.7\pm1.5$ quiescent galaxies are expected in our field. We assume in the above calculations that the selection function takes the form of a top hat filter in the range $z=3.6-4.2$ where the $H-K_S$ color samples the Balmer/4000\AA\ break. The relative change of angular diameter distance in this range is 6\%, and should result in 12\% in the expected number depending on the redshift distribution of BBGs. Taking the \citet{muzzin13} measurement as the field average, the implied overdensity of massive quiescent galaxies is $\delta\Sigma_{\rm BBG} \sim 16$! Excluding all of our post-starburst BBG candidates (assuming all are strong [O~{\sc iii}] emitters at $z\sim3.4$), the remaining BBGs correspond to $\delta\Sigma_{\rm BBG}\approx 13$. Using the \citet{spitler14} estimates, the overdensity is $\delta\Sigma_{\rm BBG}=11$ (9) with (without) the potential [O~{\sc iii}] emitters. We also compare the observed abundance of quiescent galaxies with that measured in the SSA22 protocluster at $z=3.09$. \citet{kubo13} used color criteria tuned to $z\sim3$ ($i^\prime - K>3$, $K-[4.5]<0.5$, and $K<23$), and identified 11 massive galaxies ($\gtrsim 10^{11}M_\odot$) concentrated near the overdensities of other types of galaxies with the surface density of $0.10\pm0.03$~arcmin$^{-2}$. In comparison, the overall surface density of BBGs in our field is $0.06\pm0.01$~arcmin$^{-2}$. Within a smaller rectangular region (15\arcmin$\times$16\arcmin) in which the surface density of photo-$z$ sources is enhanced by 50\% (Figure~\ref{density_BBG}, left), we find 21 quiescent BBGs there in, corresponding to the surface density of $0.09\pm0.02$~arcmin$^{-2}$. All errors are given assuming Poisson shot noise. Considering the change of angular diameter distance, the surface density per unit comoving transverse area is $0.027 \pm 0.008$~Mpc$^{-2}$ and $0.021\pm0.004$~Mpc$^{-2}$ for the SSA22 and the present structure, respectively. Similarly, \citet{lemaux14} estimated that the implied overdensity of massive ($\geq 10^{10.8}M_\odot$) red galaxies in a $z=3.29$ protocluster is $\delta_g=25.1\pm15.2$. A large population of massive quiescent galaxies found in our field implies that the formation of cluster galaxies occurred in shorter timescales and at earlier times than the field galaxies. Our results confirm an early onset of cluster red sequence \citep[e.g.,][]{kodama07,lemaux14}. This is in a broad agreement with star formation histories of present-day cluster ellipticals inferred from absorption line studies \citep{thomas05}. Little to no evolution of the cluster red sequence out to $z\sim 1.4$ further strengthens this expectation \citep[e.g.,][]{blakeslee03,mei06}. \begin{figure*}[t] \epsscale{1.1} \plotone{plot_sfr_mass_v4.eps} \caption{ The distributions of star formation rates (left), stellar masses (middle), and specific SFRs (right) are shown for the LAE protocluster members (cyan) and photo-$z$ protocluster candidates (blue) and BBG candidates (red). The errors reflect the Poisson uncertainties. For clarity, finer binsizes are used for the photo-$z$ sources than for the BBGs. As for the LAEs, stellar population parameters are derived from bootstrap realizations of image stacking analyses (see text). In all panels, the LAE distribution is rescaled to have the same peak height as the photo-$z$ members. } \label{sfr_mass} \end{figure*} The sky distribution of BBGs appears to trace the full extent of the large scale structure rather than being concentrated in the highest density environments. Few are found in either LAE or photo-$z$ overdensity peaks (see \S\ref{bbg_distribution}). We speculate that BBGs may be the central (and most massive) inhabitants of the massive halos that are in the process of merging. The implication is that they were quenched long before the final coalescence of the structure which occurred much later. Therefore, the quenching of massive cluster ellipticals is caused by the early onset of the `mass quenching' rather than by any environmental effect suppressing their formation \citep{peng10}. This is in line with a study of intermediate-redshift galaxy clusters by \citet{brodwin13}, who found that the level of star formation in cluster environment declines below that in the average field only at $z\lesssim 1.4$ \citep[also see,][]{tran10}. Recent discoveries of compact galaxy groups in protocluster environments support this view, as a fraction of quiescent galaxies in such a group is observed to be low \citep[e.g.,][]{wang16,kubo16}. \subsection{Diverse types of galaxies tracing a massive protocluster} In this work, we have identified protocluster member candidates by employing two selection methods, namely photo-$z$ selected star-forming galaxies and Balmer break galaxies. When combined with a population of LAEs in the same field \citep{lee14, dey16}, these samples showcase diverse types of inhabitants residing in a very overdense cosmic structure. In Figure~\ref{sfr_mass}, we show SFR, stellar mass, and sSFR values measured for our sample galaxies. The estimates for the photo-$z$ candidates are made on individual galaxies. As for the quiescent BBG candidates, we fix the redshift to $z=3.8$ for the SED fitting (see \S~\ref{bbg_q} for discussion on redshift degeneracy); for the UV-bright BBGs with robust photo-$z$ estimates, we fix the redshift to the best-fit value. As for the LAEs, while they have robust redshift estimates, they are too faint at infrared wavelengths to yield robust estimates of stellar population parameters on an individual basis. Instead, we perform image stacking on their positions, and measure the parameters based on the aperture photometry on the stacked images. A total of 150 LAEs are used for stacking analysis after removing those too close to nearby bright sources. To estimate the range of their physical parameters, we randomly draw a subset of the LAEs, and perform image stacking, aperture photometry, and SED fitting procedure. Their distributions of stellar population parameters shown in Figure~\ref{sfr_mass} are based on 2,500 such realizations. Since median stacking is insensitive to significant outliers, the distribution of their physical parameters should be taken as a lower limit rather than the full range spanned by the LAEs. The sample galaxies span a wide range of SFRs and stellar masses: the lack of overlap is at least in part driven by the selection effect. The lack of photo-$z$ candidates at $M_{\rm star}\lesssim 10^{10}M_\odot$ is tied to the sensitivity of our $K_S$ band data. A 10$\sigma$ detection ($K_{S,\rm{AB}}$=24.0) corresponds to the rest-frame optical luminosity of a $z=3.8$ galaxy with stellar mass $\approx 10^{10.2}M_\odot$, assuming an exponentially decaying star formation history with the $\tau$ value of 0.5~Gyr. The paucity of galaxies with ${\rm SFR}\lesssim50~M_\odot {\rm yr}^{-1}$ is also driven by the same mass limit, given the correlation between SFR and $M_{\rm star}$. The large median mass of the BBGs is driven by the IRAC color selection as discussed in Sec~\ref{selection_bbg}. The steep decline in the number of galaxies at ${\rm SFR}\gtrsim 150~M_\odot {\rm yr}^{-1}$ \citep[e.g.,][]{smit12} is likely further helped by the photo-$z$ selection which is biased against redder (dustier) galaxies than typical LBGs. The intrinsic distribution of these parameters spanned by different types of galaxies remains uncertain: such information will require careful analyses of deeper multiwavelength data and the modeling of their respective selection biases, which are outside the scope of this paper. The measured overdensities of different galaxy types highlight how they trace the same underlying large scale structure(s). Such measures are more robust against any selection biases mentioned previously as any such bias should apply equally to field and cluster galaxies, and thus should minimally impact their spatial distributions. The observed surface overdensity of photo-$z$ galaxies is $\delta \Sigma_{\rm phot}\approx 1.5$, similar to that of the LAEs over the same general area. However, we show in \S~\ref{overdensity} that the spatial overdensity of the photo-$z$ galaxies is much larger, $\delta_g=7.8\pm2.4$, than that of the LAEs. This is because the former is distributed over a much larger line-of-sight distance (i.e., larger $\Delta z$), and as a result, its surface overdensity is substantially diluted by the interlopers. It is also possible that the narrow band Ly$\alpha$ filter `misses' the core of the protocluster, and is only picking up the outer parts of the protocluster. In comparison, the surface overdensity of BBGs of the region is much higher at $\delta\Sigma_{\rm BBG}$$\approx$9--16. If all types of galaxies we consider here (LAEs, BBGs, and photo-$z$ candidates) trace the same underlying structure represented by a matter overdensity $\delta$, the implication would be that more massive BBGs are far more biased tracers of the matter distribution than less massive star-forming galaxies. Our findings are consistent with the expectation from existing clustering studies, that more luminous/massive galaxies have larger biases \citep[e.g.][]{GD01,ouchi04b,adelberger05,lee06,gawiser07,guaita10,kusakabe18}. One corollary to the luminosity/mass-dependent bias is that, everything being equal, low-mass low-bias galaxies such as LAEs are the least biased (thus most reliable) tracers of the density distribution within the large-scale structure. Using LAEs to `map out' the protocluster environment has additional advantages including the relative ease of redshift identification through the narrow-band selection technique and the abundance of low-luminosity galaxies implied by the steep faint-end slope of the UV luminosity function at this redshift range \citep[e.g.,][]{bouwens07,reddy09,alavi16,malkan17}. Given the difficulties of obtaining spectroscopic redshifts for faint distant galaxies, LAEs offer the best practical means to survey the local environment of massive protoclusters, thereby allowing for studying the impact of local environment on its galaxy constituents \citep[e.g.,][]{kubo13,umehata14,kubo16}. While large numbers of protocluster candidates are being identified from wide-field deep surveys \citep[e.g.,][]{toshikawa16,toshikawa18}, the lack of narrow-band observations targeting these structures will remain a main challenge in utilizing these structures to elucidate the physics in the main epoch of cluster formation. \begin{figure*}[t] \epsscale{1.1} \plotone{ms_env_density_v3.eps} \caption{ {\it Top left:} the location of photo-$z$ protocluster candidates (blue circles) and LAEs (red diamond) on the SFR-$M_{\rm star}$ space. The latter measurements are based on median image stacking. Grey scales show the distribution of COSMOS field galaxies at the same redshift range, and are color coded by the source density in each bin. The median scaling relation and the 16th/84th percentiles determined for the average field are shown in all top panels as solid and dashed orange lines, respectively. A prediction from a semi-analytic model by \citet{dutton10} is indicated by a green line. {\it Middle and right panels:} A zoom-in on the parameter space populated by our photo-$z$ candidates. Each galaxy is color coded by its approximate local environment determined based on the surface density of the LAEs (top middle) and photo-$z$ member candidates (top right) such that darker shades represent higher environmental densities. The sky distribution of the same galaxies are shown in bottom panels with the density maps (identical to those in Figure~\ref{fig7}) overlaid. In both panels, the scaling relation is recomputed for each environmental density bin. The same scaling law is obeyed by all environmental bins although there is a hint that the galaxies residing in the highest photo-$z$ overdensities appear to have higher SFRs than the rest. } \label{main_sequence} \end{figure*} \subsection{Impact of local environment on stellar populations}\label{env_impact} The primary challenge in investigating the environmental effect on protocluster constituents is the lack of spectroscopic redshifts, which prevents unambiguous confirmation of cluster membership and inhibits a robust mapping of the density profile of the cluster. Because our selection methods target a relatively broad range of redshift, all galaxy samples are expected to contain and may be even dominated by interlopers not associated with the structure we wish to probe. These considerations testify to the clear need of spectroscopic information in making progress. One possible way to discern any environment trend is to compare the galaxy statistic measured in a protocluster field with that obtained in a field without any strong density enhancements.. Provided that the environmental effects are strong and a substantial number of galaxies in the sample belong to the protocluster, a qualitative trend may be identified through this comparison \citep[e.g.,][]{cooke14}. However, a comparative study is only meaningful if the two datasets are well matched in depth, dynamic range, and wavelength coverage, which determine the precision with which photometric redshifts and stellar population parameters of the galaxies can be measured. With these caveats in mind, we compare the properties of protocluster candidates with those of a control sample. The control sample is constructed from the COSMOS15 catalog \citep{laigle16} where the sources whose best-fit photo-$z$ solution lies in the range $z_{\rm phot}=3.4-4.2$ are selected. After removing galaxies with multiple peaks in the photo-$z$ PDFs, the sample consists of 19,318 sources. We run the CIGALE software using the identical setup as previously, assuming constant SFHs for the both samples. While it is unrealistic to expect that all galaxies have constant SFHs, we are interested in the comparison of the two samples and not in exploring the full behavior of galaxies. A different SFH choice would generally shift measured quantities in the same direction for most galaxies, and thus would not change our conclusions. Finally, we note that the photo-$z$ precision for the COSMOS galaxies is expected to be much better ($\sigma/(1+z)\sim 0.02-0.03$) than for our sample ($\sigma/(1+z)\sim 0.06$) thanks to the better imaging depth and finer wavelength sampling in the optical/near-IR wavelengths. While the larger uncertainty can introduce a larger scatter in the overall distribution of a derived quantity, it will not impact our ability to discern any mean relation between two different quantities. In the left panel of Figure~\ref{main_sequence}, we show the locations of our photo-$z$ sources and of LAEs on the SFR-$M_{\rm star}$ plane together with those of the control sample. A prediction from a semi-analytic model \citep{dutton10} is also shown. Both our photo-$z$ candidates and LAEs occupy the same region as the field galaxies, suggesting that they obey the same star formation `main sequence' scaling relation, consistent with existing studies \citep[e.g.,][]{koyama14,cucciati14,Erfanianfar16}. From the same figure, it is evident that the COSMOS datasets can probe galaxies down to much lower masses than the present dataset. The mismatch of the sensitivities of the two datasets renders it challenging to compare how the number counts in bins of SFR or stellar mass differ in the these samples. To investigate possible environmental trends, we divide the photo-$z$ sample into several environmental bins and color-code them accordingly where darker shades represent higher densities. Given the uncertainties in the extent and center of the structure, we define local environment using the LAE and photo-$z$ surface densities. The results are shown in top middle and right panels. The overall correlation -- measured for each subsample in mass bins of $\Delta\log{M_{\rm star}}=0.25$ -- is shown in solid lines. The SFR-$M_{\rm star}$ scaling laws measured from these subsamples are generally similar to that measured in the COSMOS sample. We detect a hint of enhanced star formation activity in the highest photo-$z$ overdensity subsample. Four galaxies deviate from the field average by 0.3-0.4~dex (a factor of 2--3). The overall scaling relation in this bin has a slightly higher normalization (i.e., $\sim$0.1~dex higher SFR in a given stellar mass bin) although the scatter is substantial. Interestingly, the same bin also lacks massive galaxies above $\log{M_{\rm star}}=10.8$. The high-mass high-SFR end is well populated by galaxies residing in all environments. All in all, the environmental effects on star-forming galaxies appear to be minimal. The lack of detectable environmental effects on the galaxy properties is puzzling. Uncertain cluster membership surely plays a role in diluting any existing trend by misplacing a subset of galaxies into a wrong density bin. However, should there be an excess of high-mass or high-SFR galaxies in dense environments, our analyses would have captured it as the regions most likely to be dense are counted as such in one or the other scenario. Hence, our analysis suggests that the environmental effect on star formation is likely a subtle one. Alternatively, most of the enhanced star formation is perhaps obscured from our view by dust. \citet{koyama13} reported that while sSFRs are higher for galaxies in cluster environment than those in the field, the trend emerges only when the mid-infrared budget of the SFR is properly accounted for. They argued that their result may be explained if a higher fraction of nucleated dusty starbursts exist in cluster environments where dust properties are significantly different from normal star-forming galaxies, such that applying the same dust correction as the field galaxies would underestimate the true SFRs. The lack of extreme star-formers in our sample (in both field and protocluster) is also in part a selection effect. Extremely dusty starbursting galaxies would not be included in our sample, as they would not have a strong enough spectral break for us to identify them robustly, or perhaps, are entirely invisible in the optical or infrared wavelengths. We therefore cannot test for the prevalence of dusty starburst systems in dense environments reported by several studies \citep{hung16,casey16}. Testing these hypothesis will require deeper infrared and submillimeter coverage of the field. \subsection{Search for Extreme Sources in the Protocluster Field} The presence of powerful radio galaxies has been used as a signpost of highly overdense regions \citep{venemans05, miley06, kajisawa06, venemans07, overzier08, hatch11a, Kuiper12,cooke14,rigby14}. Likewise, highly overdense structures appear to harbor powerful AGN observed as X-ray or submillimeter luminous sources, or giant Ly$\alpha$ nebula \citep[e.g.,][]{steidel00,prescott08,lehmer09,hung16,casey15,casey16}. Motivated by these findings, we search the existing radio and X-ray source catalogs to look for a sign of enhanced AGN activity. We cross-match the {\it Chandra} X-ray point-source catalog of the Bo\"otes field \citep[XBo\"otes:][]{kenter05} with our photo-$z$, BBG, and LAE positions, and find no match. The XBo\"otes survey sensitivity of the full band (0.5--8~keV) is $7.8\times10^{-15}$~ergs~cm$^{-2}$~s$^{-1}$. \citet{lehmer09} studied X-ray detected sources in and around the SSA structure at $z=3.09$, and found that the X-ray flux for the confirmed members range in $(0.3-5.0)\times 10^{-15}$~ergs~cm$^{-2}$~s$^{-1}$. Thus, non-detection merely suggests that even the brightest X-ray sources in SSA22 would lie below the XBo\"otes detection limit. We also search for radio counterparts of our protocluster candidates (both photo-$z$ and BBG candidates) in the radio source catalog based on deep Low Frequency Array (LOFAR) 150 MHz observations (Tasse et al. in prep). The rms noise of of the data is 59 $\mu$Jy/beam. Using the matching radius of 2\arcsec, no counterpart is found. We also compare our source positions against the photometric redshift catalog of the same LOFAR-detected sources constructed following the method presented in \citet{Duncan18b,Duncan18a}, which covers roughly two thirds of our survey field and only half of the photo-$z$ overdensity region. This is because the bottom one third of our survey field lies outside of the NDWFS field \citep{ndwfs}. Once again, no credible counterpart is identified. In addition, we cross-match our candidates with deep Westerbork Synthesis Radio Telescope (WSRT) 1.4-GHz catalog covering Bo\"otes field \citep{Devries02}, and find no counterpart. Therefore, we can rule out the presence of any high-redshift radio source with the flux density $\gtrsim $ 0.2~mJy in the probed redshift range. Apart from the limited survey sensitivities, non-detection of powerful AGN in the protocluster member candidates is perhaps not surprising. As discussed previously, the majority of our photo-$z$ candidates, by design, resemble LBGs with a clean spectral break. This requirement effectively removes all galaxies that are either dusty starbursts or AGN with power-law-like SEDs similar to those identified by \citet{hung16} in the COSMOS field; robust identification of such galaxies will require improved sensitivities and wavelength baseline. % \subsection{The plausibility of a very large structure}\label{mil} We assess how likely it is to find both structures or one very large structure in our survey volume. We utilize a catalog containing 2,731 simulated clusters identified from the Millennium I+II runs as described in \citet{chiang13}. The minimum cluster mass is $10^{14} h^{-1} M_\odot$ at $z=0$. The comoving volume of the simulation is $(500/h)^3$~Mpc$^3$ or 0.364~Gpc$^3$. Our survey volume is estimated conservatively to be $2.13\times 10^6$~Mpc$^3$ assuming a flat redshift distribution at $z=3.4-4.2$ over a 28\arcmin$\times$28\arcmin\ area, which is 0.6\% of the Millennium volume. We randomly pick a region matching our survey volume, and record the number of clusters therein and the position and the mass of each cluster. The procedure is repeated 500,000 times. The median (mean) number of clusters is found to be 16.0 (16.5) with a standard deviation of 5.2; i.e., our survey volume is large enough to contain multiple clusters. If the LAE and photo-$z$ overdensities are part of a single very large structure, its combined mass would be enormous. In \citet{dey16}, based on the level and extent of the LAE overdensity alone, we estimated that the enclosed mass is $\gtrsim 10^{15}M_\odot$. As discussed in \S~\ref{overdensity}, the photo-$z$ overdensity should contain a comparable mass. Given that the two overdensities only partially overlap (and the regions of the peak overdensities do not overlap), a conservative limit on its combined mass is in the range of $(1.5-2.0)\times10^{15}M_\odot$. We find the probability of these scenarios to be 4.4\% and 0.8\%, respectively. In the entire Millennium volume, eight and one structures exist with masses above $1.5\times10^{15}M_\odot$ and $2\times10^{15}M_\odot$ respectively, corresponding to the comoving number density of $(2.2\pm0.8)\times10^{-8}$~Mpc$^{-3}$ and $(2.7\pm2.7)\times10^{-9}$~Mpc$^{-3}$, respectively. The most massive structure in the Millennium simulations has a total mass of $2.4\times 10^{15}M_\odot$. The observational counterpart of such an ultramassive cluster may be the El Gordo system, which is a merging pair of Coma-analogs at $z=0.87$ \citep{Marriage11}. To test the possibility that the two overdensities are unrelated structures, we search for the cases in which there are two Coma-like clusters (i.e., each with mass $\geq 10^{15}M_\odot$). This occurs only 3.6\% of the time. Finally, we assess how unlikely it is that the photo-$z$ overdensity lies at $z=3.72$ (see discussion in \S~\ref{sky_distribution}), which would put the distance between the two at 47~Mpc or 10~proper Mpc. Only four distinct pairs of Coma analogs exist in the Millennium sample that are within 10~Mpc (physical) from each other. Two of those pairs have the physical separation of 5.2~Mpc and 5.3~Mpc from each other, and the other two at 9.3~Mpc and 9.8~Mpc. The separation for the latter is comparable to that between PC217.96+32.3 and the putative overdensity at $z=3.72$ \citep{lee18}. The likelihood of such a configuration falling into our survey is 0.8\%. These considerations show that both scenarios are extremely unlikely to occur by chance, but also that it is not impossible. The overall density of the regions in and around PC217.96+32.3 is remarkably high. Apart from the two overdensities we discuss here, two other LAE overdensities lie within $\sim 10$~Mpc (physical) north of of PC217.96+32.3 \citep{lee14}, one of which is spectroscopically confirmed and has the estimated descendant mass of $\approx 6\times10^{14}M_\odot$ \citep{dey16}. Given the distances between these system, it is unlikely they will coalesce into a single structure within the Hubble time, but rather, will evolve separately and form structures similar to local superclusters \citep[e.g.,][]{einastoetal97,einasto14}. | 18 | 8 | 1808.07065 |
1808 | 1808.00968_arXiv.txt | Recent work indicates that the nearby Galactic halo is dominated by the debris from a major accretion event. We confirm that result from an analysis of APOGEE-DR14 element abundances and \textit{Gaia}-DR2 kinematics of halo stars. We show that $\sim$~2/3 of nearby halo stars have high orbital eccentricities ($e \gtrsim 0.8$), and abundance patterns typical of massive Milky Way dwarf galaxy satellites today, characterised by relatively low [Fe/H], [Mg/Fe], [Al/Fe], and [Ni/Fe]. The trend followed by high $e$ stars in the [Mg/Fe]-[Fe/H] plane shows a change of slope at [Fe/H]$\sim-1.3$, which is also typical of stellar populations from relatively massive dwarf galaxies. Low~$e$ stars exhibit no such change of slope within the observed [Fe/H] range and show slightly higher abundances of Mg, Al and Ni. Unlike their low~$e$ counterparts, high~$e$ stars show slightly retrograde motion, make higher vertical excursions and reach larger apocentre radii. By comparing the position in \mgfe{}-\feh{} space of high~$e$ stars with those of accreted galaxies from the EAGLE suite of cosmological simulations we constrain the mass of the accreted satellite to be in the range $10^{8.5}\lesssim M_*\lesssim 10^{9}\mathrm{M_\odot}$. We show that the median orbital eccentricities of debris are largely unchanged since merger time, implying that this accretion event likely happened at $z\lesssim1.5$. The exact nature of the low $e$ population is unclear, but we hypothesise that it is a combination of {\it in situ} star formation, high $|z|$ disc stars, lower mass accretion events, and contamination by the low $e$ tail of the high $e$ population. Finally, our results imply that the accretion history of the Milky Way was quite unusual. | \label{intro} It is now well established that accretion of lower mass systems is a fundamental component of the evolution and mass build up of galaxies \citep{1991ApJ...379...52W}. Due to its very long dynamical timescale, the stellar halo of the Milky Way keeps a record of the Galaxy's past accretion activity. That record can be accessed through the collection of precision 6D phase space and multi-element abundance information for very large samples of halo stars, which together enable fundamental tests of galaxy formation models. While this field has a long history \citep[e.g.,][]{1962ApJ...136..748E,1978ApJ...225..357S}, we highlight only a few of the main contributions from the past decade, for brevity. \citet{2010A&A...511L..10N} and \citet{2012A&A...538A..21S} were the first to identify the presence of an older, high~$\alpha$ and a younger, low~$\alpha$ halo population at metallicity lower than that of the Galactic disc in the solar neighbourhood. The kinematics of those stellar populations suggested an {\it in situ} \footnote{ By stars formed {\it in situ} we mean those that were formed within the Galaxy, either from gas originally associated with its dark matter halo or that which was accreted onto it.} or accreted origin, respectively. More recently, \citet{2015MNRAS.453..758H} proposed abundance ratio diagnostics to distinguish accreted from {\it in situ} halo stars, arguing that the accreted population dominates the nearby halo. Using APOGEE data, \citet{2018ApJ...852...50F} and \citet{2018ApJ...852...49H} studied the chemical compositions and kinematics of the metal-rich nearby halo, suggesting that much of the low \mgfe{} halo population is associated with the debris of accreted satellites, likely with a similar star formation history to the Large Magellanic Cloud (LMC). Studies of the Galactic halo are being revolutionised by the advent of large astrometric, photometric, and spectroscopic surveys of the stellar populations of the Galaxy. The \emph{Gaia} astrometric satellite has opened new avenues for exploration of substructure in phase space, with the potential for new discoveries further amplified by the addition of chemical information from spectroscopic surveys. Indeed, combining \emph{Gaia} parallaxes and proper motions \citep{2016arXiv160904303L,2018arXiv180409365G} with spectroscopic data from SDSS \citep{2000AJ....120.1579Y} and APOGEE \citep{2015arXiv150905420M}, two groups have identified what seems to be the accretion of a relatively massive stellar system that dominates the stellar populations of the nearby halo. Analysing a sample of SDSS-\emph{Gaia} DR1 main sequence stars, \citet{2018MNRAS.478..611B} showed that the velocity ellipsoid of halo stars becomes strongly anisotropic for stars with [Fe/H]$>$--1.7. Comparing their data to a suite of N-body only cosmological numerical simulations, they concluded that such orbital configurations are likely to result from the accretion of a massive satellite at about the time of the formation of the Galactic disc, roughly between $z=1$ and 3. Based on \emph{Gaia} DR2 data \citep{2018arXiv180409365G}, \citet{2018arXiv180500453M} determined the configuration of MW globular clusters (GCs) in action space. They find that 12 GCs in the halo are consistent with an origin in a single massive accretion event, consistent with the conclusions reached by \citet{2018MNRAS.478..611B}. \citet{2018arXiv180500453M} find that these clusters have highly eccentric orbits, at $e \gtrsim 0.85$, and suggest that the fact that all the clusters occupy a similar region in action space supports the idea that this highly anisotropic stellar population in the halo is mainly formed from the debris of a single accretion event. In a follow up study, \citet{2018arXiv180510288D} estimated the orbital parameters for a sample of nearby main-sequence and distant horizontal-branch stars by combining \emph{Gaia} DR2 data with spectroscopic outputs from SDSS-DR9 \citep{2012ApJS..203...21A}. They found that the apocentre radii of a significant population of stars in the halo appear to ``pile up'' at an $r_\mathrm{ap} \sim 20$ kpc. The authors link this population with that found by \citet{2018MNRAS.478..611B}. This result has special significance in light of the analysis of numerical simulations by \citet{2013ApJ...763..113D}, who proposed that the existence of a ``break radius'' in the Milky Way halo, beyond which the stellar density drops precipitously, is associated with the ``pile up'' of stellar apocenters at a comparable Galactocentric distance. \citet{2013ApJ...763..113D} argue that the observed existence of a break radius in the Milky Way halo and the absence of such a break in the Andromeda galaxy (M31) suggests that the latter had a much more prolonged accretion history than the former. Follow up work using the same sample suggests that, inside this break radius, roughly 50\% of the halo is made up of stars from this accretion event \citep{2018arXiv180704290L}. An independent analysis of \emph{Gaia} DR2 data conducted by \citet{2018ApJ...860L..11K} identified the presence of a large, old, and metal-poor slightly counter-rotating structure in phase space. They concluded that this population is associated with a relatively massive object which, they hypothesised, may have been responsible for the heating of the thick disc. Following up on that result, \citet{2018arXiv180606038H} used kinematic, chemical, and age information for a large sample of stars in \emph{Gaia} and APOGEE to identify a population of metal-poor stars with the same phase space characteristics as those reported by \citet{2018ApJ...860L..11K}. The distribution of this stellar population in the \afe{}-\feh{} plane, with relatively low \afe{} and a large spread in \feh{}, suggests the chemical evolution trend of a relatively massive system\footnote{The recent paper by \citet{2018arXiv180707269F} hints at a similar conclusion, also on the basis of APOGEE data.}. Moreover, the positions of the stars in the HR diagram are consistent with old ages (10-13 Gyr). According to \citet{2018arXiv180606038H}, the accretion of a dwarf galaxy with a mass similar to that of the Small Magellanic Cloud \citep[see also][]{2018ApJ...852...49H} $\sim 10$ Gyr ago may have been responsible for the heating of the thick disc. The notion that the thick disc was formed from the vertical heating of a thinner progenitor disc competes with the so-called ``upside-down'' formation scenario \citep[see, e.g,][]{2013ApJ...773...43B,2017arXiv170901040N} according to which the early gaseous disc was thick as a result of strong stellar feedback \citep[and/or clumpy gas accretion, e.g.,][]{2004ApJ...612..894B}, and slowly settled as the star formation waned to form the thinner components of the disc. Despite their differences, both scenarios are consistent with at least some heating of the stellar disc by satellite mergers, which in turn are also likely necessary to explain the flaring of high \afe{} mono-age disc populations \citep[e.g.][]{2015ApJ...804L...9M,2017arXiv170600018M}. In general, recent observational results do not seem to point towards a scenario where the thick disc formed thin and was heated entirely by mergers, which would produce a plateau in the age or $\alpha$~abundance against scale height relationship that is not currently borne out by the data \citep[e.g.][]{2012ApJ...751..131B,2012ApJ...753..148B,2012ApJ...755..115B,2016ApJ...823...30B,2016MNRAS.455..987C,2017arXiv170600018M} It is also important to note that the same population was identified by \citet{2018ApJ...863..113H}, who studied Gaia DR2 and APOGEE-based colour-magnitude diagrams, kinematics, and chemistry to identify a population of metal-poor stars with high transversal velocities and typically low or retrogade rotation, which they associate with the last significant merger undergone by the Milky Way. In addition to, and in support of these findings, \citet{2018MNRAS.tmp.1537K} recently inferred that the Milky Way has had a rather atypical assembly history given its mass, based on analysis of the age-metallicity relation of Galactic GCs. They found that the assembly rate of the Milky Way was among the uppermost quartile of galaxies in their simulation, and identified three recent massive accretion events. Those authors proposed that two of these accretion events correspond to the Sagittarius dwarf and Canis Major\footnote{It was acknowledged by \citet{2018MNRAS.tmp.1537K} that `Canis Major' as it is known to the community is no longer considered as a genuine accreted stellar population. The term is used there historically, as many of the GCs were those originally associated with `Canis Major' and so, for clarity, we adopt it here when discussing those results.}. The most massive of those accretion events is suggested to have no known debris, and have a stellar mass $> 10^9 \mathrm{M_\odot}$, and correspond to GCs that reside close to the Galactic center. It indeed may be possible, on the basis of the analysis of the Galactic GC population by \citet{2018MNRAS.tmp.1537K}, that the accreted satellite identified by \citet{2018MNRAS.478..611B} and \citet{2018ApJ...860L..11K} is associated with Canis Major, given that the GCs identified by \citet{2018arXiv180500453M} are further out in the halo, and those potentially associated with Canis Major are located at Galactocentric distances $> 10$ kpc. The finding that the assembly history of the Milky Way is atypical is also consistent with the work of \citet{2018MNRAS.477.5072M}, who found that Milky Way stellar mass galaxies in the EAGLE simulation with \afe{} abundance patterns similar to the Milky Way had atypical accretion histories, characterised by early, rapid accretion, which slowed at late times. In summary, the local stellar halo has been shown to be dominated by a population of moderately metal-poor, low~\afe{}, old stars on highly eccentric orbits. This population is the likely remnant of a major accretion event that took place at about the same time that the Galactic disc was itself forming. These results have important implications, which prompted us to examine the chemical and kinematic properties of the newly discovered stellar population in detail. In this paper we present an analysis of the abundance pattern of stars in common between the \emph{Gaia}-DR2 and APOGEE-DR14 catalogs, and discuss the implications of their kinematic properties in light of the EAGLE suite of numerical cosmological simulations. We extend the studies of the element abundances in these populations to include odd-$Z$ and Iron peak elements, and examine the detailed kinematics of stars in sub-populations defined by abundances and orbit eccentricity. We also extend previous theoretical work on this population by examining the kinematics of accreted debris from a fully self-consistent cosmological simulation that provides a cosmologicallly motivated sample of accreted satellite debris onto Milky Way mass haloes. In Section \ref{data} we describe our sample selection and orbital parameter determination, as well as the details of the EAGLE simulations. In Section \ref{highe} we discuss the chemical and kinematic properties of this population. In Section \ref{eagle} we contrast the kinematic properties of the newly discovered stellar population with the expectations from cosmological numerical simulations. Our conclusions are summarised in Section \ref{finale}. | \label{finale} This paper presents an analysis of chemical compositions and orbital information of halo stellar populations, based on APOGEE and Gaia data. We applied k-means clustering to identify subgroups in chemical composition and kinematics space, considering the abundances of $\alpha$, odd-Z and Fe peak elements, and orbital eccentricity. We have shown that $\sim~2/3$ of the accreted halo stars exhibit very high orbital eccentricity and display chemical compositions that are characteristic of those seen in massive dwarf galaxy satellites of the Milky Way today, suggesting that this population is likely the progeny of a single, massive accretion event which occurred early in the history of the Milky Way Galaxy, as suggested by other groups \citep[e.g.][]{2018MNRAS.475.1537M,2018arXiv180510288D,2018arXiv180606038H,2018MNRAS.478..611B}. The remaining 1/3 of the sample consists of stars with low orbital eccentricities and slightly higher abundance ratios than the high~$e$ population. The latter stars likely result from a mixture of different origins, including the remnants of less massive accretion events, {\it in situ} star formation, disc heating, and likely some contamination from the high $e$ population. We further examine this scenario by studying a numerical simulation from the EAGLE suite. We demonstrate that satellite galaxies accreted into MW mass haloes show clear trends between the time of accretion and the median eccentricity of the accreted stars at $z=0$. According to the simulation, only satellites accreted at $z\simless 1.5$ result in median debris as high as those of the high~$e$ population identified in our data ($>0.8$). This constraint also means that such satellites are likely to be accreted at relatively high stellar mass ($M_*\gtrsim 10^{8} \mathrm{M_{\odot}}$). A stricter constraint is obtained by comparing the median position of high~$e$ stars with those of EAGLE accreted systems on the Mg-Fe plane, whereby we infer a mass in the range $10^{8.5}-10^9~M_\odot$. We also showed that, according to the simulation, the median eccentricity of accreted debris generally does not appear to evolve significantly over time, further suggesting that a high orbital eccentricity is a good indicator of a relatively recent merger. Analysis of the numerical simulation further suggests that a massive accretion event such as that identified in the APOGEE/Gaia data is not very common for a Milky Way-like galaxy, indicating an unusual accretion history in same vein as suggested in our previous work \citep{2018MNRAS.477.5072M}. The high~$e$ population identified in the combined APOGEE/Gaia DR2 sample appears to be the same population as those discovered by \citet{2018MNRAS.478..611B}, \citet{2018arXiv180510288D}, \citet{2018arXiv180606038H}, and \citet{2018ApJ...863..113H}. We have shown that the kinematics of the high~$e$ group is consistent with that found in these studies, having very low, slightly negative mean $L_z$ consistent with the \citet{2018arXiv180606038H} population, and $r_\mathrm{ap}$ as high as 40 kpc, with a median of 15.1 kpc, and a suggestive secondary peak at $r_\mathrm{ap} > 20$, in rough consistency with the \citet{2018arXiv180510288D} population. Our high~$e$ population has a median eccentricity in good agreement with those of the populations discussed by \citet{2018MNRAS.478..611B} and the clusters measured by \citet{2018arXiv180500453M}. Using cosmological zoom-in simulations, \citet{2018MNRAS.478..611B} found that the growing discs of central galaxies act to radialise the orbits or accreted satellite debris as they accrete. This result is in seeming contradiction with our findings that debris eccentricity is relatively unchanged after satellite accretion (Figure~\ref{fig:echange}). However the $e_{z_\mathrm{merge}}$ we measure in the simulation is that of the debris once the satellite is fully unbound and merged to the central galaxy, and therefore likely already having undergone any radialisation from its initial orbit before accretion. Our result simply shows that the orbits do not evolve greatly following accretion onto the galaxy, and is therefore not in direct contradiction with the work of \citet{2018MNRAS.478..611B} \citep[or][who showed a similar effect in an earlier study]{2017MNRAS.464.2882A}. However, the finding that the galaxies in EAGLE which do not have a significant disc components at $z=0$ appear to follow the same trends in $e(z=0)$-$z_\mathrm{merge}$ space (Figure \ref{fig:eagle}) suggests that disc growth may not be the fundamental factor in driving these trends. \citet{2018MNRAS.tmp.1537K} suggest that the age-metallicity distribution of the Galactic globular cluster population can be used to infer the formation and assembly history of the Milky Way. They identify one very massive ($M_* > 10^9\mathrm{M_\odot}$) accretion event (\emph{Kraken}), which is associated with the overabundance of metal-rich GCs in the accreted cluster branch of the age-metallicity relation and has no known debris. They argue that the \emph{Kraken} is associated with GCs that reside within 5 kpc of the Galactic center. \citet{2018MNRAS.tmp.1537K} further point out that the GCs identified by \citet{2018arXiv180500453M} (many of which are located at $r_{GC}> 10$ kpc) closely match the sample they ascribe to the \emph{Canis Major} accretion event. That would suggest that the stellar population reported in this paper would by association also be a part of their proposed \emph{Canis Major} accretion event \citep[as would also be the case of the system identified by, e.g.,][]{2018MNRAS.478..611B,2018ApJ...852...49H,2018arXiv180606038H, 2010A&A...511L..10N}. In addition to these results based on simulations, it is worth pointing out that \citet{2013MNRAS.436..122L} associated metal poor GCs in the Milky Way with an accretion event with mass between $10^8 < M_* < 10^9\ \mathrm{M_\odot}$ (consistent with our estimation for the high $e$ population progenitor), showing that these clusters were on very low angular momentum orbits. In summary, all of these results point towards confirmation that the assembly history of the Milky Way has been very active, and quite atypical compared to other galaxies of similar mass. As mentioned previously, the notion of a massive accretion event onto the Galaxy is not an entirely new one. The earlier work of \citet{2010A&A...511L..10N} and \citet{2012A&A...538A..21S} demonstrated that the halo divides into groups in its $\alpha$-element abundances, with the kinematics of the lower \afe{} group resembling that of an accreted population. Even earlier work by \citet{2003ApJ...585L.125B} showed that a low angular momentum stellar population (resembling the one described in this paper) is present in the data used by \citet{2000AJ....119.2843C}, and possibly also in those upon which \citet{1962ApJ...136..748E} based their scenario for the formation of the halo. \citet{2003ApJ...585L.125B} suggested that this population may indeed be the debris of an accreted dwarf galaxy. Finally, \citet{2018arXiv180606038H} suggest that the merger event reported in this paper and by other groups has occurred approximately 10~Gyr ago and was responsible for the dynamical heating responsible for the formation of the thick disc. The results from analysis of EAGLE suggest that if the debris at $e \sim 0.85$ was accreted in a single satellite, then this is likely to have occurred around 8-9 Gyr ago (Figure~\ref{fig:eagle}). The \citet{2018arXiv180606038H} merger time is based on the minimum isochronal age of the stars in their sample so it is possibly indicative of the final time of star formation rather than the actual accretion time. On the other hand, EAGLE gives the time at which the satellite became bound to the central halo, so these timescales are potentially consistent. Ages of stars in the Milky Way high \afe{} disc population are generally found to be older than or similar to $\sim 10$ Gyr \citep[e.g.][]{2013A&A...560A.109H,2016MNRAS.456.3655M,2017arXiv170600018M}, so this does suggest that this population was in place before the merger occurred. It is worth mentioning, however, that analysis of the origin of $\alpha$-enhanced populations in EAGLE suggest that these stars must form in an early collapse in a period of rapid gas accretion, in order to foster the high density ISM necessary to generate a short enough gas consumption time to consume the high \afe{} gas into stars before it is polluted by SN Ia \citep{2018MNRAS.477.5072M}, rather than forming in an initially thin disc that was later heated. This scenario is consistent with the thick disc being the result of the geometric combination of the thick, centrally concentrated high \afe{} disc and the extended, flared low \afe{} disc \citep[e.g][]{2017arXiv170600018M,2016arXiv160901168M,2015ApJ...804L...9M}. Further work on this newly found halo component, and the high \afe{} disc, will surely shed more light on this discussion. | 18 | 8 | 1808.00968 |
1808 | 1808.02476_arXiv.txt | \label{abstract} We have reinvestigated the \As$(v=0)$ level of \CO\ using new high-resolution spectra obtained via multi-photon laser excitation as well as with synchrotron-based Fourier-transform absorption spectroscopy of the \AX$(0, 0)$, \eX$(1, 0)$, \dX$(4, 0)$, \apX$(9, 0)$, and \atX$(11, 0)$ bands. In addition, Fourier-transform emission spectroscopy in the visible range is performed on the \BA$(0, 0)$ band. Spectra of the \BX$(0, 0)$ band are measured in order to tie information from the latter emission data to the level structure of \As$(v=0)$. The high pressures in the absorption cell at the synchrotron and the high temperatures in the emission discharge permitted monitoring of high rotational quantum levels in \As$(v=0)$ up to $J=43$. All information, in total over 900 spectral lines, was included in an effective-Hamiltonian analysis of the A$^1\Pi(v=0, J)$ levels that are directly perturbed by the \es$(v=1)$, \ds$(v=4)$, \aps$(v=9)$, \Ds$(v=0)$, \Is$(v=0, 1)$ close-lying levels and the \es$(v=0,2)$, \ds$(v=3,5)$, \aps$(v=8,10)$ remote levels, as well being indirectly influenced by the \ats$(v=10, 11)$ state. The influence of nine further perturber levels and their interactions was investigated and are not significant for reproducing the present experimental data. This analysis leads to a much improved description in terms of molecular constants and interaction parameters, compared to previous studies of the same energy region for other CO isotopologues. | \label{sec:Intro} The spectroscopy of the carbon monoxide molecule is of major importance in view of its being the second most abundant molecule in the Universe. Its dipole moment is a decisive ingredient in the cooling process of interstellar clouds \emph{en route} to star formation. The probing of CO under a variety of conditions is crucial to an understanding of the physics and chemistry of the interstellar medium \cite{Sheffer2007}, of protoplanetary disks \cite{Perez2015}, of exoplanetary atmospheres \cite{Heng2016}, of galactic structure at large redshifts \cite{Noterdaeme2017}, and it may turn out to be a probe of temporal variation of fundamental constants \cite{Dapra2016,Dapra2017a}. In view of saturation and shielding effects of the strongest transitions, the use and investigation of lower-abundance isotope-substituted species is of relevance, in particular where photo-dissociation becomes strongly isotope dependent \cite{Eidelsberg1990,Eidelsberg1991}, in some cases connected to subtle effects of perturbations \cite{Cacciani1998,Ubachs2000}. The CO molecule is a prototypical system for investigating perturbations in the spectra of diatomic molecules, as is known since the studies by Field on the \As{} state \cite{Field1972,Field1972a}. In recent years our team has been involved in detailed re-investigations of perturbations in the \As{} state of CO, exploiting a combination of various precision spectroscopic techniques, where the lowest $v=0$ vibrational level was chosen as a main target. One of the aims of pursuing a precision study of the \As{} state was the derivation of sensitivity coefficients for probing a possible variation of fundamental constants based on the \AX\ system of CO \cite{Salumbides2012}. Thereafter, precision studies of the \AX$(0, 0)$ bands and the perturbing states were performed for $^{12}$C$^{16}$O \cite{Niu2013}, for $^{13}$C$^{16}$O \cite{Niu2016b}, for $^{13}$C$^{17}$O \cite{Hakalla2017}, and for $^{12}$C$^{18}$O \cite{Trivikram2017}. Here we extend these studies on the \CO{} isotopologue using laser-based excitation and VUV-Fourier-transform (FT-VUV) absorption spectroscopy as well as visible Fourier-transform (FT-VIS) emission spectroscopy to observe and assign the perturbations in the \As($v=0$) state. In the other isotopologues, perturbing effects of the \aps($v=9$), \ds($v=4$), \es($v=1$), \Is($v=0, 1$), and \Ds($v=0$) levels were found and these will also be investigated here. Also, perturbations by levels of the \ats{} state will be addressed. Therefore, in addition to low-pressure FT-VUV studies performed, focusing on the \AX\ excitation, high \CO{} pressures were used to observe the weak absorption of the \atX, \dX, \apX, and \eX systems. These measurements provide additional and accurate information about the perturbing effects on the \As{} state. In particular, the intensity borrowing effects between the singlet and triplet systems tightly constrain the values of the perturbation parameters. Although the \AX{} system of CO has been investigated in many studies over the decades, the information on the \CO{} isotopologue is scarce. Haridass and coworkers have performed detailed studies of \As($v=0$) by VUV emission, revealing perturbation effects from the \aps($v=10$) and \ds($v=5$) levels \cite{Haridass1994b,Haridass1994c}. Emission studies of the \AA ngstr\"{o}m (\BA) bands of \CO~\cite{Prasad1984,Malak1984} provided further information on the \As($v=0$) level, and the study of the Herzberg (\CA) systems \cite{Kepa1988,Kepa2014} also provided detailed information on the interaction with the \es($v=1$) level. The \AX\ system was reinvestigated recently with the FT-VUV spectrometer at the SOLEIL synchrotron \cite{Lemaire2016}, focusing on the determination of term values and line strength parameters. In that study, the existence of two additional dipole-allowed singlet systems, denoted as \OSX{} and \OPX, was hypothesised. Information on the perturbing triplet states in \CO{} has not yet been reported, except for the study of the \ats($v=0$) state \cite{Denijs2011}. The present study entails a high-precision re-analysis of the level structure of the \As($v=0$) state of \CO, following the rotational manifold up to the rotational quantum number $J=43$. This results in a much improved description in terms of molecular constants and interaction parameters, and a comparison is made with previous studies. | \label{sec:Concl} The present study focuses on a comprehensive analysis of spectroscopic data for the \As($v=0$) state of the \CO\ isotopologue of the carbon monoxide molecule. It is a member of a sequence of studies analysing \As($v=0$) for the isotopologues $^{12}$C$^{16}$O \cite{Niu2013}, $^{13}$C$^{16}$O \cite{Niu2016b}, $^{12}$C$^{18}$O \cite{Trivikram2017}, and $^{13}$C$^{17}$O \cite{Hakalla2017}. The complementary properties of various state-of-the-art spectroscopic instruments were exploited for gathering a wealth of accurate information from spectral lines connecting a variety of mutually interacting rovibronic states: the extreme absolute accuracy of a $2+1'$ resonance enhanced two-photon laser ionisation study employing Doppler-free excitation in a molecular beam, the photo-emission spectrum from a discharge resolved by visible Fourier-transform spectroscopy, and VUV Fourier transform absorption spectroscopy at the SOLEIL synchrotron. All studies were performed at high resolution and special techniques were employed to access high rotational states: notably high temperature and high pressure. The accuracies of measured transition frequencies for the best lines were respectively $0.002$ \wn, $0.003$ \wn, and $0.02$ \wn\ in the laser-based, visible FT and synchrotron studies. The level structure of the \As($v=0$) state of \CO {} was targeted via the \AX$(0, 0)$ and \BA$(0, 0)$ bands, while information was also gathered on the direct and indirect perturber states \es$(v=0,1,2)$, \ds$(v=3,4,5)$, \aps$(v=8,9,10)$, \Ds($v=0$), \Is($v=0,1$), and \ats$(v=10,11)$. The \BX$(0, 0)$ band was investigated by FT-VUV spectroscopy to connect the visible emission study on an absolute energy scale with respect to the ground state. Weak perturbations in the \Bs(\0) level were observed and included in the analysis. A comprehensive set of deperturbed constants and level energies for the A($v=0$) state and its perturbers is determined from this set of combined data. The complexity of the present deperturbation analysis exceeds that of the previous studies on other isotopologues and is made possible here by a more extensive highly-accurate data set. The number of modelled perturber states is extended and we determine molecular constants for some triplet levels that do not exhibit a crossing with \As($v=0$). In general, up to 87 vibronic interactions are considered between A($v=0$), A($v=1$), I($v=0,1,2$) and D($v=0,1,2$) singlet states and a large set of the a($v=10,11,12$), d($v=3,4,5$), a$'$($v=8,9,10$), and e($v=0,1,2,3$) triplet levels. Some mutual interactions of various triplet states perturbing the A($v=0$) level are determined in the analysis which had not been distinguishable in our previous studies focusing on other isotopologues. Although eight lines of the vast body of observed transitions could not be identified, there is no need to invoke additional band systems beyond those well-known to CO to describe the observed spectroscopic patterns, as was done in Ref.~\cite{Lemaire2016}. The present study surpasses in complexity any previous similar analyses of the CO molecule, which is a prototypical species for perturbations. There are 15 mutually interacting electronic-vibrational levels included to reproduce over 900 line frequencies to a high level of accuracy. The deperturbation model also reproduces the borrowing of absorption oscillator strength by the observed forbidden bands from the main transition \AX$(0,0)$. | 18 | 8 | 1808.02476 |
1808 | 1808.10325_arXiv.txt | s{Jupiter is one of the major targets for planetary exploration, and dust in the Jovian system is of great interest to researchers in the field of planetary science. In this paper, we review the five dust populations outside the ring system: grains in the region of the Galilean moons, potential dust from plumes on Europa, Jovian stream particles, particles in the outer region of the Jovian system ejected from the irregular satellites, and dust in the region of the Trojan asteroids. The physical environment for the dust dynamics is described, including the gravity, the magnetic field and the plasma environment. For each population, the dust sources are described, and the relevant perturbation forces are discussed. Observations and results from modeling are reviewed, and the distributions of the individual dust populations are shown. The understanding of the Jovian dust environment allows to assess the dust hazard to spacecraft, and to characterize the material exchange between the Jovian moons, their surface properties and distribution of non-icy constituents.} | \noindent \textbf{Interplanetary and circumplanetary} dust particles have typical sizes ranging from nanometers up to millimeters. Dust is widely distributed in the Jovian system, \textbf{where particles were first detected by the Pioneer spacecraft in the early 1970s \cite{humes1974interplanetary,humes1975pioneer}, and the dusty ring system was first observed by the cameras onboard the Voyager spacecraft in 1979 \cite{smith1979jupiter, owen1979jupiter}. Subsequently, dust particles in the Jovian system were detected in-situ by space missions, and dust rings were observed by ground- and space-based telescopes as well as cameras onboard spacecraft.} So far, eight spacecraft have made measurements/observations of dust particles/rings in the Jupiter system, including Pioneer 10 and 11 \cite{humes1974interplanetary,humes1975pioneer,zeehandelaar2007local}, Voyager 1 and 2 \cite{smith1979jupiter, owen1979jupiter, 1985Natur.316..526S,1987Icar...69..458S, throop2004jovian, showalter2008properties}, Galileo \cite{ockert1999structure, burns1999formation, 2000Icar..146....1M, 2004Icar..170...35B, throop2004jovian, showalter2008properties, 1998P&SS...47...85K, 2001P&SS...49.1285K,kruger2003impact, Kruger:2006jeb, 2009Icar..203..198K, 2010P&SS...58..965K, grun1996constraints, Thiessenhusen:2000iq,krivov2002tenuous,krivov2002dust}, Cassini \cite{throop2004jovian, 2003Sci...299.1541P,2003Icar..164..461B}, New Horizons \cite{Showalter:2007km, 2010GeoRL..3711101P}, and Ulysses \cite{grun1992ulysses,1993Natur.362..428G,2006P&SS...54..919K}. Besides, the Hubble Space Telescope \cite{1999Icar..141..253M,showalter2008properties} and the ground-based Keck telescope \cite{de1999keck,showalter2008properties, de2008keck} were used to observe the Jovian ring system. Dust particles in the Jovian system \textbf{(including the Sun-Jupiter system)} are roughly divided into the following six different populations: (1) particles in the Jovian ring system including the main ring, the halo ring and two gossamer rings \cite{smith1979jupiter, owen1979jupiter, burns1999formation}, (2) \textbf{grains in the region of the Galilean moons \cite{krivov2002tenuous,Thiessenhusen:2000iq}, which derive from impact-generated dust clouds around the Galilean moons \cite{kruger1999detection,kruger2003impact} as well as magnetospherically captured interplanetary and interstellar particles \cite{colwell1998capture, colwell1998jupiter,Thiessenhusen:2000iq}}, (3) possible dust from plumes on Europa \cite{quick2013constraints, roth2014transient, roth2014orbital, southworth2015modeling, sparks2016probing}, (4) small and fast dust streams (nanometer-sized, $>200 \, \mathrm{km\,s^{-1}}$) from Io's volcanic plumes \cite{1993Natur.362..428G,grun1996constraints,2000Natur.405...48G}, (5) particles in the outer region from the Jovian irregular moons \cite{krivov2002dust}, \textbf{and (6) dust grains in the region of Jupiter's Trojan asteroids \cite{liu2018dust, zimmer2014orbital, de2010studying}. Previous studies on the first dust population, i.e.~the Jovian ring system are well covered by several reviews \cite{de2018rings,burns2004jupiter,miner2007planetary}, including a recent one published in 2018 \cite{de2018rings}, to which the reader is referred. Thus, in the current review paper we put more emphasis on the latter five populations} (see Figure \ref{fig:galilean_outer_region_sketch} for the locations of the four Galilean moons and the outer region of the Jovian system, and Figure \ref{fig:trojan_sketch} for the locations of the Trojan asteroids associated with the Lagrange points in the Sun-Jupiter system). \textbf{The reader is also referred to an earlier review from 2004 \cite{kruger2004jovian}, by which the dust populations (2), (4) and (5) were well covered.} \begin{figure} \centering \includegraphics[width=16cm,angle=0]{galilean_outer_region_sketch.pdf} \caption{Top view showing the orbits of the four Galilean moons and the outer region. Jupiter lies \textbf{at} the origin. The orbits of Io (5.9 $R_\mathrm{J}$), Europa (9.4 $R_\mathrm{J}$), Ganymede (15.0 $R_\mathrm{J}$) and Callisto (26.3 $R_\mathrm{J}$) are denoted as I, E, G, and C, respectively. The outer region of the Jovian system extends over a range of [50, 300] $R_\mathrm{J}$.} \label{fig:galilean_outer_region_sketch} \end{figure} \begin{figure} \centering \includegraphics[width=16cm,angle=0]{trojan_sketch.pdf} \caption{Locations of the Jovian Trojan asteroids. The Sun lies at the origin. Jupiter is about 5.2 AU from the Sun. The Lagrange points in the Sun-Jupiter system are indicated as red asterisks, including three collinear Lagrange points ($L_1$, $L_2$, $L_3$) and two triangular Lagrange points ($L_4$, $L_5$). The $L_4$ and $L_5$ Trojan asteroids librate around the triangular Lagrange points $L_4$ and $L_5$, respectively.} \label{fig:trojan_sketch} \end{figure} In the near future, there are two reconnaissance missions that will visit the Jovian system. One is the JUpiter ICy moons Explorer mission \cite{plaut2014jupiter} developed by European Space Agency (ESA), which is scheduled for launch in 2022. The Europa Clipper mission \cite{phillips2014europa}, developed by National Aeronautics and Space Administration (NASA), is planned to launch between 2022-2025. The SUrface Dust Analyzer, a dedicated dust mass spectrometer instrument, is onboard Europa Clipper. This dust detector will measure the composition of the dust particles lofted from the Galilean moons. The Lucy mission developed also by NASA will visit Jupiter's $L_4$ and $L_5$ Trojan asteroids \cite{levison2017lucy}, which is scheduled for launch in 2021. | \noindent In the 2020s, there are two Jupiter missions and one Trojan mission scheduled for launch: ESA's JUpiter ICy moons Explorer mission, as well as NASA's Europa Clipper mission and Lucy mission to the Trojan asteroids. Especially onboard Europa Clipper, there is a dust instrument, the SUrface Dust Analyzer. An understanding of the Jovian dust environment will be important for the implementation of these missions, and in turn they will inform the preliminary modeling effects. In this review paper, we \textbf{have summarized} the results from previous observations and modeling work for Jovian dust outside the ring system including: particles in the region of the Galilean moons, Europa's dust plume, Jovian stream particles, grains in the outer region of the Jovian system, and dust in the region of the Jupiter Trojans. All relevant perturbation forces, the orbital evolution, and the spatial distributions of dust \textbf{were discussed}. \subsection*{Acknowledgements} \noindent This work was supported by the European Space Agency under the project ``Jovian Micrometeoroid Environment Model" (JMEM) (contract number: 4000107249/12/NL/AF) at the University of Oulu, and by the Academy of Finland under the project ``Earth and Near-Space System and Environmental Change".\\ | 18 | 8 | 1808.10325 |
1808 | 1808.09622_arXiv.txt | Starting from hydrodynamic equations, we have established a set of hydrodynamic equations for average flow and a set of dynamic equations of auto- and cross-correlations of turbulent velocity and temperature fluctuations, following the classic Reynold's treatment of turbulence. The combination of the two sets of equations leads to a complete and self-consistent mathematical expressions ready for the calculations of stellar structure and oscillations. In this paper, non-locality and anisotropy of turbulent convection are concisely presented, together with defining and calibrating of the three convection parameters ($c_1$, $c_2$ and $c_3$) included in the algorithm. With the non-local theory of convection, the structure of the convective envelope and the major characteristics of non-adiabatic linear oscillations are demonstrated by numerical solutions. Great effort has been exercised to the choice of convection parameters and pulsation instabilities of the models, the results of which show that within large ranges of all three parameters ($c_1$, $c_2$ and $c_3$) the main properties of pulsation stability keep unchanged. | \label{sec1} Great advances in understanding the pulsation of variable stars have been achieved thanks to continuous work by generations of researchers for over 5 decades. Among others, we would like to name three classical books by Ledoux \& Walraven (1958), Cox (1980) and Unno et al. (1989) which reviewed and concluded exclusively the major research work done in that period of time. The theory of stellar pulsations reached a state of art stage that makes the field probably one of the bests in astrophysics. Nevertheless, some of the fundamental questions remain. Convection inside the pulsators is one of the most difficult and long-standing problems. Revolutionary observations from space by CoRoT and Kepler spaces missions, in terms of both accuracy (down to micro-magnitude) and uninterrupted time baseline (up to months), mark a new era in stellar variability studies. Thousands of small amplitude variables of many different types are discovered, which would be otherwise undetectable with ground based instruments. Such great discovery capability greatly enhanced observations of stellar variability from $\delta$ Scuti, $\gamma$ Doradus on the main sequence to pulsating red giants. Such observations provide not only opportunities but also challenges in this field, because convection replaces radiation becoming the major energy transport mechanism in stars with very extended convective envelope. As a result, dealing with the coupling between convection and oscillations is a key factor for understanding variables with low surface temperatures. However, the treatment of stellar convection, so called mixing-length theory (MLT), developed by B\"ohm-Vitense (1958) in the middle of last century is still the most popularly used in the calculations of stellar structure, evolution and oscillations. Modified versions such as time-dependent MLT (Unno 1967; Gough 1977; Stellingwerf 1982; Grigahc\`ene et al. 2005), and non-local MLT (Spiegel 1963; Ulrich 1970) had then been made in order to account for oscillations of variable stars. Needless to say that we are still far from fully understanding the nature and principal properties of stellar turbulence, therefore a robust theory of stellar convection is still missing in the community. This led to the fact that the results cannot converge for the same observational problems when different treatments of convection were used. The theory of convection is still the most uncertain factor that prevents us from clear understandings of oscillations in low-temperature stars. In this series of papers, we are going to apply the non-local and time-dependent theory of convection we developed to the calculations of stellar oscillations. In order to cope with the great advances in observations of small amplitude red variable stars resulted from recent missions, a systematic theoretical calculations of $\delta$ Scuti, $\gamma$ Doradus and pulsating red giants are carried out, in which convection is treated by our non-local and time-dependent theory of turbulent convection. The theory was started more than 30 years ago, and has been in continuous improvements since then. Our study shows that anisotropy of turbulent convection has important effects on stellar oscillations. In the case of non-radial oscillations, neglecting anisotropy means turbulent viscosity is disregarded at the same time. Therefore the red edge of the instability strip of $\delta$ Scuti and $\gamma$ Doradus stars cannot be determined correctly. In Section~\ref{sec2}, we give a new complete version of non-local and anisotropic time-dependent convection theory and a new uniform expression for turbulent dissipation and diffusion. In Section~\ref{sec3}, we will show the general properties of the structure of stellar non-local convective envelopes. The results of theoretical calculations of non-adiabatic linear oscillations of stars are presented in Section~\ref{sec4} along with the dependance of pulsation stability on the selection of convection parameters. Conclusions and discussions are given in the last section of this paper. | \label{sec5} In this paper, we present a dynamic theory for complete non-local and anisotropic stellar convection, and the computational results on the structure of stellar envelope structure and non-adiabatic oscillations based on such a theory. This work can be summarized in the following, \begin{enumerate} \item Starting from the first principle of hydrodynamic equations and applying Reynold's decomposition for turbulence, we established a set of dynamic equations for mean fluid, and that of auto- and cross-correlations of turbulent velocity and temperature fluctuations. Following the theory of turbulence, we have introduced a proper way to deal with dissipation, diffusion and anisotropy of turbulent convection. A self-consistent and closed formalism of turbulent convection is developed, which is ready for the calculations of stellar structure and oscillations. \item Three convection parameters ($c_1$, $c_2$, and $c_3$) are included in the theory, which are respectively connected to dissipation, diffusion and anisotropy of turbulent convection in stars. \item Discussions were made on the calculations of the equilibrium envelope model and the calibration of the convective parameters. Numerical experiments suggested that ($c_1$, $c_2$, $c_3$)=(0.64, 1/2, 3) is a robust choice, which has been justified by a number of relevant observational facts including: the predicted structure of solar convective envelope that agrees with solar seismic inversion, the structures of atmospheric turbulent velocity and temperature fields of the Sun that match solar observations, and the depletions of lithium in the Sun and solar-type stars. \item When the anisotropy of turbulent velocity and overshooting mixing in stars are not the major concerns, isotropic treatment of convection is a fairly good approximation that gives good enough $T-P$ structure of stars. Only two parameters $c_1$ and $c_2$ are required in the theory. Our results show that ($c_1$, $c_2$)=(0.70, 0.35) is a good set. The quasi-anisotropy approximation eq.~(\ref{eq47}) can deliver very good measurements of the anisotropic component $\chi^{11}$ for turbulent convection, therefore can be used for linear non-adiabatic oscillation analysis for the sake of computational effort. \item The theory can be used to study both radial and non-radial oscillations of stars, and it handle both thermodynamic and dynamic couplings between convection and oscillations. \item Using the scheme of non-adiabatic oscillations in the non-local and time-dependent convection theory, we have done linear stability analysis of low degree ($l=1-4$) g9--p29 modes for stars with $M=0.6-3.0M_\odot$ from MS to RGB, and up to AGB phase. Theoretical calculations clearly show two separate $\delta$ Scuti and Mira-like instability strips in the H-R diagram. For future work, we will carry out further theoretical analysis of $\delta$ Scuti and $\gamma$ Doradus stars and pulsating red giant stars, and compare the results with observations. \item The dependence of pulsation stability of stars on the convection parameters ($c_1$, $c_2$, $c_3$) was studied very carefully. The results show that, the stability of oscillations has only weak response to the choice of the 3 convection parameters within a rather wide range. \end{enumerate} | 18 | 8 | 1808.09622 |
1206 | 1206.5819_arXiv.txt | We report the results of an investigation of particle acceleration and electron-positron plasma generation at low altitude in the polar magnetic flux tubes of Rotation Powered Pulsars, when the stellar surface is free to emit whatever charges and currents are demanded by the force-free magnetosphere. We apply a new 1D hybrid plasma simulation code to the dynamical problem, using Particle-in-Cell methods for the dynamics of the charged particles, including a determination of the collective electrostatic fluctuations in the plasma, combined with a Monte-Carlo treatment of the high energy gamma rays that mediate the formation of the electron-positron pairs. We assume the electric current flowing through the pair creation zone is fixed by the much higher inductance magnetosphere, and adopt the results of force-free magnetosphere models to provide the currents which must be carried by the accelerator. The models are spatially 1D, designed to explore the physics, although of practical relevance to young, high voltage pulsars. We observe novel behavior. a) When the current density $j$ is less than the Goldreich-Julian value ($0 < j/\GJ{j} < 1$), space charge limited acceleration of the current carrying beam is mild, with the full Goldreich-Julian charge density being comprised of the charge density of the beam, co-existing with a cloud of electrically trapped particles with the same sign of charge as the beam. The voltage drops are on the order of $m c^2/e$, and pair creation is absent. b) When the current density exceeds the Goldreich-Julian value ($j/\GJ{j} > 1$), the system develops high voltage drops (TV or greater), causing emission of curvature gamma rays and intense bursts of pair creation. The bursts exhibit limit cycle behavior, with characteristic time scales somewhat longer than the relativistic fly-by time over distances comparable to the polar cap diameter (microseconds). c) In return current regions, where $j/\GJ{j} < 0$, the system develops similar bursts of pair creation. These discharges are similar to those encountered in previous calculations of pair creation when the surface has a high work function and cannot freely emit charge, \PapI. In cases b) and c), the intermittently generated pairs allow the system to simultaneously carry the magnetospherically prescribed currents and adjust the charge density and average electric field to force-free conditions. We also elucidate the conditions for pair creating beam flow to be steady (stationary with small fluctuations in the rotating frame), finding that such steady flows can occupy only a small fraction of the current density parameter space exhibited by the force-free magnetospheric model. The generic polar flow dynamics and pair creation is strongly time dependent. The model has an essential difference from almost all previous quantitative studies, in that we sought the accelerating voltage (with pair creation, when the voltage drops are sufficiently large; without, when they are small) as a function of the applied current. The 1D results described here characterize the dependence of acceleration and pair creation on the magnitude and sign of current. The dependence on the spatial distribution of the current is a multi-D problem, possibly exhibiting more chaotic behavior. We briefly outline possible relations of the electric field fluctuations observed in the polar flows (both with and without pair creation discharges) to direct emission of radio waves, as well as revive the possible relation of the observed limit cycle behavior to microstructure in the radio emission. Actually modeling these effects requires the multi-D treatment, to be reported in a later paper. | \label{sec:introduction} Young pulsar wind nebulae (PWNe) show that rotation powered pulsars (RPPs) have dense magnetospheres, at least with regard to those regions that feed the plasma outflow (e.g., \citealt{BucciantiniAronsAmato2011}). Electron-positron pair creation in the open field line region that connects to the external world is the only known candidate for the origin of such outflows, with acceleration and convertible gamma ray emission occurring either at low altitude \citep{Sturrock71} or in the outer magnetosphere \citep{Cheng1986}. High density flows that can feed all the open field lines can exist only in the low altitude polar cap region (for a general discussion, see \citealt{Arons2009}). Theoretical studies of charged particle flow from the magnetic polar regions of rotation powered pulsars began with the observation by \citet{GJ}, that an isolated magnetic rotator in vacuum must have a charged magnetosphere almost corotating with the star. Since RPPs are strongly gravitationally bound and cool objects (thermal scale height in any atmosphere orders of magnitude less than the stellar radius) and have no external source of plasma supply (so far as we know), the only plasma source is extraction of charged particles from the stellar surface, leading to a conjectured magnetosphere whose plasma is fully charge separated, in contrast to all other known astrophysical systems, whose plasmas are charged but quasi-neutral. \citet{GJ} speculated that on polar field lines -- those that extend beyond the light cylinder located at cylindrical radius $\RLC=cP/2\pi\simeq48,000\,P$ km, $P =$ rotation period in seconds -- a charge separated outflow would form. They argued that the energy/particle in the outflow would be no more than the gravitational escape energy $GM_*/R_* \sim 0.3 mc^2 (M_*/1.4 M_{\sun}) (10 \; \mathrm{km}/R_*)$, $M_*$ and $R_*$ are star's mass and radius correspondingly -- the particles leave at non-relativistic energies, in spite of the fact that the electric potential drop \emph{across} the polar field lines is equal to the full potential of an open rotating magnetosphere with a dipole magnetic field $\Vm=\sqrt{W_{\textrm{\tiny{}R}}/c} \approx10\,(\dot{P}/10^{-15})^{1/2}P^{-3/2}$~TV, $W_{\textrm{\tiny{}R}} = $ rotational energy loss rate, with $\dot{P} = dP/dt$ . $\Vm$ vastly exceeds the rest energy and gravitational energy of the particles, either electrons or protons (or He or other ions populating the star's crust and atmosphere). The super strong magnetic field suppresses free acceleration of the particles in the transverse electric field, whose primary (``zeroth order'') consequence is corotation of the field lines with the magnetic field embedded in the neutron star (NS), with field line motion measured by the $\vec{E}\times\vec{B}$ drift of charged particles across the magnetic field (which occurs even when the particles have zero Larmor gyration). The particle loss rate in the conjectured charge separated scenario is $\dot{N}_{\textrm{\tiny{}R}} = c\Vm/e \approx 2\times10^{30}\,(\dot{P}/10^{-15})^{1/2} P^{-3/2} \; {\rm s}^{-1}$, orders of magnitude less than that inferred from the injection of plasma into the young PWNe. The electrodynamics of the magnetosphere differs drastically, depending on whether the particle loss rate falls short of or exceeds $\dot{N}_{\textrm{\tiny{}R}}$. For the young PWNe, the particle injection rate exceeds $\dot{N}_{\textrm{\tiny{}R}}$ (by a lot). In that case, the magnetosphere's basic state should be one in which $\vec{E}\cdot\vec{B}$ = 0, with no parallel acceleration sufficient to generate convertible gamma rays occurring under the pulsar's rotational control. The discovery of gamma ray pulsars in the 1970s, and their proliferation into a population with more than 100 such stars in the most recent published Fermi pulsar catalog \citep{FermiPSRCatalogI::2010}, has shown that parallel acceleration to GeV gamma ray emitting energies (indeed, multi-hundred GeV, in the Crab pulsar, \citealt{veritas_crab2011}) must occur somewhere, with energy efficiency exceeding a few tenths of a percent, as measured by $L_\gamma/W_{\textrm{\tiny{}R}}$, $L_\gamma=$ gamma-ray luminosity. If the acceleration is limited by radiation reaction, as is true in many models, $L_\gamma$ is a good proxy for the energy put into parallel acceleration. $L_\gamma/W_{\textrm{\tiny{}R}}$ can approach as much as 50\% at smaller spin down luminosities. Just how some fraction of the total potential drop gets released in acceleration along $B$, gamma ray emission and pair creation has been mysterious since the beginning of pulsar research, made relevant to the real world by the gamma ray discoveries. Since the polar cap source is the only one capable of feeding the whole (open) magnetosphere, its understanding remains of central interest to modeling pulsar magnetospheres, even though the spectral and beaming characteristics of the pulsed gamma rays are better modeled by accelerators in the outer magnetosphere. Free particle outflow from the NS surface is a common assumption in most of the current pulsar models (see \S\ref{sec:current_density}). The polar cap accelerator problem has been studied under that assumption before \citep[\emph{e.g.}][]{Michel1974,FawleyAronsScharlemann1977,Mestel1985,shibata97,Beloborodov2008}. \citet{Michel1974} and \citet{FawleyAronsScharlemann1977} obtained solutions for the non-neutral space charge limited charged particle flow for the current density almost equal to the GJ current density. All these models assume strictly steady flow in the co-rotating frame, on \emph{all} time scales. In these models, the charge density of the current carrying beam supplies almost all of the charge density needed to short out the parallel component of the electric field, while leaving a residuum $E_\parallel$ sufficient to accelerate the beam -- relativistic energies in a temporally steady flow are found if the current density $j_\parallel=-(B/P)\cos\chi + \mathrm{small~corrections} \cong \GJ{j}$; $\chi=\angle(\vec{\mu},\vec{\Omega})$, the pulsar inclination angle. \citet{Mestel1985} showed that the velocity of the beam is monotonically increasing with altitude to relativistic speeds only if the current density is larger than $\GJ{j}$. If the current density is smaller that $\GJ{j}$ the temporally steady velocity of the beam (assumed to have no momentum dispersion) oscillates spatially, i.e. particles accelerate and decelerate to a complete halt as they move outwards into the magnetosphere. \citet{Beloborodov2008} rediscovered Mestel \textit{et al.}'s solution and suggested that in the region of the polar cap where $j_\parallel<\GJ{j}$ particles will be not accelerated up to high energies as the beam velocity oscillates, but along the magnetic field lines with $j_\parallel/\GJ{j}>0$ or $j_\parallel/\GJ{j}<0$ particle acceleration will be efficient and will lead to pair formation. The quantitative model which we describe in this paper lends some support to Beloborodov's speculations, although it does not agree with them in detail. In this paper we describe our study of the physics of the polar cap accelerator in the space charge limited flow regime starting from first principles -- assuming free particle outflow from the surface of a NS we compute the electric field, particle acceleration, gamma-ray emission, propagation and pair creation simultaneously. It extends the study of current flow and pair cascades in neutron star magnetospheres using the theoretical formulation and self-consistent numerical techniques introduced in \citet{Timokhin2010::TDC_MNRAS_I}. The plan of the paper is as follows. In \S\ref{sec:current_density}, we review the properties of the current flow imposed by the magnetosphere, in the force-free model, pointing out that the current density is the main parameter which regulates the efficiency of particle acceleration. In \S\ref{sec:stationary_sclf} we review the properties of stationary solutions for the charge separated space charge limited flow problem. In \S\ref{sec:num_setup} we briefly describe our numerical model. In \S\ref{sec:cold_flow} we describe the results of numerical modeling for the case of sub-GJ current density, the regime when particle acceleration is inefficient and no pair creation is possible. In \S\ref{sec:j_pairs} we consider flow regimes with efficient pair creation. In \S\ref{sec:stationary-cascades} we pay special attention to the stationary flow regime, which up to now was assumed in (most) works on pulsar polar cap accelerators, and describe why it has limited relevance to the force-free model of the pulsar magnetosphere. We discuss the implications of our results for the physics of rotation powered pulsars in \S\ref{sec:discussion} and summarize our conclusions in \S\ref{sec:conclusions}. | \label{sec:conclusions} Our principal conclusion is simple -- pair creation can occur at pulsar polar caps, but (almost) always in the form of fully time dependent current flow (microsecond time scales for the variability). That time dependence with pair creation allows the current to adjust to any magnetospheric load, while simultaneously allowing the charge density to adjust to the requirements of the force free magnetosphere. We have also shown that a substantial fraction of the open field lines (fraction decreasing with increasing obliquity) solve the current flow problem with a low energy, non neutral beam carrying the current co-existing with a non-neutral, electrically trapped particle cloud. This is an essentially time independent local solution. Exploring the consequences of these new results for global theory and observations requires extending the calculations to multidimensional, electromagnetic models for the accelerating electric field, and perhaps to background magnetic field models more general that the star centered dipole geometry used here in the choice of the magnetic radius of curvature that enters into the pair conversion opacity. | 12 | 6 | 1206.5819 |
1206 | 1206.2925_arXiv.txt | We use new Herschel multi-band imaging of the Andromeda galaxy to analyze how dust heating occurs in the central regions of galaxy spheroids that are essentially devoid of young stars. We construct a dust temperature map of M31 through fitting modified blackbody SEDs to the Herschel data, and find that the temperature within 2 kpc rises strongly from the mean value in the disk of $17\pm1$\,K to $\sim35$\,K at the centre. UV to near-IR imaging of the central few kpc shows directly the absence of young stellar populations, delineates the radial profile of the stellar density, and demonstrates that even the near-UV dust extinction is optically thin in M31's bulge. This allows the direct calculation of the stellar radiation heating in the bulge, $U_{\ast}(r)$, as a function of radius. The increasing temperature profile in the centre matches that expected from the stellar heating, i.e. that the dust heating and cooling rates track each other over nearly two orders of magnitude in $U_{\ast}$. The modelled dust heating is in excess of the observed dust temperatures, suggesting that it is more than sufficient to explain the observed IR emission. Together with the wavelength dependent absorption cross section of the dust, this demonstrates directly that it is the optical, not UV, radiation that sets the heating rate. This analysis shows that neither young stellar populations nor stellar near-UV radiation are necessary to heat dust to warm temperatures in galaxy spheroids. Rather, it is the high densities of Gyr-old stellar populations that provide a sufficiently strong diffuse radiation field to heat the dust. To the extent which these results pertain to the tenuous dust found in the centres of early-type galaxies remains yet to be explored. | \label{sec:intro} As the nearest, massive galaxy, Andromeda (M31, NGC\,224) has offered a unique insight into the properties of galaxies. It provides the perfect stepping stone between the well-resolved interstellar medium (ISM) and stellar populations within our own Galaxy, and the integrated properties of more distant galaxies. Due to its proximity ($\sim 780$kpc), Andromeda offers more than a resolved example of an early-type spiral galaxy, but can also be used to explore the interaction of the ISM and stars in early-type galaxies (ETGs) through its large, visually dominant bulge. Andromeda's bulge dominates the stellar luminosity and mass within the central 1.5 kpc \citep[$R_{\rm eff}({\rm bulge})\sim0.5-1.1$\,kpc;][]{Courteau11}, with the disk dominating beyond this. The bulge contributes $\sim$30\% of the total stellar mass and luminosity in M31, and it is clearly the highest surface brightness feature at UV -- NIR wavelengths \citep{Geehan06,Courteau11}. While the integrated colours and luminosity of M31 may place the galaxy in the ``green valley'' \citep{Mutch11}, the optical colours of the bulge are red, with a $B-V \approx 0.9$ to 1.0 \citep{Walterbos87a}, placing it securely in the range of the red-sequence, where most early-type galaxies are found. \citet{Oke68} even used the spectral energy distribution of the centre of M31 as a representative for the average giant elliptical galaxy when determining $K$-corrections. This ``early-type'' nature of the bulge is supported by the old mean stellar age determined for the central region of M31. Resolved star colour-magnitude diagrams created by ground-based, adaptive-optics, NIR imaging reveal a population dominated by stars greater than 6 Gyr \citep{Davidge05,Olsen06}, while single-stellar population fits to absorption-line indices from slit-spectroscopy of the bulge \citep{Saglia10} find that the bulge of M31 is uniformly old ($\ge12$ Gyr, excluding the central arcsecs). High-resolution, individual star photometry from the Pan-Chromatic Hubble Andromeda Treasury survey \citep[PHAT;][]{Dalcanton12} find no population of young-stellar sources, with the UV-light dominated by evolved stars such as post-AGB stars \citep{Rosenfield12}. Given this lack of young stars and star-formation, it is unsurprising that the bulge of M31 is also extremely gas poor. Little to no CO is detected in the CO(1-0) map of \citet{Nieten06} down to low surface brightnesses. CO is detected in the central part of M31 when deeper observations of small high attenuation regions are made \citep{Melchior00,Melchior11}, however the attenuation in these regions is still relatively low ($A_{\rm B} <0.3$) and the covering fraction of these regions is very small \citep{Melchior00}, meaning diffuse, low attenuation dust (and presumably diffuse gas) is more characteristic of the bulge. Compounding this is a low CO-H$_2$ ratio \citep{Leroy11}, and a low total HI column \citep{Braun09} giving a total cool gas mass in the centre of only a few $10^6 M_{\odot}$ ($\sim0.02$\% of the bulge stellar mass), likely dominated by molecular gas \citep[e.g.][]{Li09,Melchior11}. This low gas fraction makes the M31 bulge more gas-poor than many ETGs, as recent work with the ATLAS3D sample \citep{Cappellari11} has demonstrated. \citet{Young11} observed CO(1-0) in $\sim$22\% of the sample of nearby early-type galaxies, giving corresponding gas masses of $M(\rm {H}_2) > 10^{7}M_{\odot}$ (for a sample with a median stellar mass of $M_{\star}=3\times10^{10}M_{\odot}$). Similarly, studies of nearby field ellipticals and lenticulars have found atomic gas in a large fraction of these ($\sim70$\%), with this \hi\ emission generally associated with ionized gas emission \citep{Morganti06}. Interestingly, the molecular gas in early-type galaxies is not always associated with star formation. Optical colours and emission-line ratios indicate other forms of heating in the ISM of some early-types, and only low levels, if any, of star formation \citep{Crocker11}. Given the very low level of star formation, low attenuation, and small amount of gas at the centre of M31, little dust emission was expected in the central kiloparsecs of M31. Yet when this region was examined in the far-IR with IRAS \citep{Habing84}, ISO \citep{Haas98}, and \emph{Spitzer} \citep{Gordon06}, emission at wavelengths greater than 60\,\mum\ was clearly seen, indicating the presence of warm dust. In nearby ETGs, low-levels of warm dust are also being detected, with \citet{Smith11} finding dust emission in 24\% of ellipticals and 62\% of S0s in the \emph{Herschel} Reference survey. While $M_{\rm dust}/M_*$ is far lower in spheroids than in disks, the dust appears to be warmer on average than that found in later-type galaxies. A similar result was found using \emph{Herschel} in nearby early-type spirals similar to M31 by \citet{Engelbracht10}, with the mean dust temperature of the bulges consistently hotter than the disks in these galaxies. Relatively higher dust temperatures were also found by \citet{Rowlands11} in the \emph{Herschel}-ATLAS survey of more distant ellipticals. Hence dust, when detected, tends to be in a warmer state in spheroids than that found across the disks of later-type galaxies. Given the high density of stars in bulges, stellar heating is the likeliest explanation for the observed warmer dust temperatures in ETGs. Yet the old stellar ages found in ETGs, and especially in the centre of M31, argue against the standard view that the IR luminosity and warm dust is a direct tracer of star formation \citep[e.g.][]{Kennicutt98}. Based on the IRAS observations and the extremely weak UV observed using the Astronomical Netherlands Satellite \citep[ANS;][]{Coleman80}, \citet{Habing84} put forward the argument that it is the high density of late-type giant stars that provide the strong enough radiation field to heat the dust. Based on \emph{Herschel} PACS and SPIRE maps of M31 with unprecedented resolution (Krause et al., in prep.), we follow \citet{Habing84} and use this high resolution to demonstrate how and by what stellar populations dust is heated in the bulge of this galaxy, and, by proxy, in the spheroids of other inactive early-type galaxies. We briefly review the \emph{Herschel} data and reduction in section \ref{sec:data}, and discuss the FIR geometry and integrated properties of the M31 bulge in section \ref{sec:FIR}. In section \ref{sec:bulgeheat} we determine and discuss the mean dust temperature across M31 and in the centre, and determine the heating mechanism for the rise in dust temperature in the centre. We finish with the discussion and summary in sections \ref{sec:disc} and \ref{sec:summ}. The global properties of M31 we assume throughout this paper are listed in Table \ref{tab:m31prop}. \begin{table} \caption{M31 positional data$^{\rm a}$}\label{tab:m31prop} \smallskip \begin{threeparttable}[\hsize] \begin{tabular}{ll} \hline M31 nucleus position\tnote{b} & $00^{h}42^{m}44.35^{s}$\\ ~(J2000)&$+41^{\circ}16\amin08.60\asec$\\ Position angle of major axis & $37.7^{\circ}$\\ Inclination & $75^{\circ}$\\ Distance\tnote{c} & $780\pm40$ kpc\tnote{d}\\ Distance modulus & 24.46\\ \hline \end{tabular} \begin{tablenotes} \item[a] Based on NED data and references where given. \item[b] \citep{Evans10}, and verified in \emph{Spitzer} IRAC 3.6\mum\ image. \item[c] \citet{Stanek98,Rich05}, see also NED for other determinations. \item[d] $1\amin=227\pm12$pc along major axis \end{tablenotes} \end{threeparttable} \end{table} | \label{sec:disc} As the nearest massive galaxy, the Andromeda galaxy allows us to connect the small scale physics with the integrated properties of galaxies. The central kiloparsec of M31 actually matches very well many of the observed properties of nearby early-type galaxies. Within a 1 kiloparsec (4.4\amin) circular aperture the estimated stellar mass is $\sim10^{10} M_{\odot}$, with a very old, red stellar light, estimated to be greater than 10\,Gyrs old \citep{Saglia10}. The optical colours of the bulge, e.g.~NUV-$r\approx5.0$, place it well in the realm of gas poor early-type galaxies \citep[see, e.g. ][]{Oke68,Saintonge11,Smith11}. There is a low level of dust attenuation across the centre, visible in both the difference between the observed and modelled intrinsic SEDs in Figure \ref{fig:m31sed} and in the $A_{\rm B}$ map (their Figure 1) of \citet{Melchior00}. This low level of attenuation is a result of the low dust column across the centre and connected to the relatively weak IR emission. The total dust mass within this aperture from the \citet{daCunha08} MAGPHYS model is $10^{5.2}M_{\odot}$, contributing only 0.5\% of the total dust mass to M31. However, the bulge contributes $\sim5$\% of the total IR luminosity due to the relatively warm, blue FIR emission. This dust mass results in a very low $M_{\rm dust}/M_{\star}$ for the bulge, with $\sim 10^{-4.7}$. This actually places the bulge of M31 in a similar regime as the sample of early-type galaxies explored in the \emph{Herschel} reference survey \citep[HRS, ][]{Boselli10} in \citet{Smith11}, falling somewhat in between the S0 and E galaxies (see their Figure 8). Similarly, the temperature increase from disk to bulge in M31 follows the trend of having warmer dust in earlier Hubble-types, as observed by \citet{Engelbracht10} in the KINGFISH sample. This trend was also seen by \citet{Smith11} in the HRS, who found warmer dust in E galaxies than S0, and an overall warm dust temperature for the sample (mean $T_{\rm d} =24$K). The $M_{\rm gas}/M_{\star}$ ratio is also very low in the bulge of M31, with little \hi\ and CO detected in the centre. However, ionized gas is seen in \ha\, and the FIR emission is spatially well-correlated with this gas showing a similar lower inclination, barred-spiral pattern as visible in Figure \ref{fig:m31ha_IR}, with the MIR emission also following the diffuse \ha\ morphology \citep{Li09}. Given this correlation, the \ha\ emission allows the structure of the dust distribution to be determined \citep[e.g.][]{Jacoby85}, and indicates that the ISM in the centre, including the dust, is in a thin, spiral disk. The origin of this gas and dust in the centre of M31 is still not known, and beyond the scope of this work. \citet{Li09} suggest that the stellar ejecta are more than sufficient to replenish the observed hot gas in M31's centre, and suggest the rest of this matter comes out as a hot, X-ray flow. However, the spiral pattern observed in the bulge does appear to link up with the emission in the disk (Figure \ref{fig:m31image}), even if it appears to be at a different inclination to the disk. Given the above similarities using the bulge of M31 as a resolved representative of the spheroids of other early-type galaxies is a reasonable assumption. Based on this and our resolved study of dust heating in the bulge we can extrapolate to infer that a similar heating mechanism for the dust occurs in the majority of early-type galaxies in which dust is detected (i.e., the \citet{Smith11} sample). While many early-type galaxies do have some AGN activity in the centre, and several, generally with higher gas masses, have observed active star formation \citep[e.g.][]{Crocker11}, the combination of diffuse, optically thin dust and a strong, diffuse radiation field due to the high stellar density is able to heat dust at the centres of these early-type galaxies to a significantly warmer level than that observed in most stellar disks. This increased dust temperature makes the generally dust poor early-types still visible in the recent and ongoing FIR surveys with \emph{Herschel}. However, the possible contribution of disk dust to the observed IR emission, as derived from the dust temperature offset in Figure \ref{fig:Tdist}, suggests a final cautionary note in this extrapolation. The bulge of M31 lies in a far different environment to typical early-type galaxies, which affects both the observed emission, and the evolution of the ISM in this early-type spheroid. | 12 | 6 | 1206.2925 |
1206 | 1206.2114_arXiv.txt | Magneto-atmospheres with Alfv\'en speed [$a$] that increases monotonically with height are often used to model the solar atmosphere, at least out to several solar radii. A common example involves uniform vertical or inclined magnetic field in an isothermal atmosphere, for which the Alfv\'en speed is exponential. We address the issue of internal reflection in such atmospheres, both for time-harmonic and for transient waves. It is found that a mathematical boundary condition may be devised that corresponds to perfect absorption at infinity, and, using this, that many atmospheres where $a(x)$ is analytic and unbounded present no internal reflection of harmonic Alfv\'en waves. However, except for certain special cases, such solutions are accompanied by a wake, which may be thought of as a kind of reflection. For the initial-value problem where a harmonic source is suddenly switched on (and optionally off), there is also an associated transient that normally decays with time as $\mathcal{O}(t^{-1})$ or $\mathcal{O}(t^{-1}\ln t)$, depending on the phase of the driver. Unlike the steady-state harmonic solutions, the transient does reflect weakly. Alfv\'en waves in the solar corona driven by a finite-duration train of $p$-modes are expected to leave such transients. | Alfv\'en waves in a stratified atmosphere are governed by the standard linear wave equation \begin{equation} \pderivd{\xi}{t}=a^2 \pderivd{\xi}{x}\, , \label{alfeqn} \end{equation} where $\xi$ is the plasma displacement (which is transverse to both the magnetic field and the direction of inhomogeneity $x$), and $a=a(x)=|B_x|/\sqrt{\rho}$ is the Alfv\'en speed, or more properly the Alfv\'en velocity component in the $x$-direction (the magnetic permeability is scaled to unity throughout). In large-scale open field regions of the Sun's atmosphere, the Alfv\'en speed increases monotonically with height due to the decreasing density [$\rho$], with geometric diminution of magnetic-field strength playing a secondary role. Eventually, $a$ reaches a maximum at several $R_\odot$ and decreases with distance thereafter {\new\cite{AnSueMoo90aa}}. By this stage though, solar-wind flows have become important and Equation (\ref{alfeqn}) must be modified to take these into account {\new\cite{Vel93aa}}. However, our focus in this article lies below such heights, and with wave periods of minutes rather than the hours common in the heliosphere. We simply ask, \emph{What is the nature of Alfv\'enic solutions of the simple Equation (\ref{alfeqn})?} We are all very familiar with the basic wave equation, treated at length in every text book on partial differential equations (PDEs). However, the nonuniform Alfv\'en speed introduces some features that are perhaps less well known, and that have significance for the nature of Alfv\'enic oscillations now seen in the solar corona \cite{TomMcIKei07aa,McIde-Car11aa}. We shall address a range of analytic Alfv\'en speed profiles, but the most basic is \begin{equation} a=a_1(x)=a_0\, \rme^{x/2h}\,, \label{Alf1} \end{equation} which pertains to a uniform magnetic field and an isothermal density stratification (scale height $h$). This model has been much used as a fundamental representation of Alfv\'en waves in stellar atmospheres at least since \inlinecite{Fer54aa}. \inlinecite{FerPlu58aa} noted the exact solution \begin{equation} \xi = \left[A_1 \, J_0\left(2\,\frac{\omega h}{a_0}\rme^{-x/2h}\right) + A_2\,Y_0\left(2\,\frac{\omega h}{a_0}\rme^{-x/2h}\right)\right] \rme^{-\rmi\omega t} \label{ferraro} \end{equation} for a wave of single frequency [$\omega$] in terms of Bessel functions of the first and second kind of order zero, with $A_1$ and $A_2$ arbitrary constants. They then dropped the $Y_0$ solution on the grounds that the velocity perturbation does not vanish as $x\to\infty$ (\emph{i.e.} as $\rho\to0$). We term this the regularity boundary condition. Many subsequent studies have adopted the same approach \cite[for example]{AnMusMoo89aa}. This is problematic though; it imposes a perfectly reflecting boundary at infinity thereby setting up a standing wave $J_0\left(2\rme^{-x/2h}\,{\omega h/a_0}\right)$, which may not be desirable or realistic. The regularity boundary condition is unnecessary from an energy point of view too. Despite the $Y_0$ solution being unbounded, $\mathcal{O}(x)$ in fact, the kinetic-energy density [$\half\rho\omega^2|\xi|^2$] vanishes at infinity, and the magnetic energy density $\half |b|^2$ is finite there, where $b$ is the magnetic field perturbation.\footnote{A quadratic wave-energy equation is easily constructed from the linearized momentum and induction equations: $ \partial\mathcal{E}/\partial{t} + \partial{\mathcal{F}}/\partial{x}=0\,, $ where $\mathcal{E}=\half\rho v^2 + \half b^2$ is the energy density, $\mathcal{F}=-B\,b\,v$ is the wave-energy flux, $v=\partial\xi/\partial t$ is the plasma velocity, and $b=-B\, \partial\xi/\partial x$ is the magnetic field perturbation. Energy fluxes may be attributed to solutions of the wave equation using the formula for $\mathcal{F}$, and hence reflection coefficients may be calculated if these solutions can be split into upward- and downward-propagating parts. If $\xi$ and $b$ are being modelled as complex quantities, then we should write $\mathcal{E}=\half\rho |v|^2 + \half |b|^2$ and $\mathcal{F}=-B\,\re(b\,v^*)$.} The $\xi=\mathcal{O}(x)$ behaviour is just the linear flapping of rigid field lines to be expected physically as $a\to\infty$ (see the animation attached to \opencite{CalHan11aa}). Although mathematically we are at liberty to impose the regularity boundary condition, it is often more convenient in theoretical modelling to allow waves to escape at the top so as not to confuse matters with downward travelling waves reflected from an unphysical ``infinity''. The boundary condition at infinity is particularly important in the exponential model since the Alfv\'en travel time [$\tau=2h/a(x)$] from any point $x$ to infinity is finite. To place this in a solar coronal context, assuming a 2 G magnetic field, a base density of $10^{-12}$ $\rm kg\,m^{-3}$, and a density scale height of 20 Mm, the travel time to infinity in an exponential atmosphere is around 450 seconds, comparable to the period of the waves that we are considering. Despite Alfv\'en waves undoubtedly reflecting from sharp features such as the chromosphere-corona transition region \cite{cravan05aa,HanCal12aa}, or returning along closed loops, there is reason to believe that waves in the open-field corona are preferentially outgoing. This is partly because some fraction of their energy irrevocably escapes into the solar wind, and partly because of damping by such mechanisms as turbulent cascade to the ion-cyclotron scale (see for example \opencite{MarVocTu03aa}, \opencite{Hol06aa}), neither of which we choose to model here. So, a radiation condition is a way of avoiding such complications when exploring propagation far below where they are situated. The wave-energy flux associated with the general solution (\ref{ferraro}) is \begin{equation} \begin{split} \mathcal{F} &= \frac{\omega\,B^2}{4\,h\,\pi} \left( |A_1+\rmi\,A_2|^2 -|A_1-\rmi\,A_2|^2\right)\\[4pt] &= \frac{\omega\,B^2}{h\,\pi} \left( |\Xi_2|^2 -|\Xi_1|^2\right) \end{split} \label{JYflux} \end{equation} where we define $\Xi_1=\half(A_1-\rmi\,A_2)$ and $\Xi_2=\half(A_1+\rmi\,A_2)$. This shows that the alternate but equivalent representation \begin{equation} \xi = \left[\Xi_1 \, H_0^{(1)}\left(2\,\frac{\omega h}{a_0}\rme^{-x/2h}\right) + \Xi_2\,H_0^{(2)}\left(2\,\frac{\omega h}{a_0}\rme^{-x/2h}\right)\right] \rme^{-\rmi\omega t}\,, \label{ferraroH} \end{equation} separates the solution into downgoing and upgoing parts respectively. The solution with $\Xi_1=0$, \begin{equation} \xi_\uparrow = \, H_0^{(2)}\left(2\,\frac{\omega h}{a_0}\rme^{-x/2h}\right)\,, \label{Hank2} \end{equation} was used by \inlinecite{SchCalBel84aa} to represent an outward-travelling wave (the harmonic temporal dependence is omitted from now on, but is implied). This Hankel function (Bessel function of the third kind) is well known to asymptotically reduce to a complex exponential $H_0^{(2)}(r)\sim\sqrt{2/(\pi r)}\,\exp[-\rmi(r-\pi/4)]$ for large argument $r\to\infty$ ($x\to-\infty$) \cite[formulae 10.17.5-6]{DLMF} (\inlinecite{Hol78aa} also uses a Hankel-function solution to represent a radiation boundary condition, but assumes that this is valid only ``sufficiently far from the Sun that the eikonal approximation is valid and no more wave reflections are expected''.) \inlinecite{HanCal12aa} point out that the Alfv\'en wave equation with exponential Alfv\'en speed $a_1(x)$ is isomorphic to the uniform axisymmetric two-dimensional (2D) wave equation with unit wave speed \begin{equation} \pderivd{\xi}{t} = \frac{1}{r} \pderiv{}{r}\left( r \pderiv{\xi}{r} \right) \label{axisym} \end{equation} under the transformation $r = 2 h/a$. Here the axis $r=0$ corresponds to $x=+\infty$ in the Alfv\'en wave problem. The textbook solution $J_0(\omega r)=\half[H_0^{(1)}(\omega r)+H_0^{(2)}(\omega r)]$ effectively imposes perfect reflection on the axis, resulting in a standing wave. Placing a harmonic source there instead yields the $H_0^{(1)}(\omega r)$ solution (\opencite{CouHil62aa}, Ch.~III, Section 3.2; \opencite{Whi74aa}, Section 7.4) whilst the time reverse corresponds to a perfect absorber and yields $H_0^{(2)}(\omega r)$. There is nothing reflective in this system. But neither are the waves represented by simple d'Alembert-like solutions. As is well known and understood \cite[pp.~208--210]{Had23aa,CouHil62aa}, solutions of the wave equation for uniform media in even-dimensional spaces do not obey Huygens' principle. Any propagating disturbance trails a wake, or ``reverberation''; to quote \inlinecite{Joh82aa}, ``Disturbances propagate with finite speed but after having reached a point never die out completely in a finite time at that point, like the waves arising from a stone dropped into water''. But even more restrictedly, only in one and three spatial dimensions do \emph{spherical waves} propagate ``relatively undistorted'' \cite[Ch.~VI, Section 18]{CouHil62aa}. The 2D case of interest here necessarily exhibits a wake. As noted by \inlinecite{HanCal12aa} \begin{equation} \begin{split} H_0^{(1,2)}(r) &= \frac{2}{\pi}\int_0^1\frac{\rme^{\pm \rmi\,u\,r}}{\sqrt{1-u^2}} \,\rd u \mp \frac{2i}{\pi}\,\int_0^\infty \rme^{-r\sinh\tau}\rd\tau \\[8pt] &= \alpha_\pm(r) \mp \rmi\, \beta(r) \, . \end{split} \label{Hankel2} \end{equation} Clearly, $\alpha_+$ corresponds to propagation away from $r=0$ (backward in $x$), $\alpha_-$ represents propagation towards $r=0$, and $\beta$ is the reverberation. We see that the propagation part of $\xi(r)$, \emph{i.e.} $\alpha_\pm(\omega r)$, consists of a superposition of all wavenumber components between 0 and $\omega$. Of course, $\beta$ may also be represented as a Fourier integral \begin{equation} \beta(r) = \frac{2}{\pi}\int_0^1 \frac{\sin u r\, \rd u}{\sqrt{1-u^2}} + \frac{2}{\pi} \int_1^\infty \frac{\cos u r\, \rd u}{\sqrt{u^2-1}}\,, \label{reverbstand} \end{equation} showing that the reverberation can be represented as a superposition of standing waves, in agreement with the {\new characteristics-based} findings of \inlinecite{HolIse07aa}. In terms of Bessel and Struve functions, $\alpha_\pm(r)=J_0(r)\pm \rmi\,\mathbf{H}_0(r)$ and $\beta(r)=\mathbf{H}_0(r)-Y_0(r)$; note that $\alpha_\pm$ is regular at $r=0$ \cite[Figure 10]{HanCal12aa}. {\new For small $r$, the reverberation [$\beta$] exhibits a logarithmic singularity inherited from $Y_0$, $\beta\sim -2\,\pi^{-1} \ln r$. This will be seen again later (Sections \ref{switchon} and \ref{switchonoff}) in the asymptotic form of the transients.} The fact that Alfv\'en waves in the inner corona appear to be preferentially outgoing suggests that $H_0^{(2)}(\omega r)$ is a better model of solar atmospheric Alfv\'en wave propagation than is $J_0(\omega r)$, and an indication that strong absorption occurs before the waves can reflect. In any case, we are mathematically at liberty to impose a radiation condition at large $x$, and it is certainly convenient to do so in theoretical investigations of outward wave propagation. This article, in part, addresses the consequences of this choice, both for the steady-state harmonic wave problem and for the initial-value problem. Indeed, it is very common to seek to impose a radiation condition above an exponential or similar atmosphere by simply appending a uniform plasma above some (large) height {\new\cite{Har29aa}}. However, it will be shown that this is not a good choice in general because the discontinuity in Alfv\'en speed gradient is itself highly reflective. The artifice therefore decides the issue rather than illuminates it. Another interesting suggestion for how to avoid the difficulties presented by a finite travel time to infinity and perfect reflection there is to retain the displacement current in the wave equations \cite{Ler83aa,TsaSteKop09aa}. Then the Alfv\'en speed is limited by the speed of light, and the Alfv\'en wave ultimately couples to an outgoing electromagnetic wave. (It should be noted though that \citeauthor{Ler83aa} did not mean to imply that this process actually occurs in the solar atmosphere -- see the last sentence of his article -- the device was merely introduced as a mathematical way around the troublesome infinity.) Unfortunately, we shall see in Section \ref{flat} that this model is almost totally reflective for any realistic frequency and density scale height, and so does not fulfil our requirement for optimal transmission. Reflection of harmonic waves will be addressed from several standpoints and for a variety of atmospheres in Section \ref{sec:reflect}, showing that the reflectivity of an atmosphere is governed by its smoothness, or lack thereof. Discontinuity in any derivative of the Alfv\'en speed results in a reflection coefficient that depends algebraically on the wavenumber. On the other hand, an infinitely smooth ($\mathscr{C}^\infty$) function suffers only exponentially small reflection at worst. Then we address the initial-value problem, in the exponential atmosphere, with specific focus on the decay of transients, both for the radiation and regularity boundary conditions. Finally, we draw some general conclusions about the relationship between reflectivity, wakes, and transients and how they are determined by the form of $a(x)$. | The analysis presented here may seem esoteric. Nevertheless, it has practical implications for the way that we model wave propagation in the solar atmosphere. There are any number of articles \cite[for example]{LeeHolFla82aa} that seek to calculate the ``intrinsic'' reflectivity of coronal Alfv\'en waves by placing a uniform slab above an exponential or similar model. However, this says more about the matching point than about the underlying atmosphere. The exponential and power-law profiles are cases in point. If the atmospheres are allowed to extend unimpeded to infinity without truncation, they are entirely transparent. Or, more physically, if an efficient and non-reflective wave energy sink is placed high in the atmosphere, there is no reflection from the body of the atmosphere either. A simple uniform or WKB slab does not represent such a non-reflective sink, although this is not to say that it may not be a reasonable representation of the outer corona \cite{Ler81aa}. In the absence of any Alfv\'en wave dissipation, such a WKB top would indeed induce strong reflection in the underlying atmosphere. But the point is that the underlying atmosphere is not necessarily \emph{intrinsically} reflective (\emph{viz.}, the exponential or power-law Alfv\'en-speed profiles). It is the \emph{transition} to the uniform or WKB top that reflects. This is relevant when performing numerical experiments in truncated model atmospheres. If we \emph{choose} to, we can postulate a radiation boundary condition at the top of our region of interest. {\new In numerical simulations, this is typically done using characteristic boundary conditions \cite{EngMaj77aa} or absorbing layers \cite{Ber94aa}. For steady monochromatic waves, the task may be easier, through simple matching to a known analytic solution that represents an outgoing wave.} For the exponential atmosphere, this involves adopting the $H_0^{(2)}(\omega r)$ Hankel function solution {\new\cite{CalGoo08aa}} . The $J_0(\omega r)$ solution on the other hand is appropriate if we want a reflective boundary {\new at infinity}. With this in mind, matching numerical solutions in a finite domain to a Hankel function or similar radiation solution is mathematically well founded and physically interesting. {\new This does not imply that the exponential atmosphere really does extend to infinity; it is simply an effective mathematical device for imposing a radiation condition at the top of a computational domain. A more realistic treatment of solar coronal Alfv\'en waves should in fact address the maximum and gradual decline in the Alfv\'en speed beyond a few solar radii and the loss of hydrostatic equilibrium that results in the solar wind \cite{Vel93aa}, but that is beyond the expository scope of the present analysis. It is notable though that \citeauthor{Vel93aa} finds near-total \emph{transmission} at high frequencies in this model, which further supports the use of a radiation boundary condition in simpler atmospheres.} Analysis of the initial-value problem for the exponential atmosphere verifies that the steady state $H_0^{(2)}(\omega r)$ solution does indeed fully depart the physical model through $x=+\infty$, though a weak transient remains that decays algebraically in time. Since we might expect episodic generation of Alfv\'en waves in the lower atmosphere, for example by fast-wave conversion \cite{HanCal12aa}, the ubiquitous presence of such slowly relaxing transients can hardly be avoided. These motions would not be identified as waves observationally, as they are not oscillatory in time. | 12 | 6 | 1206.2114 |
1206 | 1206.2863_arXiv.txt | The gamma-ray line from dark matter (DM) annihilation is too weak to observe, but its observation will uncover much information, e.g., the DM mass and an anomalously large annihilation rate $\sim0.1$ pb into di-photon. In this work, we construct a minimal effective theory (EFT) incorporating DM and heavier charged particles. A large annihilation rate is obtained from operator coefficients with resonance or strong coupling enhancement. The EFT is stringently constrained by the XENON100 and WMAP data. Without resonance, Dirac DM or colored charged particles are ruled out. It is pointed out that the di-gluon mode may correctly determine the DM relic density. Interestingly, this framework also provides an origin for the Higgs di-photon excess at the LHC\@. We apply the general analysis to the NMSSM, which can elegantly interpret the tentative 130 GeV gamma-ray line. A top-window model is also proposed to explain the gamma-ray line. | The existence of dark matter (DM) has been confirmed by its gravitational effects, and its energy fraction $\sim25\%$ today is also measured. However, the conclusive evidences that may reveal the DM particle properties are still absent. Among a variety of (indirect) detecting objects on DM, the gamma-ray from the DM dense region (such as the center of the Galaxy) is especially promising by virtue of weak astrophysical influence on its propagation~\cite{Bertone:2004pz}. Of particular interest is the monochromatic gamma-ray line, which has rather clear background. But it is highly suppressed because the DM $\chi$ can only annihilate to photons via the charged loop. However, once such a spectral line is observed, it will uncover very important information of DM\@. In this article, we assume an extracted DM mass from $E_\gamma$ and an anomalously large annihilation rate $\langle \sigma v\rangle_{2\gamma}\sim0.1$ pb into di-photon (it is taken as a referred value throughout the work, unless specified), then attempt to reconstruct the DM properties and dynmiacs to the most extent. % Inspired by the recent discovery of a gamma-ray line at $E_\gamma\simeq130$ GeV, which is claimed in the Ref.~\cite{Bringmann:2012vr,CW} after re-analyzing the Fermi Large Area Telescope (FERMI-LAT) data published in 2009~\cite{Atwood:2009ez}, it is conjectured that the line may originate from DM annihilating into gamma. Best fit of the data shows a DM of mass around $130$ GeV and annihilation rate at level $0.1$ pb. Later independent analysis also confirms the line~\cite{Raidal}. The line has a sharper peak which is hard to explain by FERMI-bubbles~\cite{bubble}, while DM+DM$\ra \gamma\gamma$ gives a better fit~\cite{Raidal}. The Ref.~\cite{Su:2012ft} also shows a strong evidence of the gamma-ray from the inner galaxy and draws a similar conclusion. This line has received much attention from astrophysics~\cite{bubble,Raidal,Boyarsky:2012ca,astro} and particle physics~\cite{particle}. In spite of queries~\cite{Boyarsky:2012ca}, the gamma-ray line from DM activity itself is of great theoretical interest, and deserving a deep study. The topic can be studied in the effective theory (EFT) framework, by minimally including an operator $a_C\chi^\dagger\chi C^\dagger C$ where $C$ is the charged particle. The anomalously bright gamma-ray line is due to large $a_C$. We further demand the EFT be compatible with other constraints on the DM, i.e., the WMAP and XENON100 bound~\cite{XENON100}. Independent of the mechanism generating large $a_C$, we can arrive: \begin{itemize} \item The charged particle $C$ in the loop should be heavier than the DM, otherwise it would render too large annihilation rate into $C\bar C$, which leads to too small DM relic density. On top of that, the injection from such a large flux of charged particles into the cosmic-ray probably has been excluded by the PAMELA. \item The charged particle carrying both QED and QCD charges needs careful inspections. Along with the di-photon annihilating mode, there is an enhanced di-gluon mode with estimated rate $\langle \sigma v\rangle_{2G}\sim0.1(\alpha_s^2/\alpha^2)\langle \sigma v\rangle_{2\gamma}\simeq 1$ pb, which makes an illustrative coincidence. \end{itemize} The large $a_C$ can be generated through Breit-Weigner resonance mechanism, or the strong interaction between DM and the charged loop. For the former scenario, properties of the scalar/vector resonance can be further stringently restricted by symmetries, e.g.\ the CP, and the above consideration. The next-to-minimal supersymmetric standard model (NMSSM)~\cite{Ellwanger:2009dp} is a good realization of this scenario. We find it is capable of interpreting the tentative 130 GeV gamma-ray line. For the latter scenario, the XENON100 bound excludes the Dirac DM, as well as both Dirac and Majorana DM if the charged paticle $C$ carries color. Interestingly, in any scenario, the possible SM-like Higgs $h$ to di-photon excess at the LHC~\cite{LHC:Higgs} may share the same origin, if we incorporate the operator $a^h_C hC^\dagger C$. This paper is organized as following: In the section~\ref{2}, we perform a general analysis based on the minimal EFT. In the next two sections exploration on the enhancement mechanism is presented. The Section~\ref{conclusion} includes the conclusion and discussions. And some necessary complementarity is casted in the Appendix. % | The gamma-ray line from DM annihilating in the galaxy center generically is well below the present detectable level. However, once the observation, from it we are able to extract very important information of the DM properties/dynamics. In this work, we present a minimal effective theory framework to understand the anomalously bright gamma-ray line from dark matter activity: \begin{itemize} \item In the EFT large annihilation rate is ascribed to operator coefficients with resonant or strong coupling enhancement. \item Due to the XENON100 bound, Dirac DM or colorful charged particles are ruled out in models with only strong couplings. \item If the charged particle in the loop carry $SU(3)_C$ charge, the di-gluon annihilation mode is about one order larger than the di-photon mode, that may properly account for the relic density. \item The SM-like Higgs may share the same charged loop, and therefore provide a source of Higgs di-photon excess at the LHC. \end{itemize} Applying the general analysis to the NMSSM, that is proved to accommodate neutralino LSP with large annihilation rate into di-photon and interpret the tentative 130 GeV gamma-ray line. Top-window model is also proposed to explain it. Although not the central points of this work, we would like to end up by commenting its very promising collider detection prospect, if the 130 GeV gamma-ray line from DM activity will be confirmed. In light our general analysis in the text, at the LHC or Tavertron (but beyond LEP) one can expect new light color-singlet charged particle $C$ can be produced: $q\bar q\ra C^\dagger C$. While beyond the 130 GeV line and consider more wide scope, the LHC could put very strong exclusion on the model with colored loop. | 12 | 6 | 1206.2863 |
1206 | 1206.6995_arXiv.txt | The ability to resolve all processes which drive galaxy formation is one of the most fundamental goals in extragalactic astronomy. While star formation rates and the merger history are now measured with increasingly high certainty, the role of gas accretion from the intergalactic medium in supplying gas for star formation still remains largely unknown. We present in this paper indirect evidence for the accretion of gas into massive galaxies with initial stellar masses M$_{*} > 10^{11}$~\solm and following the same merger adjusted co-moving number density at lower redshifts during the epoch $1.5 < z < 3$, using results from the GOODS NICMOS Survey (GNS). Our method utilises the observed star formation rates of these massive galaxies based on UV and far-infrared observations, and the amount of stellar and gas mass added due to observed major and minor mergers to calculate the evolution of stellar mass in these systems. We show that the measured gas mass fractions of these massive galaxies are inconsistent with the observed star formation history for the same galaxy population. We further demonstrate that this additional gas mass cannot be accounted for by cold gas delivered through minor and major mergers. We also consider the effects of gas outflows and gas recycling due to stellar evolution in these calculations. We argue that to sustain star formation at the observed rates there must be additional methods for increasing the cold gas mass, and that the likeliest method for establishing this supply of gas is by accretion from the intergalactic medium. We calculate that the average gas mass accretion rate into these massive galaxies between $1.5 < z < 3.0$, is $\dot{M} = 96\pm19$ \solm yr$^{-1}$ after accounting for outflowing gas. This is similar to what is predicted in detailed simulations of galaxy formation. We show that during this epoch, and for these very massive galaxies, 49$\pm$20\% of baryonic mass assembly is a result of gas accretion and unresolved mergers, while the remaining $\sim 25\pm10$\% is put into place through existing stars from mergers, with the remainder is gas brought in with these mergers. However, 66$\pm20$\% of all star formation in this epoch is the result of gas accretion. This reveals that for the most massive galaxies at $1.5 < z < 3$ gas accretion is the dominant method for instigating new stellar mass assembly. | Both observations and theoretical models now overwhelmingly suggest that galaxies have evolved from an early population dominated by lower mass systems undergoing significant star formation in the early universe, to the large and relatively passive galaxies that we find today (e.g., Conselice 2006; Bouwens et al. 2010). How this transformation occurs, that is how we get from young low mass galaxies to the large massive galaxies we see in today's universe, is a highly debated topic. Essentially, we want to answer the question - how do galaxies assemble their stellar masses? The answer to this question will have profound implications for both the physics of galaxy formation and for understanding properties of the universe itself. Historically, it was once thought that galaxies formed in a manner similar to stars through a collapse of gas that later, through some process, underwent intense star formation. In this paradigm the total baryonic mass of a galaxy does not change significantly with time, and its stellar mass evolves by rapidly converting gas into stars. However, it is clear that galaxies must form in a hierarchical way through mergers and accretion of material from the intergalactic medium. This view has supporting evidence from both observations of the stellar mass functions of galaxies (e.g., Bundy et al. 2006; Mortlock et al. 2011), direct observations of mergers in the distant universe (e.g., Conselice et al. 2003, 2008; Bluck et al. 2009, 2012), as well as through the evolution of galaxy sizes (e.g., Ferguson et al. 2004; Trujillo et al. 2007; Buitrago et al. 2008; Weinzirl et al. 2011). Evidence from internal kinematics also suggests that galaxy formation is driven at least in part by the accumulation of gas from the intergalactic medium falling onto a galaxy (e.g., Keres et al. 2005; Genzel et al. 2008; Dekel et al. 2009a,b; Bournaud et al. 2011). While it is now generally accepted that galaxy formation is a hierarchical process driven by the accumulation of stars and gas located outside of a galaxy after its initial formation, the details of this assembly remain largely unknown. Cold gas infall into galaxies, otherwise known as `cold gas accretion' is theorised to be an important aspect in the process of massive galaxy formation (e.g., White \& Frenk 1991; Birnboim \& Dekel 2003; Keres et al. 2005, Dekel et al. 2009a,b), and even perhaps the dominant method by which galaxies assemble their mass. However, there is little to no evidence for gas accretion onto galaxies at high redshift currently (e.g., Steidel et al. 2010), although some claims are appearing at lower redshifts (e.g., Rauch et al. 2011). This is primarily due to the difficultly of observing this process since the covering fraction of accreting cold gas is likely not high (e.g., Faucher-Giguere, Keres \& Ma 2011; Kimm et al. 2011; Fumagalli et al. 2011), nor would this gas be easily detected in, for example, absorption (e.g., Weiner et al. 2009; Giavalisco et al. 2011). In this paper we develop a new approach to this problem by analyzing the evolution of the massive galaxy population in terms of the history of its baryonic assembly. We examine how the stellar mass of a massive galaxy is built up during $1.5 < z < 3$ through various galaxy formation processes observed within a unique sample of M$_{*} >$ \mass galaxies taken from the GOODS NICMOS Survey (GNS) (Conselice et al. 2011). By examining the addition of stellar mass due to major and minor mergers (Bluck et al. 2009; 2012), and the observed star formation history (Bauer et al. 2011) and resulting stellar mass evolution using stellar synthesis modeling. we provide through this method circumstantial evidence for gas inflow, or gas imported in through extremely minor mergers, as an important process in galaxy assembly. After comparing the amount of accreted mass to the mass assembled through merging, we conclude that gas accretion is a dominant process for massive galaxy assembly at this epoch. We further discuss the comparison with theory, and describe some of the implications of our results, including how our work relates to the G-dwarf problem (e.g., Larson 1974), and the rapid gas depletion time-scales in galaxies. This paper is organised as follows: \S 2 includes a discussion of the data sources we use in this paper, and the sample selection, \S 3 is a description of our baryonic mass assembly analysis, \S 4 presents our arguments for gas accretion and \S 5 is our summary. We use a standard cosmology of H$_{0} = 70$ km s$^{-1}$ Mpc$^{-1}$, and $\Omega_{\rm m} = 1 - \Omega_{\lambda}$ = 0.3 throughout. | We present in this paper a study of the cold gas mass densities for massive galaxies with M$_{*} > 10^{11}$~\solm at redshifts of $1.5 < z < 3$. While we do not directly detect the accretion of gas within our galaxies, we are able to make a circumstantial finding for its existence. Our conclusions are as follows: I. Utilizing our measured star formation rates and galaxy sizes we find a roughly constant cold gas mass to stellar mass fraction for this sample across the redshift range of $1.5 < z < 3$. II. We utilize the star forming and merging properties of these galaxies from previous work in Bauer et al. (2011) and Bluck et al. (2012) to measure the mass budget of our sample of massive galaxies, finding that $\dot{M}_{\rm acc}$ = (96 $\pm$ 19) \solm yr$^{-1}$ of gas is needed to sustain the star formation rate outside of gas brought in via mergers. III. We derive based on these values that cold gas accretion from the intergalactic medium, or alternatively very minor galaxy mergers with mass ratios lower than 1:100 (or 1:10 in ratios of baryons), accounts for 49$\pm$20\% of the baryonic matter added to galaxies from $1.5 < z < 3$. This amount of gas mass added from accretion is larger than the amount of gas added due to the merger process (both minor and major) (e.g., Conselice 2006; Bluck et al. 2012) and is largely in agreement with models which predict on the order of 100-200 \solm yr$^{-1}$ added from cold gas accretion (e.g., Dekel et al. 2009a,b). Gas accretion is therefore the major method for producing star formation within massive galaxies between redshifts $1.5 < z < 3$. Further work with e.g., the CANDELS survey will allow us to carry out this measurement for lower mass galaxies where the mode of formation could be significantly different than the more massive systems (e.g., Dekel et al. 2009a,b). Also, we are examining in this paper massive systems in the last throws of their formation at $z < 3$. Investigating the ratio of formation due to mergers and gas accretion at $z > 3$ will reveal how the first epochs of these massive galaxies were formed. This however will require observations from JWST and the ELTs. We thank the GNS team, particularly Fernando Buitrago and Amanda Bauer, for their contributions to this survey and the previous published work utilised here. We thank the referee for a report that improved this paper significantly. The data and catalogs as used in the GNS survey are online at: {\bf http://www.nottingham.ac.uk/astronomy/gns/}. The GNS is financially supported by STFC and the Leverhulme Trust. Support was also provided by NASA/STScI grant HST-GO11082. | 12 | 6 | 1206.6995 |
1206 | 1206.2838.txt | %\boldmath We have performed the first-ever numerical N-body simulation of the full observable universe (DEUS "Dark Energy Universe Simulation" FUR "Full Universe Run"). This has evolved 550 billion particles on an Adaptive Mesh Refinement grid with more than two trillion computing points along the entire evolutionary history of the universe and across 6 order of magnitudes length scales, from the size of the Milky Way to that of the whole observable universe. To date, this is the largest and most advanced cosmological simulation ever run. It provides unique information on the formation and evolution of the largest structure in the universe and an exceptional support to future observational programs dedicated to mapping the distribution of matter and galaxies in the universe. The simulation has run on 4752 (of 5040) thin nodes of BULLÕ supercomputer CURIE, using more than 300 TB of memory for 10 million hours of computing time. About 50 PBytes of data were generated throughout the run. Using an advanced and innovative reduction workflow the amount of useful stored data has been reduced to 500 TBytes. | % no \IEEEPARstart % You must have at least 2 lines in the paragraph with the drop letter % (should never be an issue) Over the past decades cosmological observations have provided us with a clearer picture of the universe \cite{Perlmutter1999,Riess1998,York2000,Spergel2003,Komatsu2009}. On the one hand these measurements have confirmed the pillars of the Standard Hot Big-Bang scenario \cite{Peebles1993}, on the other hand they showed the existence of a class of phenomena whose study has opened a window on a completely new and unexplored territory in physics. The atoms which makes planets, stars, the diffuse gas between galaxies and ourselves account only for a small fraction of the total content of the universe. Quite astonishingly $95\%$ of the cosmos is in the form of two invisible components: $22\%$ is in Cold Dark Matter (CDM) particles, which are primarily responsible for the formation of the visible structures in the universe \cite{Peebles1980}; $73\%$ is in a unknown exotic form, dubbed ``dark energy'' (DE), which is responsible for the present phase of cosmic accelerated expansion \cite{Copeland2006}. Super-symmetric particles and extensions of the Standard Model of particles physics can provide physically motivated candidates to the role of Dark Matter (DM). In contrast, there is little clue on Dark Energy (DE). The presence of a cosmological constant term $\Lambda$ in Einstein's equations of General Relativity \cite{Weinberg1972} can account for the observed phenomenon and the so-called "concordance'' $\Lambda$CDM scenario has emerged as the minimal model to fit all available cosmological observations. However, the measured value of $\Lambda$ is hardly reconcilable with any physical interpretation so far proposed. As a result, Dark Energy may well be of different origin. Several alternative scenarios have been advanced, but to date a coherent physical understanding of DE is still missing. In the lack of a theoretical guidance, cosmologists are turning to observations and in the future several observational projects such as BOSS\cite{BOSS}, DES\cite{DES}, LSST\cite{LSST} and the EUCLID mission\cite{EUCLID} will map with great accuracy the distribution of matter in the universe. These may eventually shed new light on the problem as the clustering of matter may be key to infer the properties of DE. Indeed the physics responsible for DE may alter the time evolution of the clustering of DM which in turn shapes the formation of the visible structures in the universe. {\it What imprints does Dark Energy leave on the cosmic structures? And inversely, how can the nature of Dark Energy be inferred from observations of the distribution of matter in the universe?} These are the fundamental questions that the Dark Energy Universe Simulation\cite{DEUS} (DEUS) project seeks to answer. The galaxy and clusters we observe today are the result of the growth of tiny density fluctuations present in the early universe and which we observe today as temperature fluctuations in the Cosmic Microwave Background (CMB) radiation. The gravitational infall of initial DM density fluctuations has evolved over time to reach a highly non-linear dynamical regime in which DM particles bound into stable objects, the halos. It is inside DM halos that cooling gas falls in to form stars and galaxies and it is the succession of halo mergers that shapes the final distribution of the large scale structures we observe today. Therefore, in order to study the imprint of Dark Energy on the cosmic structure formation one has to follow the gravitational collapse of Dark Matter throughout the history of the universe and across several order of magnitude length scales. This is not realizable using solely analytical methods, which break down as soon as non-linearities develop in the dynamics of DM. Only numerical N-body simulations provide the tool to follow the entire evolution of Dark Matter particles in an expanding universe dominated by Dark Energy. During the past 10 years several groups have pushed to the limits both size and resolution of cosmological N-body simulations. The Millenium Simulation in 2005 has run a $2.2$ billion light-years simulation box with $10$ billion particles \cite{Springel2005}. Since then the performance of cosmological simulations has rapidly increased. The Millenium-XXL simulation has evolved more recently 303 billion particles in a 13 billion light-years box \cite{angulo12}, while the Horizon Run 3 has followed the evolution of 374 billion particles in a 49 billion light-years box. A simulation of the size of the entire observable universe has been a long dreamed goal to infer cosmic variance limited predictions of the properties of the distribution of cosmic structures. In this paper, we present the first-ever numerical simulation of the entire observable universe, from the Big Bang to the present day for the concordance $\Lambda$CDM model. This simulation has followed the gravitational infall of 550 billion particles in a 95 billion light-years simulation box (assuming the adimensional Hubble constant to be $h=0.72$), the size of the entire observable universe. The realization of this simulation, the first of the three planned runs of the DEUS Full Universe Runs (DEUS FUR) project, has used the totality of the CURIE supercomputer provisioned by the Grand \'Equipement National de Calcul Intensif \cite{GENCI} (GENCI) and operated at the "Tr\`es Grand Centre de Calcul" (TGCC) of "Commissariat \`a l'\'Energie Atomique et aux \'Energie Alternatives" \cite{CEA} (CEA). The other two planned runs of Dark Energy models alternative to the $\Lambda$CDM are scheduled for the next few weeks. Here, we will describe the main technical challenges that our team has faced to successfully run the first simulation of the full observable universe. To date this is the most advanced cosmological simulation ever realized. The paper is organized as follows. In Section 2 we briefly review the science implications of N-body simulations in cosmology and compare the DEUS FUR to previous "Grand Challenge'' simulations. In Section 3 we present ``A Multiple purpose Application for Dark Energy Universe Simulation'' (AMA-DEUS) that has been developed specifically for this project (a schematic representation of the application is shown in Figure \ref{AMADEUS}. This application includes the generator of the initial conditions, the numerical algorithms that have been used to solve the gravitational evolution of Dark Matter particles and an innovative reduction workflow to drastically reduce the data stored during the run. Without such a reduction workflow, it would have been impossible to perform the runs. The CURIE supercomputer is briefly presented in Section 4, while in Section 5 we describe the optimization of the numerical codes, the performances that we have been able to obtain and the numerical applications that we have used. Finally, in Section 6 we highlight some preliminary scientific results and present our conclusions. \begin{figure}[b] \centering \includegraphics[scale=0.3]{Figures/DEUS-Challenge.pdf} \caption{A Multiple purpose Application for Dark Energy Universe Simulation "AMA-DEUS": Four components: (i) Generator of initial condition, (ii) Dynamical solver of gravitational clustering, (iii) Post-processing, (iv) Numerical products and storage. } \label{AMADEUS} \end{figure} % An example of a floating figure using the graphicx package. % Note that \label must occur AFTER (or within) \caption. % For figures, \caption should occur after the \includegraphics. % Note that IEEEtran v1.7 and later has special internal code that % is designed to preserve the operation of \label within \caption % even when the captionsoff option is in effect. However, because % of issues like this, it may be the safest practice to put all your % \label just after \caption rather than within \caption{}. % % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class % option should be used if it is desired that the figures are to be % displayed while in draft mode. % %\begin{figure}[!t] %\centering %\includegraphics[width=2.5in]{myfigure} % where an .eps filename suffix will be assumed under latex, % and a .pdf suffix will be assumed for pdflatex; or what has been declared % via \DeclareGraphicsExtensions. %\caption{Simulation Results} %\label{fig_sim} %\end{figure} % Note that IEEE typically puts floats only at the top, even when this % results in a large percentage of a column being occupied by floats. % An example of a double column floating figure using two subfigures. % (The subfig.sty package must be loaded for this to work.) % The subfigure \label commands are set within each subfloat command, the % \label for the overall figure must come after \caption. % \hfil must be used as a separator to get equal spacing. % The subfigure.sty package works much the same way, except \subfigure is % used instead of \subfloat. % %\begin{figure*}[!t] %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}% %\label{fig_first_case}} %\hfil %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}% %\label{fig_second_case}}} %\caption{Simulation results} %\label{fig_sim} %\end{figure*} % % Note that often IEEE papers with subfigures do not employ subfigure % captions (using the optional argument to \subfloat), but instead will % reference/describe all of them (a), (b), etc., within the main caption. % An example of a floating table. Note that, for IEEE style tables, the % \caption command should come BEFORE the table. Table text will default to % \footnotesize as IEEE normally uses this smaller font for tables. % The \label must come after \caption as always. % %\begin{table}[!t] %% increase table row spacing, adjust to taste %\renewcommand{\arraystretch}{1.3} % if using array.sty, it might be a good idea to tweak the value of % \extrarowheight as needed to properly center the text within the cells %\caption{An Example of a Table} %\label{table_example} %\centering %% Some packages, such as MDW tools, offer better commands for making tables %% than the plain LaTeX2e tabular which is used here. %\begin{tabular}{|c||c|} %\hline %One & Two\\ %\hline %Three & Four\\ %\hline %\end{tabular} %\end{table} % Note that IEEE does not put floats in the very first column - or typically % anywhere on the first page for that matter. Also, in-text middle ("here") % positioning is not used. Most IEEE journals/conferences use top floats % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places % footnotes above bottom floats. This can be corrected via the \fnbelowfloat % command of the stfloats package. | %Using CURIE Supercomputer, we have been able to perform the first N-body simulation of the entire observable Universe. More than 10 million CPU-hours were used to follow the gravitational collapse of 8192$^3$ particles in an expanding Universe. This impressive project will be completed with the realization of two additional full universe runs for different DE cosmologies which will allows us to detect the imprints on DE on linear and non-linear cosmic structure observables. %The numerical challenge has lead us to develop highly optimized computational applications and post-processing workflow. In particular, an efficient the data reduction process has enabled us to verify on-flight the quality of the simulation outputs and conveniently store the largest amount of relevant data. %A preliminary analysis already points toward a number of important scientific results such as the non-universality of the halo mass function and the accurate resolution of the BAO signal in the matter power spectrum. Many more studies will be possible thanks to this simulation run. %Overall the strong cooperation and the continuous exchanges between the users and the CURIE support team has been key to the success of this grand challenge project. Acquiring familiarity with the machine, understanding its constraints, improving and adapting applications to the cluster has been hard, but a necessary part of the project. Running this ``grand-challenge'' simulation has been a success from which all concerned parties have benefited, giving everyone the satisfaction of developing outstanding frontier science research while proving the stability of Curis as a truly operational petascale production system. % use section* for acknowledgement | 12 | 6 | 1206.2838 |
1206 | 1206.0731_arXiv.txt | {When an image of a strongly lensed quasar is microlensed, the different components of its spectrum are expected to be differentially magnified owing to the different sizes of the corresponding emitting region. Chromatic changes are expected to be observed in the continuum while the emission lines should be deformed as a function of the size, geometry and kinematics of the regions from which they originate. Microlensing of the emission lines has been reported only in a handful of systems so far. In this paper we search for microlensing deformations of the optical spectra of pairs of images in 17 lensed quasars with bolometric luminosities between $10^{44.7-47.4}$\,erg/s and black hole masses $10^{7.6-9.8} M_{\sun}$. This sample is composed of 13 pairs of previously unpublished spectra and four pairs of spectra from literature. Our analysis is based on a simple spectral decomposition technique which allows us to isolate the microlensed fraction of the flux independently of a detailed modeling of the quasar emission lines. Using this technique, we detect microlensing of the continuum in 85\% of the systems. Among them, 80\% show microlensing of the broad emission lines. Focusing on the most common emission lines in our spectra (\CIII~and \MgII) we detect microlensing of either the blue or the red wing, or of both wings with the same amplitude. This observation implies that the broad line region is not in general spherically symmetric. In addition, the frequent detection of microlensing of the blue and red wings independently but not simultaneously with a different amplitude, does not support existing microlensing simulations of a biconical outflow. Our analysis also provides the intrinsic flux ratio between the lensed images and the magnitude of the microlensing affecting the continuum. These two quantities are particularly relevant for the determination of the fraction of matter in clumpy form in galaxies and for the detection of dark matter substructures via the identification of flux ratio anomalies. } | Soon after the discovery of the first gravitationally lensed quasar, it has been realised that microlensing (ML) produced by compact objects in the lensing galaxy towards a multiply imaged quasar could be used as an astrophysical tool to probe the inner parsecs of distant quasars \citep{Chang1979, Kayser1986, Paczynski1986, Grieger1988}. Microlenses typically magnify regions of the source on scales similar to or smaller than a few micro-arcsecs, the size of their angular Einstein radius $R_E$ \citep{Wambsganss1998, Wambsganss2006, Schmidt2010}. Hence, the quasar continuum region (accretion disc) and the broad line region are likely to be microlensed. Because the magnification varies with the source size, the power law continuum emission of quasars is expected to be more magnified as the wavelength, and hence the continuum size, decreases. Microlensing is therefore expected to produce significant color changes in macro-lensed quasar images \citep{Wambsganss1991}. The latter have indeed been observed \citep[e.g.][]{Wisotzki1993, Claeskens2001, Burud2002a, Wucknitz2003}. The effect on the broad line emitting region (BLR) has been first addressed by \cite{Nemiroff1988} who calculated the changes produced by a single microlensing-star on the emission lines. This analysis has been refined soon after by \cite{Schneider1990a} who considered the more realistic case of ML by a population of microlenses. These papers have demonstrated that microlensing of the BLR could be significant and does depend on the BLR geometry and its kinematics. They also showed that ML of a spherically symmetric BLR (in geometry and velocity field) would lead to symmetric variations of the emission lines (i.e. of the blue and red components) while ML of a keplerian disc would lead in general to asymmetric variations of the emission lines and possible shift of the line centroid. Microlensing affecting more peculiar line profiles from e.g. broad absorption lines quasars, or generated in a relativistic disc have been discussed in \cite{Hutsemekers1993, Hutsemekers1994, Lewis1998b, Belle2000, Popovic2001}. Despite these promising results, detection of microlensing in the emission lines remained elusive \citep{Fillipenko1989a, Lewis1998} or invoked to explain differences between the spectra of candidate lensed quasars \citep{Steidel1991, Small1997}. The interest in BLR microlensing got revived with the papers of \cite{Abajas2002} and of \cite{Lewis2004a}, who re-investigated this question after the discovery that the BLR was smaller than previously thought \citep{Wandel1999, Kaspi2000}. Based on the size of the BLR measured in NGC5548 and using the scaling relation $R_{BLR} \propto L^{0.7}$, \cite{Abajas2002} estimated that the BLR should be significantly microlensed in about $\sim$ 30\% of the systems. They also extended the work of \cite{Nemiroff1988}, and calculated the microlensing by a single lens for various BLR geometries and kinematics, considering BLR models described in \cite{Robinson1995}. \cite{Lewis2004a} extended the work of \cite{Abajas2002} by using more realistic microlensing patterns. Finally, microlensing of a biconical BLR, already presented in \cite{Abajas2002} and in \cite{Lewis2004a}, for two peculiar orientations of the axis of the bicone, has been discussed for more general bicone configurations in \cite{Abajas2007}. These papers have confirmed most of the earlier findings and made more detailed predictions on the line-shifts and asymetries induced by ML. They also showed that the line deformation depends only weakly on the value of the surface density $\kappa$ and shear $\gamma$ at the position of the lensed images, but more strongly on the orientation on the BLR w.r.t. to the direction of the shear. Many papers dedicated to the detection and interpretation of a microlensing signal have focused on the Einstein Cross $\equiv$ Q2237+0305, which is probably the most favourable object for microlensing studies. Indeed, this system has a negligible time-delay between the lensed images, which enables one to easily disentangle microlensing and intrinsic variability, and a low-redshift lensing galaxy which leads to a small $R_E$ and to relatively fast microlensing variations \citep{Mosquera2011}. After the first detection of microlensing in the continuum and in the broad line \citep{Irwin1989, Fillipenko1989a}, microlensing has started to be used as a tool to constrain the size of the accretion disc and of the broad line emitting region \citep{Lewis1998, Wyithe2000a, Yonehara2000, Wyithe2000b}. In the last decade, important progress in observational techniques allowed photometric and spectrophotometric monitoring of the individual lensed images to be successfully carried out \citep{Wozniak2000, Dai2003a, Anguita2008a, Eigenbrod2008a, Zimmer2011}. On the other hand, the development of more advanced numerical techniques allowed quicker calculation of magnification maps and more sophisticated analysis \citep{Kochanek2004a, Poindexter2010a, Poindexter2010b, Bate2010a, Mediavilla2011b, Garsden2011b, Bate2012a}. Owing to these two ingredients, tight constraints on the size of the accretion disc and on its temperature profile, on the size of the broad line region and on its kinematics have been obtained for Q2237+0305 \citep{Eigenbrod2008a, Poindexter2010a, Odowd2011, Sluse2011a}. Most of the recent papers focused on the study of the quasar accretion disc, which can be done using broad band photometry from X-ray to optical and near-infrared wavelengths \citep[e.g.][]{Pooley2007a, Floyd2009a, Hutsemekers2010, Dai2010a, Blackburne2011a, Munoz2011}. Studies of BLR microlensing are more sparse and detections have been reported only for a handful of systems \citep{Richards2004a, Wayth2005, Keeton2006a, Sluse2007, Hutsemekers2010}. In this paper, we present a careful re-extraction and analysis of archive spectra of a sample of 13 lensed quasars initially observed with the aim of measuring the redshift of the lensing galaxy. Our systematic analysis allow us to characterise the microlensing-induced deformation of the emission lines. To get a more complete overview of the microlensing signal, we also discuss the signal detected in four objects we presented elsewhere. From our spectra, we also derive flux ratios corrected for microlensing which are closer to the intrinsic flux ratios between pairs of images. This is important for the study of doubly imaged quasars for which the flux ratios are mandatory to constrain the lens models, because of the few observational constraints in these systems \citep[e.g.][]{Chantry2010, Sluse2011b}. Intrinsic flux ratios are also particularly relevant for the identification of flux ratio anomalies possibly produced by dark matter substructures or ML. A popular technique to study the amount of massive dark matter substructures in galaxies relies on the identification of flux ratios between lensed image pairs which deviate from lens model prediction, i.e. the so called flux ratio anomaly \citep[][ and references therein]{Mao1998, Metcalf2001, Dalal2002, Keeton2003, Fadely2011a, Zackrisson2010}. One of the current limitation of this technique is the small number of reliable flux ratios which may be used to identify an anomaly. Indeed, most of the lensed quasars are observed at visible and near-infrared wavelengths where microlensing and differential extinction significantly contaminate the flux ratios, while only a handful of systems are detected in the mid-infrared or at radio wavelengths where these two effects are negligible. In this paper we discuss how flux ratios derived using spectra may provide a good proxy to intrinsic flux ratios, allowing one to significantly extend the sample of objects where flux ratio anomalies can be studied. The structure of our paper is as follows. In Sect.~\ref{sec:data}, we present the extraction and flux calibration of the archive spectra, and the spectra from literature. In Sect.~\ref{sec:properties}, we derive the physical properties (bolometric luminosity, black hole mass, Eddington ratio) of the lensed quasars. We also discuss there the published redshifts of the quasar and provide an alternative value based on the \MgII~emission line. Sect.~\ref{sec:decomposition} is devoted to the analysis of the microlensing in the spectra. It includes a presentation of the technique used to isolate the microlensed fraction of the flux, a description of the microlensing signal observed in each object and a discussion on the accuracy of our microlensing-corrected flux ratios. In Sect.~\ref{sec:discussion}, we discuss the microlensing signal observed in the continuum, the occurrence and variety of microlensing of the broad lines and the consequences for the structure of the BLR. Finally, we summarize our main results in Sect.~\ref{sec:conclusions}. | \label{sec:conclusions} In this paper we have searched for the presence of microlensing, in the continuum and in the broad emission lines, among strongly lensed quasars based on optical spectroscopy of a sample of 13 systems (3 quadruply and 10 doubly-imaged systems). The spectra of these systems, originally targeted for detecting and measuring the redshift of their lensing galaxy \citep{Eigenbrod2006b, Eigenbrod2007}, have been re-reduced and deconvolved in order to accurately deblend the flux of the lensed images and of the lensing galaxy. For the three systems BRI~0952-0115, SDSS~J1138+0314, SDSS~J1226-0006, these are the first published spectra of the individual lensed images. In order to get a more complete overview of the variety of microlensing signals which can be detected, we have complemented our main sample with previously analysed objects, i.e. SDSS~J0924+0219, HE~2149-2745, J1131-1231, Q2237+0305 and H1413+117, extending our sample to 17 objects. We derive robust estimates of the intrinsic flux ratios $M$ between the lensed images and of the amplitude $\mu$ of microlensing of the continuum. Based on optical spectra only, we have shown that we can retrieve $M$ to typically 0.1 mag accuracy. Higher accuracy may be expected by using spectra separated by the time delay, over a wavelength range extending from UV to NIR. Our ability to derive accurate $M$ and $\mu$ is particularly relevant for the study of the so called ``flux ratio anomalies'' produced by dark matter substructures or microlensing \citep{Mao1998, Dalal2002}. Indeed, current studies of this effect are challenged by the limited number of reliable flux ratios \citep{Keeton2005, Metcalf2011, Xu2011}. Therefore, the use of our technique should help in increasing the number of interesting systems. Our results may also be used to derive the fraction of smooth matter in lensing galaxies. A study of the probability of deriving the observed values of $\mu$ in sample of lensed quasars, varying the fraction of compact/smooth dark matter along the line-of-sight of the lensed images, makes possible to constrain the fraction of matter in compact form in these galaxies \citep{Schechter2004, Pooley2009, Mediavilla2009, Bate2011, Pooley2012}. We find in our sample, which contains sources with bolometric luminosities in the range [$10^{44.7}, 10^{47.4}$]\,erg/s and black hole masses in the range [$10^{7.6}, 10^{9.8}$]$\,M_{\sun}$, that 85\% of the sources show microlensing of the continuum. The microlensing of the continuum is not systematically associated to significant chromatic changes in the optical range. These chromatic changes are not necessarily absent but relatively weak. Because we observe microlensing of the continuum in our sample in the range 0.2-0.8 mag in $R-$band (observed frame), microlensing may in general not be neglected in the $H-$band (1.6 $\mu$m). This implies that studies of the accretion disc based on microlensing will strongly benefit of a large wavelength coverage, extending at least up to the $K-$band. Another consequence is that microlensing may often exceed differential extinction in the NIR, leading to possible biases in studies of extragalactic extinction curves in lensed quasars. Using our MmD decomposition technique, we have been able to unveil microlensing-induced deformation of the emission lines independently of a detailed modeling of the quasar spectrum. Among the systems with a microlensed continuum, 80\% show deformations of at least one broad emission line. The two major characteristics of the signal are its relatively low amplitude (typically 10 \% of the line is affected) and its variety. We searched for correlation between the observed microlensing signal and the luminosity, black hole mass and Eddington ratio of the microlensed quasars, but we did not find any clear correlation. Contrary to most previous observations, we frequently detect microlensing of either the blue or the red wing of the broad emission lines instead of a signal affecting roughly symmetrically both components. This simple observation implies that the BLR does not have a spherically symmetric geometry and velocity field, at least in those objects. Microlensing of only one wing of the line has been observed recurrently in the past for SDSS~J1004+4112 \citep{Richards2004a, Lamer2006, Gomez2006}. \cite{Abajas2007} has shown that the signal observed in that system is compatible with microlensing of a biconical wind but that in general the two wings should be affected by microlensing, with different amplitudes. Such a signal is detected in only one system of our sample. This suggests that the simple biconical model is not adequate for the BLR of the lines we studied (\CIII~and \MgII). A modified keplerian disc \citep{Abajas2002} seems to be a promising alternative as a ``generic'' BLR model. | 12 | 6 | 1206.0731 |
1206 | 1206.2502_arXiv.txt | The observation of the polarization emerging from a rotating star at different phases opens up the possibility to map the magnetic field in the stellar surface thanks to the well-known Zeeman Doppler Imaging. When the magnetic field is sufficiently weak, the circular and linear polarization profiles locally in each point of the star are proportional to the first and second derivatives of the unperturbed intensity profile, respectively. We show that the weak-field approximation (for weak lines in the case of linear polarization) can be generalized to the case of a rotating star including the Doppler effect and taking into account the integration on the stellar surface. The Stokes profiles are written as a linear combination of wavelength-dependent terms expressed as series expansions in terms of Hermite polynomials. These terms contain the surface integrated magnetic field and velocity components. The direct numerical evaluation of these quantities is limited to rotation velocities not larger than 8 times the Doppler width of the local absorption profiles. Additionally, we demonstrate that, in a rotating star, the circular polarization flux depends on the derivative of the intensity flux with respect to the wavelength and also on the profile itself. Likewise, the linear polarization depends on the profile and on its first and second derivative with respect to the wavelength. We particularize the general expressions to a rotating dipole. | The present knowledge of solar and stellar magnetism derives essentially from the interpretation of polarization in spectral lines due to the Zeeman effect\footnote{There are some notable exceptions as, for example, the study of the quiet Sun magnetism by means of the interpretation of scattering polarization and its modification by the Hanle effect \citep[e.g.,][for a recent review]{trujillo_spw6_11}}. In the presence of a weak magnetic field, the radiative transfer equation for polarized light can be solved analytically and it is known as the ``weak field approximation''. Although very simple, it relies on a set of strong assumptions that we discuss later. However, the weak field approximation is applicable in many scenarios and gives very good results for the inference of magnetic fields as compared with more elaborate methods. In solar physics, it is at the heart of the success of a large number of synoptic magnetographs, like those of Big Bear \citep{varsik95,spirock01}. It has been also used recently to produce vector magnetograms with the Imaging Magnetograph Experiment (IMaX) instrument \citep{imax11} onboard the Sunrise balloon \citep{sunrise10}. In stellar spectropolarimetry, the weak field approximation is at the base of the least-squares deconvolution \citep[LSD;][]{donati97}, the most successful technique used to detect and measure magnetic fields in solar-type stars, or in some recent works on central stars of planetary nebulae \citep{jordan05,leone11}, white dwarfs \citep{aznar_cuadrado04}, pulsating stars \citep{silvester09}, hot subdwarfs \citep{otoole05} and Ap and Bp stars \citep{wade00,bagnulo02}. Most of the scientific cases commented so far deal with unresolved structures which means that the weak field approximation has to be understood in terms of fluxes of the Stokes parameters instead of specific intensities. Recently, \cite{marian_dipolo12} derived the weak field expressions in terms of fluxes, particularizing to the case of the stellar dipole. They neglected rotation to simplify the equations and to derive analytical expressions for the inference of the magnetic field. When rotation is taken into account (in other words, there is a correlation between the magnetic field and the line-of-sight velocity), the problem becomes much more challenging and it is usually solved numerically \citep[e.g.,][for a recent effort]{petit_wade12}. However, we show in this paper that it is possible to obtain analytical expressions for the Stokes vector fluxes in the weak field approximation. There are two interests on this effort. First, having an analytical expression for the Stokes flux might be of help to investigate the interplay between rotation and the magnetic field. Second, it can be used to speed up inversion codes based on the weak-field approximation because no numerical integration is needed. This will facilitate the application of Bayesian inference codes, like the one developed by \cite{petit_wade12}, that are based on Markov Chain Monte Carlo methods that need to carry out the synthesis thousands of times to sample the posterior distribution. This is the first paper of a series dealing with analytical expressions for the fluxes of the Stokes parameters in the weak field limit. This paper deals with the expressions for a rotating star with a magnetic field on its surface. The results depend on the correlation between the magnetic field and the velocity and are general for any rotation profile or any magnetic field configuration. We particularize the equations to the case of a rotating magnetic stellar dipole. | We have generalized the expressions for the Stokes parameters in the weak-field weak-line regime to the stellar case in which rotation is taken into account. This produces an intensity flux profile that is broadened by rotation while it is insensitive to the magnetic field. As a consequence, our formalism can only be applied to stars in which the intensity profile is not observed to be modulated by rotation. However, the circular and linear polarized fluxes are sensitive to the topology of the magnetic field. We have demonstrated that the inclusion of Doppler shifts generates a dependence of circular polarization of the intensity flux itself, and not only on its wavelength derivative. Likewise, the linear polarization profiles depend now on the first and second wavelength derivative and on the intensity flux itself. We have verified also that the expressions developed in this paper simplify to those obtained by \cite{marian_dipolo12} in the non-rotating dipole case. The general weak-field expressions have been particularized to a rotating dipole. The extension to a more general multipolar magnetic field is relatively easy and can be done fast if analytical expressions for the angular and radial integrals exist. In subsequent papers of this series we will deal with thin magnetized disks in Keplerian rotation and unresolved structures in the quiet Sun. Likewise, we will also explore the possibility of using more elaborate expansions to improve the convergence. | 12 | 6 | 1206.2502 |
1206 | 1206.2819_arXiv.txt | A subpopulation of neutron stars (NSs), known as central compact objects (CCOs) in supernova remnants, are suspected to be low-field objects basing on $P$~--~$\dot P$ measurements for three of them. The birth rate of low-field NSs is probably comparable with the birth rate of normal radio pulsars. However, among compact objects in High-Mass X-ray Binaries (HMXBs) we do not see robust candidates for low-field NSs. We propose that this contradiction can be solved if magnetic fields of CCOs was buried due to strong fall-back, and then the field emerges on the time scale $10^4$~--$10^5$~yrs. | 12 | 6 | 1206.2819 |
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1206 | 1206.0507_arXiv.txt | We have considered the FRW universe in loop quantum cosmology (LQC) model filled with the dark matter (perfect fluid with negligible pressure) and the modified Chaplygin gas (MCG) type dark energy. We present the Hubble parameter in terms of the observable parameters $\Omega_{m0}$, $\Omega_{x0}$ and $H_{0}$ with the redshift $z$ and the other parameters like $A$, $B$, $C$ and $\alpha$. From Stern data set (12 points), we have obtained the bounds of the arbitrary parameters by minimizing the $\chi^{2}$ test. The best-fit values of the parameters are obtained by 66\%, 90\% and 99\% confidence levels. Next due to joint analysis with BAO and CMB observations, we have also obtained the bounds of the parameters ($B,C$) by fixing some other parameters $\alpha$ and $A$. From the best fit of distance modulus $\mu(z)$ for our theoretical MCG model in LQC, we concluded that our model is in agreement with the union2 sample data. | } The combinations of different observations astrophysical data continuously testing the theoretical models and the bounds of the parameters. Different observations of the SNeIa \cite{Perlmutter,Perlmutter1,Riess,Riess1}, large scale redshift surveys \cite{Bachall,Tedmark}, the measurements of the cosmic microwave background (CMB) \cite{Miller,Bennet} and WMAP \cite{Briddle,Spergel} indicate that our universe is presently expanding with acceleration. Standard big bang Cosmology with perfect fluid fails to accommodate the observational fact. In Einstein's gravity, the cosmological constant $\Lambda$ (which has the equation of state $w_{\Lambda}=-1$) is a suitable candidate which derive the acceleration, but till now there is no proof of the origin of $\Lambda$. Now assume that there is some unknown matter which is responsible for this accelerating scenario which has the property that the positive energy density and sufficient negative pressure, know as dark energy \cite{Paddy,Sahni}. The scalar field or quintessence \cite{Peebles} is one of the most favored candidate of dark energy which produce sufficient negative pressure to drive acceleration in which the potential dominates over the kinetic term. In the present cosmic concordance $\Lambda$CDM model the Universe is formed of $\sim$ 26\% matter (baryonic + dark matter) and $\sim$ 74\% of a smooth vacuum energy component. The thermal CMB component contributes only about 0.01\%, however, its angular power spectrum of temperature anisotropies encode important information about the structure formation process and other cosmic observables.\\ If we assume a flat universe and further assume that the only energy densities present are those corresponding to the non-relativistic dust-like matter and dark energy, then we need to know $\Omega_{m}$ of the dust-like matter and $H(z)$ to a very high accuracy in order to get a handle on $\Omega_{X}$ or $w_{X}$ of the dark energy \cite{Paddy1,Paddy2}. This can be a fairly strong degeneracy for determining $w_{X}(z)$ from observations. TONRY data set with the 230 data points \cite{Tonry} alongwith the 23 points from Barris et al \cite{Barris} are valid for $z>0.01$. Another data set consists of all the 156 points in the ``gold'' sample of Riess et al \cite{Riess1}, which includes the latest points observed by HST and this covers the redshift range $1 < z < 1.6$. In Einstein's gravity and in the flat model of the FRW universe, one finds $\Omega_{\Lambda}+\Omega_{m}=1$, which are currently favoured strongly by CMBR data (for recent WMAP results, see \cite{Spergel}). In a simple analysis for the most recent RIESS data set gives a best-fit value of $\Omega_{m}$ to be $0.31\pm 0.04$. This matches with the value $\Omega_{m}=0.29^{+0.05}_{-0.03}$ obtained by Riess et al \cite{Riess}. In comparison, the best-fit $\Omega_{m}$ for flat models was found to be $0.31\pm 0.08$ \cite{Paddy1}. The flat concordance $\Lambda$CDM model remains an excellent fit to the Union2 data with the best-fit constant equation of state parameter $w=-0.997^{+0.050}_{-0.054}$(stat)$^{+0.077}_{-0.082}$(stat+sys together) for a flat universe, or $w=-1.038^{+0.056}_{-0.059}$(stat)$^{+0.093}_{-0.097}$(stat+sys together) with curvature \cite{Amanullah}. Chaplygin gas is the more effective candidate of dark energy with equation of state $p=-B/\rho$ \cite{Kamenshchik} with $B>0$. It has been generalized to the form $p=-B/\rho^{\alpha}$ \cite{Gorini} and thereafter modified to the form $p=A\rho-B/\rho^{\alpha}$ \cite{Debnath}. The MCG best fits with the 3 year WMAP and the SDSS data with the choice of parameters $A =0.085$ and $\alpha = 1.724$ \cite{Lu} which are improved constraints than the previous ones $-0.35 < A < 0.025$ \cite{Jun}.\\ In recent years, loop quantum gravity (LQG) is a outstanding effort to describe the quantum effect of our universe. Nowadays several dark energy models are studied in the frame work of loop quantum cosmology (LQC). Quintessence and phantom dark energy models \cite{Wu,Chen} have been studied in the cosmological evolution in LQC. When the Modified Chaplying Gas coupled to dark matter in the universe is described in the frame work LQC by Jamil et al \cite{jamil} who resolved the famous cosmic coincidence problem in modern cosmology. In another study \cite{Fu} the authors studied the model with an interacting phantom scalar field with an exponential potential and deduced that the future singularity appearing in the standard FRW cosmology can be avoided by loop quantum effects. Here we assume the FRW universe in LQC model filled with the dark matter and the MCG type dark energy. We present the Hubble parameter in terms of the observable parameters $\Omega_{m}$, $\Omega_{x}$ and $H_{0}$ with the redshift $z$. From Stern data set (12 points), we obtain the bounds of the arbitrary parameters by minimizing the $\chi^{2}$ test. The best-fit values of the parameters are obtained by 66\%, 90\% and 99\% confidence levels. Next due to joint analysis with BAO and CMB observations, we also obtain the bounds and the best fit values of the parameters ($B,C$) by fixing some other parameters $A$ and $\alpha$. From the best fit of distance modulus $\mu(z)$ for our theoretical MCG model in LQC, we concluded that our model is in agreement with the union2 sample data. | } Modified Chaplygin gas (MCG) is one of the candidate of unified dark matter-dark energy model. We have considered the FRW universe in loop quantum cosmology (LQC) model filled with the dark matter (perfect fluid with negligible pressure) and the modified Chaplygin gas (MCG) type dark energy. We present the Hubble parameter in terms of the observable parameters $\Omega_{m0}$, $\Omega_{x0}$ and $H_{0}$ with the redshift $z$ and the other parameters like $A$, $B$, $C$ and $\alpha$. We have chosen the observed values of $\Omega_{m0}=0.28$, $\Omega_{x0}=0.72$ and $H_{0}$ = 72 Kms$^{-1}$ Mpc$^{-1}$. From Stern data set (12 points), we have obtained the bounds of the arbitrary parameters by minimizing the $\chi^{2}$ test. Next due to joint analysis of BAO and CMB observations, we have also obtained the best fit values and the bounds of the parameters ($B,C$) by fixing some other parameters $A=1,1/3,-1/3$ and $\alpha=0.5$. The best-fit values and bounds of the parameters are obtained by 66\%, 90\% and 99\% confidence levels are shown in figures 1-9 for Stern, Stern+BAO and Stern+BAO+CMB analysis. The distance modulus $\mu(z)$ against redshift $z$ has been drawn in figure 10 for our theoretical model of the MCG in LQC for the best fit values of the parameters and the observed SNe Ia Union2 data sample. So our predicted theoretical MCG model in LQC permitted the observational data sets. The observations do in fact severely constrain the nature of allowed composition of matter-energy by constraining the range of the values of the parameters for a physically viable MCG in LQC model. We have checked that when $\rho_{c}$ is large, the best fit values of the parameters and other results of LQC model in MCG coincide with the results of the ref. [29] in Einstein's gravity. When $\rho_{c}$ is small, the best fit values of the parameters and the bounds of parameters spaces in different confidence levels in LQC distinguished from Einstein's gravity for MCG dark energy model. Also, in particular, if we consider the generalized Chaplygin gas ($A=0$), the best fit value of critical Barbero-Immirzi parameter $\gamma$ is 0.2486, where we have assumed the values of other parameters $\alpha=0.5$ and $B=0.561$ for our convenience. In summary, the conclusion of this discussion suggests that even though the effect that quantum aspect of gravity have on the CMB are small, cosmological observation can put upper bounds on the magnitude of the correction coming from quantum gravity that may be closer to the theoretical expectation than what one would expect.\\ | 12 | 6 | 1206.0507 |
1206 | 1206.2391_arXiv.txt | Using {\em RHESSI} hard X-ray imaging spectroscopy observations, we analyze electron flux maps for a number of extended coronal loop flares. For each event, we fit a collisional model with an extended acceleration region to the observed variation of loop length with electron energy $E$, resulting in estimates of the plasma density in, and longitudinal extent of, the acceleration region. These quantities in turn allow inference of the number of particles within the acceleration region and hence the filling factor $f$ -- the ratio of the emitting volume to the volume that encompasses the emitting region(s). We obtain values of $f$ that lie mostly between $0.1$ and $1.0$; the (geometric) mean value is $f = 0.20 \, \times\!/\!\div \, 3.9$, somewhat less than, but nevertheless consistent with, unity. Further, coupling information on the number of particles in the acceleration region with information on the total rate of acceleration of particles above a certain reference energy (obtained from spatially-integrated hard X-ray data) also allows inference of the specific acceleration rate (electron~s$^{-1}$ per ambient electron above the chosen reference energy). We obtain a (geometric) mean value of the specific acceleration rate $\eta(20$~keV) $ = (6.0 \, \times\!/\!\!\div \, 3.4) \times 10^{-3}$~electrons~s$^{-1}$~per ambient electron; this value has implications both for the global electrodynamics associated with replenishment of the acceleration region and for the nature of the particle acceleration process. | An important diagnostic of high-energy electrons accelerated in solar flares is the hard X-ray bremsstrahlung that they produce as they propagate through the ambient solar atmosphere. The Ramaty High Energy Solar Spectroscopic Imager ({\em RHESSI\ }) has revealed a new class of flares in which the bulk of the hard X-ray emission is produced predominantly not in dense chromospheric footpoints, but rather in the coronal loop \citep{vebr04, suetal04,krucker08}. For such sources, the corona is not only the site of particle acceleration, but also dense enough to act as a thick target, stopping the accelerated electrons before they can penetrate to the chromosphere. For suprathermal electrons with energy substantially greater than the thermal energy of the ambient electrons with which they interact, it is appropriate to use a collisional cold-target energy loss rate \citep[e.g.,][]{1978ApJ...224..241E}, for which the penetration depth of electrons increases with energy. \citet{xuetal08} analyzed a set of extended coronal flare loops located near the solar limb, and were indeed able to account for the observed behavior of loop extent with photon energy $\epsilon$ in terms of a cold-target collisional model with an extended acceleration region. \citet{guoetal2012} have extended this analysis technique to a study of the variation of loop size with {\it electron} energy $E$, in which the visibilities used to construct the electron flux images are obtained by regularized spectral inversion of the visibility data in the count domain \citep{pianaetal07}. Here we apply this new analysis technique to several simple coronal loop events observed by {\em RHESSI}. In Section~\ref{events}, we present basic data for the 22 events used in the study. In Section~\ref{analysis} we fit the variation of loop size with electron energy $E$ to the parametric model of \citet{guoetal2012} in order to determine the acceleration region length $L_0$ and density $n$ for each event. In Section~\ref{results} these values are used to determine estimates of two important properties of the acceleration region -- the filling factor $f$ (the ratio of the volume that is actively involved in electron acceleration to the overall volume that encompasses the acceleration region[s]) and the specific acceleration rate $\eta(E_0)$ (the rate of acceleration of electrons to energies $\ge E_0$ per ambient electron), and we compare the values of these quantities to the predictions of various acceleration models. | \label{results} \begin{deluxetable} {cccccccc} \tablewidth{0pt} \tabletypesize{\scriptsize} \tablecaption{Acceleration Region Characteristics\label{table:params}} \tablehead{ \colhead{Event No.} & \colhead{$L_0$ (arcsec)} & \colhead{$W$ (arcsec)} & \colhead{$V_0$ (100~arcsec$^3$) } & \colhead{$n$ ($10^{11}$~cm$^{-3}$)} & \colhead{${\cal N}$ ($10^{37}$) } & \colhead{$\eta$~(20 keV) ($10^{-3}$~s$^{-1}$) } & \colhead{$f$} } \startdata 1 & $18.6$ & $7.0$ & $7.2$ & $1.5$ & $4.1$ & $6.5$ & $0.45$\\ 2 & $16.3$ & $6.9$ & $6.2$ & $1.4$ & $3.2$ & $14.5$ & $0.83$ \\ \hline 3 & $16.7$ & $7.3$ & $7.0$ & $4.4$ & $11.7$ & $4.0$ & $0.04$\\ 4 & $16.6$ & $7.3$ & $7.0$ & $4.8$ & $12.8$ & $7.3$ & $0.11$ \\ 5 & $16.6$ & $8.2$ & $8.7$ & $10.5$ & $34.9$& $3.3$ & $0.03$\\ \hline 6 & $11.9$ & $5.9$ & $3.3$ & $4.9$ & $6.0$ & $0.6$ & $0.02$\\ 7 & $10.4$ & $6.0$ & $3.0$ & $1.8$ & $2.0$ & $12.1$ & $0.44$\\ \hline 8 & $17.8$ & $6.9$ & $6.4$ & $2.6$ & $7.1$ & $24.1$ & $0.90$\\ 9 & $18.8$ & $6.6$ & $6.5$ & $2.9$ & $7.7$ & $23.1$ & $1.05$ \\ \hline 10 & $15.1$ & $6.0$ & $4.2$ & $2.9$ & $5.4$ & $13.8$ & $0.72$\\ 11 & $16.0$ & $5.7$ & $4.1$ & $1.9$ & $3.1$ & $27.8$ & $1.95$\\ \hline 12 & $10.3$ & $6.6$ & $3.5$ & $5.1$ & $6.7$ & $4.9$ & $0.08$ \\ 13 & $9.9$ & $6.5$ & $3.3$ & $4.6$ & $5.7$ & $4.1$ & $0.18$ \\ \hline 14 & $21.5$ & $5.3$ & $4.8$ & $1.5$ & $2.8$ & $1.4$ & $0.13$ \\ 15 & $17.4$ & $6.3$ & $5.4$ & $0.8$ & $1.7$ & $1.7$ & $1.03$ \\ 16 & $17.8$ & $6.4$ & $5.8$ & $2.3$ & $5.1$ & $0.3$ & $0.18$ \\ \hline 17 & $11.0$ & $6.2$& $3.3$ &$3.9$ & $5.0$ & $2.9$ & $0.05$ \\ 18 & $9.9$ & $6.3$& $3.1$ &$3.2$ & $3.8$ & $7.0$ & $0.22$ \\ \hline 19 & $19.9$ & $6.2$ & $6.1$ &$11.1$ & $25.7$ & $13.6$ & $0.02$\\ 20 & $14.5$ & $6.1$ & $4.2$ &$5.2$ & $8.3$ & $23.4$ & $0.10$ \\ \hline 21 & $9.9$ & $6.1$ & $2.9$ &$2.2$ & $2.4$ & $16.5$ & $0.53$ \\ \hline 22 & $12.4$ & $6.0$ & $3.6$ &$1.7$ & $2.3$ & $5.2$ & $0.26$ \\ \hline Geometric Mean & 14.5 & 6.4 & 4.7 & 2.9 & 5.4 & 6.0 & 0.20 \\ $\times/\div$ & 1.3 & 1.1 & 1.4 & 1.9 & 2.2 & 3.4 & 3.9 \\ \enddata \end{deluxetable} The values of $L_0$, $W$, $V_0$, $n$, ${\cal N}$, $\eta(20$~keV) and $f$ for each event are presented in Table~\ref{table:params}. While statistical uncertainties in these values could readily be calculated through a Monte Carlo method in which noise is added to the {\em RHESSI} count visibility data and the process repeated \citep[see][]{guoetal2012}, we have intentionally refrained from doing so here, since the approximations and assumptions used in the model doubtless entail even larger uncertainties. Instead, we let the scatter of the inferred values of the parameters across the 22 events determine the extent over which the parameters range. We have calculated (Table~\ref{table:params}) the value of the (geometric) mean value of each quantity and the (multiplicative) uncertainty in this value. In particular, we obtain $n = (2.9 \times \!\!/\!\div 1.9) \times 10^{11}$~cm$^{-3}$, $f = 0.20 \, \times\!/\!\div 3.9$, and $\eta(20$~keV)~$ = (6.0 \times\!/\!\div 3.4) \times 10^{-3}$~electrons~s$^{-1}$~per ambient electron. Returning to the simplifying assumptions used in determining the form of the electron flux $F(E,s)$ (Equations~[\ref{assumptions}] and~[\ref{fes}]), we note that inclusion of electron trajectories that have a non-zero pitch angle to the guiding magnetic field and/or a guiding magnetic field that is inclined to the longitudinal axis (the direction defining the coordinate $s$) will add a factor $\mu = \overline {\cos \theta}$, where $\theta$ is the angle between the electron velocity vector and the longitudinal direction, to the energy-dependent term in Equation~(\ref{model-electron}). This will result in a decrease (by a multiplicative factor $\mu$) in the inferred density $n$, which in turn, by Equations~(\ref{number_of_particles}), (\ref{acceleration-rate}) and~(\ref{filling-factor}), will increase the values of $f$ and $\eta$ by factors of $1/\mu^2$ and $1/\mu$, respectively. Inclusion of return current Ohmic energy losses and/or energy losses to waves through collective plasma effects will also decrease the electron penetration depth, leading to further decreases in the inferred value of $n$ and so increases in $f$ and $\eta$. The values of $f$ and $\eta$ cited above are therefore in all likelihood lower limits. The inferred values of $f$ are generally somewhat less than unity, with the exception of three events (\#\# 9, 11 and 15), for which $f =$~1.05, 1.95 and 1.03, respectively. Given the uncertainties in the data, the approximations in the analysis method, and the factor of four spread in the inferred values of $f$, neither of these values exceeds unity by an alarming margin. The mean value of the filling factor obtained is consistent, within a logarithmic standard deviation or so, with unity. This result, while not entirely surprising, is nevertheless still significant. It validates the assumption used by many authors \citep[e.g.,][]{emslieetal04} that most of the observed flare volume contains bremsstrahlung-emitting electrons; the degree to which the emission is fragmented (e.g., striated into ``kernels'' or ``strands'' of emission situated within a relatively inert background medium) is quite small. The inferred mean value of $\eta$(20~keV) $\simeq 5 \times 10^{-3}$~electrons~s$^{-1}$~per ambient electron is broadly consistent with the values reported for a series of extended-loop-source events by \citet{emslie2008AIP}. It should also be noted that the value of the specific acceleration rate for Event \#4 (the ``midnight flare'' of 2002~April~15) has been determined independently by \citet{torre2012}, who used a continuity equation analysis of the variation of the electron flux spectrum throughout the source. The specific acceleration rate $\eta(20$~keV)$=11 \times 10^{-3}$~s$^{-1}$ obtained by \citet{torre2012} is consistent with the value of $7.3 \times 10^{-3}$~s$^{-1}$ deduced here. The observationally-deduced value $\eta \simeq 10^{-2}$~s$^{-1}$ implies that all available electrons would be energized and ejected towards the footpoints within a few hundred seconds. This result has significant implications for supply of electrons to the acceleration region, current closure, and the global electrodynamic environment in which electron acceleration and propagation occur \citep[see, e.g.,][]{emslie1995}. The values of the filling factor $f$ deduced herein are broadly consistent with stochastic acceleration models \citep[e.g.,][Bian et al 2012, ApJ, in press]{petrosian_liu2004, bian2011} which generally involve a near-homogeneous distribution of scattering centers. In addition, the deduced values of the specific acceleration rates $\eta$ are also broadly consistent with such models. For example, in their study of electron (and proton) acceleration in a turbulent magnetohydrodynamic wave cascade, \citet[][their Figures 6, 7, 9, 10 and 12]{1996ApJ...461..445M} derive values of the volumetric electron acceleration rate $\sim (1.5 - 4) \times 10^8$~cm$^{-3}$~s$^{-1}$ above 20~keV, with the exact value dependent on the assumptions of the various models considered. In the \citet{1996ApJ...461..445M} model, the background number density is $n=10^{10}$~cm$^{-3}$, so that $\eta \sim (1.5 - 4) \times 10^{-2}$~s$^{-1}$ above 20~keV. On the other hand, values of the filling factor $f$ close to unity pose significant challenges for particle acceleration models that involve highly localized geometries, such as super-Dreicer acceleration in thin current sheets \citep[see, e.g.,][]{litvinenko2000,turkmani2006pas}. Turning to the specific acceleration rate in such an acceleration scenario, \citet{heerikhuisen2002paa} find (their equation~[3.17]) a rate of {\it proton} acceleration $d{\cal N}_p/dt \simeq 2 \times 10^{37} \, \sqrt{\zeta}$~s$^{-1}$, where $\zeta$ \citep[$\eta$ in the notation of][]{heerikhuisen2002paa} is the Lundquist number, the ratio of the diffusive to advective terms in the magnetic diffusion equation. Following \citet{heerikhuisen2002paa}, we take $\zeta = 10^{-8}$, giving a proton acceleration rate $d{\cal N}_p/dt \sim 2 \times 10^{33}$~s$^{-1}$, and we take the number of protons available for acceleration as ${\cal N}_p \sim \varepsilon n \, L^3$, where $\varepsilon \simeq 0.4 \, \sqrt{\zeta} \simeq 4 \times 10^{-5}$ is the angle at the magnetic X-type neutral point at the origin of the acceleration region. With an ambient density $n \simeq 10^{11}$~cm$^{-3}$ and a longitudinal acceleration region extent $L \sim 10^9$~cm, ${\cal N}_p \sim 4 \times 10^{33}$ and so $\eta \simeq 2$~s$^{-1}$. Although this value is much greater than the values of $\eta$ deduced here (it corresponds to the acceleration of all ambient particles in less than a second), it must be again stressed that the \cite{heerikhuisen2002paa} model refers to highly efficient acceleration of a relatively small number of {\it protons} in a very localized geometry. We encourage calculations of specific acceleration rates for electrons in such a model, and indeed in all theoretical particle acceleration scenarios. | 12 | 6 | 1206.2391 |
1206 | 1206.2996_arXiv.txt | The PIAA is a now well demonstrated high contrast technique that uses an intermediate remapping of the pupil for high contrast coronagraphy (apodization), before restoring it to recover classical imaging capabilities. This paper presents the first demonstration of complete speckle control loop with one such PIAA coronagraph. We show the presence of a complete set of remapping optics (the so-called PIAA and matching inverse PIAA) is transparent to the wavefront control algorithm. Simple focal plane based wavefront control algorithms can thus be employed, without the need to model remapping effects. Using the Subaru Coronagraphic Extreme AO (SCExAO) instrument built for the Subaru Telescope, we show that a complete PIAA-coronagraph is compatible with a simple implementation of a speckle nulling technique, and demonstrate the benefit of the PIAA for high contrast imaging at small angular separation. | Contrast limits for the direct imaging of extrasolar planets from ground based adaptive optics (AO) observations are currently set by the presence of static and slow-varying aberrations in the optical path that leads to the science instrument \citep{2003EAS.....8..233M}. These aberrations, due to the non-common path error between the wavefront sensor and the science camera are responsible for the presence of long lasting speckles in the image. Because extrasolar planets are unresolved sources, it is difficult to discriminate them among these speckles. One family of techniques, called differential imaging, is aimed at calibrating out some of these static aberrations, by using either sky rotation (Angular Differential Imaging, or ADI), polarization (PDI), or wavelength dependence of the speckles (Spectral Differential Imaging or SDI). Of these, ADI \citep{2006ApJ...641..556M} seems very well adapted to the problem of the detection of extrasolar planets, and has been successful, most notably producing the image of the planetary system around HR 8799 \citep{2008Sci...322.1348M}. ADI uses the rotation of the sky that naturally happens while tracking with an alt-azimuthal telescope around transit. The position of static and slowly varying speckles, tied to the diffraction by the pupil, remains stable over long timescales, while the image of planetary companions rotates around the one of the host star. The rotation of the field only leads to sufficient linear displacement for angular separations of the order of one arcsecond. And in practice, below 0.5 arcsecond, the performance of ADI quickly degrades below the threshold where planets can be detected. One way to complement ADI toward small angular separation, is to use a deformable mirror (DM) to modulate speckles and introduce the diversity that will distinguish them from genuine structures like planets and lumps in disks. This type of technique is regularly used for high contrast experiments \citep{2010PASP..122...71G}, and appears as the technique of choice for a space borne mission dedicated to the direct imaging of high contrast planets. This is also the approach we propose to use for the detection of extrasolar planets at small angular separation during ground-based adaptive optics (AO) observations. In that scope we are integrating and testing the Subaru Coronagraphic Extreme AO (SCExAO) project, whose optics have been described by \citet{2009PASP..121.1232L} and \citet{2011SPIE.8151E..22M}. In comparison with other extreme-AO projects \citep{2008SPIE.7015E..31M, 2010lyot.confE..44B}, SCExAO implements an aggressive PIAA-coronagraph using a remapping of the pupil \citep{2005ApJ...622..744G, 2006ApJ...639.1129M} optimized for high-contrast detection at small angular separations (down to 1 $\lambda/D$). Laboratory high-contrast experiments relying on PIAA have demonstrated high contrast imaging capabilitty in the 2-4 $\lambda/D$ angular separation range, and achieved raw contrast of $\sim10^{-7}$ and beyond \citep{2010PASP..122...71G,2011SPIE.8151E...3K,2011SPIE.8151E...1B}, that are several orders of magnitude beyond what a ground based instrument is expected to produce \citep{2005ApJ...629..592G}. From a reasonably good starting point, these experiments can produce high contrast images in a fairly small number of iterations, using electric field conjugation (EFC) framework that relies on an acute knowledge of the system's complex amplitude response matrix \citep{2006PhDT........47G,2006ApJ...638..488B}. Ultimately, these techniques seem implementable at the telescope once an extreme AO system produces a continuous stream of stable high-Strehl images. They remain for now limited to the pampered environment of the laboratory. At this stage of its development (what is refered to as SCExAO Phase 1), SCExAO does not include a fully functioning high order wavefront sensor. The 32x32 DM it implements can be nevertheless used to actively generate speckle diversity and supplement ADI at small angular separations. SCExAO phase 1 relies on iterative speckle nulling, to produce a dark hole \citep{1995PASP..107..386M} in the field. | We have, for the first time, demonstrated focal plane wavefront control capability in a complete PIAA - focal plane mask - inverse PIAA system. Using a simple iterative speckle nulling algorithm, we successfully produced a high contrast region in the field (the so-called dark hole), and therefore confirmed that the complete set of remapping optics (PIAA and inverse PIAA) are transparent to the focal plane based wavefront control. We have also confirmed that the outer working angle allowable by the number of actuators of the deformable mirror is preserved during the double remapping. This implies that PIAA-type coronagraphs can be very well be used on ground and space-based telescopes with no loss of outer working angle and do not require complex wavefront control algorithms. High performance high efficiency coronagraphy therefore does not translate into increased system complexity. Note that while we tested PIAA with a large mask imposing a 2.2 $\lambda/D$ inner working angle), the conclusions of this paper will hold for more IWA-optimized PIAA coronagraphs, including the PIAACMC \citep{2010ApJS..190..220G} that exhibit IWA $< 1 \lambda/D$. Combined with focal plane based wavefront control to what this paper demonstrates, such aggressive designs make coronagraphy onboard small telescopes ($\sim$2 meters) in space a relevant option for the direct detection of extrasolar planets. They also offer the potential for imaging reflected light planets at very small separation with the forthcoming generation of extrely large telescopes. One should also note that the moderate contrast level results presented here were achieved in monochromatic light. Yet at the $10^{-4}$ to $10^{-6}$ raw contrast level ground-based extreme AO systems will give access to, speckle nulling remains a valid option in polychromatic light. The coronagraph currently in place in SCExAO does not take into account the spider vanes in the pupil, while these are responsible for most of the light observed in the final focal plane of the instrument. Consequently, the wavefront control algorithm must use pupil phase introduced by the deformable mirror to remove, over half of the focal plane, light diffracted by the spider vanes, as shown in figure \ref{fig:vmap}. This approach is simply not suitable in a broad spectral band, and the SCExAO coronagraph will be updated to a PIAACMC type coronagraph to solve this issue. Finally, while the results presented in this paper demonstrate the raw contrast required for ground-based system, it is unclear to which extent the approach adopted in this work is suitable for the $\sim10^{-9}$ contrast level that future space-based missions hope to reach in order to image and study Earth-like planets. While remapping propagation effects specific to the PIAA coronagraph can be included in the wavefront control algorithm \citep{2011SPIE.8151E..12K}, it is unknown to which extent such effects need to be accounted for. The approach presented in this paper should be tested, both in simulations and in laboratory experiments, at higher contrast that required for a ground-based system. This work will be conducted over the next two years on existing PIAA coronagraph testbeds. | 12 | 6 | 1206.2996 |
1206 | 1206.5578_arXiv.txt | The Sh2-294 \hii region ionized by a single B0V star features several infrared excess sources, a photodissociation region, and also a group of reddened stars at its border. The star formation scenario in the region seems to be quite complex. In this paper, we present follow-up results of Sh2-294 \hii region at 3.6, 4.5, 5.8, and 8.0 $\mu$m observed with the {\it Spitzer Space Telescope} Infrared Array Camera (IRAC), coupled with H$_2$ (2.12 $\mu$m) observation, to characterize the young population of the region and to understand its star formation history. We identified 36 young stellar object (YSO, Class I, Class II and Class I/II) candidates using IRAC color-color diagrams. It is found that Class I sources are preferentially located at the outskirts of the \hii region and associated with enhanced H$_2$ emission; none of them are located near the central cluster. Combining the optical to mid-infrared (MIR) photometry of the YSO candidates and using the spectral energy distribution fitting models, we constrained stellar parameters and the evolutionary status of 33 YSO candidates. Most of them are interpreted by the model as low-mass ($<$4 \msun) YSOs; however, we also detected a massive YSO ($\sim$9\msun) of Class I nature, embedded in a cloud of visual extinction of $\sim$24 mag. Present analysis suggests that the Class I sources are indeed younger population of the region relative to Class II sources (age $\sim$ 4.5 $\times$ 10$^{6}$ yr). We suggest that the majority of the Class I sources, including the massive YSOs, are second-generation stars of the region whose formation is possibly induced by the expansion of the \hii region powered by a $\sim$4 $\times$ 10$^{6}$ yr B0 main-sequence star. | The massive OB stars have profound influence on the evolution of molecular clouds and consequently influence star formation. The stellar radiation and winds due to massive stars in the region can sweep low density interstellar matter, consequently forming a dense layer of gas at the periphery of \hii regions or they can compress existing primordial clumps. In both the processes, the matter at the later stage becomes unstable against self gravity to form young protostars. These two are commonly known processes that can induce new generation of star formation around expanding \hii regions (see e.g., Sugitani et al. 2002; Deharveng et al. 2005; Chauhan et al. 2009; Samal et al. 2010; Ojha et al. 2011). Sh2-294 ($\alpha_{2000}=07^{h}16^{m}34.5^{s}$, $\delta_{2000}=-09^{\circ}26^{\prime}38^{\prime\prime}$) is an \hii region powered by a B0V star and is possibly interacting with a molecular cloud, thus creating a photon dominated region (PDR) which can be seen towards the eastern side as polycyclic aromatic hydrocarbon (PAH) emission in MSX A-band (Samal et al. 2007; Paper-I). Using multiwavelength observations, Samal et al. (2007) have studied the stellar content, distribution of ionized, and dust emission in the region. They identified two groups of stars, one of which is associated with the B0V star at the center of the optically visible nebula. The second group (termed as ``region A'') is situated at the eastern side of the optical cluster and near the peak of 8 $\mu$m emission along the PDR. Samal et al. (2007), using the optical colour-magnitude diagram and theoretical evolutionary models, estimated the age of the ionizing source as 4 $\times$ 10$^{6}$ yr, whereas low mass pre-main-sequence (PMS) stars show an age spread of 1-5 $\times$ 10$^{6}$ yr. On the basis of youth of the sources in ``region A" (age $\leq$ 1 $\times$ 10$^{6}$ yr) compared to the age of the ionizing source ($\sim$4 $\times$ 10$^{6}$ yr), Samal et al. (2007) suggested Sh2-294 as a site of triggered star formation. However, the mechanism that is responsible for the initiation of new star formation in this region is still not clearly understood; requires proper identification and characterization of stellar sources present in the region to put a step ahead. On the basis of high resolution near-infrared (NIR) and optical observations, Yun et al. (2008) estimated the age of the ionizing source of Sh2-294 as 4 $\times$ 10$^{6}$ yr, but suggested a higher age for the PMS sources. Due to the absence of spectroscopic or longer wavelength ($\lambda$ $>$ 2.2 $\mu$m) observations, the exact nature and evolutionary status of the PMS sources in the region could not be studied so far. Now with high angular resolution of {\it Spitzer} Space Telescope it is possible to make a more reliable membership census of the young stellar objects with disk and envelope of the region, as 3-8 $\mu$m bands of {\it Spitzer} reduce the degeneracy between selective interstellar extinction and intrinsic IR excess. Moreover, the nature of YSOs can be best accomplished using their broadband SEDs and its comparison with more sophisticated radiative transfer SED fitting models (e.g., Robitaille et al. 2007). Thus, in conjugation with the available photometric data sets for the region, the {\it Spitzer} observations will allow us to characterize the individual YSOs with their SEDs and constrained their evolutionary status, thus will help to establish spatial and temporal relationship among the YSOs. Therefore, we revisited the region at near- and mid-infrared windows for the follow up study of Sh2-294 star-forming-region (SFR), to have a better picture of star formation activity. The distance to Sh2-294 is uncertain and varies from 3.2 kpc to 4.8 kpc (Moffat et al. 1979; Samal et al. 2007; Yun et al. 2008). In this work, we adopted an average distance of 4.0 kpc for our analysis and organiged the paper with the following layout. We describe the {\it Spitzer} observations and data reduction techniques in $\S$2. In $\S$3, the observational results are presented, which includes morphology of the region, identification of the YSOs and their properties obtained with SED modelling. The star formation scenario in the region is discussed in $\S$4 and $\S$5 summarizes our results. | Star formation in a molecular cloud is more active during the first few million year of cloud lifetime. It is believed that majority of the stars in a molecular cloud form in clusters and after few million year star formation, the gas in a molecular cloud dissipates and further star formation no longer takes place (Lada \& Lada 2003). It is found that clusters with age greater than $\sim$ 5 $\times$ 10$^{6}$ yr are seldom associated with molecular gas (Leisawitz et al 1989), thus it is more likely that after $\sim$ 5 $\times$ 10$^{6}$ yr no gas is left over to form new stars. However, these type of molecular cloud complexes can still have star formation in PDRs at the interface of the \hii region and the molecular gas. Many young clusters associated with \hii regions show age spread, which is partly due to the cluster evolution and partly due to different epochs of star formation within the region (e.g., Sharma et al. 2007; Pandey et al. 2008; Jose et al. 2008). In Sh2-294 region, with the help of {\it Spitzer} observations, we detected sources with disk and envelope, evidence of youth of the region. The presence of extremely young Class I sources perhaps represents fresh star formation in the region. The SED models, within the uncertainties, indicate that the age of most of the Class II YSOs are of comparable to ionizing source and these sources are certainly older than than Class I YSOs. All the Class I sources are distributed at the outskirts of the Sh2-294 region; most of them are associated with arc-shaped H$_{2}$ structures and PAH features. The distribution of young YSOs at the outskirts of \hii regions/bubbles has been noticed in several cases (see e.g., Deharveng et al. 2005; Zavagno et al. 2006; Koeing et al. 2008; Watson et al. 2008; Deharveng et al. 2009; Chauhan et al. 2011), where it is believed that the majority of them are formed as a result of triggered star formation. Although kinematics of the Sh2-294 region is not available, the morphology, the association of Class I YSOs with H$_2$ structures and their younger ages with respect to 4 $\times$ 10$^{6}$ yr massive B0 MS star, give evidence in favor of triggered star formation in the region. On the basis of Hipparcos data, Madsen et al. (2002) calculated the velocity dispersion of $\sim$1 km s$^{-1}$ for stars in young clusters and associations. Since the Class I sources are expected to be young ($\sim$10$^{5}$ yr), their positions should roughly indicate the place where they have born, whereas with a velocity dispersion of 1 km s$^{-1}$, the Class II YSOs (median age $\sim$4.5 $\times$ 10$^{6}$ yr) might have drifted away $\sim$ 4 pc from their original position. Therefore, some of the Class II YSOs distributed away from the cluster center ($\alpha_{2000}=07^{h}16^{m}33^{s}$, $\delta_{2000}=-09^{\circ}25^{\prime}35^{\prime\prime}$; see Samal et al. 2007) might have drifted due to their motion. Figure 5 shows the spatial distribution of YSOs. The Class I source C4 is associated with the structure $\#2$ and is situated at the vertex of a finger-like structure pointing towards the ionization source. A similar kind of example can be seen in the case of RCW 120 (Zavagno et al. 2007; Deharveng et al. 2009), where a YSO located at the vertex of a structure pointing towards the exciting star (Deharveng et al. 2009). Deharveng et al. (2009) proposed that the structure results from the dynamical instability of the expanding ionization front, such as those simulated by Garcia-Segura \& Franco (1996). The regions $\#1$ and $\#3$ are associated with Class I sources. The region $\#1$ is associated with a relatively massive ($\sim$9 \msun) star and is more prominent in PAH emission in comparison to the region $\#3$, which is associated with a less massive ($\sim$2.7 \msun) star. The Class II source 25 seems to be projected near the H$_{2}$ structure $\#4$, but its parameters derived from the acceptable SED fitting models suggests that the source is possibly not embedded within the structure. Though the spatial distribution and evolutionary status of YSOs suggest in favor of triggered star formation, however, with the present data it is not possible to pinpoint the exact nature of triggering, but it is worth discussing the two most likely scenarios that might have happened in this region. In the the first case, we discuss the star formation as seen in remnants of pre-existing molecular material of a parental clumpy cloud due to interaction of an expanding \hii region. In the second case, we discuss the evolution of an \hii region in a filament and the resulting star formation. In Sh2-294 region, we have identified structures ($\#1$ and $\#3$) with YSO inside and they resembles with the numerical simulation of globules resulted due to the impact of UV photons from the near-by massive OB stars on the pre-existing dense molecular material (Lefloch \& Lazareff 1994). The structure $\#1$ shows clearly a externally heated rim, with a massive (9 \msun) source C1 inside the rim, whereas the region $\#3$ has a more globular morphology, with a less massive (2.7 $\msun$) source C3 inside. In both the cases, the structures show cometary morphology with their heads pointing toward the illuminating B0 MS star. Both the structures are approximately at the same distance form the ionizing source. The different morphological structures under the same set of initial conditions and exposed to approximately the same amount of ionizing photons, may be due to the differences in size and mass of the pre-existing clumps. Several studies show the association of YSOs with bright rims at the borders of \hii regions (Sugitani \& Ogura 1994; Ogura et al. 2002) and their formation is more likely due to effect of strong external radiation from OB stars (Morgan et al. 2004; Urquhart et al. 2006) . On the basis of cometary morphology, location, and age difference between the associated YSOs and the ionization source, one can anticipate that radiation driven implosion (RDI; Lefloch \& Lazareff 1994; Miao et al. 2006) could be the process of star formation for regions $\#1$ and $\#3$. To evaluate this hypothesis we quantitatively compare the time elapsed during the formation of the Class I YSO (C1) in the region $\#1$ with that of the age of the B0 ionization source at center. In case of RDI-induced star-formation, the pre-existing molecular clumps are surrounded by high-pressure ionized gas due to the photoionizing UV photons and the pressure exerted on the surface of the molecular clump leads to formation of a cometary globule. At an appropriate time, the high pressure will drive a shock front into the clump, leading to the formation of new stars (for details, see Lefloch \& Lazareff 1994). We estimated the time needed for the ionization front (IF) to travel to the present position of the rim of the structure $\#1$ situated at a projected distance of 1.7 pc as $\sim$1.5 $\times$ 10$^{5}$ yr, assuming that the IF expands at the sound speed of 11.4 km s$^{-1}$. The characteristic timescale for producing cometary morphologies of various shapes and inducing gravitational collapse varies from 0.1 to $\sim$1 $\times$ 10$^{6}$ yr (Lefloch \& Lazareff 1994; Miao et al. 2009), depending upon initial conditions.Hence, we presume an elapsed time to initiate star formation inside the region $\#1$ could be $\leq$ 1 $\times$ 10$^{6}$ yr. The age of the Class I source inside the rim should be of the order of 10$^{5}$ yr. Taken together, the summed time scale ($\sim$2.6 $\times$ 10$^{6}$ yr) is less than the age ($\sim$4.0 $\times$ 10$^{6}$ yr) of the ionizing source that powers the \hii region. We also evaluated the shock crossing time to the globule to see whether the star formation in regions $\#1$ and $\#3$ started due to the propagation of ionization-shock front or whether it had already taken place prior to the ionization front arrival. Assuming a typical shock velocity of 1-2 km s$^{-1}$, as found in the case of Bright Rimmed Clouds (BRCs; see e.g., Thompson et al. 2004; White et al. 1999) for the neutral gas associated with $\#1$, the shock travel time to the source C1 projected at a distance $\sim$ 0.31 pc from the photo-ionization surface layer ranges from 3.0-1.5 $\times$ 10$^{5}$ yrs. This time scale is comparable to the age of the source C1. These simple approximate estimations suggest that the formation of the source C1 and similarly C3, can be possible via the RDI mechanism. Now we will discuss the bipolar \hii region and its importance on star formation processes. In bipolar case, it is most likely that the \hii region forms in the dense region of a filamentary cloud, where the density along the equatorial axis of the filament is high, whereas it is low in the polar directions, leading to a high density contrast. As a consequence, matter can be more compressed in the equatorial plane during the expansion of the \hii region, depending upon the initial density and ionization radiation from the \hii region. A prototype example of such bipolar morphological \hii region is ``Sh2-201", where two dense ($>$ 10$^{22}$ cm$^{-2}$) and massive ($>$ 70 \msun) condensations are found at each sides of the waist of Sh2-201 (Deharveng et al. 2012). Sh2-201 is believed to be formed in a large filament that is running east-west of Sh2-201. Massive condensations are the potential sites of new star formation. Indeed, Deharveng et al. (2012) detected two 100 $\mu$m point sources possibly of Class 0 nature in the east condensation ($\sim$ 235 \msun) and hypothesized that the triggered star formation is in act at the waist of Sh2-201, which seems to be in accordance with numerical simulations of triggered star formation in a filamentary cloud due to dynamical compression of an expanding \hii region (see Fukuda \& Hanawa 2000). In the absence of long wavelength observations, it is tempting to guess about the shape and structure of original cloud in which Sh2-294 has formed. However, the morphology of Sh2-294 at 8 $\mu$m and 22 $\mu$m on a smaller scale suggests that it might be filamentary in nature. Presuming Sh2-294 formed in a filamentary cloud, we compared the observed properties with the numerical simulations. The numerical simulations by Fukuda \& Hanawa (2000), including a wide variety of physical conditions, suggest for typical conditions the \hii region takes more than five times the sound crossing time ($t_{cross}$: see Eq. (19) of Fukuda \& Hanawa 2000), to form the first generation cores (i.e., cores at the waist) in a filament. The first generation cores can be followed by two second generation cores depending on the initial conditions due to the change in self gravity in the filament. The second generation cores in a magnetized cloud are expected to be separated from the first generation cores by the wavelength of most probable fragmentation, which is thirteen times the length scale ($H$: see Eq. (18) of Fukuda \& Hanawa 2000). The $t_{cross}$ and $H$ in the simulations of Fukuda \& Hanawa (2000) depend on the sound speed and the central density of the cold filamentary cloud. In Sh2-294, we presume the H$_2$ structures $\#1$, and $\#3$, situated $\sim$ 1.7 and 1.8 pc away from the ionizing source along the long axis seen in 8 $\mu$m, perhaps represent the externally heated part of the condensations that are at the waist of Sh2-294. Assuming an effective sound speed $\sim$ 0.6 \kms, as found in central region of filaments (e.g., Heitsch et al. 2009; the observed velocity dispersion) and the average density $\sim$ 10$^5$-10$^4$ cm$^{-3}$ of the protocluster forming clumps (e.g., Mueller al. 2002; Motte et al. 2008), as the density of cluster forming filaments, we estimated the length scale and sound crossing time for Sh2-294 as $\sim$ 0.04-0.14 pc and $\sim$ 7.6-25$\times$10$^4$ yr, respectively. The presence of second generation cores cannot be assessed with the present data, but what we see today are certainly the presence of two possible H$_2$ structures ($\#$1 and $\#$3), with Class I YSOs (C1 and C3) inside of these structures. Assuming that these Class I YSOs are resulted of the cores that might have formed due to the dynamical compression of the expanding \hii region as simulated by Fukuda \& Hanawa (2000), we calculated the approximate time that might have elapsed in the entire process. In the simulations of Fukuda \& Hanawa (2000), the time required to produce dense cores depends upon several factors. We considered those models, which include magnetic field, treat the formation of \hii region on the filament axis or very close to it ($<$ 5$H$) as well as impinging the filament axis with a kinetic energy. These models predict the time required to produce two first generation cores ($\rho$ $>$ $\sqrt10$ $\rho$$_0$) is less than or equal to ten times the crossing time scale, which is $\leq$ 2.5 $\times$ 10$^6$ yr in the present case. The age of the Class I YSOs is of the order of $\sim$ 10$^5$ yr. Assuming that the age ($\sim$ 4 $\times$ 10$^6$ yr) of the ionizing source represents the age of \hii region, it seems that Sh2-294 is old enough to produce two cores, which perhaps further collapses to form the Class I YSOs The above discussion, with the present limited observations suggests that both the hypotheses can be justified being responsible for triggered star formation in Sh2-294 region. It is difficult to conclude with the present observations, which one is superior over the other, though we prefer triggered star formation at the waist of Sh2-294 in a filamentary cloud, as the overall morphology of Sh2-294 on a smaller scale resembles with a filamentary cloud. However, the proof of this would require additional informations such as determination of exact stellar properties of YSOs with infrared spectroscopic observations, a search for in favor of possible filamentary cloud with deep FIR observations and kinematics with high resolution line observations. | 12 | 6 | 1206.5578 |
1206 | 1206.2444_arXiv.txt | The shape of galaxies strongly depends on their orbital populations. Stars within galaxies belong to orbital families. In particular, the size and the shape of a galaxy determines the relative populations of these families. As a galaxy evolves, capture and escape of stars between these families takes place. Therefore, capture and escape are generic processes that will have occurred many times in the lifetime of galaxies. Each orbital family has a parent periodic orbit - that is, an orbit that describes a closed figure. For example, in a spherical galaxy, all stars belong to the family of tube orbits, whose members librate around the closed circular orbits. An oval distortion in the center of the galaxy is supported by the family of box orbits, whose parent periodic orbits are the radial orbits. As the distortion grows, stars are transferred from the loop to the box orbital family. This capture process is important in the formation, maintenance and secular evolution of non-axisymmetric structure, such as galactic bars, rings and spiral arms (e.g., Kalnajs 1973; Contopoulos, H\'{e}non \& Lynden-Bell 1973; Tremaine \& Weinberg 1984). Whether or not a trapped star remains trapped, may depend on the presence of a central massive black hole, or a simple mass concentration. Close encounters can scatter stars away from their initial orbits and thus cause a gradual disruption of the population of the orbits. The phenomenon of escaping stars from stellar systems, has been an active field of research during the last decades (e.g., Contopoulos 1990; Contopoulos \& Kaufmann 1992; Siopis et al. 1995a, 1995b; Kandrup et al. 1999; Fukushige \& Heggie 2000; Contopoulos \& Efstathiou 2004; Contopoulos \& Harsoula 2005; Contopoulos \& Patsis 2006; Papadopoulos \& Caranicolas 2007). The reader can find more details on the subject of escapes in the review of Siopis et al. 1996 and also in the book of Contopoulos 2002. When a star has a value of energy higher than the energy of escape, the equipotential curves or, what is equivalent, the zero velocity curves (ZVCs) are open and there are cases, where a star can escape from the stellar system. On the other hand, there are also cases, where stars which hold values of energy much more larger than the energy of escape do not escape at all, even though the ZVCs are open and therefore at least one channel of escape do exists. A characteristic example of such non escaping stars, are those moving in orbits with initial conditions close to those of a stable periodic orbit. Apart from galactic dynamics, the phenomenon of escaping and trapped orbits, has been also studied in the case of the three body problem (e.g., Anosova 1986; Benet et al. 1996, 1998), as well as in mappings (Bleher et al. 1988). The main scope of the present research, is to shed light on the properties of motion in a dynamical system with trapped and escaping orbits. Especially, we shall study the nature of motion (regular or chaotic) for values of energy larger than the energy of escape, that is the case when the ZVC is open. In this case, there are regular orbits which do not escape at all. We shall give the set of initial conditions leading to this kind of orbits as a function of the energy. What is much more interesting, it that there are two different kinds of chaotic orbits. The first kind of chaotic orbits contains chaotic orbits, which remain trapped inside the ZVC for long time intervals, before escaping to infinity. We shall call these orbits trapped chaotic orbits and investigate their properties, such as their time scale of escape and their degree of chaos. The second kind of chaotic orbits contains chaotic orbits which escapes from the ZVC in very short time intervals. These orbits are called fast escaping orbits. The main feature of these orbits, is that their initial conditions are very close to the neighborhood of the escape channel of the ZVC. The layout of this article is organized as follows: In Section 2, we present a mathematical analysis of our galactic type model and also a numerically obtained relationship connecting the angular momentum $L_z$ and the energy of escape $h_{esc}$. Moreover, in the same Section we study the areas of initial conditions corresponding to trapped regular orbits, as a function of the energy. In Section 3, we study the structure of the dynamical system, using the outcomes from the phase planes. A numerical relationship between the extent of the chaotic regions and the value of the energy is also presented. In Section 4 we conduct a detailed study on the trapped and escaping chaotic orbits and we also connect the degree of chaos with the value of the energy. We close with Section 5, where a discussion and the conclusions of this research are given and a comparison with previous work is also made. | (i) When evolved into the future, ensembles of orbits of fixed energy often exhibit a rapid approach towards a constant escape probability $P_0$, the value of which is independent of the details of the ensemble and exhibits interesting scaling behavior. Moreover, the values of the critical exponents appear to be relatively insensitive to the choice of Hamiltonian and (ii) at later times, the escape probability decreases in a fashion which, for at least one model system, is well fit by a power law. This nontrivial time-dependence is attributed to the fact that the possibility of escape to infinity is controlled by the cantori, which can trap chaotic orbits near regular regions for extremely long times. Fukushige \& Heggie (2000) modeled a cluster as a smooth potential plus the steady tidal field of the Galaxy. In this model there is a minimum energy below which stars cannot escape. Above this energy, however, the time-scale on which a star escapes varies with the orbital parameters of the star (mainly its value of energy). This time-scale was quantified and estimated, with both theoretical arguments and computer simulations. Within the limitations of the model, it was shown that the time-scale is long enough to complicate the interpretation of full $N$-body simulations of clusters and that stars above the escape energy may remain bound to the cluster for about a Hubble time. A detailed study regarding the dynamics of the outer parts of barred galaxies beyond corotation was made by Contopoulos \& Patsis (2006). They found that in the outer regions of barred galaxies beyond corotation, there are three types of orbits: (1) ordered (periodic or quasi periodic), (2) chaotic and (3) escaping. Papadopoulos \& Caranicolas (2007) explored the character of orbits in a ``bare" Seyfert 1 dynamical model, when the external perturbation is strong enough in order to have open Zero Velocity Curves. In this model the majority of orbits escape to infinity but there are also orbits which are trapped and do not escape at all. Thus, it is evident that our results coincide with the outcomes of previous related work, pointing out that in a Hamiltonian system with escape channel, there are two kinds of orbits (i) escaping orbits and (ii) trapped orbits. In the current research, we focused our study in the behavior of orbits when the Zero Velocity Curve (ZVC) of the dynamical system is open and therefore orbits can escape to infinity. This happens when $h > h_{esc}$, that is the case in which stars hold values of energy larger than the energy of escape. In this work we studied the possibility of escape in a dynamical system with two degrees of freedom and we have obtained quite striking results. Our results could be compared with outcomes from other studies about the non integrability of the $J_2$ problem (Irigoyen \& Sim\'{o} 1993) ar about the central manifolds and the destruction of the KAM tori in the planar Hill's problem (Sim\'{o} \& Stuchi 2000). Using the fixed values of the parameters given in Section 2, we obtained the relation (7) which connects the angular momentum and the energy of escape. Our numerical calculations show, that all tested regular orbits do not escape at all from the system. When we refer to regular orbits, we mean both the basic orbits of the system and also orbits correspond to secondary resonances. Thus, we conclude that these orbits are trapped regular orbits. Moreover, the percentage of the regular orbits increases as the values of the energy $h$ and the angular momentum $L_z$ increase. More correctly, the whole area of regular orbits, in the $\left(r,p_r\right)$ phase planes increases as we proceed to higher values of the energy. At the same time, the area in the same phase planes corresponds to chaotic orbits decreases. Note that, in all cases studied, the ZVC is open and the values of the pairs $\left[h, L_z \right]$ were chosen, using the algorithm we described in Section 2. Our numerical experiments, suggest that in addition to the regular orbits, for a particular pair of $\left[h, L_z \right]$, there are also two kinds of chaotic orbits. Chaotic orbits which spend large time intervals inside the ZVC before they escape and chaotic orbits which escape vary fast through the escape channel. It was observed, that about $62\%$ of the total tested chaotic orbits stay inside the ZVC for time intervals which are at least 100 times larger than the age of the Universe. Therefore these orbits can be considered as non escaping. On this basis, we are experienced a phenomenon of ``trapped chaos", that is when we have chaotic orbits which are trapped inside to an open ZVC. The rest $38\%$ of the tested chaotic orbits, correspond to orbits which have small escape periods and therefore can be regarded as fast escaping orbits. The main characteristic of these orbits, is that they have initial conditions very close to the critical boundary of the Lyapunov orbit. This is the boundary that orbits should be able to penetrate in order to escape to infinity. Here, we must point out that the fact that orbits with initial conditions very close to the Lyapunov orbit escape fast, is not a necessary condition for fast escape in general (e.g. in Fig. 9d we may consider the orbit starting close to the left boundary of the ZVC, far from the Lyapunov orbit and this orbit escapes fast). The numerical experiments indicate that the average value of the escape period of the chaotic orbits (trapped or fast escaping) strongly depends on the average value of the maximum $z$ component of the orbits. Our main conclusion, is that eventually all chaotic orbits, sooner or later, will escape from the system. In order to have a better estimation of the degree of chaos for the chaotic orbits in each case, we computed the average value of the Lyapunov Characteristic Exponent. Our results indicate, that as the chaotic region is reduced, this has as a result the increase of the degree of chaos. In other words, the more confined is a chaotic region, the more stronger is the degree of chaos in this region. Especially in the case of trapped chaotic orbits, we deal with ``trapped fast chaos", as in most cases the value of the computed L.C.E is much more larger than the unity. When we state that the L.C.E has a value much more larger than the unity, we mean that the L.C.E is larger than $10^{-7}$ yr$^{-1}$, that is the inverse value of the time unit. As the phenomenon of the trapped chaotic orbits is of particular interest, we shall stay in the subject with some more comments. In the case of trapped regular orbits, for values of energy larger that the energy of escape, one could say that these regular trapped orbits may have an additional third integral of motion, that keeps them inside the open ZVC forever. Of course, this can not mentioned in the case of trapped chaotic orbits, because chaotic orbits could not have any further integral of motion. So what remains, is a kind of ``stickiness" (see Karanis \& Caranicolas 2002), with a time of sticky period, larger than the age of the Universe! We consider the outcomes of the present research, to be an initial effort, in order to explore the orbital structure of this interesting dynamical system in extensive detail in a future paper. As the results are positive, further investigation will be initiated in order to explore all the available phase space and also to cover the whole range of the values of the main involved parameters, such as the value of the energy $h$ and the value of the angular momentum $L_z$. | 12 | 6 | 1206.2444 |
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1206 | 1206.4054_arXiv.txt | Synchrotron radiation mechanism, when electrons are accelerated in a relativistic shock, is known to have serious problems to explain the observed gamma-ray spectrum below the peak for most Gamma-Ray Bursts (GRBs); the synchrotron spectrum below the peak is much softer than observed spectra. Recently, the possibility that electrons responsible for the radiation cool via Inverse Compton, but in the Klein-Nishina regime, has been proposed as a solution to this problem. We provide an analytical study of this effect and show that it leads to a hardening of the low energy spectrum but not by enough to make it consistent with the observed spectra for most GRBs (this is assuming that electrons are injected continuously over a time scale comparable to the dynamical time scale, as is expected for internal shocks of GRBs). In particular, we find that it is not possible to obtain a spectrum with $\alpha>-0.1$ ($f_{\nu} \propto \nu^{\alpha}$) whereas the typical observed value is $\alpha\sim0$. Moreover, extreme values for a number of parameters are required in order that $\alpha\sim -0.1$: the energy fraction in magnetic field needs to be less than about $10^{-4}$, the thermal Lorentz factor of electrons should be larger than 10$^6$, and the radius where gamma-rays are produced should be not too far away from the deceleration radius. These difficulties suggest that the synchrotron radiation mechanism in internal shocks does not provide a self-consistent solution when $\alpha \gae -0.2$. | The dissipation mechanism responsible for the prompt emission of Gamma-Ray Bursts (GRBs) remains unknown. There have been various ideas put forth to explain it (for a review, see Piran 1999, 2004; M\'esz\'aros 2006; Gehrels et al. 2009). One of the main problems is to explain the fact that the majority of GRBs exhibit a spectrum $f_{\nu} \propto \nu^{\alpha}$, with $\alpha \sim 0$ below the peak of the spectrum (Preece et al. 2000), whereas the simplest version of the synchrotron model (in the so-called ``fast cooling regime'') predicts $\alpha=-1/2$ (see, e.g., Ghisellini et al. 2000). Recently, a modified version of the synchrotron model, in which electrons that radiate below the peak of the spectrum cool via Inverse Compton (IC) in the Klein-Nishina (KN) regime (Derishev et al. 2003) has gained popularity (Bo\v{s}njak et al. 2009, Nakar et al. 2009, Wang et al. 2009, Fan 2010, Daigne et al. 2011). The main idea is very simple: Electrons cooling via synchrotron mechanism (or IC in the Thomson regime) exhibit an energy loss rate $\propto \gamma_e^{\delta}$, where $\gamma_e$ is the electron Lorentz Factor (LF) and $\delta=2$. The observed synchrotron spectrum is then $f_{\nu} \propto \nu^{-(\delta-1)/2} = \nu^{-1/2}$. However, when the cooling of electrons is dominated by the IC in the KN regime, where the photon-electron interaction cross section scales as $\sim \gamma_e^{-1}$, then $\delta \approx 1$ and $f_{\nu} \sim \nu^{0}$. In this paper, we investigate this scenario in detail and explore its consequences. We analytically study the IC cooling in the KN regime assuming that electrons are injected continuously over a time scale comparable to the dynamical time scale, as is expected for the internal shock model of GRBs (Piran, Shemi \& Narayan 1993; Katz 1994; Rees \& M\'esz\'aros 1994). Recently, Daigne et al. (2011) have provided a detailed numerical calculation of the same context; however, they have assumed that electrons are injected instantaneously in the internal shock. Therefore, our work and the work of Daigne et al. (2011) are complementary. Essentially, Daigne et al. (2011) deals with the case when electrons are no longer being injected and they simply cool, which happens when the internal shock has already passed through the shell. They consider the superposition of emission of many shells, for which the shock has crossed all of them, and the shells simply adiabatically expand and cool. We, however, consider the shock as it traverses the shell, accelerates electrons, and these radiate. The scenario presented in this paper has been considered before (Nakar et al. 2009; Fan 2010) and our results are consistent. However, in contrast with these works and with the work of Daigne et al. (2011), the work presented here is applied to the prompt phase data of particular GRBs with $\alpha \approx 0$: we analyze the data of GRB 080916C, a burst detected by the {\it Fermi} Satellite, in the context of the scenario described above, and provide constraints on this scenario based on available $>$100 MeV data. Recent developments on prompt GRB theory have cast doubt on the internal shock model (see, e.g., Kumar \& Narayan 2009, Zou et al. 2009). New alternative models have been proposed to solve the low-energy spectral index problem described above and other prompt theory issues (see, e.g., M\'esz\'aros \& Rees 2000, Drenkhahn \& Spruit 2002; Lyutikov \& Blandford 2003; Giannios 2008; Narayan \& Kumar 2009; Kumar \& Narayan 2009; Lazar et al. 2009; Beloborodov 2010; Vurm et al. 2011; M\'esz\'aros \& Rees 2011; Ioka 2010; Ioka et al. 2011; Zhang \& Yan 2011, Bo\v{s}njak \& Kumar 2012; Pe'er et al. 2012). It is, however, still relevant to critically test the internal shock model, in the particular case where electrons cool via IC in the KN regime, to assess its feasibility. It is important to mention that there exists a fraction of GRBs with $0 < \alpha < 1/3$ (only about 25 per cent of GRBs have more than 50 per cent of their spectra with $\alpha$ in this range; see Kaneko et al. 2006), that is, with spectra consistent with synchrotron radiation mechanism; however the scenario presented here is unable to explain them. In this work we focus on the {\it majority} of GRBs, which have $\alpha \approx 0$; in particular, we study the case of GRB 080916C, which shows $\alpha = -0.02 \pm 0.02$ for most of its duration (Abdo et al. 2009). We set up our model and present the relevant time scales in Section 2. In Sections 3 and 4, we calculate the effect of IC cooling in the KN regime on the electron energy distribution and on the observed spectral slope, respectively. In Section 5 we derive the relevant physical parameters (radius of emission and total luminosity). In Section 6 we apply our results to GRB080916C, and to an average long-duration GRB. In Sections 7 and 8, we present a Discussion and our Conclusions. | In this work we have investigated the possibility that the observed low energy GRB prompt spectrum, which is $f_{\nu} \sim \nu^0$ (below the peak) for a good fraction of all long duration GRBs (Preece et al. 2000; Kaneko et al. 2006; P\'{e}langeon et al. 2008; Krimm et al. 2009; Ghirlanda et al. 2010), is due to synchrotron radiation from electrons that cool mainly via the IC mechanism in the KN regime (Derishev et al. 2003, Bo\v{s}njak et al. 2009, Nakar et al. 2009, Wang et al. 2009, Fan 2010, Daigne et al. 2011). We present an analytical method to determine the power-law index of the electron energy distribution function, $p_1$, that cools via IC cooling in the KN regime as a function of two parameters: $\eta$, which is a measure of how deep electrons of interest are in the KN regime, and $Y_{KN}$, which is the Compton-$Y$ parameter (including KN corrections) for these electrons. We have calculated the observed low energy spectral index for synchrotron radiation, $\alpha$, as a function of these two parameters as well as the power-law index of the electron energy distribution above $\gamma_i$ ($\gamma_i$ corresponds to the LF of electrons radiating at the peak). We find that $\alpha$ is not simply given by $-(p_1-1)/2$ as naively expected, but it is smaller, which makes it very difficult to explain the observed value of $\alpha\approx 0$ for a good fraction of GRBs. We find that $\alpha>-0.1$ cannot be obtained for parameters relevant for GRBs, if the radiation mechanism is the synchrotron process and electrons are accelerated in a relativistic shock, where electrons are only accelerated when they cross the shock front and are scattered back to the other side. Therefore, the $\gamma$-ray radiation from a significant fraction of long duration GRBs that have low energy spectral index larger than $-0.1$ cannot be accounted for by this mechanism. Even $\alpha \approx -0.1$ faces severe difficulties. The large radius for generation of $\gamma$-rays is in conflict with the short variability time ($\lae$ 0.1 s) of prompt GRB light curve. Moreover, the energy in the magnetic field must be extremely small, $\epsilon_B \sim 10^{-6}-10^{-4}$, and $\gamma_i \ge 10^6$ for the mechanism to be able to able to harden the spectral slope from $\alpha=-0.5$ to $\sim -0.1$ (Table 1). It is unlikely that the energy fraction in the magnetic field will be so small ($\epsilon_B<10^{-4}$) in internal shocks. If the central engine of GRBs is powered by accretion onto a black hole, we expect $\epsilon_B\sim 1$\% as magnetic fields of such a strength are likely produced in the accretion disk by the Balbus-Hawley mechanism (Hawley, Gammie \& Balbus 1996); for a magnetar based central engine this small $\epsilon_B$ is even more surprising. For the typical thermal LF of electrons to be large, $\gamma_i\gae10^6$, in internal shocks where shells collide with a relative LF of a few to 10, it is required that approximately only 1 in $\sim10^3$ electrons are accelerated when they cross the shock-front but they receive $\sim10$\% of the total energy. This is in contradiction with the numerical PIC simulations of Sironi \& Spitkovsky (2011). Moreover, the $\sim 99.9$\% of electrons which are not accelerated have a thermal LF of a few thousand due to their interaction with protons (Sironi \& Spitkovsky 2011), and these electrons produce a significant IC bump in the spectrum at $\sim$ 100 MeV which is not seen for any bursts. The SSC flux of these electrons at 100 MeV will be very large: about a factor of 10 larger than the observed flux. All these difficulties suggest that the synchrotron radiation mechanism in internal shocks does not provide a self-consistent solution when the low-energy spectral index for GRBs is larger than about $-0.2$. | 12 | 6 | 1206.4054 |
1206 | 1206.3168_arXiv.txt | This is an introductory review of the main features of leptogenesis, one of the most attractive models of baryogenesis for the explanation of the matter-antimatter asymmetry of the Universe. The calculation of the asymmetry in leptogenesis is intimately related to neutrino properties so that leptogenesis is also an important phenomenological tool to test the see-saw mechanism for the generation of neutrino masses and mixing and the underlying theory beyond the Standard Model. \begin{keywords} Early Universe; Matter-antimatter asymmetry; Neutrino Physics; Physics Beyond the Standard Model \end{keywords}\bigskip \bigskip | It was first pointed out by Andrej Sakharov in 1967 \cite{sakharov} that the non observation of primordial antimatter in the observable Universe could be related to fundamental properties of particle physics and in particular to the violation of a particular symmetry, called $C\!P$, that was discovered just three years before the Sakharov paper in the decays of newly discovered particles called $K$ mesons \cite{cpv}. The $C\!P$ transformation is the combination of the transformation of parity $P$, corresponding to flipping the sign of all space coordinates, and of charge conjugation $C$, corresponding to flip the sign of all charges of the elementary particles, including the electric charge. The fact that the laws of physics are not invariant under $C\!P$ transformation, implies that matter and antimatter can behave differently in elementary processes. Today the prescient idea of Sakharov is supported by a host of cosmological observations that show how the matter-antimatter asymmetry of the Universe has to be explained in terms of a dynamical generation mechanism, what is called a model of baryogenesis, incorporating $C\!P$ violation. At the same time it has been realised that a successful model of baryogenesis cannot be attained within the current Standard Model (SM) of particle physics and it has therefore to be regarded as a necessity of extending the SM with a model beyond the SM, or, more shortly, with some `new physics'. The discovery of neutrino masses and mixing in neutrino oscillation experiments in 1998 \cite{SuperK}, has for the first time shown directly, in particle physics experiments, that the SM is indeed incomplete, since it strictly predicts that neutrinos are massless and, therefore, cannot oscillate. Therefore, this discovery has greatly increased the interest in a mechanism of baryogenesis called leptogenesis \cite{fy}, a model of baryogenesis that is a cosmological consequence of the most popular way to extend the SM in order to explain why neutrinos are massive but at the same time much lighter than all other fermions: the see-saw mechanism \cite{see-saw}. In this way leptogenesis realises a highly non trivial link between two completely independent experimental observations: the absence of primordial antimatter in the observable Universe and the observation that neutrinos mix and (therefore) have masses. Leptogenesis has, therefore, a naturally built-in double sided nature. On one side, it describes a very early stage in the history of the Universe characterised by temperatures $T_{\rm lep} \gtrsim 100\,{\rm GeV}$, much higher than those probed by Big Bang Nucleosynthesis ($T_{BBN} \sim 1\,{\rm MeV}$) \footnote{Throughout the review, we adopt the natural system with $\hbar = c = k_B = 1$ and therefore temperatures are expressed in electronvolts, the usual unit of energy in particle and early Universe physics.}, and on another side it complements low energy neutrino experiments providing a completely independent phenomenological tool to test models of new physics embedding the see-saw mechanism. Before reviewing the main features and results in leptogenesis, we will first need to discuss, in the next section, the cosmological framework justifying the necessity of a model of baryogenesis and then, in Section 3, the main experimental results in the study of neutrino masses and mixing parameters and the main features of the see-saw mechanism. Neutrino experiments and see-saw mechanism together suggest leptogenesis to be today probably the most plausible candidate for the explanation of the matter-anti matter asymmetry of the Universe. | 12 | 6 | 1206.3168 |
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1206 | 1206.6784_arXiv.txt | The origin and structure of the magnetic fields in the interstellar medium of spiral galaxies is investigated with 3D, non-ideal, compressible MHD simulations, including stratification in the galactic gravity field, differential rotation and radiative cooling. A rectangular domain, $1\times1\times2\kpc^3$ in size, spans both sides of the galactic mid-plane. Supernova explosions drive transonic turbulence. A seed magnetic field grows exponentially to reach a statistically steady state within 1.6\,Gyr. Following \citet{G92} we use volume averaging with a Gaussian kernel to separate magnetic field into a mean field and fluctuations. Such averaging does not satisfy all Reynolds rules, yet allows a formulation of mean-field theory. The mean field thus obtained varies in both space and time. Growth rates differ for the mean-field and fluctuating field and there is clear scale separation between the two elements, whose integral scales are about $0.7\kpc$ and $0.3\kpc$, respectively. | The interstellar medium (ISM) of spiral galaxies is strongly affected by energy injection from supernovae (SNe), which drive highly compressible, transonic turbulent motions. This makes it extremely inhomogeneous, yet it supports magnetic fields at a global scale of a few kiloparsecs. Mean-field dynamo models have proved successful in modelling galactic magnetic fields and offer a useful framework to study them and to interpret their observations \citep[e.g.,][]{BBMSS96,S07}. Turbulent dynamo action involves two distinct mechanisms. The \textit{fluctuation dynamo\/} relies solely on the random nature of the fluid flow to produce \textit{random\/} magnetic fields at scales smaller than the integral scale of the random motions. The \textit{mean-field\/} dynamo produces magnetic field at a scale significantly larger than the integral scale, and requires rotation and stratification to do so. For any dynamo mechanism, it is important to distinguish the \textit{kinematic\/} stage when magnetic field grows exponentially as it is too weak to affect fluid motions, and the \textit{nonlinear\/} stage when the growth is saturated, and the system settles to a statistically steady state. The scale of the mean field produced by the dynamo is controlled by the properties of the fluid flow. For example, in the simplest $\alpha^2$-dynamo in a homogeneous, infinite domain, the most rapidly growing mode of the mean magnetic field has scale of order $4\pi\eta\turb/\alpha$, where $\alpha$ can be understood as the helical part of the random velocity and $\eta\turb$ is the turbulent magnetic diffusivity \citep{SSR83}. For any given $\alpha$ and $\eta\turb$, this scale is finite and the mean field produced is, of course, not uniform. In galaxies, the helical turbulent motions and differential rotation drive the so-called $\alpha\omega$-dynamo, where the mean field has a radial scale of order $\Delta r\simeq3|{\cal{D}}|^{-1/3}(hR)^{1/2}$ at the kinematic stage \citep{SS89}, with ${\cal{D}}$ the dynamo number, $h\simeq0.5\kpc$ the half-thickness of the dynamo-active layer and $R\simeq3\kpc$ the scale of the radial variation of the local dynamo number. For $|{\cal{D}}|=20$, this yields $\Delta r\simeq1.3\kpc$. These estimates refer to the most rapidly growing mode of the mean magnetic field in the kinematic dynamo; it can be accompanied by higher modes that have a more complicated structure. Magnetic field in the saturated state can be even more inhomogeneous due to the local nature of dynamo saturation. The mean magnetic field can have a nontrivial, three-dimensional spatial structure, and any analysis of global magnetic structures must start with the separation of the mean and random (fluctuating) parts. However, many numerical studies of mean-field dynamos define the mean magnetic field as a \textit{uniform\/} field obtained by averaging over the whole volume available, or in the case of fields showing non-trivial variations in a certain direction, as planar averages, e.g., over horizontal planes for systems that show $z$-dependent fields \citep[e.g.,][]{BS05}. The mean and random magnetic fields are assumed to be separated by a scale, $\lambda$, of order the integral scale of the random motions, $l_0$; $\lambda$ is not necessarily precisely equal to $l_0$, however, and must be determined separately for specific dynamo systems. The leading large-scale dynamo eigenmodes themselves have extended Fourier spectra, both at the kinematic stage and after distortions by the dynamo nonlinearity. Thus, both the mean and random magnetic fields are expected to have a broad range of scales, and their spectra can overlap in wavenumber space. Thus, it is important to develop a procedure to isolate a mean magnetic field without unphysical constraints on its spectral content. This problem is especially demanding in the multi-phase ISM, where the extreme inhomogeneity of the system can complicate the spatial structure of the mean magnetic field. The definition of the mean field as a horizontal average may be appropriate in simplified numerical models where the vertical component of the mean magnetic field, $\average{B_z}$, vanishes because of periodic boundary conditions applied in $x$ and $y$; otherwise, $\nabla\cdot\average{\vect{B}}=0$ cannot be ensured. An alternative averaging procedure that retains three-dimensional spatial structure within the averaged quantities is volume averaging with a kernel $G_\ell(\vect{r}-\vect{r'})$, where $\ell$ is the averaging length: $\average{f}_\ell=\int_V f(\vect{r}') G_\ell(\vect{r}-\vect{r'})\,d^3\vect{r}'$, for a random field $f$. A difficulty with volume averaging, appreciated early in the development of turbulence theory, is that it does not obey the Reynolds rules of the mean (unless $\ell\to\infty$), $\average{\average{f}_\ell g}_\ell\neq\average{f}_\ell\average{g}_\ell$, and $\average{\average{f}_\ell}_\ell\neq\average{f}_\ell$ \citep[Sect.~3.1 in][]{MY07}. Horizontal averaging represents a special case with $\ell\to\infty$ in two dimensions, and thus satisfies the Reynolds rules; however, the associated loss of a large part of the spatial structure of the mean field limits its usefulness. \citet{G92} suggested a consistent approach to volume averaging which does not rely on the Reynolds rules. A clear, systematic discussion of these ideas is provided by \citet[][Chapter~2]{E12}, and an example of their application can be found in \citet{E05}. The averaged Navier--Stokes and induction equations remain unaltered, independent of the averaging used, if the mean Reynolds stresses and the mean electromotive force are defined in an appropriate, generalized way. The equations for the fluctuations naturally change, and care must be taken for their correct formulation. An important advantage of averaging with a Gaussian kernel (Gaussian smoothing) is its similarity to astronomical observations, where such smoothing arises from the finite width of a Gaussian beam, or is applied during data reduction. Here we analyze magnetic field $\vect{B}$ produced by the rotational shear and random motions in the numerical model of the SN-driven ISM presented by \citet[][hereafter, \HDI]{FG12}, using Gaussian smoothing. We suggest an approach to determine the appropriate length $\ell$, and then obtain the mean magnetic field $\vect{B}_\ell$. The procedure ensures that $\nabla\cdot\vect{B}_\ell=0$. The random magnetic field $\vect{b}{\frcorr{_\ell}}$ is then obtained as $\vect{b}{\frcorr{_\ell}}=\vect{B}-\vect{B}_\ell$. The Fourier spectra of the mean and random magnetic fields overlap in wavenumber space, but their maxima are well separated. | \label{sect:conc} The approach used here to identify the appropriate averaging length $\ell$ (and thus the effective separation scale $\lambda$) is simple (but not oversimplified); $\ell$ can in fact depend on position, and it can remain constant in time only at the kinematic stage of all the dynamo effects involved. Wavelet filtering may prove to be more efficient than Gaussian smoothing in assessing the variations of $\ell$. At the kinematic stage, the spectral maximum of the mean field is already close to the size of the computational domain, and it cannot be excluded that the latter is too small to accommodate the most rapidly growing dynamo mode. These results should therefore be considered as preliminary with respect to the mean field; simulations in a bigger domain are clearly needed. The physically motivated averaging procedure used here, producing a mean field with three-dimensional structure, may facilitate fruitful comparison of numerical simulations with theory and observations. Although Gaussian smoothing does not obey all the Reynolds rules, it is possible that a consistent mean-field theory can be developed, e.g.\ in the framework of the $\tau$-approximation \citep[see e.g.][and references therein]{BS05}. This approach does not rely upon solving the equations for the fluctuating fields, and hence only requires the linearity of the average and its commutation with the derivatives. The properly isolated mean field is likely to exhibit different spatial and temporal behaviour than the lower-dimensional magnetic field obtained by two-dimensional averaging. | 12 | 6 | 1206.6784 |
1206 | 1206.6926_arXiv.txt | Despite the absence of viscous drag, the neutron superfluid permeating the inner crust of a neutron star can still be strongly coupled to nuclei due to non-dissipative entrainment effects. Neutron superfluidity and entrainment have been systematically studied in all regions of the inner crust of a cold non-accreting neutron star in the framework of the band theory of solids. It is shown that in the intermediate layers of the inner crust a large fraction of ``free'' neutrons are actually entrained by the crust. The results suggest that a revision of the interpretation of many observable astrophysical phenomena might be necessary. | \label{intro} No sooner did Bardeen, Cooper and Schrieffer (BCS) publish their theory of superconductivity than Migdal speculated about nuclear superfluidity in the interior of neutron stars. This possibility was further investigated by Ginzburg and Kirzhnits in 1964. The discovery of the first pulsars and the observation of frequency glitches followed by very long relaxation times of the order of months provided very strong evidence for the presence of superfluids in neutron stars. In particular, pulsar glitches are generally believed to be related to the neutron superfluid that permeates the inner crust of neutron stars at low enough temperatures~\citep[see][for a review]{lrr}. The core of a neutron star may also contain different kinds of superfluids and superconductors but their nature and their properties still remain very poorly known. The existence of a neutron superfluid in neutron-star crusts has recently found support from the observation of the initial cooling in persistent Soft X-ray Transients~\citep{shternin07,brown09}. Superfluidity is also expected to play a role in other astrophysical phenomena like the quasiperiodic oscillations detected in the giant flares from Soft Gamma Repeaters~\citep{andersson09}. | The pairing mechanism giving rise to superfluidity in neutron-star crusts is a highly non-local phenomenon involving both neutrons bound inside clusters and free neutrons. Using the band theory of solids, the critical temperature for superfluidity is found to be reduced by $\sim 10-20\%$ as compared to pure neutron matter. Non-local effects have a much stronger impact on superfluid dynamics. Due to non-dissipative entrainment effects, some regions of the crust are found to strongly resist the neutron superfluid flow. This may have implications for various astrophysical phenomena. For instance, the amount of angular momentum that the neutron superfluid can possibly transfer to the crust is limited by entrainment, thus challenging the interpretation of large pulsar glitches~\citep{cc06}. Because the neutron superfluid is coupled to the crust, entrainment leaves its imprint on the spectrum of collective excitations and their damping~\citep{pethick2010,cirigliano2011}. This could affect the thermal relaxation of the crust which has been recently monitored in several persistent soft X-ray transients. | 12 | 6 | 1206.6926 |
1206 | 1206.6117_arXiv.txt | We study the possibility that particle production during inflation could source observable gravity waves on scales relevant for Cosmic Microwave Background experiments. A crucial constraint on such scenarios arises because particle production can also source inflaton perturbations, and might ruin the usual predictions for a nearly scale invariant spectrum of nearly Gaussian curvature fluctuations. To minimize this effect, we consider two models of particle production in a sector that is only gravitationally coupled to the inflaton. For a single instantaneous burst of massive particle production, we find that localized features in the scalar spectrum and bispectrum might be observable, but gravitational wave signatures are unlikely to be detectable (due to the suppressed quadrupole moment of non-relativistic quanta) without invoking some additional effects. We also consider a model with a rolling pseudoscalar that leads to a continuous production of relativistic gauge field fluctuations during inflation. Here we find that gravitational waves from particle production can actually \emph{exceed} the usual inflationary vacuum fluctuations in a regime where non-Gaussianity is consistent with observational limits. In this model observable B-mode polarization can be obtained for \emph{any} choice of inflaton potential, and the amplitude of the signal is not necessarily correlated with the scale of inflation. | \label{sec:introduction} Inflation is currently the standard paradigm for solving the flatness, horizon and the unwanted topological relic problems in standard big bang cosmology. In addition, the quantum fluctuation of the inflaton field provides the seeds of inhomogeneity that seem to fit very well with the current observation on the Cosmic Microwave Background (CMB) and Large Scale Structure (LSS). A particularly important probe of the physics of inflation is provided by primordial gravitational waves (tensor fluctuations). A number of observational searches for gravitational wave perturbations are proposed or are currently underway; these may be probed through the B-mode polarization of the CMB \cite{Baumann:2008aq,Bock:2009xw,Farhang:2011ud} or, on smaller scales, through interferometers such as LIGO \cite{LIGO}, VIRGO \cite{VIRGO}, DECIGO \cite{Kawamura:2011zz}, Einstein Telescope \cite{ET}, or LISA \cite{LISA}. During inflation, gravitational wave fluctuations are inevitably generated by quantum fluctuations of the tensor part of the metric. These have an amplitude controlled by $\frac{H^{2}}{M_{p}^{2}}$, where $H$ is the Hubble scale and $M_p\approx 2.4\cdot 10^{18}\,\mathrm{GeV}$. The gravitational wave signal from vacuum fluctuations is detectable only when the inflaton field range is trans-Planckian \cite{Lyth:1996im}, which might be challenging to realize in a controlled effective field theory. Additional sources of Gravitational Waves (GW), which are uncorrelated with the usual quantum vacuum fluctuations, may be present in the early universe (see, for instance, \cite{Binetruy:2012ze} for a recent review). Two broad categories of mechanisms are: \begin{enumerate} \item {\bf Models involving phase transitions:} For example, in first order phase transitions, vacuum bubble collisions \cite{GWfromPT, Chialva:2010jt} and the subsequent turbulence \cite{GWfromPTturb} could source GW. The generation and decay of cosmic strings can also give rise to large GW \cite{GWfromCStr}. Along similar lines, the self-ordering of a scalar field after a second order phase transition has also been considered \cite{GWfrom2ndPT}. \item {\bf Models involving particle production:} Generically the inflaton should be expected to couple to some additional degrees of freedom, as would seem to be necessary for successful reheating \cite{Kofman:1994rk,Kofman:1997yn,Podolsky:2005bw,Barnaby:2009wr,Braden:2010wd}. In this case, there is a natural possibility that the time-dependence of the inflaton condensate during inflation leads to the production of some other degrees of freedom which may, in turn, provide an important new source of GW \cite{Cook:2011hg,Senatore:2011sp,Barnaby:2011qe}. A variety of different models have been proposed; see below for more discussion.\footnote{For gravitational waves from particle production at the \emph{end} of inflation, see \cite{Easther:2006vd,GarciaBellido:2007dg,GarciaBellido:2007af,Dufaux:2007pt,Dufaux:2008dn}; effects on the scalar fluctuations were discussed in \cite{Barnaby:2006cq,Barnaby:2006km,Chambers:2007se, Bond:2009xx}.} \end{enumerate} Given the importance of gravitational waves as a probe of inflation, it is important to understand if such mechanisms could be competitive with the usual spectrum of GW from vacuum fluctuations.~\footnote{A GW signal may also be left at the largest scales as an imprint of a pre-inflationary era if inflation had only a minimal duration \cite{Gumrukcuoglu:2008gi}.} Any mechanism which is being invoked to source gravitational waves might also source scalar metric perturbations. Therefore, one must take care not to spoil the usual prediction of a nearly scale invariant spectrum of Gaussian scalar curvature perturbations. Sometimes this concern is evaded by restricting attention to effects that take place on the small scales relevant for interferometers where the scalar fluctuations are not strongly constrained. In this work we will mostly be interested in models of particle production during inflation, where gravitational waves are sourced on CMB scales. To test the feasibility of such scenarios, it is crucial to study also the spectrum and bispectrum of the scalar fluctuations, to ensure that these are consistent with observations. Models of particle production during inflation have received considerable attention in the literature; see for example \cite{Cook:2011hg,Senatore:2011sp,Barnaby:2011qe,Berera:1995ie,Gupta:2002kn,Moss:2007cv,Chung:1999ve,Romano:2008rr,Barnaby:2009mc,Barnaby:2009dd,Barnaby:2010ke,Barnaby:2010sq,Anber:2009ua,Barnaby:2010vf,Barnaby:2011vw,Sorbo:2011rz,Green:2009ds,LopezNacir:2011kk}. One class of models involves instantaneous bursts of particle production, leading to localized features in the cosmological perturbations. Early studies focused on the production of fermion \cite{Chung:1999ve} or scalar \cite{Romano:2008rr} particles, neglecting the feed-back of the produced quanta on the perturbations of the inflaton. In Ref.~\cite{Barnaby:2009mc} it was however shown that this feed-back effect actually dominates observables for the case of scalar particle production. Ref.~\cite{Barnaby:2009mc} considered a simple model where scalar $\chi$ particles are produced through a coupling $g^2\varphi^2 \chi^2$ to the inflaton, $\varphi$, using both lattice field theory simulations and also analytical methods. Models of this same type were subsequently analyzed in the context of trapped inflation \cite{Green:2009ds}. More recently, models of instantaneous vector particle production have been studied in connection with GW at interferometer scales \cite{Cook:2011hg}. Several scenarios of GW from scalar and string production were instead studied in \cite{Senatore:2011sp}. Another possibility is that particle production occurs continuously during inflation. This is quite natural in the context of axion inflation \cite{Barnaby:2010vf}. Even in the simplest models of inflation driven by a single axion in slow roll on a smooth flat potential, pseudoscalar couplings $\varphi F\tilde{F}$ to gauge fields are ubiquitous. This interaction leads to a continuous tachyonic production of gauge field fluctuations during inflation. There are a host of interesting phenomenological signatures: observable equilateral non-Gaussianity \cite{Barnaby:2010vf,Barnaby:2011vw,Barnaby:2011pe}, GW at interferometer scales \cite{Cook:2011hg,Barnaby:2011qe}, and excess power at small scales \cite{Meerburg:2012id,Chluba:2012we}. Additionally, backreaction effects in such models can assist inflation by dissipating the kinetic energy of the inflaton \cite{Anber:2009ua,Anber:2012du}, analogously to warm inflation \cite{Berera:1995ie} and trapped inflation \cite{Green:2009ds}.~\footnote{The pseudo-scalar interaction is also used to \cite{Adshead:2012kp} to dissipate the inflaton kinetic energy from its classical interaction to a non-abelian vector field.} In~\cite{Seery:2008ms,Caldwell:2011ra,Barnaby:2012tk} a model of gauge field production through the scalar coupling $I^2(\varphi) F^2$ was considered, in connection with primordial non-Gaussianity and, perhaps, magnetogenesis (this last application is problematic \cite{Demozzi:2009fu,Barnaby:2012tk}). Above we discussed some simple models of particle production during inflation where quanta are produced by a \emph{direct coupling} between the inflaton and some additional degrees of freedom. In such a scenario the produced particles interact with the inflaton through couplings that are typically much stronger than gravitational. Hence, these produced particles will tend to source scalar curvature fluctuations much more efficiently than GW. It is not surprising, therefore, that the most stringent CMB constraints on such models often come from features and non-Gaussianity in the scalar fluctuations, rather than from GW. In this work, we investigate the possibility to source a significant GW signal on CMB scales without ruining the spectrum of curvature fluctuations. To minimize the impact on the inflaton fluctuations, we assume that particle production takes place in a ``hidden'' sector that is only gravitationally coupled to the inflaton.\footnote{Our scenario differs from the curvaton model \cite{Lyth:2002my}, in which the inflaton provide the energy density to support inflation while a light curvaton field provides the seed of scalar perturbation. The GW spectrum in the curvaton model has been considered at tree-level \cite{Fonseca:2011aa,Nakayama:2009ce} and at 1-loop level \cite{Bartolo:2007vp}, with possible detectability at future interferometer experiments \cite{Bartolo:2007vp}. See \cite{vector-curvaton} for examples of vector curvaton.} We compute for the first time the scalar perturbations induced by the gravitational coupling, and we compare their phenomenological impact with that of the produced GW. Since gravitational interactions are unavoidable, the case we investigate can be thought of as a kind of ``best case'' scenario for the production of GW while minimizing the effect on the scalar fluctuations. Concretely, we will focus on two models involving the production of spin-$1$ particles: \begin{enumerate} \item {\bf Model I:} Particle production takes place in a hidden sector where a local $U(1)$ invariance is spontaneously broken by the expectation value of some complex scalar $\psi$. Here gauge fields are produced at an isolated moment - namely, when the mass of the gauge field crosses zero during the evolution of $\psi$ - and we have localized features in the scalar spectrum and bispectrum, in addition to a localized feature in the tensor spectrum. For a single isolated burst of production, we find that observational constraints on the scalar perturbations exclude any interesting effect in GW. However, in a concrete model there may be many bursts of particle production and their resonance could enhance the effect. We note that this model could lead to interesting phenomenological signatures in the scalar fluctuations; localized features in the spectrum and bispectrum are discussed. \item {\bf Model II:} Particle production takes place in a hidden sector where a rolling pseudoscalar sources gauge field fluctuations continuously. Here we find that GW from particle production can be competitive with the vacuum fluctuations, or even larger than the vacuum fluctuations, \emph{without} violating observational bounds on non-Gaussianity. In this model the primordial tensor spectrum can be detectable for \emph{any} choice of inflaton potential (that is, also for small field inflation). In this model, GW from particle production are chiral. We show that parity violation in the tensor sector can be almost maximal, which provides a distinctive observable signature of this scenario; see also \cite{Sorbo:2011rz,Anber:2012du}. \end{enumerate} In summary: we find that the possibility to source interesting GW from particle production is rather model dependent. Even if particle production occurs in a hidden sector, coupled only gravitationally to the inflationary one, this is not a sufficient condition to ensure that observable GW can be sourced without ruining the scalar spectrum. On the other hand, we find that in some models GW from particle production can actually \emph{exceed} the usual vacuum fluctuations. The reason for the smaller GW production in Model I with respect to Model II is that in Model I the gauge quanta are highly non-relativistic after their production, which suppresses their quadrupole moment. We verified that the same suppression takes place if, instead of gauge fields, the particles produced in this mechanism have spins $0$ or $\frac{1}{2}$.~\footnote{We find that the results agree in all three cases, with only order unity differences coming from counting the number of degrees of freedom and also from spin statistics. These order unity effects can be encoded in a very simple formula, which we present.} As we mentioned, a greater GW effect may be obtained for multiple instances of particle production, or for a more complicated evolution of the gauge field mass, or if the massive particles decay into massless ones short after they are produced \cite{Senatore:2011sp}. Therefore, due to the possibility of GW from particle production, a measurement of primordial B-modes does not necessarily constitute a measurement of the scale of inflation. Nor does a detectable B-mode signal necessarily require super-Planckian excursions in field space. Fortunately, as we discuss below, the produced GW may be distinguished from the vacuum signal, either by their localization at some given wavelength (assuming that Model I can be modified so to enhance the GW signal), or by their violation of parity. In terms of observational prospects of gravitational waves on CMB scales, Model II is certainly more promising, as the gauge quanta are automatically relativistic and their quadrupole moment is not suppressed. While the focus of the present work is to examine the signatures and constraints of gravitational waves produced during inflation as a result of hidden sector particle production, the UV sensitivity of inflation motivates us to ask whether such models can be realized in string theory. Indeed, the 4D low energy spectrum of string theory contains a myriad of axion-like fields, e.g., those arise from the reduction of antisymmetric form fields on cycles of the internal space. These closed string axions couple to $U(1)$ gauge fields on the worldvolume of D-branes via $\varphi F \tilde{F}$ couplings. The axion decay constant $f$ one typically finds in string theory constructions is of the order of the GUT scale $M_{GUT} \sim 10^{16}$ GeV (see, e.g., \cite{Banks:2003sx,Svrcek:2006yi}) which sits comfortably within the allowed window for consistency of our model (see eqs.~(\ref{total_bnd}) and (\ref{bnd2-f})). It is not difficult to arrange the inflaton to have no direct coupling to the axion and the gauge field. We outline some ideas to realize Model II in string theory in the concluding section. We leave, however, a detailed study of these and other string theory embeddings for future work. This paper is organized as follows. In Section \ref{sec:formal} we develop a very general formalism which can be used to compute the effects of particle production on the scalar and tensor cosmological perturbation in a variety of models. In Section \ref{sec:model1} we apply this formalism to Model I, discussed above. In Section \ref{sec:model2} we instead apply our formalism to Model II, discussed above. In Section \ref{sec:conclusions}, we conclude. In Appendix \ref{app-longA}, we discuss the production of the longitudinal mode in Model I. This is the first time the longitudinal mode has been accounted for in a model of production of massive vector fields during inflation. In Appendix \ref{app-mod1-sourcez}, we discuss some details of the computation of the scalar perturbations for Model I. In Appendix \ref{app:modelII}, we perform an analogous computation for Model II. In Appendix \ref{app-fermions}, we discuss the production of massive fermion fields during inflation, and the amount of GW that they generate. | \label{sec:conclusions} A large experimental effort is currently taking place to detect gravitational waves from inflation. The conventional vacuum signal will be detectable only if the scale of inflation is sufficiently high, $V^{1/4} \gsim 10^{16} \, {\rm GeV}$ (corresponding to $r \gsim 0.01$, or $\epsilon \gsim 6 \cdot 10^{-4}$ in single field slow roll inflation). Does this imply that, for a lower scale, this experimental effort will be unsuccessful, or can we hope that an observable gravity wave signal can be obtained from some different mechanism ? And can we distinguish the gravity waves generated by this mechanism from the conventional vacuum ones ? Recently, \cite{Cook:2011hg} and \cite{Senatore:2011sp} considered the possible gravity signal from particle production taking place during inflation. A difficulty with this idea is that the same particle production will also source scalar perturbations; the observed scalar perturbations have properties in perfect agreement with standard vacuum fluctuations generated by the simplest inflationary model; in particular, they are gaussian to a very high degree, while there is no reason to expect that this should be the case for a generic model of particle production.~\footnote{In fact, as shown in \cite{Barnaby:2010vf}, particle production is a very simple source of observable non-gaussianity of the scalar perturbations, even for the highly motivated class of natural inflation models.} Therefore, any mechanism of gravity waves from inflation needs to explain why the mechanism has not already manifested itself in the scalar sector. To evade this problem, \cite{Cook:2011hg} studied scenarios in which the particle production takes place (or increases at a sufficient level) only towards the end of inflation, so to generate gravity waves only at scales much smaller than the CMB ones. At these scales, the scalar perturbations are only constrained by primordial black holes (see for instance \cite{Lin:2012gs} for a recent study), which is a significantly weaker bound than those from non-gaussianity at the CMB scales. One of the scenarios of \cite{Cook:2011hg} was further studied in \cite{Barnaby:2011qe} to account for the backreaction of the produced particles on the background inflaton. It was shown in \cite{Barnaby:2011qe} that in this region the sourced gravity wave signal can already be observed by the next LIGO stage \cite{LIGO}. The main purpose of the present paper is to study whether an analogous mechanism can produce an observable gravity wave signal at CMB scales, without conflicting with the limits from non-gaussianity in the scalar sector. Let us denote by $X$ the field that is produced during inflation, and that sources the gravity waves. In the models considered in \cite{Senatore:2011sp,Cook:2011hg} quanta of $X$ are produced by the motion of the inflaton, which we denote by $\varphi$. This implies a direct coupling between the inflaton and the produced quanta. As a consequence, if the inflaton is the source of cosmological perturbations $\zeta$, quanta of $X$ will source $\zeta$ with a stronger than gravitational interaction. On the contrary, the source of gravity waves from $X$ is of gravitational strength. To minimize the relative amount of produced $\zeta$ vs. produced gravity waves, in this work we made the opposite assumption of considering the weakest possible coupling (in standard gravitational theory) between $X$ and the inflaton: namely, we assumed that $\varphi$ and $X$ are coupled only gravitationally. We therefore assumed that particle production occurs in a ``hidden sector'' and in this paper, for the first time, we computed the amount of scalar perturbations $\zeta$ induced by $X$ through a purely gravitational interaction. We then computed the amounts of gravity waves produced by $X$ in these two models (for model II, we quote existing results), and we compared the two effects. Clearly, there is a large arbitrariness in the choice of the model for particle production, and we do not claim our findings to be exhaustive; in particular, we did not study here the analogous of all the scenarios considered in \cite{Senatore:2011sp}, where for instance multiple bursts of particle production, and production of strings were also studied. We study two models in which $X$ is a vector field, which is produced by the motion of a field $\psi \neq \varphi$. In model I, the vector field has a mass term $\psi \left( t \right)^2 A^2$, and quanta of $A$ are produced when the classical value of $\psi$ crosses zero. In model II the vector is continuously sourced by a pseudo-scalar $\frac{\psi}{f} F {\tilde F}$ interaction. The reasons for considering these two models is that, after the particle production, the vector quanta are highly massive in Model I, while massless in Model II. We showed that in the first case this gives rise to a strong suppression of the gravity wave signal with respect to the amount of scalar perturbations. In the remainder of this concluding section, we summarize our findings in these two models, together with some discussion. \begin{enumerate} \item {\bf Model I:} The main signature of particle production in this model is a bump in the scalar power spectrum, at the scales that exited the horizon when the gauge quanta were produced.~\footnote{This is qualitatively identical to the findings of \cite{Barnaby:2009mc}, where the sourced field is a scalar with mass depending on the inflaton.} If this bump will be observed, this mechanism can be supported / disproved by the presence/ absence of an analogous bump in the bispectrum, which we also computed here for the first time. The spectrum of gravity waves produced by the gauge quanta also presents a peak at the same scales, which - if sufficiently high - could distinguish them from the vacuum gravity waves. However, we found that - once the bound from not having observed a large bump in the scalar spectrum is respected - the amount of gravity waves produced in this model is completely unobservable ($r \lsim 10^{-6}$). The relative smallness of the gravity waves vs scalar perturbations produced in the model may come as a surprise, due to the fact that the gauge quanta are coupled gravitationally to both these quantities. The reason for the suppression is due to the fact that the quanta are highly non-relativistic after they are produced. This highly suppresses their quadrupole moment, and the amount of gravity waves that they generate. \end{enumerate} To verify this, we also computed the amount of gravity waves produced if the vector field is replaced by a fermion, with mass $\propto \psi \left( t \right)$. Ref. \cite{Cook:2011hg} computed the amount of gravity waves produced by a scalar with mass $\propto \psi \left( t \right)$. From our two results, and from the result of \cite{Cook:2011hg} for the scalar case, we actually obtained the very general formula (\ref{general-Plambda-beforpint}) for the amount of gravity waves produced in all these cases. We see that there is no large enhancement between the different spins, apart from the proportionality of the final result to the number of degrees of freedom in each case. We did not compute the amount of scalar perturbations $\zeta$ sourced in the fermionic case. However, we believe that also in this case the result will be analogous to the one that we have computed, and that therefore our conclusions on the relative importance of gravity waves vs scalar perturbations production apply for produced particles of any spin. In this model, the vector field is massive after the production, and it therefore also possesses a longitudinal component. The results for this component are more model dependent than those of the transverse components: they depend on the specific choice of the potential $U$ for $\psi$ (the results for the transverse component are independent of $U$ provided that it is smaller than the kinetic energy of $\psi$ during particle production). The longitudinal mode may drive the theory out of perturbative regime when $m \propto \psi \left( t \right) \rightarrow 0$. We showed that this is avoided if the ratio $\frac{1}{\psi} \, \frac{d U}{d \psi}$ remains finite as $\psi \rightarrow 0$. This is, for instance, the case if $U \approx \frac{1}{2} m_\psi^2 \, \psi^2$ at the origin. These considerations can be relevant for all the models in which symmetries are enhanced at some point during the cosmological evolution. For instance, we expect massive gauge modes to become massless when different branes move to the same bulk location as in the trapping mechanism of \cite{Kofman:2004yc}. We also found that, for $U \approx \frac{1}{2} m_\psi^2 \psi^2$, the longitudinal component is produced as much as each transverse component, and sources the same amount of gravity waves, for the most reasonable values of the mass $m_\psi$. Finally, it is worth pointing out that our study applies to a single instance of particle production. Things may be different in cases of multiple bursts of particle production; for instance, if the potential $U$ does not flatten at large $\psi$, so that $\psi$ performs oscillations about its minimum, gauge quanta will be produced at each oscillation, in a regime of parametric resonance \cite{Kofman:1997yn}. We have found that the gravity wave signal can reach an interesting level if the parametric resonance enhances the amount of produced quanta by a factor of $\gsim 200 \, \epsilon^{-1}$ with respect to the single episode of particle production ($\epsilon$ being the slow roll parameter). It would be interesting to study under which conditions this value can be reached in a concrete model. \begin{enumerate} \setcounter{enumi}{1} \item {\bf Model II:} The amount of gravity waves produced in this model was already computed in \cite{Barnaby:2010vf,Sorbo:2011rz,Barnaby:2011vw}. The novel computation in this work is the amount of scalar perturbations produced in this model under the assumption that the inflaton is only gravitationally coupled to the gauge field, and the comparison of the two effects. We found that coupling the inflaton only gravitationally sufficiently suppresses the amount of scalar modes generated in this model, so that the limits from non-gaussianity are irrelevant when compared to those from gravity waves. Therefore, particle production in this model can lead to gravity waves observable at the CMB scales. Differently from Model I, the gravity waves in this model are produced at all scales, and not just with a localized bump. However, this signal may be distinguishable from the vacuum one since one gravity wave helicity is produced in a much stronger amount than the other one, and this can lead \cite{Sorbo:2011rz} to observable nonvanishing TB and EB correlations in the CMB \cite{Saito:2007kt,Gluscevic:2010vv}. \end{enumerate} Ref. \cite{Sorbo:2011rz} already studied whether the parity violation in the sourced gravity waves produced by this model can be observed. Also in that case, the problem was to suppress the non-gaussianity of the scalar perturbations produced by the gauge field \cite{Barnaby:2010vf}. This was overcome in \cite{Sorbo:2011rz} by assuming the presence of $\sim 1000$ sourcing gauge fields, or the curvaton mechanism for the generation of the scalar perturbations. It was shown in \cite{Sorbo:2011rz} that, under these assumptions, and for some values of parameters, the parity-violation signal can be above the $1 \sigma$ detection line for a cosmic-variance limited experiment \cite{Sorbo:2011rz}. We have seen that in our implementation of the mechanism (namely, by assuming that the gauge field is only gravitationally coupled to the inflaton) the parity violation can, for some choice of parameters, be observed already by the ongoing / forthcoming Planck and SPIDER experiments. We have seen that backreaction bounds from this mechanism are under control for an axion scale $f$ in the interval $ 10^{-4} M_p \lsim f \lsim M_p $. Interestingly, the axion decay constant one typically finds in string theory is of the order of the GUT scale $f \sim 10^{16}$ GeV (see, e.g., \cite{Banks:2003sx,Svrcek:2006yi}) which fits comfortably within this window. Indeed, given the UV sensitivity of inflation, it is natural to ask whether one can realize our model in string theory. The low energy spectrum of string theory contains generically many axion-like particles, which arise from the reduction of antisymmetric $p$-form fields on $p$-cycles of the internal space.\footnote{In addition to these closed string axion-like particles, there are also open string axions but their presence is more model-dependent. For this discussion, we shall focus on closed string axions. Moreover, we consider only those axions that are not projected out by discrete symmetries (e.g., orientifolding), and do not receive a Stuckelberg mass.} These closed string axions have a pseudoscalar coupling $\psi F \tilde{F}$ to $U(1)$ gauge fields on the worldvolume of D-branes.\footnote{Such couplings arise from the reduction of Chern-Simons terms in the worldvolume action of D-branes, e.g., $\int_{D_{p+4}} C_p \wedge F \wedge \tilde{F}$.} In such string theory setting, it is not difficult to find inflaton candidates with no direct coupling to the axion-gauge field sector. For example, the inflaton can be another axion; the absence of direct couplings to the hidden sector follows from some topological and geometrical constraints. Consider a basis of $p$-cycles $\Sigma_i$, and their dual $p$-forms $\omega_j$ such that $\int_{\Sigma_i} \omega_j = \delta_i^j$. Two of such axions $\psi = \int_{\Sigma_i} C_p$, $\varphi = \int_{\Sigma_j} C_p$ do not have kinetic mixing if $\int \omega_i \wedge \ast \omega_j=0$. The absence of direct inflaton-gauge field $\varphi F \tilde{F}$ coupling is ensured by $\int \omega_i \wedge \tilde{\omega_j}=0$ where $\tilde{\omega_j}$ is the $6-p$ form dual to $\omega_j$, and $F$ is the gauge field to which the axion $\psi$ couples. In fact, the shift symmetries enjoyed by the axions may provide a natural explanation for why they remain as the light dynamical fields during inflation. The modest hierarchy of masses (see e.g., eq.~(\ref{mod2-cond-mpsi})) can be reasonably accommodated without necessarily assuming an ``axiverse" \cite{Arvanitaki:2009fg}.\footnote{See \cite{Acharya:2010zx,Cicoli:2012sz} for some string theory ways of generating a logarithmic hierarchy of axion masses in an ``axiverse".}, though having a hierarchy of axion masses offer more flexibilities. Clearly, more model building possibilities (with the inflaton being an axion or not) remain to be explored. We hope to return to such string theory realizations in the future. | 12 | 6 | 1206.6117 |
1206 | 1206.6103_arXiv.txt | {A first characterization of extrasolar planets by the observational determination of the radius has recently been achieved for a large number of planets. For some planets, a measurement of the luminosity has also been possible, with many more directly imaged planets expected in the near future. The statistical characterization of exoplanets through their mass-radius and mass-luminosity diagram is becoming possible. This is for planet formation and evolution theory of similar importance as the mass-distance diagram.} {Our aim is to extend our planet formation model into a coupled formation and evolution model. We want to calculate from one single model in a self-consistent way all basic quantities describing a planet: its mass, semimajor axis, composition, radius and luminosity. We then want to use this model for population synthesis calculations.} {In this and a companion paper, we show how we solve the structure equations describing the gaseous envelope of a protoplanet not only during the early formation phase, but also during the gas runaway accretion phase, and during the evolutionary phase at constant mass on Gyr timescales. We improve the model further with a new prescription for the disk-limited gas accretion rate, an internal structure model for the planetary core assuming a differentiated interior, and the inclusion of radioactive decay as an additional heat source in the core.} {We study the in situ formation and evolution of Jupiter, the mass-radius relationship of giant planets, the influence of the core mass on the radius and the luminosity both in the ``hot start'' and the ``cold start'' scenario. We put special emphasis on the validation of the model by comparison with other models of planet formation and evolution. We find that our results agree very well with those of more complex models, despite a number of simplifications we make in our calculations.} {The upgraded model yields the most important physical quantities describing a planet from its beginning as a tiny seed embryo to a Gyr old planet. This is the case for all planets in a synthetic planetary population. Therefore, we can now use self-consistently the observational constraints coming from all major observational techniques. This is important in a time where different techniques yield constraints on very diverse sub-populations of planets, and where its is difficult to put all these constraints together in one coherent picture. Our comprehensive formation and evolution model should be helpful in this situation for the understanding of exoplanets. } | The number of known transiting extrasolar planets or planet candidates has recently increased exponentially, thanks both to ground-based observations (e.g. Gillon et al. \cite{gillondoyle2011}), and to space missions like \textit{CoRoT} (e.g. L\'eger et al. \cite{legerrouan2009}) and \textit{Kepler} (Borucki et al. \cite{boruckikoch2011}). Combined with radial velocity measurements which yield the mass of the planet, one gets the planetary mass-radius ($M$-$R$) diagram, which is an observational result of similar importance as the semimajor axis-mass ($a$-$M$) diagram. The latter relation is available through the success of ongoing radial velocity surveys (e.g. Mayor et al. \cite{mayormarmier2011}). It is a goal of population synthesis models to understand the structure of the $a$-$M$ distribution, due to the multitude of clues it contains for planet formation theory (e.g. Ida \& Lin \cite{idalin2004}; Mordasini et al. \cite{mordasinialibert2009a}). A recent comparison of numerous theoretical and observational results mostly obtained by the radial velocity technique can be found in Alibert et al. (\cite{alibertmordasini2011}) and Mordasini et al. (\cite{mordasinialibert2011a}). The reason for the important role of the $M$-$R$ diagram which is now available for a statistically significant number of planets is that one can derive the mean density of the planet. This constrains the internal planetary structure which is of central importance to understand the nature (Leconte et al. \cite{lecontechabrier2011}), but also the formation of the planet. {The formation and evolution of the planetary mass-radius relationship is studied in the companion paper Mordasini et al. (\cite{mordasinigeorgy2011}), hereafter Paper II} (see also Mordasini et al. \cite{mordasinialibert2011}). Besides transiting planets, also the number of planets detected by direct imaging has increased significantly in the past few years, even though in absolute numbers, much less such planets have been found to date. But already these discoveries, like the planetary system around HR 8799 (Marois et al. \cite{maroismacinthosh2008}, \cite{maroiszuckerman2010}) have triggered numerous theoretical studies regarding the formation of these objects (e.g. Dodson-Robinson et al. \cite{dodsonrobinsonveras2009}; Kratter et al. \cite{krattermurrayclay2010}). Two points about these planets are particularly interesting: Their large semimajor axis $a$ and the fact that we measure the luminosity $L$ of young giant planets at some time $t$. Both quantities are important to understand the formation mechanism (e.g. Marley et al. \cite{marleyfortney2007}; Janson et al. \cite{jansonbonavita2011}). In the near future, more capable instruments like \textit{SPHERE} at the \textit{VLT} (Beuzit et al. \cite{beuzitfeldt2007}) or \textit{GPI} at Gemini South (McBride et al. \cite{mcbridegraham2011}) and later \textit{EPICS} at the \textit{E-ELT} (Kasper et al. \cite{kasperbeuzit2008}) will come online. We can therefore expect that the number of points we can put in the $t$-$L$, the $a$-$L$ and (for cases with an independent, dynamical mass determination) the $M$-$L$ diagram will increase from a handful at the moment to hundreds in a few years, similar to what has happened for the $M$-$R$ diagram in the past few years. This shift from an era of discovery to one of a first physical characterization of extrasolar planets by their radii and luminosities has profound implications for planet formation theory. Until recently, planet formation models studied mostly giant planets detected by radial velocity measurement, of which only the minimal mass and some orbital elements were known. Now we are confronted with a multitude of different sets of observational data and constraints, each regarding primarily planets of different types: Transiting, close-in planets, most of them with a small radius (as found by \textit{Kepler}, see also Paper II); directly imagined, self-luminous massive young giant planets at large distances from their host star; and a wide range in masses going from super-Earth to Jovian mass planets at distances varying from close to the star out to several AU found by RV measurements (e.g. Mayor et al. \cite{mayormarmier2011}). The final goal of planet formation theory to develop one theory to explain the formation (and evolution) of all these very different planets is a challenging one, and will require many efforts in the coming years. Nevertheless, the approach to bring together all these different observational data in a coherent way (which in itself is a non-trivial task, cf. Wolfgang \& Laughlin \cite{wolfganglaughlin2011}) to constrain planet formation and evolution theories seems to be a promising route. In the end, one is not interested in a theory which can explain certain types of planets, but fails for other classes. In this and the companion paper we take a first step in this direction. We present multiple upgrades of our formation model (introduced first in Alibert, Mordasini \& Benz \cite{alibertmordasini2004}). The most important addition is that we now calculate not only the formation of the planets, but couple formation in a self-consistent way with the subsequent evolution at constant mass once the protoplanetary disk is gone. With this approach, we can now calculate directly from one single model not only the planet's mass and semimajor axis, but also the planet's main physical characteristics like the radius, luminosity, surface gravity, effective temperature as well as the composition in terms of iron and silicates, ices and H$_{2}$/He. These basic characteristics are available for a planet at any time during its ``life'' starting as a tiny sub-Earth mass seed in the protoplanetary disk to a mature, billion of years old planet. A direct coupling of the planet's formation and its evolution is necessary, as it is well known that the formation has important, direct consequences for the evolution, in particular for the luminosity of giant planets at young ages (``cold'' vs ``hot'' start models, cf. Marley et al. \cite{marleyfortney2007}; Spiegel \& Burrows \cite{spiegelburrows2011}). With this model development, we can now compare our simulations directly with observational constraints coming from radial velocity (and microlensing), transits as well as direct imaging. Other upgrades are the following: a detailed description for the rate at which gas is accreted by the planet in the disk-limited gas runaway accretion phase, an internal structure model for the solid (iron/silicate and possibly ice) part of the planet, the inclusion of radioactive decay for the luminosity of the core, a new initial profile for the gaseous disk, a new prescription for the photoevaporation of the disk, including external and internal photoevaporation, and finally a realistically low grain opacity for the gaseous envelope (presented in a dedicated work, Mordasini et al. \cite{mordasiniklahr2011}). We thus deal in this paper and in Paper II mostly with improvements of the physical description of one planet. In other papers, we addressed upgrades regarding the disk model (Fouchet et al. \cite{fouchetalibert2011}), the migration of low-mass planets (Dittkrist et al. in prep) or the effect of the concurrent formation of several embryos in one disk (Alibert et al. in prep.). \subsection{Organization of the paper} The organization of the paper is as follows: In Sect. \ref{sect:combinedmodel} we give a short overview of the model. In Section \ref{sect:modelupgasenve}, we describe the modifications of the computational module that describes the gaseous envelope structure of the planet, extending it to calculate the structure not only during the pre-runaway formation phase as in our previous models, but also during the gas runaway accretion/collapse phase and the subsequent evolutionary phase after the disk is gone. In Section \ref{sect:mdotmax} we address a related subject, namely how to calculate the gas accretion rate in the disk-limited regime, i.e. once gas runaway accretion of forming giant planets has started. In Paper II, we present further upgrades regarding the planet module, namely a realistic model for the density of the solid core of the planets and the inclusion of radiogenic heating in it. In Paper II we also describe shortly some modifications regarding the protoplanetary disk model. {Finally, we use in Paper II the upgraded model in population synthesis calculations to study the formation and evolution of the planetary $M$-$R$ diagram, the distribution of planetary radii, and the comparison with observational data.} In the remainder of this first paper, we show specific results obtained with the upgraded model: In Sect. \ref{sect:examplesinsitu} we study the coupled formation and evolution of a Jovian mass planet at 5.2 AU from the Sun. Many of the effects seen during this particular simulation are characteristic for the effects encountered during the formation and evolution of the planets in a general population synthesis calculation (Paper II). In Sect. \ref{sect:radii} and \ref{sect:luminosities} we discuss our results concerning the radii and luminosities of giant planets, putting special weight on the comparison with other, more complex models. The luminosity of young Jupiters is further addressed in a dedicated paper (Mordasini et al. in prep.). | In earlier versions of the model, we calculated the internal structure of the gaseous envelope only during the attached, pre-gas runaway accretion phase. This is sufficient if one is only interested in the final mass of the planets, and thus sufficient for comparisons with planets found by the radial velocity method. Now we calculate the structure also during the gas runaway accretion phase (which is also the phase when the planet's radius collapses) and during the evolutionary phase at constant mass over Gigayear timescales. With that we now know all major quantities (mass, semimajor axis, radius, luminosity, composition) characterizing the planets during their entire formation and evolution. This allows to compare our population synthesis models directly and consistently with results coming from all major observational techniques used to detect and characterize extrasolar planets {(see Paper II for a comparison of the synthetic and actual mass-radius relationship, the predicted distribution of radii, and the comparison with \textit{Kepler})}. Extrasolar planet research has entered an era in which massive amounts of observational data regarding very different sub-populations of planets are brought to us from different techniques. They should all be explained consistently by planet formation and evolution theory, but it is a difficult task to unite the different elements and observational constraints into one consistent global picture. We think that a fruitful approach in this situation is to work with theoretical models able to make testable predictions in a consistent way for all important observational techniques. With the work presented in this paper we make a development in this direction, allowing us to test and improve theoretical formation models using the wealth of data coming from observations. | 12 | 6 | 1206.6103 |
1206 | 1206.2569.txt | Polarized emission from a quasar is produced by wavelength-independent electron scattering surrounding its accretion disc, and thus avoid the contamination from its host galaxy and reveal the intrinsic emission spectrum of the accretion disc. Ultra-violet (UV) emission from a quasar is normally free from the contamination from its host galaxy. Polarization fraction of the quasar's disc emission can therefore be determined by comparing total UV emission with polarized visible to near-infrared (NIR) emission; and the resulting continuum spectrum from UV to infrared can reveal the theoretically expected Balmer edge absorption feature. We fit the polarized spectra in visible and NIR bands together with the total UV spectra of two type-1 quasars (3C 95, 4C 09.72), to an extended geometrically thin and optically thick accretion disc model. In addition to the standard model, we include the Balmer edge absorption due to co-rotational neutral gas on a narrow annulus of the accretion disc. We find that the extended thin accretion disc model provides adequate description on the continuum spectra of the two quasars from UV to NIR wavelengths. A Monte-Carlo-Markov-Chain fitting to the continuum spectra is able to well constrain the true polarization fraction of the disk emission, which allows the Balmer edge feature to be completely revealed from polarized visible to UV continua. The Balmer edge feature is prominent in both quasars' spectra, and is significantly broadened due to the orbital motion of gas in the accretion disc. The broadening of the Balmer edge feature is therefore related to the quasar's inclination. This work proves the concept of determining quasar's inclination from the Balmer edge feature in their continuum spectra. | Quasars are the most luminous objects in the Universe. The release of gravitational energy as material is accreted onto the supermassive black hole (SMBH) heats the accretion disc and generates multi-color thermal emission from ultraviolet (UV) to infrared (IR) wavelengths (e.g., Shakura \& Sunyaev 1973; Novikov \& Thorne 1973; Lynden-Bell \& Pringle 1974; Laor \& Netzer 1989; Laor et al., 1990; Hubeny et al. 2000). However, the total emission of a quasar at visible and near-IR (NIR) wavelengths is mixed by emissions from both its accretion disc surrounding its central SMBH and its host galaxy, which complicates observations of intrinsic emission of the quasars' accretion disc. For example, the optically thick and geometrically thin ``standard" disc model predicts the emission spectrum in the optical to NIR should follow $F_{\nu}\propto\nu^{\alpha}$, where $F_{\nu}$ is the flux per frequency, $\nu$ is the frequency and $\alpha=1/3$ (e.g., Shakura \& Sunyaev 1973; Lynden-Bell \& Pringle 1974). However many quasar spectra in the optical to NIR have $\alpha<-0.2$ (Neugebauer et al. 1987; Cristiani \& Vio 1990; Francis et al. 1991; Zheng et al. 1997), consistent with significant host galaxy contaminations which are increasingly important at longer wavelengths. Polarized spectra of quasars at visible and NIR wavelengths may reveal the emissions of their accretion discs, because polarization is expected to come from the electron scattering inside the Broad Line Region (BLR) and the electron scattering is wavelength independent. Kishimoto et al. (2008) reported polarized spectra of six quasars in the rest wavelength ranging from 0.2 - 2 $\mu$m. These quasars have $\sim$ 1$\%$ of polarization in optical bands, less than 1$\%$ of polarization in NIR continuum, and little polarization in their emission lines. Indeed Kishimoto et al. (2008) found that the polarized NIR spectra manifest $\alpha=1/3$, expected from the standard disc model. We emphasize two important facts regarding quasars' polarization at visible and NIR wavelengths: first, the alignment of optical polarization with the radio structure of many quasars suggests that the emission is polarized not in the disc atmosphere but in an equatorial scattering region surrounding the disc (e.g., Stockman \& Angel 1979; Smith et al. 2005). Indeed, intrinsic polarization produced in the disc atmosphere is likely to be damped by Faraday rotation (e.g., Agol \& Blaes 1996). Second, the observed polarization percentage in the optical to NIR bands may not be the polarization percentage of the intrinsic disc emission, or the polarization percentage of the equatorial scattering region, due to possible contaminations from the quasar's host galaxy. The standard thin disc model predicts a ``bump" shape from UV to visible wavelengths, which is produced by the emission from the inner disc region and is determined by the combination of the mass of the central supermassive black hole (BH) and the inner disc boundary radius. The UV continuum is relatively free from the host galaxy's contamination, and thus should reflect the emergent spectra of the accretion disc and allow to probe the inner part of the accretion disc. Two quasars of the Kishimoto (2008) sample (3C 95, 4C 09.72) have been observed with the {\it Hubble Space Telescope} (HST) and have published UV spectra (Bahcall et al. 1993; Marziani et al. 1996; Evans \& Koratkar 2004). Combining the UV continuum and the polarized spectra in visible and NIR wavelengths, therefore, will provide powerful spectral diagnosis of the nature of the two quasars' supermassive BHs and accretion discs. It has also been reported that the quasar continuum spectra in wavelengths shorter than 120 nm can be described by a simple power law with index $\alpha_{\rm EUV}=-1.76\pm0.12$, which suggests that the extreme UV (EUV) continuum is probably due to the intergalactic medium photoionized by the integrated radiation from quasars (Telfer et al. 2002). Therefore the EUV continuum may not reflect the intrinsic emission of a quasar's accretion disc. Quasars' continuum spectra from UV to NIR wavelengths may be used to constrain the properties of their central supermassive BHs, in particular their BH spin, in a similar way to the method used for stellar mass BHs in X-ray binaries whose BH mass and disc inclination angle ($i$) are known very well for some of them (Zhang et al. 1997; Shafee et al. 2006). Czerny et al. (2011) used the standard thin accretion disc model to fit several broad-band photometric points of quasar SDSS J094533.99+100950.1. Assuming a BH mass, this procedure put constraints on its spin. However, the broad-band photometric fluxes may be contaminated by broad spectral lines, which may affect the estimates of the BH spin. Davis \& Laor (2011) also used the thin accretion disc model to fit the shape of optical continuum of a set of 80 PG quasars, and obtained their radiative efficiency and derived their BH spin. However, both methods had to assume the BH mass and the inclination angle of the accretion disc {\it a priori}. Various methods can be used to estimate the BH mass in a quasar, but normally within a factor of 2-3, as will be discussed later in section 4.1. The inclination of the accretion disc for an individual quasar is normally not well constrained. According to the unified model of active galactic nuclei, the emission from a quasar's accretion disc is not blocked by its dusty torus, which implies a disc inclination of less than $\sim60^{\circ}$ (e.g., Antonucci 1993). Advanced torus model and spectroscopy of quasars in the mid-infrared wavelengths may provide more insights on the interaction of the disc emission and the torus and better constrain the disc inclination (e.g., Alonso-Herrero et al. 2011). Another method to determine the disc inclination is to describe not only the spectra but also the morphology of active galaxies self-consistently (Kacprzak et al. 2011). For radio loud objects, inference of radio core luminosity may constrain the view angle of the radio source, i.e., the inclination of the accretion disc (e.g., Wills \& Brotherton 1995). However, the disc inclination has not been estimated from the disc emission directly. In principle, the luminosity of the accretion disc scales as $\cos(i)$, so the inclination may be constrained by photometry if the BH mass and accretion rate can be independently estimated (e.g. Czerny et al. 2011). This method so-far has large uncertainty mainly due to the large uncertainty of BH mass. The comparison between a quasar's UV emission and its polarized visible emission can be complicated by the possible Balmer edge absorption. It has been reported that the polarized flux of the two quasars manifest a discontinuity in the slope at the wavelengths shorter than $\sim$400 nm (Kishimoto et al. 2004). The feature is mostly interpreted as the buried Balmer edge of the intrinsic spectra of the quasar UV/optical continuum, or the ``Big Blue Bump" (BBB) emission. The edge absorption feature is due to the bound-free opacities in the disc atmosphere, and indeed indicates the thermal and optically thick nature of the continuum. However, the origin of the Balmer edge absorption is still unknown. An order-of-magnitude estimate of the broadening of the Balmer edge indicates that the broadening is consistent with the orbital motion of the corresponding disc annuli responsible for emission around 400 nm (Kishimoto et al. 2004). In this work, we use the extended standard thin accretion disc model to fit the polarized spectra in the visible and near-infrared bands and the total spectra in the UV band of 3C~95 and 4C~09.72, after removing prominent emission and absorption features; the extension includes the Balmer edge absorption of an optically thin layer of neutral gas co-rotating with the accretion disc. We use the Monte-Carlo-Markov-Chain (MCMC) method to fully explore the multi-dimensional parameter space of BH mass, spin, accretion rate, disc inclination and polarization. The wide spectral coverage of the total UV emission and the polarized spectra in visible and NIR bands provides a complete description of the accretion disc emission, which allows us to determine of physical properties of the BH and the accretion disc. In particular, the true polarization fraction of the disc emission can be well constrained from the spectral fitting, which leads to a continuum spectrum from UV to NIR. The spectral fitting also constrains the broadening of the Balmer edge, which is constroled by the disc inclination. | A quasar's polarized continuum spectrum at visible to NIR wavelengths, together with the total continuum spectrum at UV wavelengths, provides an unique opportunity to determine the properties of accretion discs around supermassive BHs. In this work we fitted the spectra of two type-1 quasars (3C~95 and 4C~09.72) to the standard thin accretion disc model with the Balmer-edge absorption, with the BH masses determined from stellar dynamics and reverberation measurements. We used the MCMC method to sample a parameter space of BH spin, accretion rate, polarization, disc inclination and Balmer edge optical depth. We conclude that the quasar polarized spectra at visible and NIR wavelengths and total spectra in UV wavelengths can reveal the accretion disc emission, which is indeed the thermal emission of the optically thick and geometrically thin accretion disc. At the UV wavelengths, the contamination from the host galaxy is negligible so the total spectra reflects the emission spectra of the accretion disc. At the visible and NIR wavelengths, the contamination buries the intrinsic accretion disc emission as well as the Balmer-edge feature. However the contamination does not exist in the polarized spectra. Therefore, the polarized spectra at visible and NIR wavelengths and total spectra at UV wavelengths allow us to study the entire accretion disc. The true optical polarization of the accretion disc emission can be well constrained by bridging the total emission at UV and the polarized emission at visible. We find that 3C~95 and 4C~09.72 have significantly sub-Eddington accretion rates, and their optical polarization is $1.1-1.8\%$ and $1.5-3.3\%$ (at 95\% confidence level), respectively. The true optical polarization of accretion disc derived from our continuum fitting is larger than the observed optical polarization, which indicates host galaxies' contamination in the quasars' total optical continua. The absorption feature found at the Balmer edge is prominent and significantly broadened. We found that the Balmer absorption feature for both quasars investigated can be reproduced by assuming optically thin absorbing $n=2$ hydrogen population co-rotating with the accretion disc at radii with effective temperature between 8,000 and 20,000 K. The Balmer edge feature is found to extend to UV wavelengths, whose width is the result of both photoelectric absorption cross section and the line-of-sight projection of the orbital motion. The choice of the temperature range does not significantly affect the spectral fitting. For example, for the upper boundary of temperature varying from 15,000 to 25,000 K, we did not find any significant corresponding dependency of the black hole parameters and the true optical polarization (see Table \ref{Fit}). However, we found the best-fitted Balmer edge optical depth ($\tau_0$) to be strongly dependent on the width of Balmer absorption annulus. The wider the annulus is, the deeper the Balmer edge appears, and the required $\tau_0$ to fit the data is smaller (see Table \ref{Fit}). Therefore the estimation of neutral hydrogen on the surface of the accretion disc is also sensitive to the temperature range. The sensitivity study has suggested that a reasonable uncertainty in the exact location where the Balmer edge absorption occurs has a major effect in the depth of the Balmer edge feature, but only has a minor effect on the broadening of the Balmer edge feature. Indeed, the broadening of the Balmer edge feature depends mostly on the disc's inclination. The broadening of the Balmer edge features tentatively constrain the disc's inclination of the two quasars. Our fitting results show that the quasars' BH spin parameters cannot be constrained well from the spectral fitting up to $\sim100$ nm. As shown in Figure \ref{Fit3} and Table \ref{MassT}, the posterior probability distribution of the BH spin is very wide. The best-fitted parameters for both 3C~95 and 4C~09.72 indicate non-rotating BHs; however, the full exploration to the parameter space indicates that a significant range of $a/M$ between 0 to 1 is acceptable. This is due to the combination of the uncertainties in inclination, accretion rate and BH mass. Figure \ref{3Cpair} and \ref{4Cpair} show a weak correlation between $\tau_0$ and $i$. As expected, a larger $\tau_0$ would produce a deeper absorption edge, which allows the widths of the Balmer edge feature to be better determined, and the disc's inclination to be better constrained. Indeed, the uncertainties in the observed Balmer edge depth play a major role in the uncertainty of inclination. For example, the two polarized spectra at wavelengths shorter than about 300 nm are obviously below the model predictions. The spectral features were noticed by Kishimoto et al. (2004), who did not make unambiguous identification and interpretation of these features, but suggested that they might be related to Fe II absorption and possibly the Bowen resonance-florescence lines. Nevertheless, the relatively lower signal to noise ratios of the measurements of the polarized spectra at wavelengths shorter than about 300 nm do not seem to affect the fitting results to the Balmer edge significantly. However, future better observations may allow identification and physical modeling of these features, which should allow better determination of the Balmer edge. The foreseeable improvement in tightening the inclination uncertainty is to have better polarized spectral observations around the Balmer edge in the future. In this study, we find that the Balmer edge optical depth and the disc inclination are particularly sensitive to the continuum emission at 300 - 400 nm wavelengths. The current data have low signal-to-noise ratio in this wavelength range; with high signal-to-noise ratio data in the future, it is plausible to study the visible continuum of the quasar accretion discs, and constrain the Balmer edge absorption and the disc inclination. Furthermore, since the uncertainty in inclination angle will propagate into the uncertainty in accretion rate for a given observed flux, a more accurate inclination will also result in a more accurate accretion rate. Therefore a combination of a more accurate inclination and a well observed peak emission will then allow the BH mass and accretion rate determined accurately, leading eventually to accurate BH spin measurement. \appendix | 12 | 6 | 1206.2569 |
1206 | 1206.6273_arXiv.txt | We present IACTalks, a free and open access seminars archive (http://iactalks.iac.es) aimed at promoting astronomy and the exchange of ideas by providing high-quality scientific seminars to the astronomical community. The archive of seminars and talks given at the Instituto de Astrof{\'\i}sica de Canarias goes back to 2008. Over 360 talks and seminars are now freely available by streaming over the internet. We describe the user interface, which includes two video streams, one showing the speaker, the other the presentation. A search function is available, and seminars are indexed by keywords and in some cases by series, such as special training courses or the 2011 Winter School of Astrophysics, on secular evolution of galaxies. The archive is made available as an open resource, to be used by scientists and the public. | Since April 2008, the Instituto de Astrof{\'\i}sica de Canarias (IAC) has been webcasting and archiving the weekly seminars and monthly colloquia about the most exciting topics in astronomy and astrophysics' research. The IAC is one of the leading centres for astrophysical research and related technology development in Spain, and has a staff of over 350, of which over 160 are active in astronomy research. The seminars cover both observational and theoretical astronomy and include diverse topics such as particle and stellar physics, galaxies and cosmology, and astronomical instrumentation and telescopes. The seminars are aimed at a general astronomical audience and mainly given by postdocs and staff astronomers. The speakers in our special ``colloquia'' are high-profile scientists and over the years have included leading astronomers from all over the world, covering practically the complete spectrum of current-day astrophysical research. While most of the archived seminars are on astrophysical research, the IACTalks archive also contains seminars on various topics relating to astronomical telescopes and instrumentation, and programming and (super)computing. Other on-line seminars include the webcasting and archive service of the Space Telescope Science Institute (https://webcast.stsci.edu/webcast/), going back to 2001, or the recently started seminar series at http://asterisk.apod.com/ampersand/ . IACTalks is complementary to these and other initiatives. | 12 | 6 | 1206.6273 |
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1206 | 1206.6759_arXiv.txt | Two methods are developed for solving the steady-state spherically symmetric radiative transfer equation for resonance line radiation emitted by a point source in the Intergalactic Medium, in the context of the Wouthuysen-Field mechanism for coupling the hyperfine structure spin temperature of hydrogen to the gas temperature. One method is based on solving the ray and moment equations using finite differences. The second uses a Monte Carlo approach incorporating methods that greatly improve the accuracy compared with previous approaches in this context. Several applications are presented serving as test problems for both a static medium and an expanding medium, including inhomogeneities in the density and velocity fields. Solutions are obtained in the coherent scattering limit and for Doppler RII redistribution with and without recoils. We find generally that the radiation intensity is linear in the cosine of the azimuthal angle with respect to radius to high accuracy over a broad frequency region across the line centre for both linear and perturbed velocity fields, yielding the Eddington factors $f_\nu\simeq1/3$ and $g_\nu\simeq3/5$. The radiation field produced by a point source divides into three spatial regimes for a uniformly expanding homogeneous medium. The regimes are governed by the fraction of the distance $r$ from the source in terms of the distance $r_*$ required for a photon to redshift from line centre to the frequency needed to escape from the expanding gas. For a standard cosmology, before the Universe was reionized $r_*$ takes on the universal value independent of redshift of 1.1~Mpc, depending only on the ratio of the baryon to dark matter density. At $r/r_*<1$, the radiation field is accurately described in the diffusion approximation, with the scattering rate declining with the distance from the source as $r^{-7/3}$, except at $r/r_*\ll1$ where frequency redistribution nearly doubles the mean intensity around line centre. At $r/r_*>1$, the diffusion approximation breaks down and the decline of the mean intensity near line centre and the scattering rate approach the geometric dilution scaling $1/r^2$. The mean intensity and scattering rate are found to be very sensitive to the gradient of the velocity field, growing exponentially with the amplitude of the perturbation as the limit of a vanishing velocity gradient is approached near the source. We expect the 21cm signal from the Epoch of Reionization to thus be a sensitive probe of both the density and the peculiar velocity fields. The solutions for the mean intensity are made available in machine-readable format. | \label{sect:intro} The nature of formation of the first radiating objects in the Universe is one of the paramount unsolved problems in cosmological structure formation. Searches for the earliest galaxies have broken the spectroscopically confirmed redshift barrier of $z=7$ \citep{2011ApJ...730L..35V, 2012ApJ...744...83O, 2012ApJ...744..179S}, with plausible candidates identified photometrically up to $z\lta9$ \citep{2011MNRAS.418.2074M}, and possibly as high as $z\simeq10$ \citep{2011Natur.469..504B}. These systems may well reside within the Epoch of Reionization (EoR) of hydrogen, as Cosmic Microwave Background (CMB) measurements suggest the epoch, if a sudden event, occurred at $z_r=10.4\pm1.2$ ($1\sigma$) \citep{2011ApJS..192...18K}. If so, 21cm emission from the diffuse Intergalactic Medium (IGM) would become visible near this same epoch, as the same sources would provide sufficient UV continuum to excite the line through the Wouythuysen-Field effect (WFE) \citep{1952AJ.....57R..31W, 1958PROCIRE.46..240F, MMR97}. The prospect of discovering the EoR through the associated 21cm signature from the diffuse IGM has inspired the development of a new generation of radio telescopes, such as the LOw Frequency Array (LOFAR)\footnote{www.lofar.org}, upgrades to the Giant Metrewave Radio Telescope (GMRT)\footnote{gmrt.ncra.tifr.res.in}, the Murchison Widefield Array (MWA) \footnote{www.haystack.mit.edu/ast/arrays/mwa}, the Primeval Structure Telescope/21 Centimeter Array (PaST/21CMA) \footnote{web.phys.cmu.edu/$\sim$past}, the Precision Array to Probe EoR (PAPER)\footnote{astro.berkeley.edu/$\sim$dbacker/eor}, and a possible Square Kilometre Array (SKA)\footnote{www.skatelescope.org}. A recent review of this rapidly growing area is provided by \citet{2011arXiv1109.6012P}. The interpretation of the signal will require modelling the radiative transfer of the Lyman resonance line photons, primarily Ly$\alpha$, that drive the WFE. Most estimates have presumed a homogeneous expanding medium. Early modelling neglected the effects of atomic recoil and of spatial diffusion about the emitting sources, assuming the sources were homogeneously and isotropically distributed throughout the Universe \citep{1959ApJ...129..536F, MMR97}. Allowing for recoil somewhat suppresses the \Lya photon scattering rate by an amount depending on the local temperature and expansion rate of the IGM \citep{2004ApJ...602....1C, 2006MNRAS.372.1093F}. Using Monte Carlo solutions to the radiative transfer equation to include spatial diffusion, it was found that near an emitting source the scattering rate varies as $r^{-7/3}$ \citep{2007ApJ...670..912C, 2007A&A...474..365S}, more rapidly than the geometric dilution factor $r^{-2}$ predicted without spatial diffusion. It will be shown below that the steeper dependence arises generally over all distances for which the radiative transfer of the \Lya photons may be treated in the diffusion approximation. In reality the IGM is clumpy, with structures breaking away from the cosmological expansion. Simple analytic estimates suggest that the scattering rate will be substantially modified not only by density and temperature fluctuations, but by gradients in the velocity field of the gas around individual sources \citep{2009MNRAS.393..949H}. More sophisticated methods are required for accurate solutions of the spatial and frequency dependent radiative transfer equation. Monte Carlo codes were developed for this purpose \citep{2002ApJ...578...33Z, 2006ApJ...645..792T, 2007ApJ...670..912C, 2007A&A...474..365S}. The method has recently been applied to estimate the expected cosmological 21cm signal \citep{2009A&A...495..389B, 2011A&A...532A..97V}. A difficulty with the Monte Carlo technique is the limited resolution imposed by the restricted number of photon packets that may be practically followed. An alternative grid-based method for solving the spherically-symmetric radiative transfer equation in the Eddington approximation has been developed by \citet{2009ApJ...703.1992R} for linear flow fields. Scattering in the deuterium \Lya resonance and the addition of \Lya photons produced in radiative cascades following the scattering of higher order Lyman resonance line photons will modify the \Lya mean intensity and scattering rate near a source. As these are smaller, secondary effects \citep{2007ApJ...670..912C, 2007A&A...474..365S}, they are not included in this paper. A further complication is the time required to establish a steady-state radiation field. The \Lya photon scattering rate scales like $t_s\simeq3.2 n_{\rm HI}^{-1}T^{1/2}\,{\rm s}$ for a gas with neutral hydrogen density $n_{\rm HI}$ and temperature $T$. Time-dependent radiative transfer computations suggest it may take $10^4-10^{12}$ scatterings to establish a steady-state radiation field, depending on the internal structure of the scattering system, including internal velocity gradients \citep{2009MNRAS.393..949H, 2009ApJ...694.1121R}. Timescales of $10^6-10^9\,{\rm yr}$, comparable to or longer than the evolutionary timescale of starbursts and quasars, may be required for structures that have broken away from the cosmic expansion, particularly in the presence of substantial x-ray heating. In this paper, we present two algorithms for solving the radiative transfer equation of an inhomogeneous medium, one based on finite-differences on a grid and the second Monte Carlo based. The grid-based method combines solutions to the ray equation and the moment equation based on the method of \citet{1975ApJ...202..465M, 1976ApJ...210..419M, 1977ApJ...214..337M}. The inclusion of solutions to the ray equation allows the sequence of moment equations to be closed without imposing the Eddington approximation. Since the method was developed for stellar atmospheres, modifications to the approach are described necessary to adapt the method to the problem of a source in the IGM. The method has a few restrictions:\ 1.\ it is implemented assuming spherical symmetry, 2.\ it assumes a steady state, and 3.\ it requires the velocity field around the source to be monotonically increasing or decreasing. In practice the latter is not a severe restriction because the peculiar velocity field only modulates the Hubble flow except within the turnaround radius very near the source. The assumption of spherical symmetry may not be very restrictive either, since the photons do not diffuse very far compared with the coherence length of cosmological structures. A solution along a ray in a 3D computation may therefore not differ much from that assuming the medium is isotropic with the radial properties of the ray. We are not able to test this, however, without a fully 3D solution to the radiative transfer equation, which is beyond the scope of this paper. As noted above, situations may arise in which the steady-state approximation will break down. The Monte Carlo method is similar to existing algorithms for resonance line radiation, but with two improvements. It incorporates RII frequency redistribution by interopolating on the RII redistribution function rather than directly computing collisions with atoms. This improves the speed of the computations by a factor of a few, but at the cost of requiring a frequency grid tailored to the particular problem. The second improvement is to compile the specific mean intensity based on the path lengths traversed by the photon packets rather than on frequency and position bin crossings. This improvement is general and substantially reduces the noise in the specific mean intensity for a fixed number of photon packets. The method also serves as an independent check on the solutions obtained through the ray and moments method. The paper is organised as follows. The basic framework used to solve the radiative transfer equation in spherical symmetry using the ray and moments method on a grid is presented in the next section. In Section~\ref{sect:MC_method}, we summarise the Monte Carlo method developed. We present the results of validation tests of both methods against analytic solutions for a homogeneous medium in Section~\ref{sect:HomogTest}. Both methods are applied to scattering problems in an inhomogeneous medium in Section~\ref{sect:InhomogTest}. A summary and conclusions follow. Details of the source term used for the ray and moment solution are provided in Appendix~\ref{ap:RMsource}. The Monte Carlo method is described in Appendix~\ref{ap:MC}. The solution to the radiative transfer problem for a point continuum source in a uniformly expanding homogeneous medium in the diffusion approximation is derived in Appendix~\ref{ap:hem}. Tables of solutions to a test suite of problems using the ray and moments method are provided online in machine-readable format, as summarised in Appendix~\ref{ap:solutions}. | \label{sect:concl} The $21 \, {\rm cm}$ signatures of the first luminous objects are dependent upon the \Lya scattering rate, which is necessary to decouple the \HI spin temperature from the CMB temperature through the Wouthuysen-Field effect in the diffuse IGM during the early stages of reionization and so render the hydrogen detectable against the CMB via $21 \, {\rm cm}$ observations. Realistic studies of \Lya scattering caused by the first sources during the EoR will need to make use of three-dimensional density and velocity fields derived from cosmological simulations, and treat the time-dependent radiative transfer of photons contributed from multiple sources of finite lifetime, the detailed properties and spatial distributions of which are largely uncertain and will have to be extrapolated from lower-redshift observations or estimated from galaxy formation simulations. Together with the extensive effort currently underway in removing radio foregrounds and isolating the signal of the EoR, these detailed analyses will be critical in predicting and interpreting future $21 \, {\rm cm}$ tomographic observations made by existing and future radio interferometric arrays, such as LOFAR and SKA. We develop two methods for solving the radiative transfer equation for resonance line photons in spherically symmetric systems, and apply them to idealized problems relevant to the 21cm signature of the IGM. We consider five classes of problems corresponding to a point source emitting either emission line or continuum radiation in an expanding medium, allowing for a uniformly expanding homogeneous medium, a uniformly expanding medium with an overdense shell around the source, a homogeneous medium with a quadratic velocity profile, and a medium with a self-consistent density and velocity perturbation around the source. A static medium test problem is also treated. Since these problems may serve as useful tests of Monte Carlo schemes, we provide their solutions in machine-readable format (Appendix~\ref{ap:solutions}). Following \cite{1975ApJ...202..465M} and \cite{1976ApJ...210..419M}, the first method is based on solving the ray and angular moment forms of the comoving frame radiative transfer equation in a spherically symmetric medium subject to a monotonic velocity profile $V(r)$, where $V \geq 0$ and $V' \geq 0$ for all $r$ (see Section~\ref{subsect:grid_method}). We described general boundary conditions required by these methods in order to treat the radiative transfer of \Lya scattering in a cosmological context. We also obtained an efficient prescription for the finite difference representation of the source function for partial frequency redistribution based on the diffusion approximation. We compare our results with Monte Carlo solutions to the radiative transfer equation using an implementation that determines the \Lya radiation mean intensity from the accumulated path lengths of the photons within a given volume and frequency range. This greatly improves the accuracy over a technique that uses spatial and frequency bin crossings to estimate the intensity. For 200 logarithmically-spaced grid zones covering three decades in radius, the noise level in the scattering rate is kept under 10 per cent per radial bin using $2\times10^5$ photon packets. The code computes the Doppler redistribution of the frequencies upon scattering both directly and by interpolating on the RII redistribution function. The latter speeds the computations by a factor of a few, but requires a grid tailored to a specific application, so lacks generality. In Section~\ref{sect:HomogTest} we validated our schemes using various test problems for resonance line photon scattering in spherical symmetry, including:\ (i) \Lya scattering in an optically thick static sphere \citep{DHS_06} and (ii) the \Lya scattering halo of a monochromatic \Lya point source in a uniformly expanding homogeneous medium \citep{1999ApJ...524..527L}. We found the ray and moment method results agreed with the analytic solutions, at least in the optically thick regime where the analytic solutions are valid, while in case (ii) our solution matched the Monte Carlo solution found by Loeb \& Rybicki. A final test problem was described for a continuum source in a uniformly expanding homogeneous medium. We utilised the analytic solution of \cite{1999ApJ...524..527L}, valid in the zero-temperature diffusion approximation, as a Green's function to obtain the equivalent solution for a flat source spectrum in the diffusion approximation. The solution gives a radial profile for the \Lya scattering rate that varies as $r^{-7/3}$, steeper than the free-streaming dependence $r^{-2}$, and the same dependence found by other authors in Monte Carlo studies of this problem. Our analytic solution also allows for a maximum frequency cutoff from the source; both of our numerical methods recover the effects of the cutoff. The photon production rate between \Lya and \Lyb required to couple the spin temperature to the gas kinetic temperature is found to be ${\dot N}_{\alpha, {\rm th}}^{\rm cont}\simeq4.39\times10^{55}[(1+z)/11] r_{\rm Mpc}^{7/3}\,{\rm s}^{-1}$, where $r_{\rm Mpc}$ is the distance from the source in megaparsecs. This is less demanding than for an emission-line source by several orders of magnitude at a distance of 1~Mpc. We solve the test problem of a continuum source in a uniformly expanding homogeneous IGM numerically, outside of the diffusion limit, using our ray/moment and Monte Carlo methods for spherical symmetry. In suitable spherically symmetric problems such as this test problem, the combined ray/moment equation solution method may be used to quickly produce noise-free results, in contrast to the Monte Carlo approach for a practical number of photon packets. For more general situations, the Monte Carlo method is more readily extended to treat cartesian grids with general configurations of sources and arbitrary density, temperature and peculiar velocity fields within the scattering medium. For precision results, however, a grid-based scheme such as the method presented here may be desirable. In this case, the diffusion approximation may be used as an inner boundary condition on the surface of an inner core region. For non-monotonic velocity fields, the problem would need to be divided into monotonic flow regions and pieced together. It may not, however, be necessary to solve the coupled moment and ray equations to obtain the scattering rates. We find for all solutions that the linear approximation $I_\nu\simeq J_\nu + 3H_\nu\mu$ holds to high accuracy over a very broad frequency region (at least 100 Doppler widths for $T=10$~K gas) across the line centre, giving the Eddington approximation value $f_\nu\simeq1/3$, for linear flow fields before converging to the free-streaming value $f_\nu=1$ far in the wings. Allowing for a perturbed velocity flow gives close to the expected value $g_\nu=3/5$ over a similarly broad region. This considerably simplifies the radiative transfer computation, as solving the ray equation may be circumvented, requiring only solutions to the moment equations. We found frequency redistribution produces solutions with different features across the line centre compared with the coherent scattering case near the source, resulting in variations in the scattering rate of up to $\sim50$ percent about the coherent scattering results. Further from the source the solutions for a homogeneous expanding IGM were found to agree closely with the solution for coherent scattering, and roughly follow the analytically predicted $r^{-7/3}$ radial dependence out to $\tilde{r}\simeq1$, beyond which the diffusion approximation breaks down. For $\tilde{r}>1$, the scattering rate more nearly approaches the free-streaming value $1/4\pi\tilde{r}^2$ before becoming causally truncated. Recoils are found to suppress the scattering rate by approximately 20 percent for a medium at a temperature of $T=10$~K, in good agreement with estimates based on the diffusion approximation solution for the radiation produced by a uniform and isotropic distribution of sources in a uniformly expanding homogeneous medium. Our computations extend the result beyond the diffusion approximation, and show that nearly the same suppression factor applies for an isolated source. Very near the source, frequency redistribution modifies the suppression factor by up to 15 percent. In Section~\ref{sect:InhomogTest} we examined the continuum source \Lya scattering problem allowing for inhomogeneities in the surrounding scattering medium, namely an overdense shell and a quadratic velocity profile. We found substantial deviations in the profile of the \Lya scattering rate in each case compared with a homogeneous medium. The overdense shell produces not only an enhancement of the \Lya scattering rate within the shell, but boosts the scattering rate between the shell and the source as well as a consequence of backscattering. A shadowed region with a deficit in the scattering rate compared with the homogeneous medium solution extends beyond the shell some distance before recovering to the homogeneous medium value. The scattering rate produced by the quadratic velocity profile is enhanced over the rate for the corresponding linear velocity profile, except near the outer boundary, where the rate is lower. As a less-contrived example of an inhomogeneous medium we considered a spherically symmetric density and velocity perturbation in a uniformly expanding homogeneous IGM that satisfies the linear continuity equation. We found that the resulting scattering rate increases non-linearly with increasing values of the perturbation amplitude for perturbations beginning to become nonlinear, and grows exponentially with the amplitude once nonlinear as the velocity profile flattens near the source. We infer that the \Lya scattering rate will depend sensitively on the velocity structure of the IGM. \begin{appendix} | 12 | 6 | 1206.6759 |
1206 | 1206.0349_arXiv.txt | We present a comparative study of the manufacture of binary pupil masks for coronagraphic observations of exoplanets. A checkerboard mask design, a type of binary pupil mask design, was adopted, and identical patterns of the same size were used for all the masks in order that we could compare the differences resulting from the different manufacturing methods. The masks on substrates had aluminum checkerboard patterns with thicknesses of 0.1/0.2/0.4/0.8/1.6$\mu$m constructed on substrates of BK7 glass, silicon, and germanium using photolithography and chemical processes. Free-standing masks made of copper and nickel with thicknesses of 2/5/10/20$\mu$m were also realized using photolithography and chemical processes, which included careful release from the substrate used as an intermediate step in the manufacture. Coronagraphic experiments using a visible laser were carried out for all the masks on BK7 glass substrate and the free-standing masks. The average contrasts were 8.4$\times10^{-8}$, 1.2$\times10^{-7}$, and 1.2$\times10^{-7}$ for the masks on BK7 substrates, the free-standing copper masks, and the free-standing nickel masks, respectively. No significant correlation was concluded between the contrast and the mask properties. The high contrast masks have the potential to cover the needs of coronagraphs for both ground-based and space-borne telescopes over a wide wavelength range. Especially, their application to the infrared space telescope, SPICA, is appropriate. | The direct detection and spectroscopy of exoplanets is expected to play an essential role in the understanding of how planetary systems were born, how they evolve, and, ultimately, in finding biological signatures on these planets. For the direct observation of exoplanets, the enormous contrast in luminosity between the central star and the planet is a critical difficulty. For example, the contrast between the sun and the earth observed from outside is $\sim$10$^{-10}$ at visible light wavelengths and $\sim$10$^{-6}$ in the mid-infrared wavelength region, respectively(\cite{Traub2002}). Therefore, the number of exoplanets detected directly is quite a lot smaller than the number of those detected by other methods (e.g., \cite{Mayor1995}; \cite{Charbonneau2000}), though the first direct observation was finally achieved (e.g., \cite{Marois2008}; \cite{Kalas2008}; \cite{Lagrange2010}). Coronagraphs, which were first developed for solar observations (\cite{Lyot1939}), is special optics to reduce the contrast. It is considered that advanced coronagraphs have the potential to make possible further extended direct observations of exoplanets. Among the various current coronagraphic methods, coronagraphs using binary pupil masks have some advantages, and has been studied(\cite{Jacquinot1964}; \cite{Spergel2001}; \cite{Vanderbei2003a}; \cite{Vanderbei2003b}; \cite{Vanderbei2004}; \cite{Kasdin2005a}; \cite{Kasdin2005b}; \cite{Belikov2007}; \cite{Enya2007}; \cite{Enya2008}; \cite{Haze2009}; \cite{EnyaAbe2010}; \cite{Carlotti2011}; \cite{Haze2011}; \cite{Enya2011a}; \cite{Haze2012}). The function of a binary pupil mask coronagraph to produce a high contrast point spread function(PSF) is so less sensitive to wavelength (except the effect of scaling the size of the PSF), and also be quite less sensitive to telescope pointing errors than other coronagraphs. Simplicity is another advantage of this optics. Because of these advantages, the use of a binary pupil mask coronagraph is being considered (e.g., \cite{Enya2011b}) for the Space Infrared Telescope for Cosmology and Astrophysics(SPICA) mission (e.g., \cite{Nakagawa2009}). For the development of a binary pupil mask coronagraph, both free-standing masks and masks constructed on substrates are possible. In laboratory demonstration experiments, a high contrast of 6.7$\times 10^{-8}$ was achieved with a high precision mask constructed on a glass substrate by electron beam lithography(\cite{Enya2008}). On the other hand, masks on substrates have undesirable properties. The substrates give rise to transmittance losses, and the applicable wavelength of the coronagraph is limited by the substrate material. Multiple reflections at the front and back surfaces of the mask are another disadvantage. Considering this background, we carried out a comparative study of mask manufacturing processes. Aluminum(Al) mask patterns of various thicknesses were manufactured on substrates of BK7 glass, silicon(Si), and germanium(Ge). Free-standing masks made of copper (Cu) and nickel (Ni) of various thicknesses were also manufactured. The design of the mask pattern was common to all the masks manufactured so that we were able to carry out a systematic comparison of the coronagraphic performance focusing on the differences in the manufacturing processes. In this work, we set the primary goal contrast to be 10$^{-6}$ because of the need to observe exoplanets using space infrared telescopes. The design, manufacture, and the results of laboratory tests of the coronagraphic performance are presented in the following sections. | The contrasts obtained are distributed from 5.3$\times10^{-8}$ to 2.1$\times10^{-7}$. It should be noted that all the contrasts exceed the goal set at the beginning of this work, $10^{-6}$. The average contrasts were 8.4$\times10^{-8}$, 1.2$\times10^{-7}$, and 1.2$\times10^{-7}$ for the masks on BK7 glass substrates, and the free-standing masks of Cu and Ni, respectively. The average contrast for the masks on BK7 glass substrates is higher than those of the free-standing masks. However, because of the dispersion of the data, the statistical significance of this is not valid. Also, significant correlation is not concluded between the contrast and the mask thickness for each of the three types of mask. Because the contrast in the design is 10$^{-10}$, it is obvious that there is a practical limiting factor that gives rise to the speckle patterns observed in the DRs. However, identification of this limiting factor was not easy. Using a mask having same specification with \#FC020, detail study about the limiting factor was performed as shown in \citet{Haze2012}: For example, mask rotation methods were tested. In these tests, it is expected that the speckle patterns are rotated with the mask if the speckle patterns were produced simply by error of the mask shape. However, less correlation was confirmed between the speckle pattern before and after the mask rotation. Finally suggested candidates of the limiting factor are imperfectness of incident beam(e.g., wavefront error, inhomogeneity of amplitude, and so on) and error in repeatability of the mask position before and after the rotation. Influence of instability of the experimental system is also suggested. For more detail, please see \citet{Haze2012}. The wavefront error, can be corrected by deformable mirrors \citet{Trauger2007} pioneered ultra high contrast using the wavefront control with High Contrast Imaging Testbed. Using one of early generation of our free-standing mask, \citet{Kotani2010} demonstrated improvement of the contrast by factor of $\sim$100 at a part of the dark region close to $IWA$ in the air with a visible laser. For the use in infrared wavelength region, development of cryogenic deformable mirror is ongoing. Actuation of a proto-type of Micro Electro Mechanical Systems(MEMS) deformable mirror with 32 actuators were demonstrated at $\sim$95K(\cite{Enya2009}). Toughness tests, vibration tests and rapid pumping tests were also carried out for the proto-type(\cite{Enya2011a}). Coronagraphic experiments for the masks on Ge and Si substrates were not carried out in this work since visible light was used as the light source and the experiments were carried out at ambient temperature in air. Important future work is to demonstrate the coronagraphic performance directly in the mid-infrared wavelength region at cryogenic temperatures in vacuum. Following results, indirectly, suggest applicability of the masks on Ge and Si substrates: 1) The high contrast was achieved using the masks on BK7 glass substrates in this work. 2) The masks on Ge and Si substrates and the masks on BK7 glass substrates were manufactured using same process. 3) The masks on Ge and Si substrates survived the cooling tests. It is also important to evaluate coronagraph using the free-standing masks in infrared at cryogenic temperature. Finally, performance of the all the masks for an infrared coronagraph should be compared. Only one mask design, a checkerboard type without pupil obscuration, was used in this work to compare the various manufacturing processes. On the other hand, recent progress in mask design allows the binary pupil mask coronagraph to be applied to a normal telescopes with pupil obscuration, which is not specially designed for a coronagraph. \citet{Carlotti2011} presented a 2-dimensionally optimized pupil design which provides the ultimate efficiency possible in terms of throughput for a pupil coronagraph mask. An integral 1-dimensional coronagraph pupil mask also gives a higher throughput than conventional ones, and a generalized design of the dark region at the focal plane was introduced to realize a more efficient distribution of the $IWA$, $OWA$, and contrast at the focal plane (\cite{EnyaAbe2010}; \cite{Enya2011a}). As a result, these high contrast masks have the potential to cover the needs of coronagraphs for ground-based telescopes(e.g., current 8-10m class telescopes like SUBARU, and larger future ones such as TMT, EELT), and space telescopes (e.g., JWST, SPICA) over a wide wavelength region. Indeed, the use of a binary pupil mask coronagraph is planned for the SPICA Coronagraph Instrument(SCI), for which the results of this work are quite encouraging. Because of less wavelength dependence of binary pupil mask coronagraphs, it would be worthy to evaluate benefit of applying binary pupil masks for instruments for SPICA for longer wavelength; Mid-infrared Camera and Spectrometer(MCS; \cite{Kataza2010}) and/or SPICA FAR-infrared Instrument(SAFARI; e.g., \cite{Goicoechea2012}). In the work presented in this paper, we carried out a comparative study of the manufacturing processes of binary pupil masks for coronagraphs. Both masks on substrates and free-standing masks were manufactured with various materials and thicknesses. Coronagraphic experiments in the visible light region confirmed the high contrast, in which obtained average contrasts were 8.4$\times10^{-8}$, 1.2$\times10^{-7}$, and 1.2$\times10^{-7}$ for the masks on BK7 substrates, the free-standing copper masks, and the free-standing nickel masks, respectively. Significant correlation was not concluded between the contrast and the mask properties. We consider such masks have the potential to cover needs of coronagraphs for various telescopes. \bigskip We are grateful to the all pioneers in this field, especially to R. J. Vanderbei. The work is supported by the Japan Society for the Promotion of Science, the Ministry of Education, Culture, Sports, Science and Technology of Japan, and the Japan Aerospace Exploration Agency. We thank A. Suenaga, T. Ishii and their colleagues in Houwa-sangyo Co. and Photo-precision. Co. We also thak to referee's fruitful comments for this paper. Lastly, we would like to express special thanks to S. Tanaka, and wish him well in his current field. | 12 | 6 | 1206.0349 |
1206 | 1206.0039_arXiv.txt | We have constructed a five station 12~GHz atmospheric phase interferometer (API) for the Submillimeter Array (SMA) located near the summit of Mauna Kea, Hawaii. Operating at the base of unoccupied SMA antenna pads, each station employs a commercial low noise mixing block coupled to a 0.7 m off-axis satellite dish which receives a broadband, white noise-like signal from a geostationary satellite. The signals are processed by an analog correlator to produce the phase delays between all pairs of stations with projected baselines ranging from 33--261 m. Each baseline's amplitude and phase is measured continuously at a rate of 8 kHz, processed, averaged and output at 10 Hz. Further signal processing and data reduction is accomplished with a Linux computer, including the removal of the diurnal motion of the target satellite. The placement of the stations below ground level with an environmental shield combined with the use of low temperature coefficient, buried fiber optic cables provides excellent system stability. The sensitivity in terms of rms path length is 1.3 microns which corresponds to phase deviations of about 1\arcdeg\ of phase at the highest operating frequency of the SMA. The two primary data products are: (1) standard deviations of observed phase over various time scales, and (2) phase structure functions. These real-time statistical data measured by the API in the direction of the satellite provide an estimate of the phase front distortion experienced by the concurrent SMA astronomical observations. The API data also play an important role, along with the local opacity measurements and weather predictions, in helping to plan the scheduling of science observations on the telescope. | Astronomical radio and millimeter interferometers combine signals from multiple antennas in order to produce images of the sky. The signals must be combined with a predictable phase relationship based on the array geometry and the direction of the target field \citep{Ryle60}. In the vacuum of space, the signal propagates from an astronomical source as a plane wave front. However, the atmosphere of the Earth is not a homogeneous transmission medium, and spatial and temporal variations in its constituents and properties along the line of sight distort the original plane wave front \citep{Baars67}. The resulting wave front aberration reduces the observed source visibility as compared to the true source visibility, a phenomenon often termed ``radio seeing'' \citep{Baldwin90,Hargrave78}. If the variations become too large or too rapid, then they cannot be calibrated with the standard technique of phase referencing in which astronomical point sources are periodically observed to order to solve for the drift of each antenna's complex gain vs. time \citep[e.g.][]{Carilli99,Wright96,Shapiro79}. In this situation, the data will often become unusable, especially on the longer baselines and at higher frequencies. Therefore, in order to survey potential sites for future interferometers and to promote optimal scheduling of observations in different frequency bands on an existing interferometer, it is desirable to construct an ancillary device to measure atmospheric phase variations on a continuous basis. Furthermore, these measurements should be performed on baseline lengths comparable to those of the existing (or planned) array configuration. In this paper, we describe the design and operation of a novel, broadband, multi-baseline atmospheric phase interferometer (API) operating at the Submillimeter Array (SMA)\footnote{The Submillimeter Array (SMA) is a collaborative project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy \& Astrophysics of Taiwan.} telescope site located near the summit of Mauna Kea, Hawaii. There are many examples of previous and currently operating instruments that correlate geostationary satellite beacon signals at astronomical observatory sites \citep{Middelberg06,Hiriart02,Radford96,Ishiguro90,Masson90} and elsewhere \citep{Kirkland00,Shao99}. In contrast, rather than using a beacon tone, our instrument correlates broadband digital television emission from satellites which contains far more power than the beacon tones, thereby enabling a high signal to noise ratio while avoiding the many drawbacks of a very narrow bandpass filter . The use of the transponder signal rather than the satellite beacon to measure the atmospheric phase is derived from the Berkeley Illinois Maryland Array (BIMA) phase monitor design \citep{Lay98b}. In addition to higher signal to noise, the broadband system eliminates the possibility of signal loss due to frequency drifts of the beacon tone that can exceed the bandwidth of the narrow band filters required in beacon detection systems. The API acronym which we adopt in this paper for our system is synonymous with the term Radio Seeing Monitor adopted by \citet{Ishiguro94}. | We have successfully developed and deployed a five-station 12~GHz API for the SMA. Each of the ten baselines correlates a broadband digital signal from a geostationary television broadcast satellite. The stations are installed in the covered pits of SMA antenna pads, protecting them from environmental disturbances, and yielding a path length sensitivity of $\approx 1$ micron. The real-time phase stability data correlates well with the observed phase stability of the SMA interferometer data stream. Preliminary statistics on the rms path length and the behavior of the root phase structure function (slope and corner time) are consistent with the previous single baseline atmospheric phase monitor experiment on Mauna Kea. The SMA API is used regularly along with other measurements of weather conditions and forecasts to schedule science observations in appropriate conditions for the desired frequency band, and to help ensure that these observations are completed successfully. Future studies of the phase stability statistics for Mauna Kea will become possible as the archive of API data grows. | 12 | 6 | 1206.0039 |
1206 | 1206.3330_arXiv.txt | We report on the analysis of two \xmm\ observations of the recently discovered soft gamma repeater \src, taken in September 2005 and one month after the source went into outburst on 2011 August 7. We performed timing and spectral analyses on the point source as well as on the extended emission. We find that the source period is consistent with an extrapolation of the \chandra\ ephemeris reported earlier and the spectral properties remained constant. The source luminosity decreased to a level of $1.6\times10^{34}$ erg~s$^{-1}$ following a decay trend of $ \propto t^{-0.5}$. Our spatial analysis of the source environment revealed the presence of two extended emission regions around the source. The first (Region A) is a symmetric ring around the point source, starting at 25\arcsec\ and extending to $\sim$50\arcsec. We argue that Region A is a dust scattering halo. The second (Region B) has an asymmetrical shape extending between 50\arcsec\ and 150\arcsec, and is detected both in the pre- and post-outburst data. We argue that this region is a possible magnetar wind nebula (MWN). The X-ray efficiency of the MWN with respect to the rotation energy loss is substantially higher than those of rotation powered pulsars: $\eta_{\rm X}\equiv L_{\rm MWN,0.5-8~keV}/\dot{E}_{\rm rot}\approx0.7$. The higher efficiency points to a different energy source for the MWN of \src, most likely bursting activity of the magnetar, powered by its high magnetic field, $B=1.4\times10^{14}$ G. | \label{Sec:Intro} Soft Gamma Repeaters (SGRs) and Anomalous X-ray Pulsars (AXPs) are two empirical classes of objects widely accepted to comprise the magnetar population, i.e., isolated neutron stars with ultra-strong magnetic fields ($B\gtrsim10^{14}-10^{15}$~G). Their existence was predicted theoretically in 1992 \citep{duncan92ApJmagnetars, paczynski92AcA:magnetars}, but was only confirmed in 1998 with {\it RXTE} observations (\citealt{kouv98Natur:1806, kouveliotou99ApJ:1900}; for detailed magnetar reviews please refer to \citealt{woods06csxs:magnetars}, \citealt{ mereghetti08AARv:magentars}). SGRs and AXPs share many characteristics such as long spin periods (2-12 s) and large spin-down rates that imply very high surface dipole magnetic fields of $10^{14}-10^{15}$~G. They are all persistent X-ray emitters with luminosities significantly larger than those expected from rotational energy losses; instead the magnetar X-ray emission is attributed to the decay of their powerful magnetic fields and sub-surface heating \citep{thompson96ApJ:magnetar}. Magnetars enter active episodes during which they emit short (0.1\,s) bursts of hard X-/soft $\gamma-$rays with luminosities ranging from $10^{37}$ to 10$^{41}$~erg~s$^{-1}$; very rarely, they emit Giant Flares (GFs) that last several minutes with luminosities $\gtrsim10^{46}$~erg~s$^{-1}$. The typical magnetar bursts are attributed to neutron star crust quakes caused by the evolving magnetic field under its surface \citep{thompson95MNRAS:GF}. \begin{figure}[th] \begin{center} \includegraphics[angle=0,width=0.48\textwidth]{fig1-1.pdf}\\ \includegraphics[angle=0,width=0.48\textwidth]{fig1-2.pdf}\\ \includegraphics[angle=0,width=0.48\textwidth]{fig1-3.pdf} \caption{Post-outburst {\it XMM-Newton} EPIC-PN observation of \src\ in 2011 (obs.~2, upper and middle panels) and pre-outburst 2005 EPIC MOS1+MOS2 observation (obs.~1, bottom panel). The middle and bottom images are Gaussian smoothed with a FWHM of 5.0 pixels (20\arcsec). The smallest green circle with a 25\arcsec-radius represents the \src\ point-source emission. The annulus with 25\arcsec$\le r\le$50\arcsec\ represents the symmetrical extended emission around the point source (region A). The ellipse of major (minor) axis of 145\arcsec\ (95\arcsec) encloses the asymmetrical extended emission around \src\ (region B). Other sources in the field are labeled. North is up and west is right.} \label{imagxray} \end{center} \end{figure} An interesting question in the magnetar field is their evolutionary link, if any, to their less magnetically-powerful counterparts, rotation powered pulsars (RPPs). The latter sources are known to produce particle outflows, often resulting in spectacular Pulsar Wind Nebulae (PWNe, see \citealt{kargaltsev08PWN} for a review) of which the Crab is the most famous example \citep{weisskopf00ApJ}. The PWN X-ray emission is due to synchrotron radiation from the shocked relativistic outflow of electrons and positrons produced by the pulsar. Magnetars are also expected to produce particle outflows, either steady or released during outbursts accompanying bright bursts or GFs \citep{thompson98PhRvD:mag, harding99ApJ:mag,tong12arXiv1205:mwn}. The GF of 2004 December 27 from SGR\,J$1806-20$ released at least $4\times10^{43}$ ergs of energy in the form of magnetic fields and relativistic particles \citep{gaensler05Natur:1806}. Given the strong magnetic fields associated with this class of neutron stars, the idea, therefore, of a Magnetar Wind Nebula (MWN) seems very plausible. Only a few claims have been made so far for the detection of a nebula around a magnetar. The first one was the radio nebula around SGR~J$1806-20$ \citep{kulkarni94Natur:1806}, which was shown later to be enshrouding a Luminous Blue Variable star, unrelated to the SGR \citep{hurley99ApJsgr1806}. Elongated and expanding radio emission was unambiguously identified following the GF of SGR~J$1806-20$ \citep{gaensler05Natur:1806,gelfand05ApJ:sgr1806}, most likely associated with jets produced by the flare. A variable radio source indicating particle outflow was also seen after the giant flare of SGR~1900+14 \citep{frail99Natur:sgr1900}. Recently, \citet{rea09ApJpwn}, \citet[][see also \citealt{ gonzalez03ApJ:PSR1119}]{safiharb08ApJ:PSR1119} and \citet{vink09ApJ:PWN} reported the discovery of unusual extended emission around three high $B-$field sources, a Rotating Radio Transient, RRAT~J1819$-$1458, a high-B pulsar PSR J1119-6127, and a magnetar 1E~$1547.0-5408$ (SGR~J$1550-5418$) respectively. The latter case was shown to be a halo on the basis of correlated flux variations in the extended emission and the magnetar \citep{olausen11ApJ:sgr1550}. In summary, to date there is no unambiguous evidence for the existence of a PWN/MWN around a magnetar. Confirmed detections of MWNe would reconcile observations with theoretical predictions of their existence and would shed light on the nature of magnetar outflows and the environmental properties of magnetars. \src\ is the last in a long line of magnetar discoveries during the last three years, owing to the synergy between NASA's three observatories, \swift, \rxte, and \fermi. It was discovered on 2011 August 7, when it triggered the \swift/Burst Alert Telescope (BAT) and the Fermi/Gamma-ray Burst Monitor (GBM) with a soft, short burst \citep{delia11GCN1834,guiriec11GCN:1834}. The magnetar nature of \src\ was established with {\it RXTE}/PCA and \chandra\ Target of Opportunity observations, which revealed a coherent X-ray pulsation at a spin period $P=2.482295$~s \citep{gogus11ATel:1834,gogus11ATel:1834B}, and a spin-down rate $\dot{\nu}=-1.3(2)\times10^{-12}$~Hz~s$^{-1}$ \citep{kuiper11:1834}, implying a dipole surface magnetic field $B=1.4\times10^{14}$~G, and a spin-down age and energy loss rate $\tau=4.9$~kyr and $\dot{E}_{\rm rot}=2.1\times10^{34}$~erg~s$^{-1}$, respectively. \citet[][K+12 hereinafter]{kargaltsev12apj:1834} studied the spatial, temporal, and spectral properties of \src\ using the available \swift, \rxte, and \chandra\ post-outburst observations, and one \chandra\ pre-outburst observation taken in June 2009. The persistent X-ray light curve of the source, spanning 48 days after the first burst, showed that the $2-10$~keV flux decayed steadily as a power-law with index $\alpha=0.53\pm0.07$ ($F\propto t^{-\alpha}$). The source spectrum ($2-10$\,keV) was well fit with either an absorbed power-law with a photon index $\Gamma\approx3.5\pm0.5$ or an absorbed blackbody with a temperature $kT=1.1\pm0.1$~keV, and an emitting area radius of 0.26 km (assuming a source distance of 4 kpc, see below). The hydrogen column density was of the order of $10^{23}$~cm$^{-2}$, depending on the model spectrum. Finally, K+12 reported the presence of an extended emission up to a radius of 10\arcsec\ from the center of the source, most likely a dust scattering halo, considering the large absorption toward the source position. However, an even more extended emission, with radius $>$30\arcsec, was detected in the 2009 pre-outburst \chandra\ observation. The asymmetrical shape of this emission, northeast-southwest of the source, poses a challenge to the dust scattering halo interpretation, especially since this extended component was detected while the point source was not seen down to a limit of $10^{-15}$~erg~cm$^{-2}$~s$^{-1}$. Here we report the analysis of two \xmm\ observations of \src, taken in September 2005 and September 2011 (one month after the source outburst), with emphasis on the analysis of the environment around the source. Section 2 describes the observations and data reduction techniques. We present our results of the spatial, timing and spectral analysis in Section~3. We discuss the spectral and temporal results of \src\ and the implication of our extended emission analysis in the context of Magnetar Wind Nebula (MWN) in Section~4. Given a plausible association between Swift J1834.9–0846 and the SNR W41, we will assume that both are at the same distance ($\sim4$ kpc, \citealt{tian07ApJ:1834,leahy08AJ:w41}; K+12) throughout the paper. | \label{sec:discuss} \subsection{\src} The effects of bursting activity on the magnetar persistent X-ray flux have been discussed by several authors. The increase of the source intensity during bursting episodes is also often accompanied by spectral variability \citep[e.g. ][]{vasisht00ApJ:ax1845, gotthelf04ApJ:xte1810, gogus10ApJ:0501}. It would then be reasonable to assume that the detection of \src\ in the 2005 \xmm\ observation at $F_{\rm 2-10\,keV}\approx10^{-13}$~erg~cm$^{-2}$~s$^{-1}$, could be due to a bursting episode that had occurred prior and close to that observation (if such an episode comprised only one burst similar to the 2011 episode, it could have easily been missed by {\it Swift}, which was the only all sky monitor in the $25-350$\,keV range at the time). Indeed, assuming a (constant) flux decay trend between 2005 and 2009 similar to the one exhibited by the source after its 2011 outburst ($\alpha=-0.5$, Figure~\ref{nebulavar}) results in an expected flux level in 2009, consistent with the estimated upper limit of $10^{-15}$~erg~cm$^{-2}$~s$^{-1}$ (K+12). However, there maybe other sources of neutron star surface heating that might not result in SGR bursts, such as was the case of the transient magnetar SGR~J$1810-197$ \citep{ibrahim04ApJ:xtej1810}. The source was serendipitously discovered with \rxte\ as a transient during observations of a nearby magnetar (SGR~J$1806-20$); the increase of its X-ray flux was not associated with any bursting activity during that period. This behavior could be explained within the framework of the twisted magnetosphere model of \citet{thompson02ApJ:magnetars} as follows. Variations of the twist angle of the magnetic field lines would lead to a sudden release of energy accompanied by possible changes in the cyclotron resonant scattering depth in the magnetosphere and heating of the neutron star surface. Heating by such a $B-$field reconfiguration should also be associated with sharp spectral changes. Unfortunately, with the currently available data we cannot distinguish between the two scenarios. \begin{figure}[!th] \begin{center} \includegraphics[angle=0,width=0.48\textwidth]{fig8.pdf} \caption{The post-outburst persistent X-ray light curve of \src\ based on 48 days of \swift/XRT data (dashed-line, K+12); day 1 corresponds to the \swift\ trigger. The dots represent the \chandra\ and \xmm\ post-outburst point source fluxes ($2-10$\,keV), respectively, while the diamonds represent the fluxes of Region A during the same observations. The dashed line represents the \swift/XRT decay slope of $-0.5$; the solid and dot-dashed lines are decay trends of the point source and Region A with the same slope.} \label{halosrcvar} \end{center} \end{figure} Magnetar X-ray spectra are usually fit by a two component model, e.g., two BBs with temperatures $kT_{1}\sim0.3$~keV and $kT_{2}\sim0.8$~keV, or a BB and a PL with $kT\sim0.5$~keV and $\Gamma\sim3.0-4.0$ \citep[e.g., ][]{mereghetti05ApJ:sgr1806, halpern05ApJ:xte1810,tiengo08ApJ:cxouj010043, bernardini09:axp1810, bernardini11:1E1547, rea09MNRAS:sgr0501, gogus11ApJ:1900,woods07ApJ:1806, kouveliotou03ApJ:1627, kouveliotou01ApJ:1900}. The 2005 pre-outburst spectral properties of the source could not be inferred due to very low statistics. The post-outburst X-ray spectrum of \src\ seems unusual at first glance, as it is well fit by a single, heavily absorbed ($N_{\rm H}\sim10^{23}$~cm$^{-2}$) component, either a blackbody with $kT=1.1$~keV or a power-law with $\Gamma=4.2$ (see also K+12). It could be that we see here the effects of the environment within which \src\ resides; e.g., dense giant molecular clouds (GMCs, \citealt{tian07ApJ:1834}), which, in principle, could absorb the soft part of the spectrum, eliminating the requirement of a soft spectral component \citep[see also ][]{esposito11MNRAS:1833}. The single BB spectral model for \src\ gives a small decrease in the BB temperature ($\Delta kT=0.14\pm0.06$~keV), and a consistent BB emitting area radius ($\Delta R=0.02\pm0.05$) between the \chandra\ and \xmm\ post-outburst observations separated by a month, similar to the behavior of XTE~J$1810-197$ \citep{woods05ApJ:xte1810}. The BB fluxes between the two observations are consistent with the same power-law decay $\alpha\approx-0.5$, estimated using the PL fits. K+12 discussed the possibility of a hot spot emitting thermal radiation at the surface of the neutron star, noting that in such a scenario it would be difficult to explain the high pulsed fraction due to light bending in the neutron star gravitational field, unless the radiation is anisotropic, having a narrow peak along the magnetic field direction \citep{pavlov94AA:magnetars}. \subsection{A Halo around \src: Region A} The spectrum and flux of the symmetrical extended emission (region A) fits well a dust scattering halo interpretation. First, the heavy absorption ($N_{\rm H}\approx10^{23}$~cm$^{-2}$) towards the source, inferred from the X-ray spectral fits, should cause the scattering of the point source X-ray emission, resulting in a dust scattering halo. Since the scattering cross section of the dust particles is proportional to $E^{-2}$, a halo is expected to have a softer spectrum than the illuminating source, i.e., \src. Indeed, in Obs.~2, the spectrum of region A is marginally softer than the \src\ spectrum (although consistent within the uncertainties, see Section 3.3 and Table~1). Second, a dust scattering halo is expected to vary in flux proportionally to the illuminating source flux \citep{mathis91ApJ:halo}, with a time lag depending on the distance of the scattering material from the source \citep{mauche86ApJ:halo,olausen11ApJ:sgr1550}. This trend is evident from Figure~\ref{halosrcvar}, which shows the flux evolution of region~A and \src, between the post-outburst \chandra\ (K+12) and \xmm\ observations (diamonds). Finally, we estimate the fractional intensity of the halo during Obs.~2 to be $I_{\rm frac}=F_{\rm halo}/(F_{\rm halo}+F_{\rm source})=0.20_{-0.10}^{+0.25}$. During Obs.~1 the spectrum of region A was harder, $\Gamma=1.7^{+1.4}_{-1.1}$, with a fractional intensity $I_{\rm frac}=0.36^{+0.2}_{-0.1}$, somewhat higher than, but consistent within the error bars with the $I_{\rm frac}$ calculated for Obs.~2. However, the \src\ spectrum during obs.~1 is unknown due to the poor statistics. The harder spectrum during obs.~1 could then be explained if there were another component contributing to the flux in region A. Indeed, the flux of region B (the putative MWN, see Section 4.3) dominates the emission from the vicinity of \src\ during Obs.~1 (Table~1), which could explain both the hard spectrum and the slightly higher $I_{\rm frac}$ seen during this observation. Another explanation could be that the \src\ spectrum during Obs.~1 is much harder than it is during obs.~2, which would make the region A spectral shape consistent with a solely dust scattering halo explanation. \subsection{Asymmetrical Extended emission (Region B): a MWN?} \begin{figure}[!th] \begin{center} \includegraphics[angle=0,width=0.48\textwidth]{fig9.pdf} \caption{Long term light curves of the fluxes ($2-10$\,keV) of \src\ (black dots) and Region B (red stars).} \label{nebulavar} \end{center} \end{figure} Rotation Powered Pulsars (RPP) with magnetic fields $B\sim10^{11-13}$~G and periods $P\lesssim1$~s are believed to lose their rotational energy in the form of a relativistic magnetized particle wind. Pulsar wind nebulae (PWNe) are often observed around these pulsars and are believed to be the synchrotron radiation of the shocked wind \citep[see ][for reviews]{kaspi06csxs:PWN,gaensler06ARA:PWN, kargaltsev08PWN}. The efficiency at which the rotational energy loss of a pulsar, $\dot{E}_{\rm rot}$, is radiated by the PWN is characterized by $\eta_{\rm X}=L_{\rm X, PWN}/\dot{E}_{\rm rot}$, which ranges from 10$^{-6}$ to 10$^{-2}$. Magnetars, on the other hand, have longer spin periods and lower $\dot{E}_{\rm rot}$ values, making the production of a steady and bright rotationally-powered nebula unlikely. Nonetheless, \citet{thompson98PhRvD:mag} showed that particle outflows, either steady or released in short periods of time due to the flares, could be driven by Alfv\'en waves \citep[see also ][]{harding99ApJ:mag}. Furthermore, a jetted baryonic outflow was observed in the radio wavelengths after the GF of SGR~J$1806-20$ \citep{gaensler05Natur:1806,fender06MNRAS:1806}. These processes could lead to the emergence of nebulae around magnetars. There has not been yet a ubiquitous detection of a magnetar wind nebula (MWN) in X-rays, but ``magnetically powered'' nebulae around pulsars with relatively high magnetic fields have been suggested. \citet{rea09ApJpwn} reported that the nebula around the rotating radio transient RRAT\,J$1819-1458$ has a nominal X-ray efficiency $\eta_{\rm X}\approx0.2$, too high to be rotationally powered. The authors suggested that the occurrence of the nebula might be connected with the high magnetic field ($B=5\times10^{13}$~G) of the pulsar. The nebula around \src\ shares some characteristics with the nebula around RRAT\,J$1819-1458$. The X-ray efficiency of the \src\ nebula is very high, $\eta_{\rm X}\approx0.7$, for a $0.5-8$\,keV luminosity of $1.5\times10^{34}$~erg~s$^{-1}$\footnote{We have chosen the 0.5-8 keV energy range to enable comparison with the efficiency of RRAT\,J$1819-1458$ and other pulsars, Figure~\ref{LpwnEdot}.}. Considering the source's relatively low rotational energy loss ($\dot{E}_{\rm rot}=2.1\times10^{34}$ erg~s$^{-1}$), it is in the low-$\dot{E}_{\rm rot}$/high-$L_{\rm X, PWN}$ region in Figure~\ref{LpwnEdot}, similar to RRAT~J$1819-1458$. Moreover, the nebula around \src\ shows small flux variability (owing to large uncertainties) between the three different epochs (Figure~\ref{nebulavar}). Its flux slightly decreased, although within uncertainties, when the source went to quiescence in 2009 ($F_{\rm X}<10^{-15}$~erg~s$^{-1}$), then increased by a factor of 7 (at the $\sim$2 sigma level) after the September 2011 outburst, in line with a variable wind nebula scenario. \begin{figure}[t] \begin{center} \includegraphics[angle=0,width=0.49\textwidth]{fig10.pdf} \caption{Luminosity of normal PWNe as a function of the rotational energy loss of their corresponding pulsars. Data presented as black dots are taken from \citet{kargaltsev08PWN}, whereas the blue star represents the high B source RRAT\,J$1819-1458$ \citep{rea09ApJpwn}. The dashed line represents the $\eta_{\rm X}=0.2$ of RRAT\,J$1819-1458$, and the solid line represents the $\eta_{\rm X}=0.7$ of \src. The three red dots represent the luminosity of the candidate MWN around \src\ at the detected epochs. [Figure adapted from \citet{rea09ApJpwn}].} \label{LpwnEdot} \end{center} \end{figure} An obvious difference between the MWN around \src\ and the ``usual'' PWNe is the very soft spectrum of the former, $\Gamma =3.5\pm0.6$, compared to $\Gamma\sim1 - 2$ of PWNe of RPPs. It is worth pointing out that the nebula around RRAT~J$1819-1458$ also shows a soft spectrum, $\Gamma=3.0\pm 0.5$, which suggests that the two nebulae are in some respects similar, in particular, the electrons are accelerated by similar mechanisms (we note, however, that the nebula around RRAT~J$1819-1458$ is about 10 times smaller in size than the nebula around \src, for similar distances). For the most plausible assumption that we are observing synchrotron radiation of relativistic electrons, this large index implies a very steep electron spectrum, with a slope $p = 2\Gamma - 1 \approx 6$. What could produce such an electron population? A different mechanism (other than the typically invoked Fermi mechanism) of electron acceleration, such as, e.g., magnetic field line reconnection might be at work. We can only conjecture that the twisted magnetic field model by \citet{thompson02ApJ:magnetars} could lead to reconnection, facilitating the production of the required electron population distribution. We can estimate the termination shock radius $R_s$ depending on our assumptions about the energy flux provided by the magnetar. In quiescence, the balance of pressures $\dot{E}_{\rm rot}/(4\pi f c R_s^2) = p$, where $4\pi f$ is the solid angle in which the wind (including the Poynting flux) is blowing ($f =1$ for an isotropic wind), and $p$ is the ambient pressure (this equation assumes that the magnetar's speed is essentially subsonic). For the $\dot{E}_{\rm rot} = 2.1\times 10^{34}$ erg s$^{-1}$, this equation gives $R_s = 2.4\times 10^{16} f^{-1/2} p_{-10}^{-1/2}$ cm, where $p_{-10}$ is the pressure in units of $10^{-10}$ erg cm$^{-3}$. This corresponds to the angular size of $0\farcs4 f^{-1/2} p_{-10}^{-1/2} d_{4}^{-1}$. Such a small size cannot be resolved by \xmm, and it is hidden within the dust scattering halo (Region A), assuming reasonable values for the ambient pressure. The size of an X-ray PWN is typically a factor of a few times larger than $R_s$ (e.g., \citealt{kargaltsev08PWN}), which is still much smaller than the observed size of $\sim150$\arcsec. Therefore, not only the unrealistically high ``efficiency'' $\eta_{\rm X}\sim 0.7$, but also the large size support the hypothesis that the observed asymmetrical nebula (Region B) could not be produced by the magnetar in quiescence via rotation-powered wind. When a magnetar is in an active state, the pressure of its wind (ejected particles and magnetic fields) is much higher than that in quiescence. In this state, the energy loss rate, $\dot{E}_{\rm burst}$, can be much higher than $\dot{E}_{\rm rot}$. It can be crudely estimated as a ratio of the magnetar's X-ray luminosity in the bursting state, $L_X = 10^{34} L_{X,34}$ erg s$^{-1}$, to some reasonable magnetar X-ray efficiency $\eta_{\rm X} = 10^{-4}\eta_{\rm X,-4}$: $\dot{E}_{\rm burst} = 10^{38} L_{X,34} \eta^{-1}_{\rm X,-4}$ erg s$^{-1}$. Using $\dot{E}_{\rm burst}$ instead of $\dot{E}_{\rm rot}$, we obtain $R_s = 1.6\times 10^{18} L_{X,34}^{1/2} \eta_{\rm X,-4}^{-1/2} f^{-1/2} p_{-10}^{-1/2}$ cm, which corresponds to the angular shock radius of $\sim$25\arcsec\ $L_{X,34}^{1/2} \eta_{\rm X,-4}^{-1/2}f^{-1/2} p_{-10}^{-1/2} d_{4}^{-1}$, and a factor of a few larger size of the X-ray nebula, comparable with the observed nebula radius of $\sim150$\arcsec. This allows one to assume that the detected nebula was created in a burst (or a series of bursts), which is in line with our first assumption in Section 4.1, that likely the magnetar experienced a bursting episode before obs.~1, which was not directly detected. We can in principle connect the nebula size (and even the softness of the spectrum) with synchrotron cooling. First of all, it is worth noting that the magnetic field at the shock (if there is a shock) does {\em not} depend on the neutron star surface magnetic field -- it is determined by the balance of the wind pressure and the ambient pressure and depends on the latter and the magnetization parameter $\sigma$ (i.e., the ratio of the electromagnetic energy flux to the kinetic energy flux): $B_s \sim [8\pi\sigma p/(1+\sigma)]^{1/2} \sim 50 [p_{-10}\sigma/(1+\sigma)]^{1/2}$ $\mu$G, upstream of the shock, and it can be a factor of 3 higher immediately downstream of the shock \citep{kennel84ApJ:mhdwind}. This, in particular, means that the softness of the nebula spectrum is not due to a higher magnetic field in the nebula. The magnetization parameter $\sigma$ is, unfortunately, quite uncertain for the putative magnetar winds. It is believed to be $\ll 1$ for PWNe (e.g., $\sim 10^{-3}$ for the Crab), but it may be higher in magnetars. Therefore, the actual value of the magnetic field in the shocked magnetar flow remains uncertain; it might be as low as a few $\mu$G (for small $\sigma$ and low-pressure ambient medium) or as high as a few mG (for large $\sigma$ and high-pressure medium). Therefore, we will simply scale the field as $B = 10^{-4} B_{-4}$ G. The synchrotron cooling time for an electron with Lorentz factor $\gamma$ can be estimated as $\tau_{\rm syn} = 5\times 10^8 \gamma^{-1} B^{-2}\, {\rm s} \sim 5\times 10^{8} \gamma_8^{-1} B_{-4}^{-2}\, {\rm s} \sim 5\times 10^{8} B_{-4}^{-3/2}$ s, where for synchrotron emission in the X-ray band we used $\gamma^2_8 B_{-4} \sim (E/5\,{\rm keV}$). The shocked wind flows from the magnetar with mildly relativistic velocities (e.g., $c/3$ for an isotropic outflow -- see \citealt{kennel84ApJ:mhdwind}). Multiplying $\tau_{\rm syn}$ by the flow velocity, we obtain a distance from the magnetar where the X-ray synchrotron radiation still can be observed: $R_{\rm MWN} \sim 5\times 10^{18} B_{-4}^{-3/2}$ cm, which corresponds to an angular distance of $\sim 84\arcsec\ B_{-4}^{-3/2}$, quite close to the observed size for $B\sim 60$ $\mu$G. Thus, the observed size can be explained by the synchrotron cooling of the outflowing electrons in a reasonable magnetic field. The cooling time also determines the lifetime of the putative MWN after the end of the magnetar activity period. For instance, for $B\sim 60$ $\mu$G, $\tau_{\rm syn} \sim 30$ years, which means that the MWN can be observable in X-rays around quiescent (even undetectable) magnetars if these were in an active state years ago; it would also explain the detection of the MWN in Obs.~1. Finally, we would like to discuss some other possibilities for the origin of the extended X-ray emission around \src. The source lies in the center of a crowded field filled with many other high energy sources. It lies almost at the center of the extended TeV source HESS~J1834$-$087 \citep{aharonian06ApJ:HESSsur1}, and within the SNR W41 (K+12) and a dense GMC \citep{tian07ApJ:1834}. The high absorbing column density toward \src\ is most likely related to the GMC, which in turn is causing the scattering halo emission. An anisotropic dust distribution within the GMC could cause an asymmetrical halo emission, leading to region A and region B emanating from the same region and having the same physical origin. To test this hypothesis we extracted the spectrum of region~A+region~B during obs.~2 and fit it with an absorbed power-law. We find a hydrogen column density $N_{\rm H}=17_{-3}^{+4}\times10^{22}$~cm$^{-2}$, consistent with the point source absorbing column, and a power-law photon index $\Gamma=3.4\pm0.5$, harder than the point source spectrum, indicating that a halo interpretation for region~A+region~B is unlikely. Hence, the nature of these two regions is indeed different as indicated by their different spectral properties (Section~\ref{sec:spec}). Moreover, the detection of region~B during obs.~1, when the source was in quiescence, poses a challenge to such an interpretation. Another possibility for the region B emission could be some contribution from the SNR W41, in the form of either thermal emission from shocked gas or non-thermal synchrotron emission \citep[see][for a review]{vink12AARv:SNR}. However, the fluxes of both region~A and region~B varied with the source flux, implying a tight connection between the two and the SGR. Deeper high-resolution multiwavelength observations would be of great value to better understand the physical properties and emission processes of the \src\ putative MWN, and would help shed light on the connections between the many point-like and extended sources existing in this crowded field. | 12 | 6 | 1206.3330 |
1206 | 1206.1335_arXiv.txt | We examine the constraints on soft X-ray photon emissions from the reionization era. It is generally assumed that the Universe was reionized by ultraviolet photons radiated from massive stars. However, it has been argued that X-ray photons associated with the death of these stars would have contributed $\sim 10\%$ to the total number of ionizations via several channels. The parameter space for a significant component of cosmological reionization to be sourced by X-rays is limited by a few observations. We revisit the unresolved soft X-ray background constraint on high-redshift X-ray production and show that soft X-ray background measurements significantly limit the contribution to reionization from several potential sources: X-rays from X-ray binaries, from Compton scattering off supernovae-accelerated electrons, and from the annihilation of dark matter particles. We discuss the additional limits on high-redshift X-ray photon production from (1) $z\sim3$ measurements of metal absorption lines in quasar spectra, (2) the consensus that helium reionization was ending at $z\approx 3$, and (3) measurements of the intergalactic medium's thermal history. We show that observations of $z\sim3$ metal lines allow little room for extra coeval soft X-ray emission from a nonstandard X-ray sources. In addition, we show that the late reionization of helium makes it quite difficult to also ionize the hydrogen at $z>6$ with a single source population (such as quasars) and that it likely requires the spectrum of ionizing emissions to soften with increasing redshift. However, we find that it is difficult to constrain an X-ray contribution to reionization from the intergalactic temperature history. We show that the intergalactic gas would have been heated to a narrower range of temperatures than is typically assumed at reionization, $2-3 \times 10^4~$K, with this temperature depending weakly on the ionizing sources' spectra. | Extreme ultraviolet (EUV) radiation from stars within diminutive galaxies is the leading candidate for what sourced hydrogen reionization at $z\sim 10$ (e.g., \citealt{wyithe03}). This scenario has been the focus of the majority of theoretical and numerical work on reionization (e.g., \citealt{furlanetto04, iliev06, mcquinn07, trac07, finlator11b}). However, other models may still be viable, such as models with a significant contribution to reionization from active galactic nuclei (AGN; \citealt{volonteri09}). The bright end of the AGN luminosity function declines drastically between $z=3$ and $z=6$ \citep{fan01}, precluding rare AGN (i.e., quasars) as the primary driver of reionization. Nevertheless, reionization by fainter AGN may still be possible (\citealt{siana08, shankar07, glikman11}, although see \citealt{willott10}). In addition, at least a fraction of reionization could have been sourced by soft X-rays produced from inverse Compton scattering of cosmic microwave background (CMB) photons off supernova-accelerated electrons \citep{oh01}, by emission produced directly in supernova remnant shocks \citep{johnson11}, by high-mass X-ray binaries \citep{power09, mirabel11}, by mini-quasars \citep{madau04}, by halo accretion shocks \citep{dopita11, wyithe11}, or by dark matter annihilations \citep{belikov09}. Even if stars reionized the bulk of the intergalactic hydrogen, \citet{oh01}, \citet{johnson11}, and \citet{mirabel11} argued that X-rays associated with the remnants of these stars should contribute $\sim 10\%$ of the ionizations via any of a few mechanisms. X-ray reionization scenarios have recently received renewed attention (e.g., \citealt{haimanopinion}), particularly for two reasons. Firstly, soft X-ray photons would have had little difficulty in escaping from $z\sim 10$ galaxies and ionizing the intergalactic medium (IGM). This is in contrast to EUV photons, for which it is unclear whether they would have escaped at all (e.g., \citealt{gnedin08}). Empirically, observations of $z\sim 3-4$ Ly$\alpha$ emitters suggest that a non-negligible fraction of ionizing photons was escaping into the IGM \citep{nestor11}. Curiously, for Lyman-break galaxies the escape fraction is constrained to be smaller. \citet{vanzella10} placed an upper bound on the escape fraction of $3.4 <z<4.5$ Lyman breaks of $<5-20\%$. Secondly, there is evidence that high-mass X-ray binaries (HMXBs) and ultra-luminous X-ray sources (ULXs) anti-correlate with metallicity \citep{crowther10, kaaret11}. This anti-correlation suggests that these X-ray sources -- which already dominate the X-ray production of low-redshift star-forming galaxies -- were even more prevalent at high redshifts \citep{mirabel11}. A full or partial reionization by soft X-rays would have resulted in a different morphology of intergalactic \HII\ regions during this process compared to a full reionization by EUV photons alone. The mean free path of soft X-ray photons is much longer than EUV photons owing to the strong energy dependence of the photoionization cross section. A photon with energy $E_\gamma$ has a mean free path, $\lambda_{\rm HI}$, to be absorbed by hydrogen of \begin{equation} \lambda_{\rm HI} \approx 7 \, x_{\rm HI}^{-1} \, \left( \frac{E_\gamma}{200 {\rm ~eV}} \right)^{2.6} \left( \frac{1+z}{10} \right)^{-2}~{\rm cMpc}, \label{eqn:LHI} \end{equation} where $x_{\rm HI}$ is the fraction of hydrogen that is neutral.\footnote{The mean free path to be absorbed by \HeII\ and \HeI\ is comparable, with $\lambda_{\rm HeI} = 4 \, x_{\rm HeI}^{-1}~$cMpc and $\lambda_{\rm HeII} = 5 \, x_{\rm HeII}^{-1}~$cMpc, assuming $E_\gamma = 200$~eV and $z=9$. $\lambda_{\rm HeI}$ has a softer scaling with $E_\gamma$ than $\lambda_{\rm HI}$ such that the \HeI\ would be the first species to be ionized by a background of just soft X-ray photons.} If a significant fraction of the IGM were reionized by $E_\gamma \gtrsim 200~$eV photons, the inhomogeneous structure on scales of $\sim 10$~comoving~Mpc that is anticipated by most models of this process would have been largely erased. A more homogeneous reionization scenario than that preferred by models may be more consistent with limits on the kinetic Sunyaev-Zeldovich anisotropy from reionization \citep{reichardt11, mesinger11}. High-redshift X-ray production is also important for the reheating of the Universe and determines whether redshifted 21cm radiation appears in emission or absorption \citep{furlanettoohbriggs, mcquinn12}. This study investigates the constraints from current data on high-redshift X-ray emissions. Because the Universe is optically thin to $\gtrsim 1~$keV photons from $z\sim 10$, such photons produced during the reionization era would have streamed freely and altered the ionization state of intergalactic metals at $z\sim 3$ as observed in quasar absorption spectra. They also would contribute to the observed soft X-ray background \citep{dijkstra04, salvaterra07}. In addition, the hardness of the high-redshift EUV and X-ray emissions determines whether the electrons of helium were ionized concurrently with those of the hydrogen or well after. An early reionization of the second electron of helium appears to be in conflict with the mounting evidence that helium reionization ended at $z\approx 2.7$ \citep{theuns02, hui03, furlanettodixon, mcquinnGP, shull10, becker11, worseck11}. Finally, measurements of the thermal state of the IGM have been extended to $4 <z< 6.5$ in the past few years \citep{becker11, bolton11}, redshifts more sensitive to the heating during hydrogen reionization. Reionization by a harder spectrum than stars would have injected more heat into the IGM, potentially resulting in higher temperatures. Section \ref{sec:sources} summarizes the leading candidates for sourcing the production of high-redshift soft X-ray and EUV photons. Section \ref{sec:constraints} discusses the constraints on high-redshift X-ray production from the unresolved soft X-ray background, from $z\sim 2.5$ metal absorption line observations, from our knowledge of the reionization history of the hydrogen and helium, and, finally, from constraints on the thermal history of the IGM. In our calculations, we assume a flat $\Lambda$CDM cosmological model when necessary with $\Omega_m=0.27$, $h=0.71$, $\sigma_8= 0.8$, $n_s=0.96$, and $\Omega_b = 0.046$, consistent with recent measurements \citep{larson11}. | Several studies have suggested that the production of soft X-ray photons was more efficient per unit star formation rate at $z\sim10$ than it is at $z\sim 0$ and that these photons contributed significantly to the reionization of the Universe \citep{oh01,madau04, mirabel11, johnson11}. In addition, reionization by quasars may not yet be ruled out. While it has often been reasoned that quasars could not have reionized the Universe, this rationale has traditionally relied on observations of the decreasing number density of bright, $L>L_*$ quasars at $z>3$ \citep{madau99, faucher08b}. This paper presented a census of constraints on high-redshift soft X-ray photon production. We discussed the constraints from (1) the unresolved soft X-ray background (SXB), (2) intergalactic metal line observations, (3) the late reionization of helium, and (4) the temperature of the intergalactic medium. We found that the unresolved SXB places interesting bounds on the contribution to reionization of sources with a spectral index in intensity per unit frequency, $\alpha$, greater than $ -1$. This bound limits the total number of ionizing photons radiated per hydrogen atom to be $<1$ from several potential sources: inverse Compton scattering off supernova-accelerated electrons, HMXBs (under empirically motivated spectral models), and dark matter annihilations. It limits the contribution to be $\ll 1$ in the latter two cases. All of these sources have been proposed as important contributors to hydrogen reionization. However, we showed that the SXB is consistent with quasars reionizing the Universe, correcting a common misperception. In addition, we showed that if high-redshift galactic X-ray emissions account for the unresolved SXB intensity, significant evolution in hard X-ray luminosity--SFR relationship from that observed at low redshifts is required (unless there was more than an order of magnitude additional star formation at $z\sim 8$ than has been observed). We showed that $z\approx 2.5$ intergalactic metal line observations (which constrain the coeval EUV background) are consistent with quasar-like sources with $\alpha \approx -1.7$ dominating the extragalactic background. Metal absorption line observations do not allow a harder component than quasars to source more than half of the $\sim 200~$eV background at $z= 2.5$. In addition, if a source population with $\alpha = -1$ contributed even just $10\%$ of the $1~$Ry emissivity at $z=2.5$, it would overshoot measured bounds on the unresolved SXB. We found that the contribution of faint AGN to high-redshift ionizing backgrounds is most constrained by our knowledge of the reionization history of hydrogen and helium (but recent luminosity function measurements also exclude much of the parameter space for AGN reionization; \citealt{willott10}). We showed that quasars cannot finish ionizing the helium until $z=2.7$, while also ionizing the \HI\ at $z>6$, unless theoretical estimates for the clumpiness of intergalactic gas are low and the EUV emissivity of quasars/AGN stays constant or increases with increasing redshift. Lastly, we investigated models for the heating of the IGM owing to reionization with a $1$D radiative transfer code. Our calculations account for the finite speed of light as well as secondary heating and excitation processes, effects that had previously either been ignored or treated in an approximate manner, but are in fact important to include when soft X-ray photons contribute to reionization. We argued that the bulk of the intergalactic gas would have been heated at reionization to temperatures greater than $17,000~$K and less than $25,000~$K for reionization by a wide range of spectral models (with an even narrower range if the sources cannot doubly ionize the helium). The narrowness of this range owes to the efficiency of cooling at the ionization front for plausible front speeds. The higher temperatures in this range did not necessarily imply that the gas was ionized by the hardest spectra, as our intermediate $\alpha=-1.5$ case resulted in the highest post-front temperatures. In addition, the speed of the ionization front was as important for determining the post-front temperature as the emitted spectrum. Therefore, it would be difficult to distinguish models for the sources of reionization based on measurements of the intergalactic thermal history. Instead, the timing and duration of reionization is most important for establishing the average temperature of the post-reionization IGM.\\ We are grateful to Rosanne Di Stefano, Ryan O'Leary, Joop Schaye, and Jennifer Yeh for useful discussions. We thank the Aspen Center for Physics (NSF grant \#1066293), where this work was initiated. MM is supported by the National Aeronautics and Space Administration through Einstein Postdoctoral Fellowship Award Number PF9-00065 issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under contract NAS8-03060. | 12 | 6 | 1206.1335 |
1206 | 1206.6515_arXiv.txt | We have used deep $V$ and $R$ images acquired at the ESO Very Large Telescope to identify the optical companion to the binary pulsar \psr, one of the black-widow millisecond pulsars recently detected by the Fermi Gamma-ray Telescope in the Galactic plane. We found a faint star ($V\sim26.7$) nearly coincident ($\delta r \sim0\arcsec.28$) with the pulsar nominal position. This star is visible only in half of the available images, while it disappears in the deepest ones (those acquired under the best seeing conditions), thus indicating that it is variable. Although our observations do not sample the entire orbital period ($P=0.28$ d) of the pulsar, we found that the optical modulation of the variable star nicely correlates with the pulsar orbital period and describes a well defined peak ($R\sim25.6$) at $\Phi=0.75$, suggesting a modulation due to the pulsar heating. We tentatively conclude that the companion to \psr\ is a heavily ablated very low mass star ($\approx 0.02\Msun$) that completely filled its Roche Lobe. | It is generally accepted that millisecond pulsars (MSPs) are formed in binary systems containing a neutron star that is eventually spun up through mass accretion from an evolving companion. Among these systems those characterized by relatively small eccentricity and very small mass function (typically the companion mass is only $\mcom \lsim 0.1\Msun$) are classified as ``black-widow'' pulsars (BWPs). In several cases the pulsar shows eclipses in the radio signal suggesting that the companion is a non-degenerate, possibly bloated star. In some cases the eclipse of the radio signal is so extended that it implies a size of the companion larger than its Roche lobe, suggesting that the obscuring material is plasma released by the companion because of the energy injected by the pulsar. However since the size of the eclipse depends on the inclination angle (King et al. 2005), not all BWPs are expected to show eclipses. As suggested by King et al. (2003), the formation of BWPs needs two phases: a first one in which the companion spins-up the neutron star to millisecond periods and a second where the companion is ablated by the pulsar. While it is difficult to describe the two phases using the same star as a companion to the MSP, in globular clusters (GCs), where encounters and exchange interactions are frequent, the white dwarf (WD) companion responsible for the pulsar spinning-up can be replaced by a main sequence star via an exchange interaction. The following evolution of this newly assembled binary system can cause the progressive vaporization of the companion because of the energy injected by the MSP. Since dynamical interactions are less probable in low density environments, BWPs were thought to be mainly generated in GCs and then ejected in the field. However, the increasing number of BWPs discovered in the Galactic field suggests that they must form in the disk as well. In this paper we focus on a BWP in the galactic plane: \psr. \psr\ is a MSP with period $P=3.8$ ms and a radio flux at 1.4 GHz of $S_{\rm 1.4}= 0.4 \pm 0.2$ mJy discovered during the Parkes High-Latitude pulsar survey (Burgay et al.\ 2006, hereafter B06). The period derivative $\dot{P}=1.235\times10^{-20}$s s$^{-1}$ implies a characteristic age $\tau=5$ Gyr, a magnetic field $B=2.18 \times 10^8$ G, and a rotational energy loss rate $\dot{E}= 2.3 \times 10^{33}$ erg s$^{-1}$, similar to the values measured for other MSPs. \psr\ is in a binary system, with an orbital period of $\sim 0.28$ d. In particular, it is one of 53 binary MSPs with $P < 10$ ms currently known in the Galactic disk (http://www.atnf.csiro.au/research/pulsar/psrcat/expert.html; Manchester et al. 2005). It is located at a distance of $3.5\pm 1.5$ kpc, estimated from its dipersion measure (DM=60.666 pc cm$^{-3}$) and the Galactic electron density model of Cordes \& Lazio (2002). The pulsar has a proper motion of $\mu_{\alpha} cos\delta = 7 \pm 3$ mas yr$^{-1}$ and $\mu_{\delta}=11\pm 3$ mas yr$^{-1}$ (B06), which implies a transverse velocity of $228\pm53$ km s$^{-1}$, one of the highest measured for Galactic MSPs. The system mass function ($f=5\times10^{-6}$) implies a lower limit of $0.02 \Msun$ for the mass of the companion, assuming $1.35 \Msun$ for the pulsar (B06). Thus, in agreement with the definition above, \psr\ is probably a BWP seen at a low inclination angle (in fact no eclipse is detected). Until a few years ago just two other BWPs were known in the Galactic field, namely PSR B1957+20 (Fruchter et al. 1988a) and PSR J2051-0827 (Stappers et al.\ 1996a). But very recently, thanks both to dedicated surveys of $\gamma$-ray sources and to new blind searches, seven new BWPs have been discovered, most of them having been detected in $\gamma$-rays (see Roberts 2011 and references therein). Also \psr\ has been detected in $\gamma$-rays by the Large Area Telescope (LAT) on board the {\em Fermi} Gamma-ray Space Telescope. Based upon positional coincidence with the LAT error box, it was initially associated with the $\gamma$-ray source 1FGL\, J0610.7$-$2059 (Abdo et al.\ 2009; 2010). The detection of $\gamma$-ray pulsations at the radio period of \psr\ has been recently reported and used to confirm it as the $\gamma$-ray counterpart to the MSP (Espinoza et al., in preparation). In the X-rays \psr\ has not been detected, neither by the {\em ROSAT} All Sky Survey (Voges et al.\ 1999), nor by {\em Swift} (Marelli, private communication). Studying the optical emission properties of binary MSP companions is important to better constrain the orbital parameters and to clarify the evolutionary status of these systems and then to track back their history and characteristic timescales. In spite of their importance, only two optical companion to BWPs in the Galactic field have been detected to date (Fruchter et al. 1988b, Reynolds et al. 2007, and Van Kerkwijk et al.2011; Stappers et al.\ 1996b, Stappers et al. 1999 and Stappers et al. 2000). The binary MSP PSR B1957+20 is the first discovered BWP and one of the best studied members of this class. The optical companion to PSR J1957+20 was identified by Kulkarni et al. (1988), while subsequent observations found the companion to vary by a fraction of 30\%-40\% in flux over the course of the orbital period (Callanan et al. 1995). Reynolds et al. (2007), modelling the light curve over all the orbital period, constrained the system inclination $63 ^{\circ}<i<67^{\circ}$ and the filling factor of the Roche Lobe ($0.81<f<0.87$). Moreover, they ruled out the possibility that the companion is a white dwarf, suggesting that most probably is a brown dwarf. A recent spectroscopic analysis, combined with the knowledge of the inclination angle inferred from models of the light curve, suggested that the PSR B1957+20 is massive with $M_{\rm PSR}=2.4\Msun$ ($M_{\rm PSR}>1.66\Msun$ being conservative; van Kerkwijk et al. 2011). The optical companion to binary PSR J2051-0827 was identified by Stappers et al. (1996b). They found that the amplitude of the companion's light curve was at least 1.2 mag, and that the variation was consistent with the companion's rotating synchronously about the pulsar and one side being heated by the impinging pulsar flux. In subsequent works it has been possible to study the entire lightcurve, measuring amplitudes of 3.3 and 1.9 magnitudes in the $R$-band and $I$-band respectively. The companion star has been modelled by a gravitationally distorted low-mass secondary star which is irradiated by the impinging pulsar wind. The resulting best-fit model is of a Roche lobe filling companion star which converts approximately 30\% of the incident pulsar spin down energy into optical flux (Stappers et al., 2000). Here we present the first identification of the optical companion to \psr, from data acquired at the ESO {\em Very Large Telescope} (\vlt). The observations and data analysis are described in Sect. 2, while the results are presented in Sect. 3 and discussed in Sect. 4. | We have determined the physical parameters of \com\ from the comparison of its position in the CMD (Figure \ref{cmd}) with a reference zero age main sequence, assuming an interstellar extinction of $E(B-V)\sim0.074$\footnote{ from NED, Nasa/ipac Extragalactic Database - Galactic Extinction Calculator available at the web site {\it http://ned.ipac.caltech.edu/forms/calculator.html}.} and the typical metallicity of the Galactic disk ($Z=0.02$). The resulting effective temperature and bolometric luminosity of the star are $T_{eff}\sim3500$ K and $L_{bol}\sim 0.0017 L_{\odot}$ respectively, with a conservative uncertainty of $\pm 500$ K and $\pm0.0001L_{\odot}$. Under the assumption that the optical emission of \com\ is well reproduced by a blackbody (BB), it is possible to derive its radius: $R_{\rm BB}\sim 0.14R_{\odot}$. However, since the companion to a BWP is expected to be affected by the tidal distortion exerted by the pulsar and to have filled its Roche Lobe, the dimension of the Roche Lobe might be a more appropriate value (i.e., see PSR J2051-0827; Stappers et al. 1996b and Stappers et al. 2000). According to Eggleton (1983) we assume: \begin{displaymath} \rrl \simeq \frac{0.49q^{\frac{2}{3}}}{0.6q^{\frac{2}{3}}+\ln \left(1+q^{\frac{1}{3}}\right)} \end{displaymath} where $q$ is the ratio between the companion and the pulsar masses ($\mcom$ and $\mpsr$, respectively). This relation can be combined with the PSR mass function $f(i,\mpsr,\mcom)=(\mcom\sin i)^3/(\mcom+\mpsr)^2$ by assuming a NS mass $\mpsr=1.5 \Msun$ (as recently estimated for recycled pulsars by Ozel et al. 2012; see also Zhang et al. 2011 and Kiziltan et al. 2011), thus yielding $\rrl(i)\sim0.24-0.47 R_{\odot}$, depending on the inclination angle ($i$) of the orbital system. These values are about 1.7-3.4 times larger than $R_{\rm BB}$. In the following discussion we assume the value of the Roche Lobe as a measure of the size of \com\ and we discuss how the scenario would change by using $R_{\rm BB}$ instead of $\rrl$. While these assumptions trace two extreme possibilities, the situation is probably in the midway. In fact, in the case of a completely filled Roche Lobe, the mass lost from the companion should produce some detectable signal in the radio band (unless for very small orbital inclinations) and ellipsoidal variations could be revealed in the light curve (unless the heating from the pulsar is dominating). Under the assumption that the optical variation shown in Figure \ref{lc} is mainly due to irradiation from the MSP reprocessed by the surface of \com\, we can estimate how the re-processing efficiency depends on the inclination angle and, hence, on the companion mass. To this end, we compare the observed flux variation ($\Delta F_{obs}$) between the maximum ($\Phi=0.75$) and the minimum ($\Phi=0.25$) of the light curve, with the expected flux variation ($\Delta F_{exp}$) computed from the rotational energy loss rate ($\dot{E}$). Actually, since we do not observe the entire light curve, $\Delta F_{obs}$ can just put a lower limit to the reprocessing efficiency. Moreover, since these quantities depend on the inclination angle of the system (see below) we can just estimate the reprocessing efficiency as function of $i$. At first we have to convert the observed magnitude variation into a flux. We limited our analysis to the $R$ band since we have more observations and a more reliable sampling of the light curve. At maximum ($\Phi=0.75$) we assume $R=25.6$, and between $\Phi=0.75$ and $\Phi=0.25$ we estimate an amplitude variation $\Delta R \gapp 1.5$. Hence we obtaine $\Delta F_{obs} \sim 1.88 \times 10 ^{-30}$ erg s$^{-1}$ cm$^{-2}$ Hz$^{-1}$ and considering the filter width ($\Delta \lambda = 165$ nm) we have $\Delta F_{obs} \sim 3.4 \times 10 ^{-15}$ erg s$^{-1}$ cm$^{-2}$. On the other hand, the expected flux variation between $\Phi=0.75$ and $\Phi=0.25$ is given by \begin{displaymath} \Delta F_{exp}(i)= \eta \frac{\dot{E} }{A^2} \rcom^2 \frac{1}{4\pi d^2_{\rm PSR}} \varepsilon (i) \end{displaymath} where $\eta$ is the re-processing efficiency under the assumption of isotropic emission, $A$ is semi-major axis of orbit which depends on the inclination angle, $\rcom$ is the radius of the companion star, which we assumed to be equal to $\rrl(i)$, $\dpsr$ is the distance of pulsar (3.5 kpc \footnote{In these calculations we adopted a distance of 3.5 kpc, while we discuss below how the scenario changes by varying the distance between the range of values within the quoted uncertainty.}) and $\varepsilon (i)$ is the fraction of the re-emitting surface visible to the observer\footnote{ In the following we assume $\varepsilon (i)=i/180$. In fact, for a face-on configuration ($i=0^{\circ}$) no flux variations are expected, while for an edge-on system ($i=90^{\circ}$) the fraction of the heated surface that is visible to the observer varies between 0.5 (for $\Phi=0.75$) to zero (for $\Phi=0.25$).}. By assuming $\Delta F_{obs}=\Delta F_{exp}(i)$ between $\Phi=0.75$ and $\Phi=0.25$, we can derive a relation linking the re-processing efficiency and the inclination angle. The result is shown in Figure \ref{repr}. The absence of eclipses in the radio signal allows us to exclude very high inclination angles. As shown in Figure \ref{repr}, pulsar companions with stellar mass above the physical limit for core hydrogen burning star (i.e., with $M\ge0.08\Msun$) necessarily imply a non-isotropic emission mechanism of the pulsar flux (otherwise a larger than $100\%$ physical efficiency would be required). On the contrary a re-processing efficiency between 40\% and 100\% is sufficient for less massive companions and intermediate inclination angles. Taking into account the uncertainty on the pulsar distance, only re-processing efficiencies larger than $\sim60\%$ for inclination angles in excess to $~50^{\circ}$ and companion masses lower than $\sim0.03\Msun$ are allowed in the case of the distance upper limit (5 kpc). Instead, in case of a closer distance $\eta$ decreases for all inclination angles, thus making acceptable also companion stars with masses larger than $0.08 \Msun$. For instance, for companions masses between $0.08$ and $0.2 \Msun$ and a 2 kpc distant pulsar, the re-processing efficiency ranges between $30\%$ and $60\%$ for any value of $i$. The observed optical modulation can be reproduced considering a system seen at an inclination angle of about $60^{\circ}$, with a very low mass companion ($\mcom\sim0.02\Msun$) that has filled its Roche Lobe, and a re-processing efficiency of about $50\%$. On the other hand, if we use $R_{\rm BB}$ instead of the $\rrl$, the efficiency becomes larger than 100\% for every inclination angle, and the only possible scenario would be that of an anisotropic pulsar emission. However, even with this assumption it is very difficult to obtain an acceptable value for $\eta$. This seems to confirm that $R_{ \rm BB}$ is too small to provide a good estimate of the star physical size. Forthcoming studies will allow us to better constrain the system parameters. | 12 | 6 | 1206.6515 |
1206 | 1206.1759_arXiv.txt | {The energy source that maintains the solar chromosphere is still undetermined, but leaves its traces in observed intensities.}{We investigate the statistics of the intensity distributions as function of the wavelength for \ion{Ca}{ii}\,H and the \ion{Ca}{ii}\,IR line at 854.2\,nm to estimate the energy content in the observed intensity fluctuations.}{We derived the intensity variations at different heights of the solar atmosphere as given by the line wings and line cores of the two spectral lines. We converted the observed intensities to absolute energy units employing reference profiles calculated in non-local thermal equilibrium (NLTE). We also converted the observed intensity fluctuations to corresponding brightness temperatures assuming LTE.}{The root-mean-square (rms) fluctuations of the emitted intensity are about 0.6 (1.2) Wm$^{-2}$ster$^{-1}$pm$^{-1}$ near the core of the \ion{Ca}{ii}\,IR line at 854.2\,nm (\ion{Ca}{ii}\,H), corresponding to relative intensity fluctuations of about 20\,\% (30\,\%). Maximum fluctuations can be up to 400\,\%. For the line wing, we find rms values of about 0.3 Wm$^{-2}$ster$^{-1}$pm$^{-1}$ for both lines, corresponding to relative fluctuations below 5\,\%. The relative rms values show a local minimum for wavelengths forming at about 130\,km height, but otherwise increase smoothly from the wing to the core, i.e., from photosphere to chromosphere. The corresponding rms brightness temperature fluctuations are below 100\,K for the photosphere and up to 500\,K in the chromosphere. The skewness of the intensity distributions is close to zero in the outer line wing and positive throughout the rest of the line spectrum, caused by a frequent occurrence of high-intensity events. The skewness shows a pronounced local maximum on locations with photospheric magnetic fields for wavelengths in between the line wing and the line core ($z\approx\,150-300$\,km), and a global maximum at the very core ($z\approx\,1000$\,km) for both magnetic and field-free locations.} {The energy content of the intensity fluctuations is insufficient to create a similar temperature rise in the chromosphere as predicted in most reference models of the solar atmosphere. The increase of the rms fluctuations with height indicates the presence of upwards propagating acoustic waves with an increasing oscillation amplitude. The intensity and temperature variations show a clear increase of the dynamics from photosphere towards the chromosphere, but fall short of fully dynamical chromospheric models by a factor of about five. The enhanced skewness between photosphere and lower solar chromosphere on magnetic locations indicates a mechanism which solely acts on magnetized plasma. Possible candidates are the Wilson depression, wave absorption, or magnetic reconnection.} | The solar chromosphere shows prominent emission lines when viewed near the solar limb, e.g., during an eclipse, but also on the solar disc chromospheric spectral lines such as H$\alpha$, \ion{Ca}{ii}\,H and K, \ion{Mg}{ii}\,h and k, or the \ion{Ca}{ii}\,IR triplet revert to transient emission. Because the gas density is so low that the material is transparent and the radiation temperature is decreasing above the continuum forming layers in the photosphere, the emission lines require an energy supply other than radiative transfer. The different types of possible heating mechanisms vary from purely mechanical processes to all processes that can be related to the presence of magnetic field lines \citep[see, e.g.,][]{biermann_48,schatzman1949,liu1974,anderson+athay1989,davila+chitre1991,rammacher+ulmschneider1992,narain+ulmschneider1996,carlsson+etal2007,rezaei+etal2007,beck+etal2008,fontenla+etal2008,beck+etal2009,khomenko+collados2012}. In addition to the fact that ``the'' heating mechanism of the chromosphere could not be identified yet, the exact amount of energy required to maintain the chromosphere as it is observed is not fully clear. There exists a series of static atmospheric stratification models for the solar photosphere and chromosphere \citep[e.g.,][]{gingerich+etal1971,vernazza+etal1976,vernazza+etal1981,fontenla+etal2006,avrett+loeser2008} that were determined from temporally and/or spatially averaged spectra. These models mainly share the existence of a temperature reversal at a certain height in the solar atmosphere, the location of the temperature minimum. Using temporally and spatially resolved spectra, it seems that the assumption of a static background temperature with minor variation around it is not fulfilled \citep[e.g.,][]{liu+skumanich1974,kalkofen+etal1999,carlsson+stein1997,rezaei+etal2008}. The spectra indicate in some cases that no chromospheric temperature rise is present at all \citep{liu+smith1972,cram+dame1983,rezaei+etal2008}, as is also required by the observations of CO molecular lines in the lower chromosphere \citep[][]{ayres+testerman1981,ayres2002} that only form at temperatures below about 4000\,K. Numerical hydrodynamical (HD) simulations of the chromosphere show even lower temperatures down to 2000\,K \citep[][]{wedemeyer+etal2004,leenarts+etal2011}. In the first paper of this series \citep[][BE09]{beck+etal2009} we investigated the energy content of velocity oscillations in several photospheric spectral lines and the chromospheric \ion{Ca}{ii}\,H line. The main finding of BE09 was that the energy of the root-mean-square (rms) velocity of a spectral line in the wing of \ion{Ca}{ii}\,H, whose formation height was estimated to be about 600\,km, was already below the chromospheric energy requirement of 4.3\,kWm$^{-2}$ given by \citet{vernazza+etal1976}, with a further decrease of the energy content towards higher layers. The observations used had a spatial resolution of about 1$^{\prime\prime}$, similar to those of \citet{fossum+carlsson2005,fossum+carlsson2006} that also found an insufficient energy in intensity oscillations observed with TRACE. \citet{wedemeyer+etal2007} and \citet{kalkofen2007} demonstrated later that the spatial resolution can be critical for the determination of the energy content, because the spatial smearing hides high-frequency oscillations with their corresponding short wavelengths. % Recently, several papers addressed the energy flux of acoustic and gravity waves using data of higher spatial resolution from, e.g., the G\"ottingen Fabry-Perot Interferometer \citep[GFPI,][]{puschmann+etal2006}, the Interferometric BI-dimensional Spectrometer \citep[IBIS,][]{cavallini2006}, or the Imaging Magnetograph eXperiment (IMaX) onboard of the Sunrise balloon mission \citep{jochum+etal2003,gandorfer+etal2006,martinezpillet+etal2011}. \citet{straus+etal2008} found an energy flux of solar gravity waves of 5\,kWm$^{-2}$ at the base of the chromosphere in simulations and observations, usually an order of magnitude higher than the energy flux of acoustic waves at the same height. \citet{nazi+etal2009,nazi+etal2010} found an acoustic energy flux of 3 and $>$\,6\,kWm$^{-2}$ at a height of 250\,km, using GFPI and IMaX data, respectively \citep[see also Table 2 in][]{nazi+etal2010}. Much of the wave energy was found in the frequency range above the acoustic cut-off frequency of about 5\,mHz; these high-frequency waves are able to propagate into the chromosphere without strong (radiative) losses \citep[cf.~also][]{carlsson+stein2002,reardon+etal2008}. The energy content was, however, basically determined from {\em photospheric} spectral lines, and thus refers to the upper photosphere, where also at lower spatial resolution sufficient mechanical energy is seen (BE09). Interestingly, the (lower) chromospheric lines used in \citet{straus+etal2008}, \ion{Na}{i} D and \ion{Mg}{i} $b_2$, showed an energy flux {\em below} 4\,kWm$^{-2}$ (their Fig.~3). It is therefore unclear how reliable the extrapolation of the photospheric energy fluxes actually is. Another point to be considered is the influence of the photospheric magnetic fields on the chromospheric behaviour \citep[e.g.,][]{cauzzi+etal2008}. Photospheric magnetic fields also cause an enhancement of the chromospheric emission, even if the underlying process may be a kind of wave propagation in the end \citep[e.g.,][]{hasan2000,rezaei+etal2007,beck+etal2008,hasan+etal2008,khomenko+etal2008,vigeesh+etal2009,fedun+etal2011}. The usage of velocity oscillations to estimate the energy content is in general also less direct than to use the intensity spectrum. If energy is deposited into the upper solar atmosphere by a process without a clear observable signature, either because of missing spatial or temporal resolution, or because of physical reasons such as for the case of transversal wave modes, the emitted intensity will still react to the energy deposit, even if the non-local thermal equilibrium (NLTE) conditions in the chromosphere make the reaction neither instantaneous nor necessarily linear to the amount of deposited energy. For instance, \citet{reardon+etal2008} found evidence that the passage of shock fronts induces turbulent motions at chromospheric heights. The dissipation of the energy of these turbulent motions then would effect an energy transfer from mechanical to radiative energy, but with some time delay and over some period longer than the duration of the shock passage itself \citep[see also][]{verdini+etal2012}. In this contribution, we investigate the intensity statistics of two chromospheric spectral lines, \ion{Ca}{ii}\,H and the \ion{Ca}{ii}\,IR line at 854.2\,nm, to estimate the energy contained in their intensity variations at all wavelengths from the wing to the very line core. Section \ref{sec_obs} describes the observations used. The data reduction steps are detailed in Sect.~\ref{add_data}. In Sect.~\ref{sec_int}, we investigate the intensity statistics of the two lines. The results are summarized and discussed in Sect.~\ref{summ_disc}, whereas Sect.~\ref{concl} provides our conclusions. \begin{figure*} \centering \fbox{\begin{minipage}{8.8cm}\centerline{Observation No.~3}$ $\\\resizebox{8.8cm}{!}{\hspace*{.7cm}\includegraphics{fov_overview_cair.ps}}$ $\\$ $\\\end{minipage}}\hspace*{.25cm}\fbox{\begin{minipage}{8.3cm}\centerline{Observation No.~4}$ $\\\resizebox{8.3cm}{!}{\hspace*{.7cm}\includegraphics{fov_overview_cair_ts.ps}}$ $\\$ $\\\end{minipage}} \caption{Overview maps of the observation No.~3 ({\em left panel}) and No.~4 ({\em right panel}). {\em Bottom row, left to right}: continuum intensity at 1083\,nm, 854\,nm, 630\,nm, and 396\,nm. {\em Top row, left to right}: unsigned wavelength-integrated Stokes $V$ signal around \ion{Si}{i} at 1082.7\,nm, line-core intensity of the \ion{Ca}{ii}\,IR line at 854.2\,nm, unsigned wavelength-integrated Stokes $V$ signal around 630\,nm, line-core intensity of \ion{Ca}{ii}\,H at 396.85\,nm. The {\em red contours} outline strong polarisation signals. The {\em white squares} denote co-spatial local darkenings.\label{overview_2009}} \end{figure*} \begin{table} \caption{Overview of the observations.\label{tab_obs}} \begin{tabular}{cccccc} No. & date & type & $t_{\rm int}$ & size & \ion{Ca}{ii}\,IR\cr\hline 1 & 24/07/06 & map & 6.6 sec & 75$^{\prime\prime}\times 70^{\prime\prime}$ & no\cr 2 & 24/07/06 & time series & 3.3 sec & 60 min & no \cr 3 & 29/08/09 & map & $\sim 30$\, sec & 40$^{\prime\prime}\times 70^{\prime\prime}$ &yes \cr 4 & 08/09/09 & time series & 5 sec & 50 min &yes \cr \end{tabular} \end{table} | } The intensity distributions of the chromospheric lines of \ion{Ca}{ii}\,H and the \ion{Ca}{ii}\,IR line at 854.2\,nm show a minimum of rms fluctuations for wavelengths forming in the low photosphere caused by the inversion of the granulation pattern. Wavelengths forming above the height of minimal rms show a nearly monotonic increase of rms fluctuations towards the line core that indicates propagating acoustic waves with increasing oscillation amplitudes. A conversion of these intensity fluctuations to corresponding brightness temperature variations yields rms values of about 100\,K in the lower photosphere and a few hundred K in the chromosphere, favoring dynamical models of the solar chromosphere. The fluctuations fall still short of those in numerical simulations and would not suffice to lift an atmosphere in radiative equilibrium to the temperature of, e.g., the HSRA model. The positive skewness for most wavelengths indicates a higher occurrence frequency of high-intensity events, presumably the hot shock fronts formed by the steepening acoustic waves. A prominent difference in skewness between magnetic and field-free locations for wavelengths forming in the mid photosphere indicates the existence of a mechanism that operates only in the presence of magnetic fields and enhances the intensity in the line wing. Single-case studies of such events will allow one to identify the exact process and its relation to the structure of the magnetic field. | 12 | 6 | 1206.1759 |
1206 | 1206.1790_arXiv.txt | The radio pulsar models based on the existence of an inner accelerating gap located above the polar cap rely on the existence of a small scale, strong surface magnetic field $B_s$. This field exceeds the dipolar field $B_d$, responsible for the braking of the pulsar rotation, by at least one order of magnitude. Neither magnetospheric currents nor small scale field components generated during neutron star's birth can provide such field structures in old pulsars. While the former are too weak to create $B_s \gtrsim 5\times 10^{13}$G$\;\gg B_d$, the ohmic decay time of the latter is much shorter than $10^6$ years.\\ We suggest that a large amount of magnetic energy is stored in a toroidal field component that is confined in deeper layers of the crust, where the ohmic decay time exceeds $10^7$ years. This toroidal field may be created by various processes acting early in a neutron star's life. The Hall drift is a non-linear mechanism that, due to the coupling between different components and scales, may be able to create the demanded strong, small scale, magnetic spots.\\ Taking into account both realistic crustal microphysics and a minimal cooling scenario, we show that, in axial symmetry, these field structures are created on a Hall time scale of $10^3$-$10^4$ years. These magnetic spots can be long-lived, thereby fulfilling the pre-conditions for the appearance of the radio pulsar activity. Such magnetic structures created by the Hall drift are not static, and dynamical variations on the Hall time scale are expected in the polar cap region. | The Partially Screened Gap Model relies on an intimate interplay of the cohesive energy in the polar cap surface layer and the corresponding surface temperature $T_s$ as well as on the partial screening by the thermal outflow of iron ions (\cite{2003_Gil}). Both quantities depend on the local surface field strength $B_s$. The condition for the existence of an accelerating gap has been calculated by \cite{2007_Medin}. The balance of heating by the bombardment with ultrarelativistic particles and cooling by radiation returns for typical radio pulsar parameter $T_s \gtrsim 10^6$ K \cite{2003_Gil}, a significantly higher value than the cooling age predicts. In order to enable the creation of a gap for such high $T_s$, $B_s$ has to be larger than $5\times 10^{13}$ G, perhaps even larger than $10^{14}$ G. Simultaneous X-ray and radio observations with X-ray spectra that can be fitted by blackbody radiation (\cite{2006_Kargaltsev,2005_Zhang}) support these estimates. Though these fits have to be considered with caution (see ERPM talk of W. Hermsen) they may be indicating that the base of the open field lines on the stellar surface (heated to temperatures above $10^6$ K) is much smaller than the conventional polar cap (\cite{1975_Ruderman}). Flux conservation arguments lead to $B_s \gtrsim 5\times 10^{13}$ G $\gg B_d \sim 5\times 10^{12}$ G (for a typical radio pulsar). In order to allow an efficient electron-positron pair creation rate within the accelerating gap, the curvature radius of the magnetic field lines must be $R_{B_s} \ll R_{B_d} \sim 100$ km (\cite{1975_Ruderman}). This is valid when either curvature radiation or inverse Compton scattering are the dominating processes (\cite{2000_Melikidze},\cite{2011_Szary}). Polar cap surface fields of the required strength and curvature cannot be present since the birth of the neutron star, because the electric conductivity during the first $\sim 10^4$ yr is relatively low and, for small-scale structures is $\lesssim 1$ km, the ohmic decay time in the subsurface crustal layers is typically only a few $10^2$ - a few $10^3$ yrs. Therefore, the demanded $B_s$ has to be (re-)created and maintained over the lifetime of radio pulsars, i.e. $\sim 10^6-10^7$ yr. Therefore, there must be a large reservoir of magnetic energy, stored in regions where it can survive for $\gtrsim 10^6$ yr, which, at some point over the lifetime of radio pulsars, can be tapped for forming this $B_s$. Since magnetospheric currents are not a plausible mechanism to create the demanded $B_s$ - structures (\cite{2001_Hibschman}), the Hall drift of the crustal magnetic field turns out to be a possible alternative to explain the existence of the of small scale, strong surface fields. We propose that the energy reservoir is a large scale crustal toroidal field whose maintaining currents circulate in deeper layers, where the high electric conductivity ensures a sufficiently long lifetime. Due to the non-linear interaction of the crustal and/or core based poloidal field $\sim B_d$ with the toroidal crustal field, a magnetic spot in the vicinity of the polar cap can be created. | Our main conclusion is, therefore, that the Hall drift is a viable process, that might create both on a correct time scale and on proper scale lengths the surface magnetic field configurations that enable a neutron star to appear as radio pulsar. Although the model is limited to the 2D, axially symmetric case, so that no "real" spots, limited both in meridional and azimuthal direction, can arise, the results are promising and should motivate further investigations in this field. | 12 | 6 | 1206.1790 |
1206 | 1206.3871_arXiv.txt | The \an reaction is an important source of neutrons for the s-process. In massive stars responsible for the weak component of the s-process, \an is the dominant source of neutrons, both during core helium burning and in shell carbon burning. For the main s-process component produced in Asymptotic Giant Branch (AGB) stars, the \reaction{13}{C}{$\alpha$}{n}{16}{O} reaction is the dominant source of neutrons operating during the interpulse period, with the \Nepa source affecting mainly the s-process branchings during a thermal pulse. Rate uncertainties in the competing \an and \ag reactions result in large variations of s-process nucleosynthesis. Here, we present up-to-date and statistically rigorous \Nepa reaction rates using recent experimental results and Monte Carlo sampling. Our new rates are used in post-processing nucleosynthesis calculations both for massive stars and AGB stars. We demonstrate that the nucleosynthesis uncertainties arising from the new rates are dramatically reduced in comparison to previously published results, but several ambiguities in the present data must still be addressed. Recommendations for further study to resolve these issues are provided. | \label{sec:intro} The s-process is responsible for creating about half of the elements heavier than iron that are observed in the solar system\ \citep{SNE08}. This process involves the slow capture of neutrons (slower than the average $\beta$-decay rate of unstable nuclei) onto seed material, hence nucleosynthesis follows the nuclear valley of stability. By considering the solar system abundances of s-only nuclei (that is, nuclei that can only be produced in the s-process) it can be shown that there are two key components of the s-process: the ``main'' component and the ``weak'' component\ \citep{KAP11}. The main component produces s-nuclei with masses of $A>90$, while the weak component enriches the s-nuclei abundances at $A \lesssim 90$. The main component of the s-process arises from neutron captures during He-burning in $M \leq 4 M_{\odot}$ Asymptotic Giant Branch (AGB) stars (a detailed discussion of nuclear burning in AGB stars can be found in Refs.~\cite{AGBBook} and \cite{HER05}). In low mass (0.8 to 4\ $M_{\sun}$) AGB stars of solar metalicity, most neutrons are released through the $^{13}$C($\alpha$,n)$^{16}$O reaction during the inter-pulse period, while the \an reaction produces an additional burst of neutrons during thermal pulses. This burst of neutrons affects mainly the branchings in the s-process path. In intermediate-mass AGB stars ($M>4M_{\odot}$), where the temperatures are expected to be higher, the \an reaction is thought to be the main source of neutrons and could explain the enhancement of rubidium seen in some metal poor AGB stars \citep{PIG05,GAR06,LUG08,GAR09,KAR12}. % In addition to s-process elements, the \an and \ag rates influence the relative production of \nuc{25}{Mg} and \nuc{26}{Mg}, whose abundance ratios can be measured to high precision in circumstellar (``presolar'') dust grains. Magnesium is also one of the few elements for which the isotopic ratios (\nuc{25}{Mg}/\nuc{24}{Mg} and \nuc{26}{Mg}/\nuc{24}{Mg} can be derived from stellar spectra (for example, Refs.~\cite{YON03a,YON03b}). However, \textcite{KAR06} showed that with their estimated \an and \ag reaction rate uncertainties, the relative abundances of \nuc{25}{Mg} and \nuc{26}{Mg} predicted by their stellar models can vary by up to 60\%. The weak component of the s-process arises from nuclear burning in massive stars. The core temperature in these stars (typically with $M \gtrsim 11M_{\odot}$) becomes high enough during He-burning for the \an reaction to produce a high flux of neutrons shortly before the helium fuel is exhausted. Any remaining \nuc{22}{Ne} releases a second flux of neutrons during convective carbon shell burning. The s-process yield in these stars is therefore sensitive to the temperature at which the \an reaction starts to produce an appreciable flux of neutrons. \textcite{THE07} showed that the s-process during the core He-burning stage in massive stars depends strongly on both the \Nepa and the \reaction{16}{O}{n}{$\gamma$}{17}{O} reaction rates. They also found that not only are the overall uncertainties in the rates important, but also the temperature dependence of the rates. % The \Nepa reactions also affect nucleosynthesis in other astrophysical environments. During type II supernova explosions, two $\gamma$-ray emitting radionuclides, \nuc{26}{Al} and \nuc{60}{Fe} are ejected, % and their abundance ratio provides a sensitive constraint on stellar models \cite[][and references therein]{WOO07}. The species \nuc{60}{Fe} is mainly produced in massive stars by neutron captures during convective shell carbon burning\ \citep[e.g.,][]{PIG10}. Its abundance, therefore, depends strongly on the \Nepa rates. The \Nepa rates also play a role in type Ia supernovae. Throughout the ``simmering'' stage, roughly 1000 years prior to the explosion, \textcite{PIR09} suggested that neutrons released by the \an reaction affect the carbon abundance, thus altering the amount of \nuc{56}{Ni} produced (i.e., the peak luminosity) in the explosion. \textcite{TIM03} also found that during the explosion, neutronisation by the \an reaction affects the electron mole fraction, $Y_e$, thus influencing the nature of the explosion. In this work we will evaluate new reaction rates for \mbox{\Nepa}. Compared to previous results\ \citep{ANG99,JAE01,KAR06} our new rates are significantly improved because (i) we incorporate all the recently obtained data on resonance fluorescence absorption, $\alpha$-particle transfer etc., and (ii) we employ a sophisticated (Monte Carlo) method to estimate the rates and associated uncertainties. % We have recently presented new \Nepa rates in Ref.\ \cite{ILI10a}, but did not give a detailed account of their calculation. Since the latter results were published, we found, and could account for, a number of inconsistencies in data previously reported in the literature. In addition, new data from Ref.\ \cite{DEB10} became available, which have been included in the present work. Thus the rates presented here supersede our earlier results\ \citep{ILI10a}. The paper will be organised as follows: in Sec.\ \ref{sec:formalism} a detailed discussion of the Monte Carlo method used to calculate reaction rates is discussed. This method is described in detail elsewhere\ \citep{LON10} but will be summarised to show its applicability to the specific cases of the \Nepa reactions. The \Nepa rate calculations and comparisons with the literature will be presented in Sec.\ \ref{sec:rates}. The reaction rates will then be used to present new nucleosynthesis yields along with their uncertainties in Sec.~\ref{sec:results}. Conclusions will be presented in Sec.\ \ref{sec:conclusions}. | \label{sec:conclusions} Both the \an and the \ag reactions influence the neutron flux available to the s-process in massive stars and AGB stars. Uncertainties in the rates, therefore, lead to large uncertainties in s-process nucleosynthesis. In this paper, we have estimated greatly improved \Nepa reaction rates, based on newly available experimental information published since the works of Refs.\ \cite{JAE01} and \cite{ANG99}, and by applying a sophisticated rate computational method\ \citep{LON10}. Subsequently, we explored the astrophysical consequences for massive stars and for AGB stars. In massive stars, simple one zone models of core helium-burning were utilised to determine the influence of the new rates on the weak component of the s-process. The most important result of our study is a significant reduction of nucleosynthesis uncertainties. The yield uncertainty has been reduced by between a factor of 5 and 10 across the s-process mass region considered here (A $< 100$). For example, the yields of key isotopes, \nuc{26}{Mg} and \nuc{70}{Zn}, have uncertainty reduction factors of about 5 and 10, respectively. When comparing abundances obtained from our new recommended rates with those derived from previous recommended rates, the final yield of \nuc{26}{Mg} is found to have been reduced by roughly a factor of three, while s-process isotopes were affected only marginally. However, s-process nucleosynthesis is more concentrated around the iron peak when using the new reaction rates. This relative insensitivity to changes in neutron flux is partially caused by captures on the neutron poisons \nuc{12}{C}, \nuc{16}{O}, and \nuc{25}{Mg}, which are present in large quantities. In our AGB star models, the final abundance uncertainties have also been improved significantly with the new rates, with reductions by up to an order of magnitude. The key rubidium and zirconium isotopes, for example, have undergone yield uncertainty improvements of roughly a factor of two. We have also found that s-process nucleosynthesis is more active when including the new \Nepa reaction rates. While only small changes are found in the low-mass s-process path ($A < 80$), at higher masses production increases by up to a factor of 2. This is especially evident by counting the number of captures at the end of our network, yielding an increase of over 70\%. Further calculations should be performed to study the effect of our new rates on lower mass AGB stars, while paying special attention to their effects on branchings in the s-process path. The Monte-Carlo method used in the present study to calculate the \Nepa reaction rates has the distinct advantage of calculating the uncertainties in a robust and statistical meaningful manner. Although our rates include some of the systematic uncertainties in the nuclear data, there are still open questions regarding the resonance properties that could affect the rates. Clearly, the remaining ambiguities in the nuclear data for the \Nepa reaction rates need to be resolved. The discrepancies discussed here, by \textcite{KOE02}, and by \textcite{KAR06}, make it difficult to assign some \nuc{26}{Mg} levels to \Nepa resonances. Furthermore, the \Erlab{831} resonance should be re-measured with high precision. More information should also be gathered on the structure of \nuc{26}{Mg} levels near the $\alpha$-particle and neutron thresholds. Indirect methods such as particle transfer measurements are useful here, since the Coulomb barrier inhibits direct measurements. | 12 | 6 | 1206.3871 |
1206 | 1206.1045_arXiv.txt | The formation of brown dwarfs (BDs) poses a key challenge to star formation theory. The observed dearth of nearby ($\leq 5$ AU) brown dwarf companions to solar-mass stars, known as the brown dwarf desert, as well as the tendency for low-mass binary systems to be more tightly-bound than stellar binaries, have been cited as evidence for distinct formation mechanisms for brown dwarfs and stars. In this paper, we explore the implications of the minimal hypothesis that brown dwarfs in binary systems originate via the same fundamental fragmentation mechanism as stars, within isolated, turbulent giant molecular cloud cores. We demonstrate analytically that the scaling of specific angular momentum with turbulent core mass naturally gives rise to the brown dwarf desert, as well as wide brown-dwarf binary systems. Further, we show that the turbulent core fragmentation model also naturally predicts that very low-mass (VLM) binary and BD/BD systems are more tightly-bound than stellar systems. In addition, in order to capture the stochastic variation intrinsic to turbulence, we generate $10^4$ model turbulent cores with synthetic turbulent velocity fields to show that the turbulent fragmentation model accommodates a small fraction of binary brown dwarfs with wide separations, similar to observations. Indeed, the picture which emerges from the turbulent fragmentation model is that a single fragmentation mechanism may largely shape both stellar and brown dwarf binary distributions during formation. | \subsection{Derivation} Turbulence in the core provides it with a net angular momentum \citep {burkertbodenheimer00}. Intuitively, as Landau originally suggested long ago \citep {landaulifshitz59, davidson09}, we can understand the net angular momentum generated by a turbulent power spectrum consistent with Larson's linewidth-size relation \citep {larson81} by realizing that although the net angular momentum induced by the numerous small-scale turbulent modes will tend to cancel out, the few large-scale turbulent modes which fit within the core will tend to result in a small net angular momentum. Turbulence is inherently a stochastic physical process, and different realizations of a turbulent velocity field will endow a core with differing levels of angular momentum. However, the resulting net mean angular momenta of models of turbulent cores are nonetheless consistent with the low mean rotation rates implied by the linewidth gradients of cores mapped in NH$_3$ \citep {goodmanetal93, jijinamyersadams99}. \citet {burkertbodenheimer00} showed that because most of the angular momentum endowed by turbulence is generated at the scale of the core, the mean specific angular moment of a population of turbulent cores could be reasonably estimated even under the simplifying assumption of uniform core rotation. We therefore assume uniform rotation to derive estimates for the specific angular momenta of model cores. Expanding upon this, we derive estimates for binary properties, including the scaling of semimajor axes, periods, and binding energies with system mass from the isolated turbulent core fragmentation model. These estimates capture the essential physical description of turbulent fragmentation, which we will subsequently elaborate upon in \S \ref {methodology} in more detailed calculations, taking into account a fuller description of the stochastic variation inherent in different realizations of turbulence, as well as the inhomogeneous, turbulent GMC background within which individual cores are embedded. In our derivation of the scaling relations, we assume that the core is a critical Bonnor-Ebert sphere \citep{ebert55, bonnor57} with a density distribution modeled using an analytic lowered power law approximation \citep{natarajanlyndenbell97}. We calculate the moment of inertia $I$ and the gravitational potential energy $\Omega$ of this core as $ I = cM_{\rm core}R_{\rm core}^2$ and $\Omega = -dGM_{\rm core}^2/R_{\rm core}$, where $c\approx 0.34$ and $d\approx 0.55$ are constants numerically determined for a critical Bonnor-Ebert sphere, in terms of the core mass $M_{\rm core}$ and radius $R_{\rm core}$. We take the parameter $\beta =cR_{\rm core}^3\omega^2/(2dGM_{\rm core}) $ to describe the ratio of rotational energy to gravitational binding energy of the core, and find the specific angular momentum of the critical Bonnor-Ebert core $J_{\rm core}/M_{\rm core}$ scales as the square root of the mass and radius of the core; $J_{\rm core}/M_{\rm core} = \sqrt{2cd \beta GM_{\rm core}R_{\rm core}}$. We combine the Larson turbulent velocity dispersion relation with an exponent of $1/2$, $\sigma = 1.10 $ km s$^{-1} L$(pc$)^{0.5}$, with the condition that the core is in virial balance; in terms of the virial parameter, $\alpha = 5 \sigma^2 R/(GM)$, $\alpha \sim 1$. Consequently, we find that $J_{\rm core}/M_{\rm core} \propto M_{\rm core}^{3/4} \propto R_{\rm core}^{3/2} \ $\citep{larson81, leungetal82, myers83}. The latter scaling reflects the increase of line width with increasing size, and is the same scaling reported by \citet {burkertbodenheimer00}. These lead to a scaling estimate of the specific angular momentum with the mass of the core: \begin{equation} {J_{\rm core}\over M_{\rm core}} = 2.6 \times 10^{20}\left({\alpha \over 1.3}\right)^{1/4} \left({\beta \over 0.02}\right)^{1/2}\left({M_{\rm core}\over M_{\odot}}\right)^{3/4} {\rm cm}^2\ {\rm s}^{-1} \label {jovermscaling} \end{equation} Crucially, $lower$-$mass$ turbulent cores in virial balance naturally have a lower specific angular momentum than more massive cores. This scaling of the specific angular momentum with mass has profound consequences for binary properties. While most of the mass and angular momentum in a core is carried away during the star formation process and does not end up in the final binary, we can describe the fractions of mass and angular momentum transferred from the core to the binary system in terms of a star formation efficiency, $\epsilon_* = M/M_{\rm core}$, and an angular momentum efficiency, $\epsilon_J = J/J_{\rm core}$, where $M = M_1 + M_2$ and $J$ are the total mass and angular momentum of the binary system, with a primary mass $M_1$ and a companion mass $M_2$. Studies have suggested that the star formation efficiency is fairly constant over a wide range of formation conditions, with a typical value of $0.3$ \citep{alvesetal07}. Less information is known about the angular momentum efficiency, but F04 demonstrated that the stellar period distribution could be reproduced by a constant value of $\epsilon_J$ for a given model star formation efficiency $\epsilon_*$. Thus, we use the two efficiencies to derive the scaling of the system specific angular momentum with total mass from the core scaling: \begin{equation} { J \over M}= 3.37 \times 10^{19} \left({\epsilon_J \over 0.016}\right)\left({0.30\over \epsilon_*}\right)^{7/4}\left({\alpha \over 1.3}\right)^{1/4}\left({\beta \over 0.02}\right)^{1/2}\left({M \over M_{\odot}}\right)^{3/4} {\rm cm}^2\ {\rm s}^{-1} \end{equation} We may then use this scaling to estimate the typical periods $P$ and semimajor axes $a$ of binary systems : \begin{equation} P = 159 \left({\epsilon_J \over 0.016}\right)^3\left({0.30\over \epsilon_*}\right)^{21/4}\left({\alpha \over 1.3}\right)^{3/4}\left({\beta \over 0.02}\right)^{3/2}\left({M \over M_{\odot}}\right)^{1/4}{1 \over (1-e^2)^{{3 \over 2}} } { (1+q)^6 \over q^3 } {\rm days} \end{equation} \begin{equation} a = 0.57 \left({\epsilon_J \over 0.016}\right)^2\left({0.30\over \epsilon_*}\right)^{7/2}\left({\alpha \over 1.3}\right)^{1/2}\left({\beta \over 0.02}\right)\left({M \over M_{\odot}}\right)^{1/2} {1 \over (1-e^2) } {(1+q)^4\over q^2 } {\rm AU}, \end{equation} where $e$ is the eccentricity of the system and $q = M_2 / M_1$ is the mass ratio. As seen above, the period and semimajor axis scale weakly with mass, to the $1/4$ and $1/2$ powers respectively. Moreover, the mass ratio of the system, $q$, is crucial for shaping the primordial distributions, as most of the angular momentum that is transferred from the core to the binary system will be associated with the orbit of the companion. To illustrate the significance of the mass ratio concretely, consider two $1 \ M_{\odot}$ systems: one a stellar binary with $q = 1$ and the second a BD/stellar binary with $q = 0.04$. For simplicity, we assume both have the mean eccentricity of a thermal distribution, $e = 2/3$. With our fiducial scalings, the semimajor axes of the stellar and BD/stellar binary will be 16 AU and 750 AU, respectively. The wider separation of the BD/stellar binary systems is typical of the brown dwarf desert. Thus, the desert naturally arises in the turbulent fragmentation model primarily as a mass ratio effect. Furthermore, consider a $0.16 \ M_{\odot}$ binary brown dwarf system with $q = 1$, which will have a semimajor axis of 6.6 AU with our fiducial scalings. Consequently, the turbulent fragmentation model also naturally predicts that VLM and binary brown dwarf systems will be narrower than stellar binary systems, as they are formed within low-mass turbulent cores with lower specific angular momenta than stellar-mass turbulent cores. Moreover, these lower-mass systems will have nearer-equal mass ratios than stellar systems; this trend toward equal mass ratios further favors narrow-binary brown dwarf systems. We may expand upon our semimajor axis estimates to construct the turbulent fragmentation model prediction for the scaling of the minimum binding energy with the system mass. A system of mass $M$ has binding energy of approximately $E_{\rm bind} = GM_1M_2/a \propto M^{3/2}(q^3/(1+q)^6)$. Such a binary is most weakly bound when it has a brown dwarf companion; these systems establish the minimum binding energies of a binary with total mass $M$. For a companion dwarf with a much lower mass than the primary, $M_2 << M_1$, this scaling will approximately follow $E_{\rm bind, min} \propto M^{-3/2}$. As an example, let us consider a $0.10 \ M_{\odot}$ and a $1.00 \ M_{\odot}$ system, each with a $0.01 M_{\odot}$ companion. We find that the former system is bound $\approx 22$ times more tightly than the latter. Our result is similar to the conclusion derived by Close et al. 2003 that VLM and binary brown dwarf systems tend to be 10 - 20 times more tightly bound that solar mass systems. | 12 | 6 | 1206.1045 |
|
1206 | 1206.6981_arXiv.txt | { The low multipole anomalies of the Cosmic Microwave Background has received much attention during the last few years. It is still not ascertained whether these anomalies are indeed primordial or the result of systematics or foregrounds. An example of a foreground, which could generate some non-Gaussian and statistically anisotropic features at low multipole range, is the very symmetric Kuiper Belt in the outer solar system. In this paper, expanding upon the methods presented in \cite{Burigana}, we investigate the contributions from the Kuiper Belt objects (KBO) to the WMAP ILC 7 map, whereby we can minimize the contrast in power between even and odd multipoles in the CMB, discussed in \cite{Jkim1,Jkim2}.\\ We submit our KBO de-correlated CMB signal to several tests, to analyze its validity, and find that incorporation of the KBO emission can decrease the quadrupole-octupole alignment and parity asymmetry problems, provided that the KBO signals has a non-cosmological dipole modulation, associated with the statistical anisotropy of the ILC 7 map. Additionally, we show that the amplitude of the dipole modulation, within a $2\sigma$ interval, is in agreement with the corresponding amplitudes, discussed in \cite{Lew}. } | The departure of the CMB from statistical isotropy and homogeneity has attracted very serious attention since the first publications of the WMAP data \cite{WMAP1, WMAP3, WMAP5}. Investigations of the low multipole anomalies of the WMAP co-added map and the ILC whole sky map can clarify possible sources of ``contamination" \cite{Jkim1, Chiang03, Coles, Vielva, Eriksen2, Eriksen1, Larson, Oliveira-Costa1, Park1, Copi1, Land1, Coldspot1, Copi2, Schwarz1, Hoftuft1}. The low multipole non-Gaussian features and departure from statistical anisotropy of the CMB can be related to the foreground residuals \cite{Burigana, Naselsky2, Naselsky1, Naselsky3}, systematic effects \cite{Hansen1}, or it could even have a primordial origin, for instance by a violation of the Copernican principle \cite{Odd_C}, a primordial magnetic field \cite{PMF_anomaly, alfven}, or by a non-trivial topology of the Universe \cite{low_quadrupole, spherical_tessellation, Land_Bianchi}. Usually, discussing uncounted residuals of the foregrounds as a source of low multipole anomalies, one can assume that most of those residuals are associated with the Galactic plane, while for instance, the observed quadrupole -octupole alignment \cite{Copi1} is connected with the ecliptic plane. Spergel et al. \cite{spergel} have pointed out, that low multipole anomalies, like a power asymmetry and statistical anisotropy of the CMB signal, correlates with the ecliptic North and South poles, and more generally, reflect the morphology of the map of number of observations (MNO). Indeed, \cite{groeneboom1, groeneboom2} building on the work of \cite{hanlew} and \cite{ack} have identified a quadrupolar power asymmetry, confirmed by the WMAP team \cite{WMAP7:anomaly}. Most likely, this anomaly indicates an influence of the beam asymmetry on the CMB signal, discussed in \cite{hlc}. However, as it was pointed out by \cite{wehus}, in spite of significant distortions of the phases of the CMB signal, an anisotropic beam could only change the beam window function with less then $0.6\%$ at $l\gg 400$, and it is insignificant for estimation of the CMB power spectrum at the low multipole range $l\ll 200$, with changes at the level of $<0.1\%$.\\ Most of these tests are based on the CMB maps, meaning that a high quality of data reduction is essential. In contrast, as recently proposed in \cite{Jkim1, Jkim2}, the parity test requires only the CMB power spectrum, which is usually estimated with significantly better accuracy than the CMB map \cite{Odd_bolpol}.\\ The idea of the parity test is based on the analysis of the ratio $g(l)$ of the powers, stored in even and odd multipoles. For a statistically homogeneous and isotropic random CMB signal, $g(l)$ should have no preferences in respect to $l=even$ or $l=odd$ (see \cite{Kim2011, Parity_review} for discussions).\\ In this paper we would like to focus on an extension of the parity test, quadrupole-octupole alignment and lack of angular correlations at $\theta\ge 60^o$ \footnote{As it was shown in \cite{Kim2011} the anomaly of the correlation function can be explained as manifestation of the parity asymmetry of the CMB power} for the whole sky CMB map, taking under consideration the possible contributions from ``new foregrounds" like the Kuiper Belt objects KBO, (see for review \cite{Dikarev}), counting them as a source of contamination of the CMB \cite{Burigana}. Under the standard assumption that the KBOs is localized mainly in the Ecliptic plane, this foreground is potentially "dangerous" for the quadrupole-octupole alignment. More importantly, due to the high degree of symmetry, the morphology of the KBO signal could be remarkably similar to the morphology of the MNO, for instance at the V-band, and at least at the low multipole range $l\le 20-30$, where the power is comparable to the CMB power spectrum.\\ In \cite{Lew}, the concept of dipole modulation of the CMB is presented. The dipole modulation is effectively an addition of a term in harmonic space, with an amplitude $A$. This extra dipole term multiplies the primordial (true) cmb temperature value, at a given location on the sphere, with a number between $-A$ and $A$. If the location coincides with the direction of the dipole modulation, the number is $A$, and if opposite the dipole modulation direction, the number is $-A$. Effectively this introduces a dipole component in the measured map. See \cite{Lew} for further details. The critical point of our analysis is the assumption, that the dipole modulation of the CMB, is associated with an unknown systematic effect. Thus it affects not only the measured primordial CMB signal, but all the measurements of the foregrounds, including the KBO, as well.\\ We estimate the temperature change which the model-KBOs contribute to the CMB. We show that unlike the model of \cite{Burigana}, de-correlation of the ILC 7 and KBO leads to a decrease of the power of even and odd harmonics, improving the shape of the parity parameter $g(l)$.\\ Moreover, we will show that a KBO-ILC 7 de-correlation could change the significance of the quadrupole-octupole alignment, down to the level of spontaneous (chance) correlations. Thus, if the KBOs are responsible for the parity asymmetry of the CMB, one should be cautious of the alignment of quadrupole and octupole components of the CMB.\\ The outline of the paper is the following. In section 2 we introduce the basic characteristics of the parity asymmetry. In section 3, we discuss the model of the Kuiper Belt. Then, in section 4, we present a method of cross-correlations of the KBO foreground and the WMAP ILC 7 map at low multipole range. Section 5 is devoted to the analysis of general properties of the cross-correlations between ILC 7 and KBO signal. In section 6 we investigates the distortion of even and odd component of the ILC 7 map. Section 7 is devoted to the cleaning of the ILC 7 map by de-correlation with KBO emission. Additionally we look at the implications for the parity asymmetry and the quadrupole-octupole alignment, and test various properties of the KBO filtered signal in section 8. Finally, in section 9, we summarize our results and draw our conclusions. | In this paper, we have investigated a possible solution to the anomalous parity asymmetry in the Cosmic Microwave Background and the quadrupole-octupole alignment, related to the solar system foreground. The Kuiper Belt objects in the solar system plane can contribute to the microwave sky, and thus create a power contrast between even and odd multipoles. We have built a model of the KBO emissivity, based on the symmetry of the KBO in ecliptic coordinates. An essential part of the model is the incorporation of the dipole modulation of the ILC 7 map and KBO foreground, which transform the symmetric KBO foreground into an asymmetric part. An important point of our analysis is that by maximizing the cross-correlations between that asymmetric component and the ILC 7 odd harmonics for $l=3$, and separately for $l=5$, we can fix the direction of dipole modulation, and significantly change the balance between even and odd multipoles in the ILC map.\\ To illustrate the possible changes to the morphology of the low multipole domain of the CMB power spectrum, we have applied the strongest de-correlations between the ILC 7 map and dipole modulated KBO foreground, in order to illuminate the clear improvement of the parity asymmetry and the quadrupole-octupole alignment.\\ We have developed a method for cleaning the ILC 7 $a_{l,m}$-values from the contribution of the dipole modulated KBO, thus retaining only the intrinsic CMB signal in the Ecliptic plane. It is possible to apply different weights to this filtering, allowing for various levels of parity symmetry for the low multipoles, depending on the normalization of the dipole modulation direction in the sky, and the corresponding amplitude of modulation. We have shown, that at the level where the parity is effectively restored, the quadrupole-octupole alignment would be significantly reduced down to the level of a chance correlation.\\ In conclusion, the removal of the KBO contribution, in the framework of the dipole modulation model, requires a statistical anisotropy of the CMB of non-cosmological origin. We believe, that the coming PLANCK data, with different systematics compared to the WMAP experiment, can put a light on the problem of low multipole anomalies in the CMB. | 12 | 6 | 1206.6981 |
1206 | 1206.5982_arXiv.txt | {CW Leo has been observed six times between October 2009 and June 2012 with the SPIRE instrument on board the \it Herschel \rm satellite. Variability has been detected in the flux emitted by the central star with a period of 639 $\pm$ 4 days, in good agreement with determinations in the literature. Variability is also detected in the bow shock around CW Leo that had previously been detected in the ultraviolet and Herschel PACS/SPIRE data. Although difficult to prove directly, our working hypothesis is that this variability is directly related to that of the central star. In this case, fitting a sine curve with the period fixed to 639 days results in a time-lag in the variability between bow shock and the central star of 402 $\pm$ 37 days. The orientation of the bow shock relative to the plane of the sky is unknown (but see below). For an inclination angle of zero degrees, the observed time-lag translates into a distance to CW Leo of 130 $\pm$ 13 pc, and for non-zero inclination angles the distance is smaller. Fitting the shape of the bow shock with an analytical model (Wilkin 1996), the effect of the inclination angle on the distance may be estimated. Making the additional assumption that the relative peculiar velocity between the interstellar medium (ISM) and CW Leo is determined entirely by the star space velocity with respect to the local standard of rest (i.e. a stationary ISM), the inclination angle is found to be ($-$33.3 $\pm$ 0.8)\degr\ based on the observed proper motion and radial velocity. Using the Wilkin model, our current best estimate of the distance to CW Leo is 123 $\pm$ 14 pc. For a distance of 123 pc, we derive a mean luminosity of 7790 $\pm$ 150 \lsol\ (internal error). } | CW Leo (= IRC~+10~216 = AFGL~1381) was discovered by Becklin et al. (1969) in the pioneering \it Two-micron Sky Survey \rm as an extremely red object. It soon turned out to be a carbon star (Miller 1970, Herbig \& Zappala 1970) in an advanced stage of stellar evolution called the asymptotic giant branch (AGB). It is pulsating and surrounded by an optically thick dust shell and a large molecular circumstellar envelope (CSE). In the near- and mid-infrared (IR) it is one of the brightest objects in the sky, thus a typical target for any new instrument or telescope operating from the infrared to the millimetre. With the {\it Herschel} satellite (Pilbratt et al. 2010) two important discoveries have already been published on CW Leo: the discovery of many high-temperature water lines that have shed new light on the origin of water around carbon stars (Decin et al. 2010), and the confirmation of a bow shock, produced by the interaction of the stellar wind with the interstellar medium (ISM), originally discovered by Sahai \& Chronopoulos (2010) in the ultraviolet with {\it Galex}, by Ladjal et al. (2010, hereafter L10). Although an important object, its distance is uncertain, which is reflected in the uncertain estimates of basic quantities such as the luminosity and mass-loss rate. One of the most in-depth studies was conducted by Groenewegen et al. (1998), where dust and molecular radiative-transfer models were used to fit simultaneously the available photometric data, the {\it Low Resolution Spectrometer} spectrum taken by the {\it Infrared Astronomical Satellite}, near- and mid-IR interferometric observations, and CO J= 1-0 up to 6-5 molecular line emission data, available at that time. The conclusion was that the distance must be in the range 110-135 pc (corresponding to a luminosity of 10~000 \lsol\ to 15~000 \lsol), which was consistent with the luminosity of 7~700 \lsol\ to 12~500 \lsol\ based on the Mira period-luminosity (PL-) relation (Groenewegen \& Whitelock 1996), taking into account the scatter in that relation. Other distances quoted in the literature are based on slightly different versions of the PL-relation, e.g. 120 pc (Scho\"ier et al. 2007) or 140 pc (Menzies et al. 2006). In this work, an independent distance estimate to CW Leo is provided, based on the phase-lag between the flux variations of the central star and the bow shock. In Section~2, the observations are presented, and the analysis is described in Section~3. The model that was used to correct for the inclination angle of the bow shock is outlined in the Appendix. | A sine curve of the form $F(t) = F_0 + A \cdot \sin \left( 2\, \pi\, (t-T_0)/P \right)$ was fitted to the data, using the program Period04 (Lenz \& Breger 2005). The Monte Carlo option was used to estimate the error bars. For the PSW, PMW, and PLW filters separately, periods of, respectively, $P$ = 635 $\pm$ 4, 638 $\pm$ 10, and 646 $\pm$ 4 days are found. Independently, the PMW and PLW fluxes were scaled to the average level of the PSW flux, and the period was determined for the combined data set of 18 points to give a period of 639 $\pm$ 4 days, which is consistent with the values above. The derived period compares well to other determinations in the literature: Le Bertre (1992) presented lightcurves in many bands in the near- and mid-IR, and found an overall best-fit period of 649 days (no error bar given), and periods based on $K$-band lightcurves of 644 $\pm$ 17 days (Witteborn et al. 1980), 636 $\pm$ 3 days (quoted in Ridgway \& Keady 1988, based on unpublished material), and 638 days (Dyck et al. 1991, no error bar given). For the period fixed to 639 days, the amplitude, $A$, and zero level, $F_0$, of the sine curve were determined, and are listed in Table~\ref{TabRes}. The time of maximum light is $T_o$ = 2455256.8 $\pm$ 2.2 for the lightcurve of the central star. Taking the working hypothesis that the flux variation of the bow shock follows that of the central star, the time lag between the maximum light on the bow shock and the central star was determined to be 402 $\pm$ 37 days. Figure~\ref{FigStar} shows the lightcurve of the star and the bowshock in the PSW filter, and the model fit to the observations. The fit to the lightcurve of the bow shock flux is less secure, and the five flux determinations may be equally well fitted by either a constant or a line. A model with one parameter (a constant of 1.250, which is the average of the five determinations) results in $\chi^2$ of 24.0, and a value for the Bayesian information criterion\footnote{This is essentially a $\chi^2$ added with a term that penalizes models with more free parameters.} (Schwarz 1978) of BIC = 2.6. The sine model (with three parameters, as the period is fixed) naturally results in a lower $\chi^2$ of 13.0, but also in a lower BIC of -5.2. The fit with a straight line (two parameters) formally fits the data best, with $\chi^2$ = 4.7, and BIC = -15.0. We do not have a plausible physical model that can explain why the flux on the bow shock would decrease exactly linearly with time. To illustrate our working hypothesis for the physical situation, the dust radiative transfer model of Groenewegen (1997) for CW Leo was updated with a newer version of the code (Groenewegen 2012), by fitting the spectral energy distribution (SED), near- and mid-infrared visibility curves, and PACS and SPIRE radial intensity profiles (Groenewegen, in prep.). The fit to the SED at mean light is illustrated in Fig.~\ref{fig-sed}. For the model shown in the figure, the dust temperature at the location of the bow shock is 24.5~K. This is in excellent agreement with the fit to the PACS and SPIRE photometry in L10, who derived 25 $\pm$ 3~K. At that temperature, the dust is primarily heated by photons emitted at about 110 $\mu$m. The optical depth at that wavelength is predicted to be 0.05, hence optically thin. The variation in flux of the central star and inner dust region would therefore be felt directly at the location of the bow shock. In a second model to represent the variation from minimum to maximum light, the effective temperature of the central star was increased by 300~K (see Men'shchikov et al. 2001) and the luminosity then increased as to reproduce the observed increase in SPIRE PSW flux of the central star. In this model, the dust temperature at the location of the bow shock was increased from about 22.5~K to 27.5~K. This temperature variation alone would lead to a variation in flux of about 70\%, which is larger than is observed (20\%). The exact change in the dust temperature depends however both on details of the model and the flux variation of the central star, which in turn depends on the details of the SPIRE calibration. The model is also simplistic in the sense that the temperature calculated is that in the free expanding wind and not that in the bow shock, which is the result of the interaction of the wind with the interstellar medium. The calculation did show that the variation in theflux of the central star could lead to a variation in temperature and hence flux at the location of the bow shock, and that the flux variation is expected to follow the variation of the central star. The change in flux could also be due to a variation in dust density, but the timescale for the bow shock to adjust to changes in either the mass-loss rate of the central star (of order 500-1700 years, Decin et al. 2011) or the local density of the ISM is expected to be much longer than the pulsation period of the star (1.7 years). Hydrodynamical models (van Marle et al. 2011, Cox et al. 2012) tuned to CW Leo may in the future lead to a better understanding of the nature of the dust emission. \begin{figure} \includegraphics[angle=-0,width=82mm]{lcSTAR.ps} \includegraphics[angle=-0,width=82mm]{lcBS.ps} \caption[]{ Observations and fitted sinusoidal curve to the SPIRE PSW 250 \mm\ data on the central star (top panel), and the bow shock (lower panel). The bottom panel also includes the best fit to the data using a constant (the red dashed line), and a line (the blue dotted line) } \label{FigStar} \end{figure} \begin{table}[!ht] \caption{Amplitude and zero level of the lightcurves in the SPIRE filters used to observe the central star and bow shock (Cols.5-7)} \begin{tabular}{rrrrrrrrccc} \hline \hline filter & $F_o$ & $A$ & $A/F_o$ & $F_o$ & $A$ & $A/F_o$ \\ & (Jy) & (Jy) & & (Jy) & (Jy) & \\ \hline PSW & 158.3 & 20.8 & 0.13 & 1.258 & 0.109 & 0.09 \\ % PMW & 63.4 & 7.22 & 0.11 \\ % PLW & 25.8 & 2.69 & 0.10 \\ % \hline \end{tabular} \label{TabRes} \vspace{-6mm} \end{table} The phase lag between the lightcurve measured on the central star and the bow shock allowed us to determine the distance to CW Leo. The phase lag of (402 $\pm$ 37) light days corresponds to (1.041 $\pm$ 0.096) 10$^{18}$ cm, and this translates to a relation between distance, $d$ (in pc), and angular separation ($\Delta \theta$) between the emission of the central star and the bow shock of $d \Delta \theta$ = (6.96 $\pm$ 0.64) 10$^{4}$ (\arcsec $\cdot$ pc). The distribution of the angular distance $\Delta \theta$ of all points inside the aperture shown in Fig.~\ref{fig-contour} and the central star was determined, and found to be (534 $\pm$ 16)\arcsec, based on the median value and the error estimated from half the difference between the 69\% and 31\% percentiles of the distribution. If the bow shock were located in the plane-of-the-sky, the distance to CW Leo would follow immediately as $d$ = 130 $\pm$ 13 pc. This is also an upper limit to the distance, as for bow shocks inclined with respect to the plane-of-the-sky the distance will be smaller. To improve on this result, and obtain an estimate for the distance rather than just an upper limit, we employed a model that describes analytically the shape of a bow shock in the thin-shell limit (Wilkin 1996). The model was used in L10 (also see Ueta et al. 2008, 2009). In L10, we had assumed that the column density reaches its highest value where the bow shock cone intersects with the plane of the sky including the central star. The Monte Carlo simulations of the three-dimensional (3-D) structure described in Appendix~A now show that this is not the case, and that for non-zero inclinations of the bow shock the surface brightness peaks at a location away from this plane (also see Cox et al. 2012). Using these Monte Carlo simulations, it was possible to estimate for any inclination the distribution of angular distances $\Delta \theta$ to the central star of all points on the "Wilkinoid" that fall in the aperture when projected on the sky. The results are listed in Table~\ref{TabIncl}, together with the distance that then follows. We note that the fitting of the Wilkin model to the observed trace of the bow shock in itself does not allow the inclination to be determined. For zero inclination, the model gives a distance of (534.4 $\pm$ 18.3)\arcsec, in good agreement with the observed value of (534 $\pm$ 16)\arcsec. \begin{table}[!ht] \caption{Angular distance to the central star of all points on the "Wilkinoid" that fall in the aperture when projected on the sky \rm for various inclination angles based on the Wilkin model, and the derived distance to CW Leo.} \begin{tabular}{ccccclccc} \hline \hline inclination & $\Delta \theta$ & distance \\ (\degr) & (\arcsec) & (pc) \\ \hline 0 & 534.4 $\pm$ 18.3 & 130.2 $\pm$ 12.7 \\ % 10 & 540.9 $\pm$ 19.8 & 128.6 $\pm$ 12.7 \\ % 20 & 550.5 $\pm$ 25.6 & 126.4 $\pm$ 12.9 \\ % 30 & 561.2 $\pm$ 30.4 & 124.0 $\pm$ 13.1 \\ % 33.3 & 564.7 $\pm$ 37.4 & 123.3 $\pm$ 13.7 \\ % 36 & 568.1 $\pm$ 39.0 & 122.5 $\pm$ 13.7 \\ % 50 & 600.6 $\pm$ 56.0 & 115.9 $\pm$ 14.5 \\ % 60 & 655.7 $\pm$ 77.0 & 106.1 $\pm$ 14.8 \\ % \hline \end{tabular} \label{TabIncl} \vspace{-4mm} \end{table} \begin{figure} \includegraphics[angle=-0,width=80mm]{cwleo_sed.ps} \caption[]{ Fit to the SED (top panel), with a zoomed image of the 10 $\mu$m region in the lower panel. For a distance of 123 pc, the luminosity is 7790 \lsol. The horizontal lines in the lower panel indicate the wavelength regions excluded from the fitting. } \label{fig-sed} \vspace{-4mm} \end{figure} Making one further assumption, we further refine our estimate for the distance to CW Leo. The radial velocity of CW Leo is V$_{\rm LSR}= -25.5$ \ks\ (Groenewegen et al. 2002), corresponding to V$_{\rm helio}= -18.6$ \ks, and its proper motion (PM) is $\mu_{\rm \alpha} \cos \delta = +35 \pm$1, $\mu_{\rm \delta} =+12 \pm$1 mas$\cdot$yr$^{-1}$ (Menten et al. 2012). At this point, we assume that the relative peculiar velocity between the ISM and the star is determined entirely by the star space velocity with respect to the local standard of rest (LSR) (i.e. a stationary ISM). Then, following Cox et al., one can calculate the inclination angle. Unfortunately, there is a typographical error in Table~1 of Cox et al. for CW Leo. The correct values should read (for a distance of 123 pc, see below): a total PM of $\mu$ = 65 mas$\cdot$yr$^{-1}$, a peculiar space velocity of $v_{\star}$ = 45.7 \ks, position angle of PA = 66\degr, and, taking into account the errors in PM and RV (0.5 \ks\ adopted), an inclination angle of $i = -33.3$ $\pm$ 0.8\degr. For this angle, one can take the true angular distance between the points located on the bow shock and the central star from Table~\ref{TabIncl}, and find our current best estimate of the distance to CW Leo of 123 $\pm$ 14 pc. The model illustrated in Fig.~\ref{fig-sed} leads to a luminosity of 7790 $\pm$ 150 \lsol\ for a distance of 123 pc. Taking into account the error in the distance, we find $M_{\rm bol} = (-4.94 \pm 0.25$). This is in agreement with the Mira PL-relation of Feast et al. (2006), $M_{\rm bol} = -2.54 \log P + 2.06 (\pm 0.24)$, which gives $(-5.07 \pm 0.24)$ for $P = 639$ days. Menten et al. (2012) recently estimated the luminosity at phase 0.75 of the lightcurve (i.e. approximately mean light) from VLA observations to be $(8640 \pm 430)$ \lsol\ for 130 pc, or $(7730 \pm 380)$ \lsol\ for 123 pc, in excellent agreement with us. | 12 | 6 | 1206.5982 |
1206 | 1206.0796_arXiv.txt | We perform a joint analysis of dwarf galaxy data from the Fermi Gamma-ray Space Telescope in search of dark matter annihilation into a gamma-ray line. We employ a novel statistical method that takes into account the spatial and spectral information of individual photon events from a sample of seven dwarf galaxies. Dwarf galaxies show no evidence of a gamma-ray line between 10 GeV and 1 TeV. The subsequent upper limit on the annihilation cross section to a two-photon final state is $3.9^{+7.1}_{-3.7}\times 10^{-26} {\mathrm{cm^3s^{-1}}}$ at 130 GeV, where the errors reflect the systematic uncertainty in the distribution of dark matter within the dwarf galaxies. | 12 | 6 | 1206.0796 |
||
1206 | 1206.4127_arXiv.txt | {A new paradigm for active galactic jet kinematics has emerged through detailed investigations of BL Lac objects using very long baseline radio interferometry. In this new scheme, most, if not all, jet components appear to remain stationary with respect to the core but show significant non-radial motions. This paper presents results from our kinematic investigation of the jets of a statistically complete sample of radio-loud flat-spectrum active galaxies, focusing on the comparison between the jet kinematic properties of BL Lacs and flat-spectrum radio-quasars. It is shown that there is a statistically significant difference between the kinematics of the two AGN classes, with BL Lacs showing more bent jets, that are wider and show slower movement along the jet axis, compared to flat-spectrum radio-quasars. This is interpreted as evidence for helically structured jets.} | Black holes have been at the center of astronomical research for many years, being one of the most prominent predictions of the theory of General Relativity. There is a large amount of indirect evidence supporting that most, if not all, galaxies host a supermassive black hole (SMBH) at their centers (e.g., \citealt{Blandford1986}). It is widely believed that this SMBH is the main constituent of activity in active galactic nuclei (AGN) (for a review see e.g., \citealt{Begelman1984}). Given their very luminous nature, AGN are therefore some of the best probes that we have today to study the properties and evolution of SMBH out to the earliest times of the Universe. It is believed that AGN are made up of a number of building blocks including a central SMBH, an accretion disk, an obscuring molecular screen (usually referred to as a torus), ionization regions producing broad and narrow emission lines, and in some cases powerful collimated outflows, known as AGN jets (e.g., \citealt{Antonucci1993}, \citealt{Urry1995}). Jets are found in a plethora of astrophysical environments, among which, young stellar objects, massive X-ray binaries, possibly pulsars, $\gamma$-ray bursts, and AGN. They\linebreak have been observed for the first time in the optical in the nearest active galaxy to us, M87 (\citealt{Curtis1918}). Given their ubiquity, astrophysical jets research has been a booming field of astronomy, especially after the advent of high-\linebreak resolution imaging instruments and techniques (e.g., very long baseline interferometry, VLBI). Although observed in the minority of active galaxies ($\sim15\%$; \citealt{Krolik1999}), extragalactic jets are some of the most pronounced morphological features in AGN research. Their, presumably direct, connection to the active core and the SMBH residing there, makes them invaluable tools in the effort to characterize the properties and the underlying physics of activity in galaxies. Although observable at different wavelengths (see Fig. \ref{fig:AGNmultijet}), VLBI observations enabled the direct imaging of AGN jets at the highest possible resolutions and thus the detailed study of their properties. \begin{figure} \includegraphics[width=0.49\textwidth]{0131_multi.pdf} \caption{The active galactic nucleus 3C273 and its jet observed in three different wavelength regimes, the optical (left panel, \textit{HST}), the X-ray (middle panel, \textit{Chandra}), and the radio (right panel, MERLIN). Credit: NASA/STScI, NASA/CXC, MERLIN.} \label{fig:AGNmultijet} \end{figure} VLBI techniques have allowed the mapping of jets in the radio. A result of this was the discovery of the knotty nature of AGN jets, observed as a consecutive series of brightness maxima and minima. Observations at different times revealed that these brightness maxima actually move. The investigation of extragalactic jet kinematics had begun. One of the most prominent discoveries, related to jet kinematics, was that of the superluminal movement of these jet components, which was first theoretically predicted by\linebreak \citet{Rees1966}. The effect is a combination of relativistic expansion speeds (close to the speed of light) and the projected geometry onto the plane of the sky. Superluminal movement was indeed detected, first indirectly (\citealt{Whitney1971}), and then by direct imaging (\citealt{Pearson1981}). Superluminally moving components have become the staple of blazars, i.e., radio-loud AGN seen at the smallest viewing angles to their jet axis. Jet kinematics, as investigated through the study of distinct components, is currently explained in terms of the\linebreak shock-in-jet model (e.g., \citealt{Marscher1985}, also see Fig. \ref{marscher}), where the observed jet knots are manifestations of shocks propagating at relativistic speeds down the jet. As discussed above, beaming and projection effects regulate the observed properties of the jets. Analysis of samples of active galaxies containing large number of sources, selected following stringent criteria, has been of fundamental importance to this end (e.g., \citealt{Ghisellini1993}; \citealt{Vermeulen1994}; \citealt{Vermeulen1995}; \citealt{Taylor1996}; \citealt{Hough2002}; \citealt{Lister2005}; \citealt{Britzen2007a}). There has been a continuous effort to distinguish whether the different types of radio-loud active galaxies (e.g., quasars, BL Lacs, etc.) and their jet properties are an effect of different viewing angles, or whether these objects have intrinsically different properties. The current paradigm is that the differences observed can be attributed to geometrical effects, although some indications to the contrary also exist (e.g., \citealt{Gabuzda1995}; \citealt{Gabuzda2000}; \citealt{Britzen2009}; \citealt{Britzen2010b}). For example, using a sample of 39 superluminal sources,\citet{Ghisellini1993b} find no appreciable difference between the Doppler factors distributions of BL Lacs and quasars, with radio galaxies showing smaller values. \begin{figure} \begin{center} \includegraphics[width=0.45\textwidth]{marscher.pdf} \caption{An illustration of the AGN core, comprising the SMBH, the accretion disk, line emission regions, and the jet. Different jet regions and the effects observed in them are presented. Illustration reproduced from \citet{Lobanov2007} (adapted from \citealt{Marscher2005}).} \label{marscher} \end{center} \end{figure} | We develop a number of tools to investigate both the morphology and kinematics of the CJF jet ridge lines: \begin{enumerate} \item Monotonicity Index \item Apparent jet width \item Apparent jet linear evolution \end{enumerate} \noindent We summarize our results: \begin{itemize} \item Using the M.I., we find that BL Lacs jet ridge lines more often resemble a sinusoidal curve compared to FSRQs. In contrast, 2/3 of the FSRQs have an M.I. lower than 0.5 (indicating fairly monotonic jets). \item 22.4\% of the CJF sources have apparent jet widths larger than 20 degrees. 47.3\% of BL Lacs, over 13.6\% for FSRQs, have $dP>20$ degrees. \item BL Lacs exhibit substantially apparently wider jets than FSRQs. This effect persists for a smaller redshift range. This supports the effects seen in individual BL Lac objects (i.e., 1803+784, 0716+714, etc.). \item The distribution of apparent jet ridge line widths for BL Lacs appears to extend towards higher values, with \mbox{FSRQs} mainly contained at lower values. A K-S test indicates a $0.7\times10^{-3}\%$ probability that FSRQs and BL Lacs are drawn from a single parent population. \item BL Lac objects, on average, show weaker apparent linear evolution of their jet ridge lines compared to FSRQs. \item We use a helical jet model to show that a helical geometry combined with a small viewing angle can explain the large widths seen in BL Lac objects. \end{itemize} In conclusion, by statistically analyzing the CJF sample, we provide detailed insight concerning the morphology and evolution of AGN jet ridge lines. The statistical investigation of the CJF sources lends independent support to the different kinematic scenario recently seen in a number of BL Lac objects (1803+784, \citealt{Britzen2010}; 0735+178, \citealt{Britzen2010b}). 25\%-30\% of the CJF sample show apparently considerably wide jets and strong apparent width evolution. BL Lac objects appear to deviate the strongest from the kinematic paradigm, widely accepted for blazars, of outward superluminally moving jet components. BL Lacs appear to evolve their jet ridge lines (with respect to the core) less than the other source classes, hence indicating a slower apparent flow in their jets. On the other hand, they show significantly apparent wider jets than FSRQs. We have argued that the combination of a helically structured jet (as a universal property of all AGN jets) and projection effects would produce the apparent kinematic properties observed here. Viewing a source at a small angle to its jet axis possibly allows us to uncover this peculiar kinematic behavior that would otherwise be inaccessible at larger viewing angles. This would then imply that BL Lac objects are preferentially seen at smaller viewing angles than FSRQs. Combined with the significant number of (non-BL Lac) CJF\linebreak sources showing evidence that support this different kinematic scheme imply a rather universal effect, rather than something unique to BL Lacs. Finally, it should be noted that the above results underline the fact that the notion of linear, ballistic trajectories for AGN jet components usually employed until recently is a very crude approximation and, more often than not, deviates grossly from the reality. It is of great interest to uncover the physical process that leads to the properties of AGN jet ridge lines as studied in this paper. | 12 | 6 | 1206.4127 |
1206 | 1206.3531_arXiv.txt | {Gamma Ray Burst prompt emission is believed to originate from electrons accelerated in a highly relativistic outflow. ``Internal shocks'' due to collisions between shells ejected by the central engine is a leading candidate for electron acceleration. While synchrotron radiation is generally invoked to interpret prompt gamma-ray emission within the internal shock model, synchrotron self-Compton (SSC) is also considered as a possible candidate of radiation mechanism. In this case, one would expect a synchrotron emission component at low energies, and the naked-eye GRB 080319B has been considered as such an example. In the view that the gamma-ray lightcurve of GRB 080319B is much more variable than its optical counterpart, in this paper we study the relative variability between the synchrotron and SSC components. We develop a ``top-down'' formalism by using observed quantities to infer physical parameters, and subsequently to study the temporal structure of synchrotron and SSC components of a GRB. We complement the formalism with a ``bottom-up'' approach where the synchrotron and SSC lightcurves are calculated through a Monte-Carlo simulations of the internal shock model. Both approaches lead to the same conclusion. Small variations in the synchrotron lightcurve can be only moderately amplified in the SSC lightcurve. The SSC model therefore cannot adequately interpret the gamma-ray emission properties of GRB 080319B. } | \label{Intro} Gamma Ray Burst (GRB) prompt emission lightcurves are complex with superimposed rapid short-scale variabilities. Variabilities of the order of milliseconds in the prompt phase, detected in $\gamma$-rays, were known since the discovery of the earliest GRBs and has led to the subsequent proposal of the ``internal shock'' model, where the energy in the relativistic flow is dissipated through multiple collisions within the ejecta. In the internal shock model \citep{1994ApJ...430L..93R}, the ultra-relativistic outflow from the central engine (ejecta) consists of a succession of shells with random lorentz factors. When a fast moving shell (with lorentz factor $\Gamma_f$) collides with one moving slowly (with $\Gamma_s$) ahead of it, a pair of internal shocks develops which dissipates the kinetic energy in the flow. Each pulse in the burst lightcurve corresponds to one such collision \citep{1997ApJ...490...92K, 2009ApJ...707.1623M}. The physical parameters of the dissipation region, magnetic field and electron distribution, depend on the masses and initial lorentz factors of the colliding shells, and the unknown microphysics of relativistic shocks \citep{1998MNRAS.296..275D}. Hence they vary erratically between collisions and so does the final flux. Almost in all cases, prompt emission has been observed only in the narrow $\gamma$-ray band until very recently. This has limited our understanding of the underlying emission process. Observed spectra suggest that the radiative process is non-thermal. The most likely candidate is synchrotron radiation. Nonetheless, synchrotron self-Compton (SSC) process has been also suggested (e.g. \citep{2000ApJ...544L..17P, 2008MNRAS.384...33K}). For such models, one would expect a synchrotron component peaking in the lower energy band, and prompt optical emission is expected. In recent years, a few rapidly responding GRB-dedicated optical telescopes (e.g. RAPTOR, TORTORA, ROTSE) have become instrumental in detecting optical emission simultaneous to the $\gamma$-ray burst \citep{2005Natur.435..178V, 2006Natur.442..172V}. Most often these detections were limited to a few observations in the entire duration of the burst. Nevertheless, in a few cases a temporal correlation could be established between the optical and the $\gamma$-ray lightcurves, indicative of their possible origin from the same dynamical process \citep{2007ApJ...657..925Y,2007ApJ...663.1125P}. This improved spectral coverage has led to a better understanding of the prompt emission region \citep{2009MNRAS.398.1936S}. The optical flash of GRB080319B seen in unison with the $\gamma$-ray emission was exceptionally bright \citep{2008Natur.455..183R}. Optical prompt emission was observed throughout the entire duration of the $\gamma$-ray component with remarkable time resolution. The onset is simultaneous in both bands and the overall shape of the lightcurves are similar, indicating that emission in the two bands are possibly physically related. Flux in V-band was almost four orders of magnitude higher than the extrapolation of the $\gamma$-ray spectrum, implying that the two lightcurves are likely to have originated from two different emission processes. High and low energy emission tracking each other but belonging to two different radiative processes naturally led to the conjecture that optical prompt emission in GRB080319B is due to synchrotron mechanism in the internal shocks and these photons were up-scattered to the $\gamma$-ray band by the SSC process \citep{2008Natur.455..183R,2008MNRAS.391L..19K}. Despite its advantage of interpreting the rough tracking behavior between the two bands, this model also has several difficulties. For example, a few seconds lag between the two lightcurves is not straightforwardly expected in this model. Several later calculations claimed that the emission radius required under this scenario will be much larger if internal shocks were to occur \citep{2009MNRAS.395..472K,2009ApJ...692L..92Z}. Another drawback of this model is the energy crisis that occurs due to the presence of the bright 2nd order SSC component \citep{2009MNRAS.393.1107P,2009A&A...498..677B,2009ApJ...692L..92Z}. The non-detection of this second SSC bump in the prompt emission spectra as observed by Fermi LAT (e.g. \cite{2009ApJ...706L.138A,2011ApJ...730..141Z}) also places a great constraint on the synchrotron + SSC model. Alternative models to interpret the rough tracking optical/$\gamma$-ray behavior of GRB 080319B have been proposed. \cite{2009PhRvD..79b1301F} advanced the idea of a neutron loaded fireball where both optical and $\gamma$-ray emission are synchrotron in origin but from two different electron populations, one being the original electrons in the plasma while the other originates from the $\beta$-decay process. \cite{2009ApJ...692.1662Y} suggested that a pair of internal forward and reverse shocks could be responsible for the $\gamma$-ray and optical emission respectively. Acknowledging the difficulty of the simplest internal shock SSC model, \cite{2009MNRAS.395..472K} invoked relativistic turbulence to improve the SSC model (cf. \cite{2009ApJ...695L..10L}). One interesting observational feature of GRB 080319B is that its $\gamma$-ray lightcurve is much more variable than its optical counterpart \citep{2008Natur.455..183R}. The time resolution of optical observation is poorer than $\gamma$-rays, but even if one re-bins the $\gamma$-ray lightcurve to the same temporal resolution as the optical lightcurve, the $\gamma$-ray lightcurve still appears much more variable. This feature would give important constraints on the models. For example, the FS/RS internal shock model \citep{2009ApJ...692.1662Y} would predict a similar variability in both the optical and $\gamma$-ray lightcurves, so it cannot interpret the above feature. The two-zone model \citep{2009PhRvD..79b1301F}, on the other hand, is more consistent, since the optical emission is expected to occur at a larger radius, where the angular spreading time is longer. The synchrotron + SSC model \citep{2008MNRAS.391L..19K,2008Natur.455..183R} is more difficult to access since the relative variability between the two emission components has not been studied in the past. In this paper, we study the relative variability within the framework of the synchrotron + SSC model. We approach the problem through two complementary methods. In the `top-down' method, we use the observed optical lightcurve as the input synchrotron component, derive the fluctuations in the underlying physical parameters, and self consistently calculate the SSC lightcurve. In the `bottom-up' method, we follow the standard formalism to simulate the lightcurves in the frame work of the internal shock model. We generate a set of basic physical parameters through Monte-Carlo simulations, calculate both the synchrotron and SSC lightcurves and compare the fluctuations. The aim is to compare the relative variability between the two lightcurves and then address whether the observational features of GRB 080319B can be interpreted. In section-2 and section-3 respectively, we describe our methods and results from the two approaches mentioned above. | 12 | 6 | 1206.3531 |
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1206 | 1206.4916_arXiv.txt | One possible interpretation of the holographic principle is the equality of the number of degrees of freedom in a bulk region of space and the number of degrees of freedom on the boundary surface. It is known that such an equality is maintained on equipotential surfaces in any static spacetime in the form of an equipartition law $\Delta N_{\rm bulk}\equiv[\Delta E/ (1/2)k_B T]= \Delta N_{\rm sur} $. In the cosmological context, the de Sitter universe obeys the same holographic equipartition. I argue that the difference between the surface degrees of freedom and the bulk degrees of freedom in a region of space (which has already emerged) drives the accelerated expansion of the universe through a simple equation $\Delta V = \Delta t (N_{\rm sur} - N_{\rm bulk})$ where $V$ is the Hubble volume in Planck units and $t$ is the cosmic time in Planck units. This equation reproduces the standard evolution of the universe. This approach provides a novel paradigm to study the emergence of space and cosmology, and has far reaching implications. | 12 | 6 | 1206.4916 |
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1206 | 1206.6122_arXiv.txt | The white-light flares observed on the surfaces of UV Ceti-type stars and their process could not be absolutely understood, although these subjects have been heavily studied \citep{Ben10}. In this study, we obtained the largest data set from the observations of DO Cep in the literature. The data are very useful for a statistical analysis of the white-light flare property. Observed star, DO Cep (= Kr\"{u}ger 60B = KR 60B), is classified as a UV Ceti-type star in the SIMBAD database from spectral-type dM4V \citep{Hen02}. The star is a component of HD 239960, which is a visual binary \citep{Lac77, Sod99}. The other component of the binary is GJ 860 A, which classified as dM3V by \citet{Hen02, Tam06}. Unlike DO Cep, GJ 860 A (= KR 60A) is not active as seen from the literature. In the studies of the system, the semi-major axis of the orbit ($a$) was found to be 2.420 $arcsec$, while the orbital inclination ($i$) was calculated as 172 $deg$ by \citet{Sod99}. The orbital period was found to be 44.64 years, while the orbit eccentricity ($e$) was computed as 0.41 in the same study. The distance of the system is given as 4.0 $pc$ by \citet{Pet91}, while it is given as 4.04 $pc$ by \citet{Sch04}. Some basic properties taken from \citep{Lac77} are listed in Table 1 for each component. According to \citet{Vee74}, DO Cep is an old disk star. In fact, taking $M_{bol}=9.72$ mag and $log(T_{eff})=3.525$, its age was computed as about $5.0 \times 10^{8}$ years by \citet{Van83}. The equatorial rotational velocity ($v \sin i$) of DO Cep was found to be 4.7 $kms^{-1}$ by \citet{Gle05, Jen09}. There are several flare patrols for DO Cep in the literature \citep{Har55, Her69, Nic75, Con82}. For the first time, \citet{Har55} suspected that DO Cep is a flare star. Then, \citet{Her69} observed the star along 27.8 hours, and they detected 10 flares. Secondly, \citet{Nic75} detected 22 flares in 57.4 hours flare patrol, while \citet{Con82} detected no flare in 59.13 hours flare patrol. As seen from the literature, DO Cep has a high level flare activity. In this study, DO Cep was observed in $U$-band for flare patrol in 2006 and 2007, and 89 white-light flares were detected. In order to classify the flares detected from DO Cep, the method described by \citet{Dal10} was used. In the literature, there are several studies about classifying the white-light flares \citep{Har69, Osa68, Mof74, Gur88}. The classification of the flare light-variations is important due to modelling these events \citep{Gur88, Ger05}. The white-light flare events were generally classified into two subtypes as slow and fast flares \citep{Har69, Osa68}. However, some studies, such as \citet{Osk69} and \citet{Mof74}, revealed that the white-light flares can be classified in more than two subtypes. \citet{Kun67} revealed that the observed flare light-curves should be a combination of slow and fast flares. Recently, \citet{Dal10} developed a rule to classifying white-light flares. The rule depended on the ratios of flare decay times to flare rise times demonstrates that the flare, whose decay time is 3.5 times longer than its rise time, is a fast flare. If the decay time of a flare is shorter than 3.5 times of its rise time, the flare can be classified as a slow flare. In fact, there are two possible energy sources for the white-light flares \citep{Gur88}. According to the author, the thermal processes are dominant in the slow flare events, while the nonthermal processes are dominant in the fast flare events. A rapid increasing is generally seen in light curves, if the energy source is caused by the nonthermal processes \citep{Ben10, Ger05, Gur88}. Apart from the shapes of the flare light-variations, the upper and lower limits of both flare-power and flare timescales are also important to understand the flare processes occurring on a star. In order to compare the flare-powers of different stars, several studies have been done. In these studies, the flare energy spectra were derived for each star \citep{Ger72, Lac76, Wal81, Ger83, Pet84, Mav86}. According to the results of these studies, the energy levels of stars vary from a star to next one. The variations seem to be caused by different ages of stars. On the other hand, the analyses based on the flare energies could not give the real results. Because the flare energy depends on the luminosity of a star as well as the power of the flare. Thus, if the stars are from different spectral-types, the energies of these flare will be different, even if their real powers are the same. In this respect, the flare-equivalent duration was based on the analyses in this study in order to determined the behaviour of the white-light flares of DO Cep. These method recently developed by \citet{Dal11a} is based on the modelling the distributions of the flare-equivalent durations versus flare total durations. The authors demonstrated that the best function is the one-phase exponential association function (hereafter the OPEA) to model the distribution. As it is seen in the OPEA model, the flare-equivalent durations can not be higher than a specific value, and the flare's total duration does not matter. \citet{Dal11a} defined this level as an indicator for the saturation level for the white-light flare processes. In fact, white-light flares are detected in some large active regions, where compact and two-ribbon flares are occurring on the surface of the Sun \citep{Rod90, Ben10}. It is possibly expected that the energies or the flare-equivalent durations of white-light flares can also reach the saturation. Generally, flare activity seen on the surfaces of dMe stars is modelled concerning the processes of the solar flare event. This is why the magnetic reconnection process is accepted as the source of the energy in these events \citep{Ger05, Hud97}. According to both some models and observations, it is seen that some parameters of magnetic activity can reach the saturation \citep{Ger05, Sku86, Vil83, Vil86, Doy96a, Doy96b}. | \subsection{Flare Activity and Flare Types} In this study, 89 white-light flares were detected in $U$-band observations of DO Cep. 88 flare were detected in 44.85 h flare patrol of 2007, while only one flare was detected in 22.76 h flare patrol of 2006. Therefore, 0.044 flares were detected per hour in 2006, while 3.866 flares were detected per hour in 2007. There is a large difference between the flare frequencies ($N_{2006}$ and $N_{2007}$) of consecutive observing seasons. A large differences between the flare frequencies obtained in different years are also seen in the literature \citep{Her69, Nic75, Con82}. According to the results of \citet{Her69}, $N$ value is 0.360 in 1968. The flare frequency ($N$) is 0.509 flares per hour in 1970, and it is 0.208 flares per hour in the observing season of 1972 - 1973 \citep{Nic75}. However, \citet{Con82} detected no flare in 1975. Consequently, the largest frequency was obtained with 3.866 flares per hour in this study. It seems that DO Cep is active as well as EV Lac, EQ Peg and AD Leo \citep{Mof74, Dal10}. The flare frequency variation of UV Ceti type stars has been examined in several studies \citep{Ish91, Let97}. \citet{Ish91} found no variation for a few stars, while \citet{Let97} demonstrated that the flare frequency of EV Lac is dramatically increasing. It must be noted that DO Cep should be taken to observing programs, because its flare frequency is remarkably varying. The flares detected in this study are examined one by one. The flares, whose rise times are equal, were determined. It was seen that the flares are accumulating into two groups. It was seen that even if the rise times of two flares are equal, their equivalent durations can be different from each other. Apart from their equivalent durations, the main difference between two type flares is light-variation shapes. As seen from Figures 1 - 5, the some flares slowly increase and slowly decrease, while some of them rapidly increase, but slowly decrease. In logarithmic scale, the flare distributions were obtained for both groups. First of all, two group flares were analysed with t-test. Then, they were modelled with the linear function, and the models of two groups were analysed to compare. Using t-test, the averages of equivalent durations for two types of flares were computed. The average of equivalent durations was found to be 1.871 s for the fast flares, and it is 1.544 s for the slow flares. The difference of 0.327 s between these values in the logarithmic scale is equal to the 39.282 s difference between the equivalent durations. As can be seen from equation (2), this difference between average equivalent durations affects the energies in the same way. Therefore, there is 39.282 times difference between the energies of these two types of flares. This difference must be the difference mentioned by \citet{Gur88}. On the other hand, according to \citet{Dal10}, this difference between two flare types is about 157 times. In the case of DO Cep, the energies of the slow and fast flares occurring on the surface of the star seem to be closer to each other. Apart from the average of equivalent durations, the parameters of the linear fits were also compared. The slope of the linear fit is 1.046 for the slow flares, which are low-energy flares, and it is 1.232 for the fast flares, which are high-energy flares. According to the $p-value$, the slopes are almost close to each other. It demonstrates that the flare-equivalent durations versus the flare rise times increase in similar ways for both groups. However, the fast flare (Flare A) seen in Figure 3 is seen out of the general trend of the fast flares. This flare is the most powerful flare detected in the study. It seems to be an extreme example. In the case of the extreme examples, some effects must be involved in the fast flare process towards the long rise times. These effects can make fast flares seem more powerful than they actually are. However, comparing the $y-intercept$ values of the linear fits, it is seen that there is a 0.313 times difference in the logarithmic scale. There is a 0.327 times difference between general averages. Both values are close to each other. It means that the energy emitting processes behave similarly except the extreme flare. Apart from the equivalent durations, the differences between these two flare types are seen in the lengths of their rise times and their amplitudes. The maximum rise time seen among the slow flares is 1164 s, but it is 270 s for fast flares. In addition, the amplitudes of slow flares can reach to 0.791 mag at most, the amplitudes of fast flares can reach to 1.900 mag. \citet{Dal10} computed the ratios of flare decay times to flare rise times for two types of flares. They have demonstrated that there is a limit values between two flare types. This limit value of the ratio of flare decay time to flare rise time is 3.50. In this study, the limit value of this ratio is found to be 3.40 for the flares detected from DO Cep. Providing this limit value between flare types, it was found that the fast flare rate is 20.22$\%$ of the 89 flares observed in this study, while the slow flare rate is 79.78$\%$. It means that one of every five flares is the fast flare, other four flares are the slow flare. This result is close to what \citet{Gur88} stated. According to \citet{Gur88}, slow flares with low energies and low amplitudes make up 95$\%$ of all flares, and the remainder are fast flares. \subsection{The Saturation Level in the Detected White-Light Flare} The distributions of flare-equivalent durations versus flare total duration were modelled by the OPEA function expressed by equation (6) for 89 white-light flares detected in observations of DO Cep. To model the distribution, the best model curve was searched. Considering $p-value$ and the correlation coefficient ($r^{2}$) parameters, the OPEA function was found as the best model function. The main characteristic feature of the OPEA is that this function has a $plateau$ phase. According to the observations, the flare-equivalent durations increase with the flare total duration until a specific total duration value. After the specific total duration, the flare-equivalent durations are constant, and the total duration does not matter. There is just one flare among all of them. This flare is Flare A seen in Figure 3. It must be an extreme sample. Some parameters such as $plateau$ value, $half-life$, etc., were derived from the OPEA model. The $plateau$ value was found to be 2.810. The value is in agreement with the mean average of the equivalent durations. It had been found to be 2.808. Considering the standard deviations of two values, they can be assumed to be equal. Besides, the found $plateau$ value is also in agreement with the $plateau$ values found from other stars by \citet{Dal11a}. According to the $B-V$ colour index of DO Cep, it is seen that the star is among its analogues. This result supports that the upper limit of the energy producing by white-light flare mechanism really increase towards the later spectral types. It is well known that the white-light flares occur in the regions, where the compact and two-ribbon flare events are seen \citep{Rod90, Ben10}. In the analyses, the flare-equivalent durations were used instead of the flare energies. In fact, the derived $plateau$ values depend only on the power of the white-light flares. According to observations, the $plateau$ phase exists in the model. The flare-equivalent durations can not be higher than a particular value, and the flare's total duration does not matter. Apart from the timescales, the power of the flares must depend on some other parameters, such as magnetic field flux and/or particle density in the volumes of the flare processes. However, \citet{Doy96a} and \citet{Doy96b} suggested that the saturation in the active stars does not have to be related to the filling factor of magnetic structures on the stellar surfaces or the dynamo mechanism under the surface. It can be related to some radiative losses in the chromosphere, where the temperature and density are increasing in the case of fast rotation. This phenomenon can occur in the chromosphere due to the flare process instead of fast rotation, and this causes the $plateau$ phase to occur in the distributions of flare-equivalent duration versus flare total duration. On the other hand, the $plateau$ phase cannot be due to some radiative losses in the chromosphere with increasing temperature and density. This is because \citet{Gri83} demonstrated the effects of radiative losses in the chromosphere on the white-light photometry of the flares. According to \citet{Gri83}, the negative H opacity in the chromosphere causes the radiative losses, and these are seen as pre-flare dip in the light curves of the white-light flares. Unfortunately, considering the results of \citet{Dal11a}, it is seen that the $plateau$ values vary from one star to the next. This indicates that some parameters or their efficacies, which make the $plateau$ increase, are changing from star to star. According to Standard Magnetic Reconnection Model developed by \citet{Pet64}, there are several important parameters giving shape to flare events, such as Alfv\'{e}n velocity ($\nu_{A}$), $B$, the emissivity of the plasma ($R$) and the most important one, the electron density of the plasma ($n_{e}$) \citep{VanB88, VanA88}. All these parameters are related with both heating and cooling processes in a flare event. \citet{VanA88, VanB88} have defined the radiative loss timescale ($\tau_{d}$) as $E_{th}/R$. Here $E_{th}$ is the total thermal energy, while $R$ is emissivity of the plasma. $E_{th}$ depends on the magnetic energy, which is defined as $B^{2}/8\pi$, and $R$ depends on the electron density ($n_{e}$) of the plasma. $\tau_{d}$ is firmly correlated with $B$ and $n_{e}$, while $\tau_{r}$ is proportional to a larger loop length ($\ell$) and smaller $B$ values. Consequently, it is seen that both the shape and power of a flare event depend on mainly two parameters, $n_{e}$ and $B$. As seen from the OPEA model, the flare-equivalent durations start to reach maximum value in a specific total duration, and the $half-life$ value was found to be 433.1 s from the model. In addition, the maximum flare rise time was found to be 1164 s, while the maximum flare total duration was found to be 3472 s. These results demonstrated that the flare timescales of the flares detected from DO Cep are in fact shorter than they are in the earlier spectral types. However, the flares get the maximum energy limits in longer times. It is well known from the X-Ray observations of the flares that the timescales of the X-Ray flares give some clues about the flaring loop geometry on the stars \citep{Ree02, Ima03, Fav05, Pan08}. The white-light flares can exhibit the same behaviour with its counterpart observed in X-Ray \citep{Ger05, Ben10}. If this case is valid, the timescales derived from the white-light flares can also give some clues about the the flaring loop geometry or the flaring area geometry (at least for the photosphere). The obtained timescales from the observations of DO Cep demonstrated that the flaring loop or area are smaller than those seen on the stars from the earlier spectral types. Because, the obtained maximum flare duration for DO Cep flares is 3472 s. The observed maximum duration is 5236 s for V1005 Ori, and 4164 s for AD Leo \citep{Dal11a}. The flare timescales of both stars are dramatically longer than that of DO Cep. However, considering the $half-life$ value, the flares detected from DO Cep get maximum energy in longer times, while the geometries of flaring loops or areas get smaller. | 12 | 6 | 1206.6122 |
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1206 | 1206.4311_arXiv.txt | To investigate possible variations in the stellar initial mass function (IMF) in red-sequence galaxies, we have obtained infrared spectroscopy with Subaru/FMOS for a sample of 92 red-sequence galaxies in the Coma cluster. Velocity dispersions, ages and element abundances for these galaxies have been previously determined from optical data. The full range of velocity dispersions covered by the sample is $\sigma$\,=\,50--300\,\kms. By stacking the FMOS spectra in the rest frame, removing sky-subtraction residuals and other artefacts fixed in the observed frame, we derive composite spectra in the 9600--10500\,\AA\ range for galaxies grouped according to their velocity dispersion or Mg/Fe ratio. We measure the Wing--Ford band of FeH and a new index centred on a Ca{\,\sc i} line at 10345\,\AA; these features are strong in cool dwarf stars, and hence reflect the form of the IMF at low mass ( $<$\,0.5\,$M_\odot$). The Ca{\,\sc i} line, unlike the Wing--Ford band and other ``classical'' IMF indicators (Na{\,\sc i} doublet, Ca{\,\sc ii} triplet), is unaffected by the abundance of sodium. We compare the measured indices against predictions from spectral synthesis models matched to the element abundances estimated from the optical data. Binning galaxies by velocity dispersion, we find that both the Wing--Ford and Ca{\,\sc i} index measurements are best reproduced by models with the Salpeter IMF. There is no clear evidence for an increase in dwarf-star content with velocity dispersion over the range probed by our sample (which includes few galaxies at the highest velocity dispersions, $\sigma>250$\,\kms). Binning the observed galaxies instead by Mg/Fe ratio, the behaviour of both indices implies a trend of IMF from Chabrier-like, at abundance ratios close to solar, to Salpeter or heavier for highly $\alpha$-enhanced populations. At face value, this suggests that the IMF depends on the mode of star formation, with intense rapid star-bursts generating a larger population of low-mass stars. | \label{sec:intro} The stellar initial mass function (IMF) is a crucial ingredient in interpreting extragalactic observations: without constraints, or assumptions, for the IMF, observed luminosities cannot be converted into estimates of assembled stellar mass. For old galaxies with a Salpeter (1955) IMF, the great majority of output luminosity is contributed by giant-branch and main-sequence stars with mass $\sim$1$M_\odot$. However, some 80 per cent of the stellar mass is locked up in cool dwarfs with mass $<$0.5$M_\odot$, which collectively provide less than ten per cent of the bolometric luminosity. The total stellar mass-to-light ratio is hence very sensitive to the form of the IMF at low masses. In the Milky Way, resolved star counts indicate that the IMF follows a Salpeter-like power law ${\rm d}N(M)$\,$\propto$\,$M^{-2.35}{\rm d}M$ for $M$\,$\ga$\,$M_\odot$, but becomes shallower at lower masses. This form can be well represented either by a broken power law (e.g Kroupa, Tout \& Gilmore 1993), or by a log-normal distribution (Chabrier 2003). Extensive searches for variation in the IMF in different environments within the Milky Way have not found conclusive evidence for non-universality (e.g. see the review by Bastian, Covey \& Meyer 2010). For extragalactic systems, low-mass stars are not directly observable, and the application of a Chabrier-like IMF to distant galaxies must be regarded with caution until empirically tested. Limits on the contribution of dwarf stars to the mass budget can be inferred from total mass estimates from dynamical modelling (e.g. Bell \& de Jong 2001; Cappellari et al. 2012) or gravitational lensing (e.g. Treu et al. 2010), but this approach cannot unambiguously discriminate dark mass in cool dwarfs (bottom-heavy IMF) from that in stellar remnants (top-heavy IMF) or in non-baryonic dark matter. An alternative method to constrain the mass locked in low-mass stars is to exploit stellar spectral features that depend strongly on surface gravity, and hence distinguish giant from dwarf stars at similar effective temperature. In particular, red-optical and near-infrared spectral features that are strong in M-dwarfs and not present in cool giants (or vice versa) can potentially discriminate the low-mass stellar content in unresolved galaxies. The Wing--Ford band (WFB) of FeH at 9915\,\AA\ (Wing \& Ford 1969) and the Na\,{\sc i} doublet (8190\,\AA) were identified as possible giant-to-dwarf star indicators and exploited in early works (e.g. Spinrad \& Taylor 1971; Whitford 1977; Cohen 1978; Faber \& French 1980; Carter, Visvanathan \& Pickles 1986; Couture \& Hardy 1993). Some of these papers (e.g. Spinrad \& Taylor, Faber \& French, both based on Na{\,\sc i}) suggested a substantial fractional contribution of dwarf stars to the integrated light of nearby galaxies, while others (e.g. Whitford, based on the WFB) inferred a much lower dwarf-to-giant ratio. Similarly, Carter et al. reported tension between the two indicators for a sample of 14 galaxies, with Na{\,\sc i} requiring a larger fraction of dwarf light than the WFB. The work of the 1970s--1990s was hampered by the limitations of spectral synthesis models at that time. In particular, there were no large empirical infrared stellar libraries covering the full range of spectral types relevant to the problem. Moreover, knowledge of the range of elemental abundance variations in galaxies was not yet well constrained; nor was the machinery required to account for such variations through synthetic spectral modelling yet developed. Emphasis in the study of the IMF from resolved populations shifted somewhat to the Ca\,{\sc ii} triplet (which is strong in giants and weak in dwarfs), with Cenarro et al. (1993) concluding that either calcium was underabundant in giant ellipticals or that a dwarf-enriched IMF was required. A new impetus was given to such studies by the publication of the IRTF spectral library by Rayner, Cushing \& Vacca (2009), which finally provided empirical library spectra for cool stars across the red/infrared regime. Building models from these stars to predict the integrated spectra of old populations, and comparing them to observations of eight giant elliptical galaxies, van Dokkum \& Conroy (2010) argued that a strongly dwarf-enriched IMF was required to account for the strength of the Na{\,\sc i} and (to a lesser extend) the WFB. Their spectra could be fit only by adopting very bottom-heavy IMFs, e.g. a power law with exponent $x$\.=\,3 (where ${\rm d}N(M)$\,$\propto$\,$M^{-x}{\rm d}M$), in which a majority of the mass is in $\la$0.15$\,M_\odot$ stars with $T_{\rm eff}\la3000$\,K. The stellar mass-to-light ratio $M_*/L$ for the IMF favoured by van Dokkum \& Conroy is a factor of 3--4 times larger than the Chabrier-like IMF often assumed in extra-galactic contexts. Hence verifying this result, and determining the types of galaxies affected, has wide implications. Conroy \& van Dokkum (2012a, hereafter CvD12a) have since generalized their spectral synthesis models to make predictions for simple stellar populations (SSPs) with a range of IMFs, ages, metallicities and abundance ratio patterns. Spurred in part by the original van Dokkum \& Conroy (2010) result, several groups have recently investigated the behaviour of IMF-sensitive indices in larger galaxy samples. Spiniello et al. (2012) studied the Na{\,\sc i} doublet in luminous red galaxies from the Sloan Digital Sky Survey (SDSS) with velocity dispersions $\sigma$=200--335\,\kms), finding this feature to increase with $\sigma$, requiring an steepening IMF or an increase in Na/Fe enhancement (or both), with increasing galaxy mass. Subsequently, Conroy \& van Dokkum have analysed new high-S/N spectroscopy including the WFB, the Na\,{\sc i} doublet and the Ca\,{\sc ii} triplet, as well as blue/optical features, for a sample of 38 nearby galaxies (van Dokkum \& Conroy 2012; Conroy \& van Dokkum 2012b, the latter CvD12b hereafter). In this work, they apply a sophisticated full-spectrum fitting method with many model components to describe abundance variations and possible confounding parameters. They conclude that dwarf-enrichment increases with velocity dispersion and (perhaps more strongly) with [Mg/Fe], ranging from Chabrier-like to heavier-than-Salpeter IMFs. Although all three of the ``classical'' indicators employed in this work seem to support dwarf-enriched IMFs in the most massive ellipticals, the details depend on which spectral features are included in the fit. Perhaps to compensate for this tension, the models require enhancements of Na/Fe by up to an order of magnitude over the solar ratio. Most recently, Ferreras et al. (2012) used a very large sample of SDSS early-type galaxies to confirm the strong increase in Na{\,\sc i} with velocity dispersion in the $\sigma$\,=\,100--300\,\kms\ range, interpreting the results as a steepening of the IMF slope. (They did not explicitly consider the effects of Na/Fe variations.) For all but the most nearby galaxies, the Wing--Ford band is redshifted beyond the limits of current ``optical'' CCDs, and infrared detectors are required. In this paper we present new observations of the Wing--Ford band for red-sequence galaxies in the Coma cluster, using the infrared Fibre Multi-Object Spectrograph (FMOS; Kimura et al. 2010) at the 8.2m Subaru telescope on Mauna Kea. Although galaxies at the distance of Coma are individually fainter than those studied by Conroy \& van Dokkum (2012b), we can exploit the dense concentration of galaxies in the cluster, and the multiplex capability of FMOS, to observe dozens of galaxies simultaneously. Because the Coma galaxies have a range of radial velocities due to their motions within the cluster potential, stacking their spectra in the rest-frame allows rejection of pixels contaminated by OH sky-line residuals and other artefacts fixed in the observed wavelength frame. Our galaxy sample spans a range in velocity dispersion and other properties, derived in previous work from optical spectroscopy (Price et al. 2011; Smith et al. 2012), so that we can explore possible variations in the IMF with galaxy mass and control for element abundance effects. Besides the WFB, our spectral range also includes a Ca{\,\sc i} line which we exploit as an IMF indicator for the first time. The outline of this paper is as follows. Section~\ref{sec:obs} describes the observations and data reduction. The construction of composite spectra is detailed in Section~\ref{sec:compo}. The results are presented in Section~\ref{sec:results}, starting with the global composite spectrum (Section~\ref{sec:globalcomp}), the measurement of spectral indices and their comparison to model predictions (Section~\ref{sec:indices}), and then dividing the sample into four bins in velocity dispersion (Section~\ref{sec:sigmabin}) and Mg/Fe ratio (Section~\ref{sec:mgfebin}), to explore the dependence of the IMF on mass and star-formation timescale. In Section~\ref{sec:discuss}, we discuss our results in the context of relevant recent work, and summarize our conclusions in Section~\ref{sec:concs}. \begin{figure*} \includegraphics[angle=270,width=178mm]{compo_fullwav.eps} \caption{Composite spectrum constructed from the 59 observed galaxies with $\sigma$\,$>$\,100\,\kms\ (top, black). The lower spectra show SSP models from CvD12a, with different IMFs, smoothed to match the effective velocity dispersion of the stacked data. The $x$\,=\,3.5 IMF is extremely bottom-heavy and is plotted here to emphasize the IMF dependence of the WFB and Ca{\,\sc i} line. Subsequent figures show only on the rest-frame 9600--10500\,\AA\ region (white background) where the atmospheric transmission is clean and which includes the IMF-sensitive spectral features. For reference, we show a gaussian profile representing the shifts induced by the velocity dispersion within the cluster; any residual sky-subtraction artefacts are effectively smoothed over this scale in the composite spectrum.} \label{fig:compo_fullwav} \end{figure*} | \label{sec:concs} We have presented new infrared spectroscopy for red-sequence galaxies in Coma, and measured gravity-sensitive absorption features to probe their low-mass stellar content. Compared to other recent work in this field, our study differs in targetting cluster galaxies, and in sampling ``typical'' red-sequence galaxies, rather than only the most massive objects. By comparing line-strength indices against state-of-the-art spectral synthesis models, tuned to match element abundances estimated from optical data, we derive constraints on the average IMF and its variation with velocity dispersion and $\alpha$-abundance ratio. Our main conclusions are as follows: \begin{itemize} \item The average rest-frame 1$\mu$m spectra for sizable samples of galaxies at the distance of Coma can be recovered with Subaru/FMOS, thanks to its wide-field multiplex capability which is currently unique in the infrared. \item The observed spectral features are generally in good qualitative agreement with the latest stellar libraries and synthesis models, although some localised discrepancies are seen. \item The Ca{\,\sc i} line at 10345\,\AA\ is promising as a new gravity-sensitive feature, which unlike the ``classical'' IMF indicators is independent of the sodium abundance. \item The strength of the Wing--Ford band and Ca{\,\sc i} 10345\,\AA\ line indicate that red-sequence galaxies in Coma have (on average) a dwarf-star content similar to that in a Salpeter IMF. \item There is no clear trend in the derived IMF as a function of velocity dispersion, with Salpeter models an adequate fit from $\sigma$\,$\approx$\,100\,\kms\ to $\sigma$\,$\approx$\,250\,\kms. \item A more dwarf-dominated IMF cannot be ruled out at the highest velocity dispersions ($\sigma$\,$\ga$\,300\,\kms), which are not well sampled by our observations. \item The derived IMF is correlated with Mg/Fe ratio suggesting that galaxies which underwent intense rapid starbursts formed a larger number of low-mass stars per solar-mass star. \end{itemize} Our work adds to a developing consensus that massive red-sequence galaxies have heavier IMFs, with a greater contribution from low-mass stars, than found in the Milky Way. A Salpeter-like IMF is favoured by recent spectroscopic (CvD12b; Spiniello et al. 2012; Ferreras et al. 2012; this work), dynamical (Thomas et al. 2011; Cappellari et al. 2012) and lensing analyses (Spiniello et al. 2011; Sonnenfeld et al. 2012). For spiral galaxies, in contrast, recent lensing results are consistent with Chabrier-like IMFs similar to the Milky Way (Brewer et al. 2012), consistent with earlier dynamical results (Bell \& de Jong 2001). Together with the apparent correlation of dwarf-star content with Mg/Fe ratio found here and in CvD12c, these results strongly suggest that the low-mass IMF may be dictated in part by the dominant mode of star-formation: quiescent star formation yields Kroupa-like IMF, while star-bursts lead to an excess of low-mass stars. | 12 | 6 | 1206.4311 |
1206 | 1206.6252_arXiv.txt | {\object{HD 327083} is a supergiant B[e] star that forms a binary system with an orbital semi-major axis of approximately 1.7~AU.} {Our previous observations using the VLTI and AMBER in the medium resolution $K-$band mode spatially resolved the environment of HD 327083. The continuum visibilities obtained indicate the presence of a circumbinary disc. CO bandhead emission was also observed. However, due to the limited spectral resolution of the previous observations, the kinematic structure of the emitting material could not be constrained. In this paper, we address this and probe the source of the CO emission with high spectral resolution and spatial precision.} {To determine the properties and kinematics of its CO emitting region, we have observed HD~327083 with high spectral resolution (25 \& 6~$\mathrm{km\,s^{-1}}$) using AMBER and CRIRES. The observations are compared to kinematical models to constrain the source of the emission.} {The multi-epoch AMBER spectra obtained over 5~months contain no evidence that the CO $\mathrm{1^{st}}$ overtone emission of HD~327083 is variable. This indicates that the structure of the emitting region is not strongly dependent on orbital phase. It is shown that the CO bandhead emission can be reproduced using a model of a Keplerian disc with an inclination and size consistent with our previous VLTI observations. The model is compared to AMBER differential phase measurements, which have a precision as high as $\sim$30~$\mu$as. A differential phase signal corresponding to 0.15~mas ($\sim$5~$\sigma$) is seen over the bandhead emission, which is in excellent agreement with the model that fits the CRIRES observations. In comparison, a model of an equatorial outflow, as envisaged in the standard sgB[e] scenario, does not reproduce the observations well.} {We present a direct test of the circumstellar kinematics of the binary sgB[e] star HD 327083 using both spatial and spectral information. The excellent agreement between the disc model and observations in the spatial and spectral domains is compelling evidence that the CO bandhead emission of HD~327083 originates in a circumbinary Keplerian disc. In contrast, the model of an equatorial outflow cannot reproduce the observations well. This suggests that the standard sgB[e] scenario is not applicable to HD~327083, which supports the hypothesis that the B[e] behaviour of HD~327083 is due to binarity.} | Massive stars play a crucial role in multiple areas of astrophysics. As a result, a complete understanding of many astrophysical phenomena requires an understanding of the evolution of massive stars. In turn, this requires knowledge of how massive stars lose mass \citep[see e.g.][]{Puls2008}. Supergiant B[e] {{(sgB[e])}} stars are important objects in this regard as they are massive objects in a late evolutionary stage which also exhibit signs of enhanced mass loss \citep[see e.g.][]{Lamers1998}. In addition, it has been suggested that there could be an evolutionary link between sgB[e] stars and the luminous blue variables \citep[LBVs,][]{Zickgraf2006}. In turn, LBVs are generally thought to be the precursors of the Wolf-Rayet stars; the final phase in massive star evolution \citep[see e.g.][]{Jorick_lbv}. Therefore, the asymmetric geometries that are required to produce phenomena such as gamma ray bursts may be constructed in the sgB[e] stage. Consequently, it is important to study the circumstellar geometry of sgB[e] stars and determine what is responsible for their mass loss. \smallskip With this in mind, we recently studied the sgB[e] star HD~327083 with the VLTI and AMBER in the medium resolution $K-$band mode \citep[see][hereafter W12]{Me_HD_327083_1}. High spatial resolution observations were required to probe the geometry of the object's circumstellar environment on milli-arcsecond scales. In turn, this was necessary to elucidate the ``bracket'' behaviour of HD~327083, for which there have been several hypotheses. On the basis of a comparison between optical spectroscopy and a NLTE model of an expanding atmosphere, \citet{Machado2003} suggest that the object may be close to the {{LBV phase}}. This would make it a key object to study the link, if any, between the sgB[e] and LBVs. However, there is an alternative hypothesis. \citet[][hereafter M2003]{Miro2003} detected an unresolved binary companion via radial velocity variations. Based on the relatively short period of the variations, $\sim$6~months, these authors suggest that the system is close enough to interact. In this case, the material traced by the object's infrared excess may be mass lost as the result of binary interactions, as proposed for other objects showing the B[e] phenomenon \citep[see][]{Millour2009,Millour2011,Kraus_v921_2012}. \smallskip We now briefly summarise the results from W12. Our observations with the VLTI and AMBER spatially resolved the material responsible for the $K-$band excess of HD~327083. Using simple geometrical models, we found that the continuum visibilities could be reproduced by an elongated ring with a central radius of approximately 6.6~AU. The location of this ring is consistent with the expected dust sublimation radius of a star with the stellar parameters reported by M2003; $6<R_{\rm{sub}}<25$~AU using the standard equation \citep[see][]{Monnier2002}. A non-zero closure phase was observed over the continuum emission and this was attributed to the binary companion. The closure phase suggested that the companion should be located within the elongated ring. Therefore, the geometrical model was associated with the inner rim of a dusty, circumbinary disc. Such a configuration is more reminiscent of mass lost as the result of binary interactions \citep[see e.g.][]{Millour2011} than intrinsic mass loss via an equatorial outflow, as depicted in the standard sgB[e] scenario \citep[see e.g.][]{Zickgraf1985}. Therefore, the observations to date favour the interacting binary hypothesis. \smallskip Probing the mass loss process of the system further requires constraining the kinematics of the circumbinary material and the conditions that give rise to the occurrence of the B[e] phenomenon. Such constraints can be determined from spectrally resolved observations of CO bandhead emission. Therefore, we obtained new high spectral resolution (25 \& 6~$\mathrm{km\,s^{-1}}$) observations of HD~327083's CO bandhead emission with AMBER and CRIRES. Here we present these observations, which provide sub-milli-arcsecond precision constraints on the geometry of the emitting material. The CO bandhead emission of HD~327083, initially observed by \citet{McGregor1988}, is spectrally resolved for the first time and we observe a differential phase signature over the emission. This paper presents the observations and modelling of the CO emitting material, and it is structured as follows. In Sect. \ref{obs_and_data} we describe the observations and subsequent data reduction. We present the observational results in Sect. \ref{res}. These are then analysed and modelled in Sect. \ref{ana} and the implications are discussed in Sect. \ref{disc}. The conclusions are presented in Sect. \ref{conc}. | \label{conc} This paper presents high spectral resolution (25 \& 6~$\mathrm{km\,s^{-1}}$) AMBER and CRIRES observations of the supergiant B[e] star HD~327083. The observations spectrally resolve the CO bandhead emission of this object for the first time and provide new insights into its immediate environment. Here we list the key results. \begin{itemize} \item[--]{We find no evidence that the CO bandhead emission of HD~327083 is variable. Since the observations span the majority of the estimated period of the binary system, this suggests that the structure of the CO emitting region is not strongly dependent on orbital phase.} \item[--]{The CRIRES observations of HD~327083's CO $\mathrm{1^{st}}$ overtone bandhead emission are fit to an excellent degree by a model of a Keplerian rotating disc.} \item[--]{A differential phase signature corresponding to a photo-centre displacement of $\sim$0.15~mas is observed. This is well reproduced by the same model that fits the high spectral resolution CRIRES spectrum. The agreement between the model and observations in both the spatial and spectral domains is compelling evidence that the CO emission of HD~327083 originates in a Keplerian disc.} \item[--]{The inner edge of the best fitting CO disc is approximately 3$\pm$0.3~AU. This places it interior to the previously detected continuum emitting disc (which has an inner radius of approximately 5~AU), but is sufficiently large for the CO emitting disc to be circumbinary.} \item[--]{We show that a model of an equatorial outflow cannot reproduce the data as well as the Keplerian disc model. This suggests that the standard sgB[e] scenario is not applicable to HD~327083, which supports the hypothesis that the B[e] behaviour of HD~327083 is due to binarity.} \end{itemize} | 12 | 6 | 1206.6252 |
1206 | 1206.2647_arXiv.txt | We investigate the evolution of the surface density of a circumbinary accretion disc after the mass loss induced by the merger of two supermassive black holes. We first introduce an analytical model, under the assumption of a disc composed of test particles, to derive the surface density evolution of the disc following the mass loss. The model predicts the formation of sharp density peaks in the disc; the model also allows us to compute the typical timescale for the formation of these peaks. To test and validate the model, we run numerical simulations of the process using the Smoothed Particle Hydrodynamics (SPH) code PHANTOM, taking fluid effects into account. We find good agreement in the shape and position of the peaks between the model and the simulations. In a fluid disc, however, the epicyclic oscillations induced by the mass loss can dissipate, and only some of the predicted peaks form in the simulation. To quantify how fast this dissipation proceeds, we introduce an appropriate parameter, and we show that it is effective in explaining the differences between the analytical, collisionless model and a real fluid disc. | Supermassive black holes (SMBHs) are hosted in the nuclei of most galaxies \citep{1995ARA&A..33..581K}. If two host galaxies merge, as predicted by hierarchical galaxy formation models, the two black holes can form a supermassive black hole binary \citep{1980Natur.287..307B} via dynamical friction. Mergers of gas rich galaxies also drive a large quantity of gas in the centre, potentially forming massive, rotationally supported disc \citep{2005ApJ...630..152E,2007MNRAS.379..956D}. If this gas can cool efficiently, it settles into a thin accretion disc surrounding the black hole binary. If the binary hardens up to sub-parsec scales through gravitational slingshot ejection of stars \citep{2003ApJ...596..860M} or other processes, such as the interactions with a gaseous accretion disc \citep{1999MNRAS.307...79I,2009MNRAS.398.1392L,2011MNRAS.412.1591N}, eventually gravitational waves (GW; \citealt{PhysRev.136.B1224}) will carry away the remaining orbital energy and induce the coalescence in less than a Hubble time. The detection of these GWs is expected by proposed experiments such as the \emph{Laser Interferometer Space Antenna (LISA)}. General relativity predicts \citep{2005PhRvL..95l1101P,2006PhRvD..74d1501C,2008PhRvD..78h1501T} that the gravitational waves emitted during the merger of the black holes carry away energy and momentum, thus resulting in a \emph{mass loss} and in a \emph{recoil} of the remnant black hole. Many authors \citep[e.g.][]{2008ApJ...684..835S,2010MNRAS.401.2021R,2010MNRAS.404..947C,2010A&A...523A...8Z} have explored the second possibility, with the final aim of predicting an electromagnetic (EM) afterglow of the coalescence. The detection of such an afterglow would help in constraining the properties of the merged black holes and of the host galaxies. In this paper we explore the first possibility, studying the response of the accretion disc to the mass loss. For the rest of this paper, we neglect the effect of recoil. Previous work for this physical case have been done by \citet{2009PhRvD..80b4012M,2009ApJ...700..859O,2010MNRAS.404..947C} by means of numerical simulations. In the present paper, we present an analytical model for the surface density evolution of the disc following the merger, derived under the assumption of a collisionless disc. To assess the validity of our model, we compare it with the outcome of 3D numerical hydrodynamical simulations, using the Smoothed Particle Hydrodynamics (SPH) code \textsc{phantom} \citep{2010MNRAS.406.1659P,lodatoprice2010}. The geometry of the accretion disc before the merger has been discussed by \citet{2002ApJ...567L...9A} and by \citet{2005ApJ...622L..93M}. We assume that the plane of the disc coincides with the orbital plane of the binary \citep{1997MNRAS.285..288L,1999MNRAS.307...79I}. For such a configuration, the secondary black hole will open a gap \citep{1994ApJ...421..651A} in the disc, creating a hollowed region of size approximately $2a$, where $a$ is the semi-major axis of the binary. The evolution of the system will then progress at the viscous timescale, the disc and the binary being in contact due to tidal interactions. When the gravitational wave emission sets in, the structure of the circumbinary disc and of the binary rapidly decouple, and the coalescence occurs on a very fast timescale compared to the disc dynamical one. We can then assume that at the moment immediately preceding the merger the disc is in rotation around a point mass, whose magnitude is given by the total mass of the binary. For our purposes, the merger of the two black holes can be described as an instantaneous reduction of the mass of the central object. The paper is organised as follows. In Section 2, we derive an analytical model for the evolution of the surface density of the disc after the merger, and thus the mass loss, occurs. The model is then compared with numerical simulations, described in Section 3; we present our results in section 4. Finally, in Section 5, we draw our conclusions. | In this paper, we have investigated the evolution of the dynamics of an accretion disc after the massloss of two merging black holes. Under the assumption of a disc composed of test particles, we were able to derive an analytical model for the surface density evolution of the disc following the mass loss. The model predicts the formation of sharp density peaks in the disc. Once formed, these peaks travel outwards. However, we showed that they are not a type of hydrodynamical wave, but rather follow only from the kinematics of the disc. We derived also a timescale for the formation of these peaks, finding it of the same order of magnitude as previous findings. However, our model is fully time-dependent. To test the validity of our model, we set up numerical simulations, capable of taking into account the full hydrodynamics of the gaseous disc, using the SPH code PHANTOM. We found a good agreement in the shape and position of the peaks between the model and the simulations. There are however small differences, depending on the disc parameters, in the position and shape of the peaks from the model predictions. To account for these discrepancies, we introduced the $\mathcal{M}_\epsilon$ parameter. We showed that lower values of this parameter correspond to discs that deviate more strongly from the analytical model, because hydrodynamical effects are more important. We also showed that the timescale introduced is effective in predicting the formation of the density peaks. In the fluid disc, after some of the density peaks have formed, the epicyclic oscillations dissipate, thus causing the inner disc, where the dynamical timescales are faster, to significantly differ from the analytical model. We showed that the $\mathcal{M}_\epsilon$ parameter is also effective in explaining how fast this dissipation proceeds, that is, how many peaks form in the disc. In our work we did not consider the radiation emitted by the fluid. We modelled two limiting cases, using an isothermal and an adiabatic equation of state, accounting for a very fast cooling timescale and a very long one, respectively. Further work is needed to quantify in which physical regime real discs lie. | 12 | 6 | 1206.2647 |
1206 | 1206.3312.txt | Rotation is expected to have an important influence on the structure and the evolution of stars. However, the mechanisms of angular momentum transport in stars remain theoretically uncertain and very complex to take into account in stellar models. To achieve a better understanding of these processes, we desperately need observational constraints on the internal rotation of stars, which until very recently were restricted to the Sun. In this paper, we report the detection of mixed modes --- i.e. modes that behave both as g modes in the core and as p modes in the envelope --- in the spectrum of the early red giant \cible, which was observed during one year with the \textit{Kepler} spacecraft. By performing an analysis of the oscillation spectrum of the star, we show that its non-radial modes are clearly split by stellar rotation and we are able to determine precisely the rotational splittings of 18 modes. We then find a stellar model that reproduces very well the observed atmospheric and seismic properties of the star. We use this model to perform inversions of the internal rotation profile of the star, which enables us to show that the core of the star is rotating at least five times faster than the envelope. This will shed new light on the processes of transport of angular momentum in stars. In particular, this result can be used to place constraints on the angular momentum coupling between the core and the envelope of early red giants, which could help us discriminate between the theories that have been proposed over the last decades. | Understanding the effects of rotation on stars is currently one of the key steps to making progress in stellar modeling. Angular momentum transport plays a central role in star and planet formation (see \citealt{bodenheimer95} and \citealt{bouvier08}, respectively). Stellar rotation is intimately linked with the star formation process. The distribution of main sequence rotation rates in stars indeed arises from the hydrodynamic assembly phase and the subsequent interaction of protostars and their accretion disks (\citealt{shu94}). Rotation also impacts stellar structure and evolution by inducing a mixing of the chemical elements inside stars. Meridional circulation is expected on general grounds in rotating stars (\citealt{eddington26}, \citealt{mestel53}, \citealt{mathis04}), and internal shears can generate hydrodynamic instabilities (see \citealt{maeder00}, \citealt{pinsonneault97} for reviews on mixing in high and low-mass stars, respectively). Despite its importance, very little is currently known about the internal rotation of stars, the timescales over which it is modified, or the major mechanisms responsible for doing so. The theoretical problem is complex because rotation, convection, and magnetism are intricately tied to one another. Three classes of mechanisms --- hydrodynamic, wave-driven (\citealt{charbonnel05}, \citealt{mathis08}, \citealt{mathis09}), or magnetic (\citealt{gough98}, \citealt{spruit99}, \citealt{spada10}) --- could transport angular momentum or induce mixing, and their relative importance is a matter of active debate. To understand the mechanisms of angular momentum transport in stars better, observational data on stellar rotation are needed. Unfortunately, in most cases these are limited to observations of surface rotation. Seismology is currently the only tool that allows us to probe the internal rotation profiles of stars through the detection of rotational splittings of mode frequencies. Observations of solar p-mode splittings have established that the convective envelope of the Sun is in mild differential rotation, whereas the radiative interior rotates as a solid body down to about 0.2 $R_\odot$ (e.g., \citealt{schou98}). This discovery revolutionized our understanding of the solar interior and raised some questions, such as the thinness of the solar tachochline (\citealt{spiegel92}), that are still open. It also showed that although rotational mixing processes have been successful in reproducing the observations for massive and intermediate-mass stars (\citealt{talon97}, \citealt{maeder00}), they predict a solar core rotation rate that is too fast (\citealt{pinsonneault89}). As a result, other more powerful transport processes, such as internal gravity waves (\citealt{charbonnel05}) or magnetic fields (\citealt{gough98}), have to be invoked. However, the Sun alone cannot give us information about the timescale for effective angular momentum transport in stellar interiors. Indirect methods, involving the evolution of surface rotation in stellar populations, have been the only tools to study this matter so far. The spin down of sun-like stars can be used to estimate the timescale over which the radiative core responds to a magnetized wind torque. Timescale estimates range from $\sim10$ Myr (\citealt{keppens95}) to $\sim500$ Myr (\citealt{irwin07}), with a dependence on mass and rotation rate. The survival of rapid rotation in old horizontal branch stars (\citealt{peterson83}, \citealt{behr03}) requires that they preserve a core reservoir of angular momentum, even when taking into account mass loss on the red giant branch. Differential rotation in red giants is required to explain this data (\citealt{sills00}). This was corroborated by evolutionary models of red-giant stars taking into account self-consistently the latest prescriptions of angular momentum transport (\citealt{palacios03}, \citealt{palacios06}). %There have also been suggestions about dynamo-driven mixing processes in evolved giants (\citealt{nordhaus08}). While interesting, these methods are relatively insensitive to rotation in deep stellar cores and apply only to special evolutionary stages. %Rotation plays a central role in the formation of stars (see \citealt{bodenheimer95}) and planets (\citealt{bouvier08}), and also in stellar evolution by redistributing the chemical elements inside stars (\citealt{maeder09}). There is compelling observational evidence for such rotational mixing in radiative regions of stars (\citealt{maeder00}, \citealt{pinsonneault10}). However, very little is currently known about the internal rotation profiles, and evolution thereof, of stars. The reason for this uncertainty is that the transport of angular momentum inside stars is generated by processes that are not only theoretically uncertain, but also intricately coupled to one another. For instance, differential rotation is expected to cause meridional circulation and shear-induced turbulence (\citealt{zahn92}), which transport angular momentum and in turn modify the rotation profile inside the star. And although transport processes that are induced by rotation have been found quite successful in reproducing the observations for massive and intermediate-mass stars (\citealt{talon97}, \citealt{maeder00}), they fail to predict the rotation profile of the Sun and usually predict a core rotation rate that is too fast (\citealt{pinsonneault89}). As a result, other more powerful transport processes, such as internal gravity waves (\citealt{charbonnel05}) or magnetic fields (\citealt{gough98}), have to be invoked. %To understand the mechanisms of stellar angular momentum transport better, observational data on stellar rotation are needed. Unfortunately, in most cases these are limited to observations of surface rotation. Seismology is currently the only tool that allows us to probe the internal rotation profiles of stars through the detection of rotational splittings of mode frequencies. Observations of solar p-mode splittings have established that the convective envelope of the Sun is in mild differential rotation, whereas the radiative interior rotates as a solid body down to about 0.2 $R_\odot$ (e.g., \citealt{schou98}). This discovery revolutionized our understanding of the solar interior and raised some questions, such as the thinness of the solar tachochline (\citealt{spiegel92}), that are still open. Performing the same type of analysis for other stars requires very long and high-precision data sets, that until very recently were out of reach. In this paper, we are able to estimate the internal rotation profile of a halo early red giant star using seismology. One of the main asteroseismic goals of the space missions \corot\ (\citealt{baglin06b}) and \textit{Kepler} (\citealt{borucki10}) is to probe the rotation profile of stars. These missions are currently providing us with exquisite asteroseismic data (see \citealt{michel12} and \citealt{gilliland10} for overviews of the asteroseismology programs of \corot\ and \kepler, respectively). They have already made it possible to extract averaged seismic parameters of hundreds of solar-like stars (e.g. \citealt{2009A&A...506...41G}, \citealt{2011Sci...332..213C}, \citealt{verner11}), thousands of red giants (e.g. \citealt{2009A&A...506..465H}, \citealt{2011A&A...525L...9M}), and also of stars in open clusters (e.g. \citealt{2010ApJ...713L.182S}). With these averaged seismic parameters, the validity of the scaling relations proposed by \cite{kjeldsen95a} could be observationally established (\citealt{huber11}) and global stellar parameters such as the mass and radius were estimated for stars in a wide range of evolutionary stages covering the HR diagram (e.g. \citealt{2009ApJ...700.1589S}, \citealt{2010A&A...522A...1K}, \citealt{2011ApJ...729L..10B}). Moreover, the excellent quality of the photometry provided by these instruments enabled us to measure individual p-mode parameters for many modes (e.g. \citealt{2010ApJ...713L.169C}, \citealt{2011A&A...530A..97B}), leading to a very precise modeling of the structure of the observed stars (e.g. \citealt{2011ApJ...740L...2S}). Observations of individual modes lead directly to observations of rotational splittings once the frequency resolution allows us to do so. Evolved stars such as subgiants and red giants are among the most promising objects for the purpose of studying core rotation. Indeed, these stars have higher-amplitude modes than main-sequence stars because of their higher luminosity, and more importantly, many of their non-radial modes are so-called \textit{mixed modes}. As a star evolves past the end of the main sequence, the frequencies of g modes become comparable to those of p modes owing to the high core density. When a p mode and a g mode of same degree meet, they are known to avoid each other and exchange natures, instead of simply crossing. This phenomenon, known as \textit{avoided crossing}, is caused by the coupling between the p-mode and the g-mode cavities. During this process, both modes have a mixed character: they behave as p modes in the envelope and as g modes in the core. These mixed modes are very useful because, unlike pure g modes, they have large enough surface amplitudes so we can detect them and yet are sensitive to the structure of the core. Mixed modes have been theoretically known since \cite{osaki75} discovered them in stellar evolution models. They were first observed from the ground (\citealt{kjeldsen95b}) and later from space with \corot\ (\citealt{analyse_49385}) and \textit{Kepler} (e.g. \citealt{campante11}, \citealt{2011ApJ...733...95M}). These modes enabled us to probe the structure of the core of subgiants (\citealt{deheuvels11}, \citealt{metcalfe10}) and red giants (\citealt{2011Sci...332..205B}, \citealt{2011A&A...532A..86M}), thus making it possible to discriminate between evolutionary scenarios (\citealt{2011Natur.471..608B}, \citealt{mosser12}, see \citealt{bedding12} for a review). The detection of mixed modes that are split by rotation will allow us to probe the rotation rate of stars even in their deepest interior (\citealt{kawaler99}, \citealt{lochard04}). Very recently, \cite{beck12} were able to measure the rotational splittings of mixed modes in three red giant stars observed with \textit{Kepler} and they concluded that the core must rotate at least ten times faster than the surface in these objects. We here report on the detection of rotationally-split mixed modes in the oscillation spectrum of the star \cible, lying on the lower giant branch and observed with the \textit{Kepler} spacecraft. We use these modes to probe the internal rotation profile of this star. The rest of the paper is organized as follows: we first give an overview of the atmospheric parameters of the star in Sect. \ref{sect_atm}. We analyze in detail the oscillation spectrum of the star, obtained from one year of \textit{Kepler} data, in Sect. \ref{sect_sismo}. This spectrum is made very complex by the presence of many mixed modes. We show that the observed non-radial modes are rotationally split and that the rotational splitting varies from one mode to the other, which we interpret as a possible evidence for radial differential rotation in the star. To study this hypothesis, we search for a stellar model that is in good agreement with both the atmospheric and the seismic constraints of the star in Sect. \ref{sect_model}. Finally, in Sect. \ref{sect_inversion}, we use the observed rotational splittings and our closest stellar models to infer information about the rotation of the star. In particular, we perform inversions of the rotational profile using both the Regularized Least Squares method and the Optimally Localized Averages technique. | In this paper, we obtained a precise seismic determination of the rotation rate in the core of the early red giant \cible\ and we proved that it spins at least five times faster than the surface. \cible\ is a low-mass evolved star, which is located at the bottom of the red giant branch. Solar-like oscillations have been detected in the oscillation spectrum of the star, derived from one year of \textit{Kepler} observations (quarters Q5-6-7-8). Due to the evolution stage of the star, many of its non-radial modes have a mixed nature, which means that they behave both as g modes in the core and as p modes in the envelope. We found that many of these mixed modes are very clearly split by stellar rotation and we therefore set out to probe the rotation profile of the star. We performed a seismic analysis of the oscillation spectrum of the star and were able to determine precisely the rotational splittings of 19 $l=1$ and $l=2$ modes. They were found to range from 0.13 to 0.41 $\mu$Hz, with error bars of $0.03\,\mu$Hz on average, thereby suggesting that the interior of the star is differentially rotating in radius. We then found a stellar model reproducing very well both the atmospheric and the seismic properties of the star. We used this model to study the relation between the observed rotational splittings and the regions in the star where the modes are trapped. We found a clear correlation between these quantities that unambiguously indicated that the core rotates faster than the envelope in \cible. Finally, we performed inversions of the rotation profile of the star, using the observed splittings and the rotational kernels of our best-fit models. We used both the RLS (Regularized Least Square) and the OLA (Optimally Localized Averages) methods and obtained the following results: \begin{itemize} \item We were able to determine a very robust and precise estimate of the core rotation of the star. \textit{All the methods} that we used (RLS, OLA) provided a core rotation rate consistent with $\Omega\ind{c}=710\pm51$ nHz within 1-$\sigma$ error bars. Besides, we obtained similar values when using the rotational kernels of other models of the star computed with different metallicities, so this result seems to be only weakly model-dependent. We showed, using the OLA method, that this rotation rate in fact corresponds to a very good approximation of the average of $\Omega(r)$ in the innermost 1.4\% of the stellar radius. It is ironic that the core rotation rate of \cible\ could be measured while the solar core rotation is still uncertain for $r < 0.2R_\odot$ (\citealt{chaplin99}). \item We obtained an upper limit for the surface rotation of $\Omega\ind{s}<150\pm19$ nHz. This enabled us to establish that the core rotates at least five times faster than the surface in this star. \end{itemize} %\cible\ is a low-mass evolved star, which is located at the tip of the red giant branch. Solar-like oscillations have been detected in the oscillation spectrum of the star, derived from nine months of \textit{Kepler} observations. Due to the evolution stage of \cible, many of its non-radial modes have a mixed nature, i.e. behave both as g modes in the core and as p modes in the envelope. By analyzing the oscillation spectrum of the star, we found that the non-radial modes are very clearly split by stellar rotation. %We performed a seismic analysis of the oscillation spectrum of \cible, applying both an MLE (maximum likelihood estimation) method and an MAP (maximum a posteriori) method to determine the parameters of the observed oscillation modes. We obtained estimates of the frequencies, amplitudes, and linewidths of about 40 modes of degrees $l=0,1,$ and 2. We were also able to tightly constrain the inclination angle of the star to $i=85\pm5^\circ$ and to obtain robust estimates of the rotational splittings for 15 $l=1$ modes. The observed splittings range from 0.15 to 0.41 $\mu$Hz, with error bars of $0.03\,\mu$Hz on average. These significant variations of the splitting between the modes already suggested at this point that the interior of \cible\ is differentially rotating. %To study this differential rotation, we searched for a stellar model reproducing both the spectroscopic and the seismic properties of \cible. For this purpose, we adapted the method proposed by \cite{deheuvels11} and designed for the modeling of subgiants to the case of more evolved stars such as \cible. By applying this method to \cible, we showed that the mass of the star ranges from 0.75 to 0.9 $M_\odot$, and that its age is about $12\pm2$ Gyr. More precise estimates of these stellar parameters could possibly be obtained by performing a more thorough modeling. However, the obtained models were sufficient to successfully identify the mixed modes of \cible\ and to determine their rotational kernels. This way, we could confront the observed rotational splittings to the trapping of the modes. We found a clear correlation between these quantities that unambiguously indicated that the core rotates faster than the envelope in \cible. %We then tried to obtain quantitative information about the rotation profile of \cible\ using the observed splittings along with the rotational kernels of our best-fit models. We first followed a forward approach, assuming simple rotation profiles for the star and adjusting their parameters to fit the observed splittings at best. Since we had the unprecedented opportunity (except for the Sun) to have access to both precise estimates of the rotational splittings for many oscillation modes and to the rotational kernels of these modes from a model fitting the observations quite well, we estimate the rotation profile by inversion techniques. We performed inversions using both the RLS (Regularized Leat Square) and the OLA (Optimally Localized Averages) methods. Here is a summary of the results we obtained: %\begin{enumerate} %\item We were able to obtain an extremely robust and precise estimate of the core rotation of \cible. \textit{All the methods} that we used (forward, RLS, OLA) provided a core rotation rate consistent with $\Omega\ind{c}=729\pm40$ nHz within 1-$\sigma$ error bars. Besides, we obtained similar values when using the rotational kernels of other models of \cible\ computed with different metallicities, so this result seems to be only weakly model-dependent. We showed, using the OLA method, that this rotation rate in fact corresponds to a very good approximation to the average of $\Omega(r)$ in the innermost 1.4\% in radius of the star. This constitutes the first precise absolute determination of the core rotation in a star (we recall that even in the Sun, the core rotation rate is still uncertain). %\item It is striking to remark that very simple rotation profiles, such as two-zone models and linear profiles, give a fairly good agreement with the observations ($\chi^2\approx1.7$). The use of more sophisticated profiles did not provide a closer agreement in spite of the increase in number of free parameters to describe $\Omega(r)$. %\item The inversion techniques that were used in this study (RLS, OLA) were severely limited by the small data set we have. The only region were these methods proved to be efficient is the core. Elsewhere, the averaging kernels that we obtained are poorly localized and the estimate of the rotation profile that are obtained cannot be trusted. %\item One important point is the question of the surface rotation. Estimates of the \vsini\ of the star have shown that $-270\leqslant\Omega\ind{s}\leqslant270$ nHz and the values that we obtained with the different methods are summarized in Table \ref{tab_omegas}. We note that if the rotation is solid in the envelope, the surface rotation is very well determined by both the two-zone model and the OLA method and is around 60-90 nHz. %\end{enumerate} We note that in this study we essentially focused on the rotational splittings of $l=1$ modes. This is partly caused by the SNR of modes of degree $l\geqslant2$, which in most cases remains too low to reliably determine their rotational splittings. This problem should be at least partially solved by the growing data set from the \textit{Kepler} spacecraft (this star will continue to be on the short-cadence target list at least through Q12 and hopefully for the remainder of the mission). However, we also showed that the profiles of certain $l=2$ mixed modes split by rotation significantly differ from the expected one and it is our opinion that some theoretical work still remains to be done to better understand the effects of rotation on mixed modes of degree $l\geqslant2$. We are entering a new era in the study of the transport of angular momentum in stars because we now have access to observational constraints on the internal rotation profiles of stars, which were longed for since a very long time. We will very likely find among the \textit{Kepler} targets other subgiants and red giants whose internal rotation can be inferred by interpreting the rotational splittings of mixed modes. For instance, if we assume that the rotation is nearly rigid at the end of the main sequence (as it is in the Sun), then the differential rotation observed in subgiants and red giants is entirely caused by the core contraction in the post main sequence stage. The ratio between the core rotation and the surface rotation at different luminosities along the giant branch should bring very valuable constraints on the timescale of the exchange of angular momentum between the core and the envelope. This should help us determine which mechanisms of angular momentum transport dominate and how efficient they are. %We insist that the seismic study of subgiants observed with \textit{Kepler} is only starting. The oscillation spectra of many more of them will be analyzed shortly and we can hope to detect the signature of rotation in mixed modes for several of them. The present work definitely shows that if we find such objects, we can expect to derive quantitative estimates of the rotation in their interior. %This work also opens many interesting perspectives to investigate about the transport of angular momentum in stars. It should be very instructive to confront the results of this study to the rotation profiles that are predicted by the state of the art models of transport of angular momentum for a star such \cible. For instance, we know that when evolved stars are moving toward and climbing up the red giant branch, their core contracts while their envelope expends. The rotation in the %interior of the star is likely to be affected by these phenomena. The resulting rotation profile should strongly depend on the coupling between the core and the envelope and stars like \cible\ are very good candidates to constraint this coupling. | 12 | 6 | 1206.3312 |
1206 | 1206.2537_arXiv.txt | \vskip 1mm \noindent We discuss the phenomenology and cosmology of a Standard-like Model inspired by string theory, in which the gauge fields are localized on D-branes wrapping certain compact cycles on an underlying geometry, whose intersection can give rise to chiral fermions. The energy scale associated with string physics is assumed to be near the Planck mass. To develop our program in the simplest way, we work within the construct of a minimal model with gauge-extended sector $U (3)_B \times Sp (1)_L \times U (1)_{I_R} \times U (1)_L$. The resulting $U (1)$ content gauges the baryon number $B$, the lepton number $L$, and a third additional abelian charge $I_R$ which acts as the third isospin component of an $SU(2)_R$. All mixing angles and gauge couplings are fixed by rotation of the $U(1)$ gauge fields to a basis diagonal in hypercharge $Y$ and in an anomaly free linear combination of $I_R$ and $B-L$. The anomalous $Z'$ gauge boson obtains a string scale St\"uckelberg mass via a 4D version of the Green-Schwarz mechanism. To keep the realization of the Higgs mechanism minimal, we add an extra $SU(2)$ singlet complex scalar, which acquires a VEV and gives a TeV-scale mass to the non-anomalous gauge boson $Z''$. The model is fully predictive and can be confronted with dijet and dilepton data from LHC8 and, eventually, LHC14. We show that $M_{Z''} \approx 3 - 4~{\rm TeV}$ saturates current limits from the CMS and ATLAS collaborations. We also show that for $M_{Z''} \alt 5~{\rm TeV}$, LHC14 will reach discovery sensitivity $\agt 5\sigma$. After that, we demostrate in all generality that $Z''$ milli-weak interactions could play an important role in observational cosmology. Finally, we examine some phenomenological aspects of the supersymmetric extension of the D-brane construct. | With the turn on of the Large Hadron Collider (LHC) at CERN, a new era of discovery has just begun~\cite{ATLAS:2012ae,Chatrchyan:2012tx,ATLASnew,CMSnew}. The $SU(3)_C \times SU(2)_L \times U(1)_Y$ Standard Model (SM) of electroweak and strong interactions was once again severely tested with a dataset corresponding to an integrated luminosity of $\sim 5~{\rm fb}^{-1}$ of $pp$ collisions collected at $\sqrt{s} = 8~{\rm TeV}$. The LHC8 data have shown no evidence for new physics beyond the SM. However, there is another side to the story. The concordance model of cosmology --the flat expanding universe containing 5\% baryons, 20\% dark matter, and 75\% dark energy-- continues to be put on a firmer footing through observations of the Supernova Search Team~\cite{Riess:1998cb,Riess:2001gk,Tonry:2003zg}, the Supernova Cosmology Project~\cite{Perlmutter:1998np,Knop:2003iy,Kowalski:2008ez}, the Wilkinson Microwave Anisotropy Probe (WMAP)~\cite{Spergel:2003cb,Komatsu:2010fb}, the Sloan Digital Sky Survey (SDSS)~\cite{Abazajian:2003jy,Tegmark:2003ud,Abazajian:2008wr,Percival:2009xn}, and the Hubble Space Telescope~\cite{Riess:2009pu}. While not yet rock solid experimentally, from these observations it is evident that in order to describe the physics of the early universe, and thereupon particle interactions at sub-fermi distances, new theoretical concepts are necessary, which go beyond the SM.\footnote{It appears likewise from experimental evidence of neutrino flavor oscillations by the mixing of different mass eigenstates that the SM has to be extended~\cite{GonzalezGarcia:2007ib}.} Arguably, another major driving force behind the consideration of physics beyond the SM is the huge disparity between the strength of gravity and of the SM forces. This hierarchy problem suggests that new physics could be at play at the TeV-scale. To be more specific, the non-zero vacuum expectation value of the scalar Higgs doublet sets the scale of electroweak interactions. However, due to the quadratic sensitivity of the Higgs mass to quantum corrections from an aribitrarily high mass scale, with no new physics between the energy scale of electroweak unification, $M_{\rm EW} \sim 1~{\rm TeV}$, and the vicinity of the Planck mass, $M_{\rm Pl} \sim 10^{19}~{\rm GeV}$, the Higgs mass must be fine-tuned to an accuracy of ${\cal O}(10^{32})$. Therefore, it is of interest to identify univocal footprints that can plausible arise in theories with the capacity to describe physics over this colossal range of scales. Among various attempts in this direction, string theory is perhaps the most successful candidate and also the most ambitious approach since besides the SM gauge interactions it includes also the gravitational force at the quantum level~\cite{Green:1987sp,Green:1987mn}. In recent years there has been achieved substantial progress in connecting string theory with particle physics and cosmology. Important advances were fueled by the realization of the vital role played by D-branes~\cite{Polchinski:1995mt,Polchinski:1996na} in connecting string theory to phenomenology. This has permitted the formulation of string theories with string scale setting in at TeV scales, and together with large extra dimensions~\cite{Antoniadis:1998ig}. There are two peerless phenomenological consequences for TeV scale D-brane string compatifications: the emergence of Regge recurrences at parton collision energies $\sqrt{\hat s} \sim$ string scale $\equiv M_s;$ and the presence of one or more additional $U(1)$ gauge symmetries, beyond the $U(1)_Y$ of the SM. The latter follows from the property that the gauge group for open strings terminating on a stack of $N$ identical D-branes is $U(N)$ rather than $SU(N)$ for $N > 2$. (For $N = 2$ the gauge group can be $Sp(1) \cong SU(2)$ rather than $U(2)$.) In a series of recent publications we have exploited both these properties to explore and anticipate new-physics signals that could potentially be revealed at LHC. Regge recurrences most distinctly manifest in the $\gamma +$ jet~\cite{Anchordoqui:2007da,Anchordoqui:2008ac} and dijet~\cite{Lust:2008qc,Anchordoqui:2008di,Anchordoqui:2009mm,Dong:2010jt,Nath:2010zj} spectra resulting from their decay.\footnote{The amplitudes of lowest massive Regge excitations that include $2 \to 2$ scattering processes involving 4 gauge bosons, or 2 gauge bosons and 2 quarks, are {\it universal}~\cite{Lust:2008qc}. Therefore, the $s$-channel pole terms of the average square amplitudes contributing to $\gamma +$ jet and dijet topologies can be obtained independent of the details of the compactification scheme. For phenomenological purposes, the poles need to be softened to a Breit-Wigner form by obtaining and utilizing the correct total widths of the resonances~\cite{Anchordoqui:2008hi}. The recent search for such narrow resonances in data collected during the LHC8 run, excludes a string scale below 4.69~TeV~\cite{cms_dijet8tev}.} The extra $U(1)$ gauge symmetries beyond hypercharge have (in general) triangle anomalies, but are cancelled by the Green-Schwarz mechanism~\cite{Green:1984sg}. In addition there can be also massive $U(1)$ gauge bosons, which are associated to 4D non-anomalous Abelian gauge symmetries, but however originate from anomalous $U(1)$'s in six dimensions. In both cases, these $U(1)$ gauge bosons get St\"uckelberg masses. Since in these D-brane models $M_s$ is assumed to be ${\cal O} ({\rm TeV})$, the presence of these generic $U(1)$'s may be amenable to experimental tests at the LHC~\cite{Ghilencea:2002da,Berenstein:2008xg,Anchordoqui:2011eg}. In this work we take a related but different approach studying new physics effects of D-brane models with the conventional assumption ${\rm TeV} \ll M_s \alt M_{\rm Pl}$. The gauge symmetry also arises from a product of $U(N)$ groups, guaranteeing extra $U(1)$ gauge bosons in the spectrum. The weak hypercharge is identified with a linear combination of anomalous $U(1)$'s which itself is anomaly free. As indicated in the preceding paragraph, the extra anomalous $U(1)$ gauge bosons generically obtain a string scale St\"uckelberg mass. The $U(1)$ symmetries survive as global selection rules in the effective low energy theory. Such anomalous gauge bosons are now very heavy and out of the LHC reach. However, in some D-brane models there exists non-anomalous and also massless $U(1)$ gauge symmetries in addition to hypercharge. Namely, under certain topological conditions the associated gauge bosons can remain massless and obtain a low mass scale via the ordinary Higgs mechanism. Some phenomenological aspects of these kind of $U(1)$ gauge bosons were recently discussed in~\cite{Cvetic:2011iq}. In this paper we first revisit the prospects of detecting such TeV-scale gauge bosons in particular at the LHC, and then we show in all generality that their milli-weak interactions could play an important role in observational cosmology. Before proceeding with an outline of the paper, we sketch some issues surrounding the choice of a non-supersymmetric formulation. To avoid the fine tuning inherent in the hierarchy problem, the overwhelmingly favored approach is the introduction of supersymmetry (SUSY). However, for the present study, this presents a difficult technical problem: the full complexity of the scale of SUSY breaking has been pushed by experiment into the TeV region, which coincides with the energy scale involved in searching for the extra $U(1)$ gauge bosons. In the absence of an experimental signal for the onset of SUSY breaking, we will extract from string theory the choice of the $U(1)$ gauge assignments, as well as the quiver structure of the fermionic couplings. In principle, SM-like non-SUSY vacua exist in the string landscape~\cite{Bousso:2000xa,Susskind:2003kw,Douglas:2003um}. Throughout most of this work we will operate within that vacuum structure. However, before concluding we will also discuss in some detail the phenomenology of supersymmetric vacua and the technical problems associated with a phenomenologically viable breaking of an additional $U(1)$ symmetry in a SUSY background. The layout of the paper is as follows. In Sec.~\ref{SEC-II} we outline the basic setting of intersecting D-brane models and discuss general aspects of the effective low energy theory inhereted from properties of the overarching string theory. After that, we particularize the discussion to the $U(3)_B \times Sp(1)_L \times U(1)_L \times U(1)_{I_R}$ intersecting D-brane configuration that realizes the SM by open strings~\cite{Cremades:2003qj}. In Sec.~\ref{SEC-III} we study the associated phenomenological aspects of non-anomalous $U(1)$ gauge bosons related to experimental searches for new physics at the LHC. In Sec.~\ref{SEC-IV} we explore cosmological predictions of intersecting D-brane models in light of recent data, which seem to favor the existence of roughly one additional neutrino species (in addition to the 3 contained in the SM), challenging the earliest observationally verified landmarks: big bang nucleosynthesis (BBN) and the cosmic microwave background (CMB). The gist of Sec.~\ref{SEC-IV} extends the previous study of TeV-scale string compactifications~\cite{Anchordoqui:2011nh} to D-brane models where some of the $U(1)$ masses are at a high string scale. In Sec.~\ref{SEC-V} we examine the consequences of possible supersymmetric extensions. Our conclusions are collected in Sec.~\ref{SEC-VI}. | \label{SEC-VI} The main purpose of this paper has been to cast D-brane ideology in as bottoms-up, phenomenologically driven a way as possible. The energy scale associated with string physics is assumed to be near the Planck mass. To develop our program in the simplest way, we considered a minimal model with gauge-extended sector $U (3)_B \times Sp (1)_L \times U (1)_{I_R} \times U (1)_L$. The resulting $U (1)$ content gauges the baryon number $B$, the lepton number $L$, and a third additional abelian charge $I_R$ which acts as the third isospin component of an $SU(2)_R$. Rotation of the $U(1)$ gauge fields to a basis exactly diagonal in hypercharge $Y$ and very nearly diagonal in (anomalous) $B$ and (non-anomalous) $I_R$ fixes all mixing angles and gauge couplings. The anomalous $Z'$ gauge boson obtains a string scale St\"uckelberg mass via a 4D version of the Green-Schwarz mechanism, ${\rm TeV} \ll M_{Z'} \alt M_s \alt M_{\rm Pl}$. To keep the realization of the Higgs mechanism minimal, we add an extra $SU(2)$ singlet complex scalar, which acquires a VEV and gives a TeV-scale mass to the non-anomalous gauge boson $Z''$. It is noteworthy that there are no dimension 4 operators involving $H''$ that contribute to the Yukawa Lagrangian in our D-brane construct. This is very important since $H''$ carries the quantum numbers of right-handed neutrino and its VEV breaks lepton number. However, this breaking can affect only higher-dimensional operators which are suppressed by the high string scale, and thus there is no phenomenological problem with experimental constraints for $M_s$ higher than $\sim 10^{14}~{\rm GeV}$. Since all freedom of determining coupling constant and mixing angles has been exercised, there remains only constraints on the possible value of $M_{Z''}$. We have shown that $M_{Z''} \approx 3 - 4~{\rm TeV}$ saturates current limits from the CMS and ATLAS collaborations. We have also shown that for $M_{Z''} \alt 5~{\rm TeV}$, LHC14 will reach discovery sensitivity $\agt 5\sigma$. Armed with our D-brane construct, we developed a dynamic explanation of recent hints that the relativistic component of the energy during the CMB and BBN epochs is equivalent to about 1 extra Weyl neutrino. Requiring that the $B-L$ current be anomaly free implies existence of 3 right-handed Weyl neutrinos. The task then reverts to explain why there are not 3 additional r.d.o.f. We showed that for certain ranges of $M_{Z''}$ the decoupling of the $\nu_R$'s occurs during the course of the quark-hadron crossover transition, just so that they are only partially reheated compared to the $\nu_L$'s --- the desired outcome. Roughly speaking, if decoupling requires a freezout of the annihilation channel (loss of chemical equilibrium), then for a $Z''$ which is mostly $I_R$, $3.6~{\rm TeV} < M_{Z''}< 4.8~{\rm TeV}$, whereas for a $Z''$ which is mostly $B-L$, $4.5~{\rm TeV} < M_{Z''}< 6.1~{\rm TeV}$. This range will be probed at LHC14. If thermal equilibrium via scattering is sufficient, for a $Z''$ which is mostly $I_R$, $5.4~{\rm TeV} < M_{Z''}< 7.4~{\rm TeV}$, and for a $Z''$ which is mostly $B-L$, $6.3~{\rm TeV} < M_{Z''}< 8.2~{\rm TeV}$. To carry out this program, we needed to make use of some high statistics lattice simulations of a QCD plasma in the hot phase, especially the behavior of the entropy during the confinement-deconfinement changeover. Interestingly, the behavior of the trace anomaly (shown in Fig.~15 of~\cite{Bazavov:2009zn}), which is very sensitive to the nature of the crossover region, shows a sharp peak at $200~{\rm MeV}$ and our range for $T_{\rm dec}$ straddles this region. Throughout this paper we remained agnostic with respect to SUSY breaking and the details of the low energy effective potential. However, we do subject the choice of quantun numbers for $H''$ to the stringent holonomic constraints of the superpotential at the string scale. This forbids the simultaneous presence of scalar fields and their complex conjugate. As an illustration, if the quantum numbers of $H''$ are those of $N_R^c$, then higher dimensional operators such as $\overline N_R N_R^c {H''}^2$, which can potentially generate a Majorana mass, are absent. Because of holonomy this absence cannot be circunvented by including $\overline N_R N_R^c {H''}^{*2}$. In summary, we have studied the $U(1)$ phenomenology of D-brane models endowed with a high mass string scale. We have incorporated some elements of SUSY, discussing evolution of the gauge couplings to the string scale and enforcing the holonomic constraints on the superpotential. We have shown that LHC8 data set upper limits on the mass of the $Z''$ gauge boson: $M_{Z''} \alt 3 - 4~{\rm TeV}$. We have also shown that $Z''$ milli-weak interactions, which are within reach of LHC14, could play an important role in observational cosmology. It is important to stress that the $Z''$ production cross section and its branching fractions are {\it universal} and have been evaluated in a parameter-free manner. Therefore, the $U(1)$ phenomenology presented in this paper is completely independent of the details of the compactification scheme, such as the configuration of branes, the geometry of the extra dimensions, and whether the low energy theory is supersymmetric or not. | 12 | 6 | 1206.2537 |
1206 | 1206.0532_arXiv.txt | We test the assumption of strict hydrostatic equilibrium in galaxy cluster MS2137.3-2353 (MS~2137) using the latest CHANDRA X-ray observations and results from a combined strong and weak lensing analysis based on optical observations. We deproject the two-dimensional X-ray surface brightness and mass surface density maps assuming spherical and spheroidal dark matter distributions. We find a significant, 40\%--50\%, contribution from non-thermal pressure in the core assuming a spherical model. This non-thermal pressure support is similar to what was found by \cite{Molnar2010} using a sample of massive relaxed clusters drawn from high resolution cosmological simulations. We have studied hydrostatic equilibrium in MS~2137 under the assumption of elliptical cluster geometry adopting prolate models for the dark matter density distribution with different axis ratios. Our results suggest that the main effect of ellipticity (compared to spherical models) is to decrease the non-thermal pressure support required for equilibrium at all radii without changing the distribution qualitatively. We find that a prolate model with an axis ratio of 1.25 (axis in the line of sight over perpendicular to it) provides a physically acceptable model implying that MS~2137 is close to hydrostatic equilibrium at about 0.04--0.15 \Rvir and have an about 25\% contribution from non-thermal pressure at the center. Our results provide further evidence that there is a significant contribution from non-thermal pressure in the core region of even relaxed clusters, i.e., the assumption of hydrostatic equilibrium is not valid in this region, independently of the assumed shape of the cluster. | Galaxy clusters are the largest gravitationally bound and virialized systems in our universe. They are important cosmological tools to probe the curvature, mass and energy density of the universe. One of the most important parameters of galaxy clusters for cosmology is the total mass. Cosmological simulations make specific predictions for the total mass distribution of clusters and the distribution of mass in individual clusters. The total mass of clusters is a particularly important scaling parameter when using galaxy clusters to constrain cosmological parameters. Unfortunately, the mass of clusters can not be observed directly, it has to be derived from observations with some additional assumptions. The most widely used (and independent) methods to determine cluster masses are based on gravitational lensing and X-ray observations. The method based on gravitational lensing is independent of dynamics because the masses is derived from the tangential shear of the background galaxies distorted by the gravitational potential of the cluster. On the other hand, cluster masses estimated from X-ray observations is based on dynamics. The X-ray method assumes that the gas is relaxed and in strict hydrostatic equilibrium (i.e. the cluster is supported only by the thermal pressure). However, there is a long-standing problem that these two methods sometimes result in significantly different cluster masses \citep{Wu1998,Allen1998,Hicks2000,Hoekstra2007,Piffaretti2008,Peng2009,Riemer2009,Meneghetti2010, Zhang2010,Okabe2010,Morandi2011,Morandi_Pedersen2011}. The most popular method to derive the total mass of relaxed clusters from X-ray observations assumes that they are in strict hydrostatic equilibrium and have spherical symmetry. Unfortunately, there are several physical processes which would break the strict hydrostatic equilibrium in clusters, for example: turbulent gas motion, cosmic rays, heating, cooling, and magnetic fields \citep{Ensslin1997,Norman_Bryan1998,Rasia2004,Sarazin2004,Rasia2006,Nagai2007,Pfrommer2007_1,Pfrommer2008_2,Pfrommer2008_3,Guo2008,Skillman2008,Fang2009,Lau_Kravtsov_Nagai2009,Vazza2009,Lagana2010,Valdarnini2011,Parrish2012}. Numerical simulations suggest that turbulent motions of the intracluster gas (ICG) caused by mergers and shocks provide a significant non-thermal pressure support which varies as a function of radius \citep{Norman_Bryan1998,Dolag2005,Vazza2006,Rasia2006,Iapichino2008,Lau_Kravtsov_Nagai2009,Vazza2009,Molnar2010}. Based on smooth particle hydrodynamics (SPH) simulations, \cite{Vazza2006} showed that the turbulence energy of gas particles scales approximately with thermal energy of clusters. In the outskirts of clusters, the ICG is also supported by the bulk gas motion and turbulence created by accretion shocks \citep{Burns2010}. The scaling relations between the thermal and turbulence energy in the different radii among the different redshifts have been investigated by \cite{Vazza2011}. Their results suggest that the non-thermal energy increases with radius and it may be more than 20\% of the thermal energy near the \Rvir. \cite{Parrish2012} conducted magnetohydrodynamics simulations to study the turbulences deduced from the magnetothermal instability in the outskirts of the clusters, and suggested that non-thermal pressure can provide 5 -- 30\% support against gravity beyond $R_{500}$. \cite{Lau_Kravtsov_Nagai2009} studied the effect of gas motion in the mass estimation of simulated clusters, and concluded that the non-thermal pressure due to residual gas motion at large radii, if not taken into account, would result an underestimate of the cluster mass of about 15\% confirming previous results. Based on an analysis of massive clusters drawn from cosmological simulations, \cite{Molnar2010} suggested that the non-thermal pressure can provide a significant, about 30\%, support in the central region, a minimum support at about 0.1--0.2 \Rvir, and increases with radius to about 35\% at \Rvir. \cite{Fang2009} suggest that the pressure from rotation and streaming motions are significantly comparable to the pressure raised from random turbulent pressure out to certain radius range. The hydrostatic equilibrium assumption could result an underestimate of the mass of clusters due to the neglected contribution from turbulent bulk motion \citep{Rasia2006}. The mass estimation of the cluster could be fairly reconstructed if the gas motion pressure is taken into account in the hydrostatic equilibrium equation \citep{Rasia2004,Lau_Kravtsov_Nagai2009}. In addition, inappropriate assumption of the gas and the dark matter halo distributions could also bias the mass estimation of the clusters \citep{Gavazzi2005,Corless2008,Oguri2010,Morandi2011,Morandi_Pedersen2011,Morandi_Limousin_Sayers_2011,Sereno_Umetsu2011,Sereno2012_a,Sereno2012_b}. On the other hand, gravitational lensing of background galaxies is an unique, direct probe of the distribution of matter in galaxy clusters, determining the mass profiles from two-dimensional (2D) projected physical quantities such as reduced shear for example. However, it is extremely hard to fully reconstruct the three-dimensional (3D) mass distribution even with triaxial models fitting to the lensing data, because the lensing technique is sensitive to all the projected mass in the line of sight (LoS) \citep{Corless2008}. Methods based on lensing assuming spherical symmetry would possibly overestimate (underestimate) the cluster masses if the mass distributions are prolate (oblate) with the non-degenerated principle axis aligned in LoS (see for example \citealt{Gavazzi2005}). Moreover, in order to derive accurate mass profiles at all radii, it is necessary to combine strong and weak lensing observations which are sensitive to small and large radii. Molnar et al. (2010, hereafter M10) studied Abell~1689 using the latest CHANDRA data and three massive clusters of galaxies drawn from cosmological adaptive mesh refinement (AMR) simulations. Assuming spherical geometry, they found a significant, about 45\% and 35\%, contribution from non-thermal pressure in the core regions of Abell~1689 and simulated clusters respectively. \cite{Morandi2011} fitted triaxial dark matter mass models with their major axis aligned with the LoS to the full lensing and X-ray data simultaneously, and derived the dark matter axis ratio is 2.02 $\pm$ 0.01 (1.24 $\pm$ 0.13) along the LoS (in the plane of sky) for Abell~1689. But, unlike M10, \cite{Morandi2011} assumed that the non-thermal pressure contribution is constant throughout the all radii. They found that the non-thermal pressure contributes about 20\% to the total pressure needed if the hydrostatic equilibrium holds. Using similar methods, \cite{Morandi2011} and \cite{Morandi_Limousin_Sayers_2011} presented a triaxial model analysis fitting simultaneously to the multiple-wavelength data of Abell~383, and Abell~1835, and derived the non-thermal pressure contribution, about 11\% -- 20\%, out to $R_{200}$. In this paper we continue our previous analysis of non-thermal pressure support in relaxed clusters assuming more general, non-spherical (ellipsoidal) geometry for the matter distribution. Since we are interested in the physics of the mass discrepancy, instead of comparing the total masses of clusters determined from X-ray and lensing observations, we test (as in M10) the assumption of strict hydrostatic equilibrium by comparing the two competing physical processes, self-gravity, acting inward, and the gradient of the pressure, acting outward. In particular, we study strict hydrostatic equilibrium in cluster MS~2137. MS~2137 ($z=0.313$) has been studied extensively by using X-ray and optical (lensing) data \citep{Hammer1997,Gavazzi2005,Comerford2006,Shu2008,Sand2008,Merten2009,Donnarumma2009,Comerford2010}. \cite{Comerford2006} modeled the central mass distribution of MS~2137 assuming an asymmetric NFW profile with the observed gravitational arcs. They found that the reconstructed lens system and the estimated mass profile are in a good agreement with simulations. \cite{Donnarumma2009} (hereafter D9) estimated the mass of MS~2137 in the central and the outer regions by analyzing strong lensing data observed by Hubble Space Telescope and CHANDRA X-ray data, respectively. Assuming spherical and elliptical cluster models with the major axis aligned in the LoS, \citealt{Gavazzi2005} (hereafter G5) derived the total mass profile in MS~2137 between 0.02 and 1.0 Mpc by fitting the conventional and general NFW models to the strong and weak lensing data. G5 found a better agreement between masses determined from X-ray and lensing observations using prolate models. G5 carried out a detailed combined weak and strong gravitational lensing analysis of MS~2137 (the same data were used by D9), therefore we use their results as our reference for lensing. MS~2137 is a relaxed cluster with a round morphology (close to circular) in projection (in the plane of the sky). In order to simplify the modeling, in this case, with a good approximation, we can derive the thermal and equilibrium pressure profiles for this cluster assuming spherical or the elliptical (prolate) models with the non-degenerated axis aligned in the LoS. The outline of our paper is as follows: in section 2, we discuss our X-ray data analysis of CHANDRA data for MS~2137, and the derivation of the thermal pressure, \Pth, based on our analysis. We discuss our method to derive the equilibrium pressure, \Peq, in section 3, based on published results from strong and weak gravitational lensing. We present our test of the assumption of hydrostatic equilibrium in MS~2137, we discuss the possible sources of non-thermal pressure support and systematic biases in section 4 and draw our conclusion in section 5. Throughout in this paper, we assume a concordance cosmological model with $\Omega_m$ = 0.3, $\Omega_\Lambda$ = 0.7, and $H_0$ = 70 km s$^{-1}$ Mpc$^{-1}$. Based on this model, the angular size 1$\arcmin$ = 0.275 Mpc for MS~2137. Unless otherwise stated, all errors, error bars and dashed lines are represented 1$\sigma$ confident intervals. | We have derived thermal and non-thermal pressure ratio profiles for cluster MS~2137 from X-ray and gravitational lensing observations assuming spherical and elliptical models. Since MS~2137 show nearly circular projected morphology, with a good approximation, in our analysis, we could assume elliptical (prolate) models with the non-degenerate axis aligned in the LoS. Analyzing the pressure ratio profiles, we have found, in accord with previous studies based on different arguments, that a prolate model with \qDM = 1.25--1.5 for MS 2137 provides an adequate description for the distribution of the ICG. We have found that the contribution from non-thermal pressure varies with radius. Based on our analysis of the pressure ratios (\Rpr and \Rnpr), spherical symmetry does not seem to be a good assumption for MS~2137. Assuming \qDM = 1.25--1.5, \Rnpr reaches its minimum value of 0\%--20\% at about 0.08 \Rvir, and the non-thermal component contributes about 10\%--40\% and 20\%--60\% at small (within 0.03 \Rvir) and large (0.2--0.5 \Rvir) radii, respectively. We conclude that MS~2137 is not in hydrostatic equilibrium in these two regions even assuming non-spherical symmetry. Our results from comparing the shapes of pressure ratio profiles, \Rnpr, for MS~2137, A1689, and those derived from relaxed clusters drawn from cosmological simulations, suggest that A1689 is not a typical relaxed cluster. Our results based on X-ray and gravitational lensing observations, and numerical simulations of relaxed massive galaxy clusters provide further evidence that there is a significant contribution from non-thermal pressure in the core region of even relaxed clusters, i.e., the assumption of hydrostatic equilibrium is not valid in this region, independently of the assumed shape of the cluster (spherical or elliptical). | 12 | 6 | 1206.0532 |
1206 | 1206.1314_arXiv.txt | We estimate the fraction of core-collapse supernovae (CCSNe) that remain undetected by optical SN searches due to obscuration by large amounts of dust in their host galaxies. This effect is especially important in luminous and ultraluminous infrared galaxies, which are locally rare but dominate the star formation at redshifts of $z$ $\sim$ 1-2. We perform a detailed investigation of the SN activity in the nearby luminous infrared galaxy Arp~299 and estimate that up to 83\% of the SNe in Arp~299 and in similar galaxies in the local Universe are missed by observations at optical wavelengths. For rest-frame optical surveys we find the fraction of SNe missed due to high dust extinction to increase from the average local value of $\sim$19\% to $\sim$38\% at $z$ $\sim$ 1.2 and then stay roughly constant up to $z$ $\sim$ 2. It is therefore crucial to take into account the effects of obscuration by dust when determining SN rates at high redshift and when predicting the number of CCSNe detectable by future high-$z$ surveys such as LSST, JWST, and Euclid. For a sample of nearby CCSNe (distances 6-15 Mpc) detected during the last 12 yr, we find a lower limit for the local CCSN rate of 1.5$^{+0.4}_{-0.3}$ $\times 10^{-4}$ yr$^{-1}$Mpc$^{-3}$, consistent with that expected from the star formation rate. Even closer, at distances less than $\sim$6 Mpc, we find a significant increase in the CCSN rate, indicating a local overdensity of star formation caused by a small number of galaxies that have each hosted multiple SNe. | Much of the massive star formation and hence a substantial fraction of the core-collapse supernovae (CCSNe) in the universe may be hidden behind dust. At higher redshifts, obscured star formation in luminous (10$^{11}$$L_{\odot}$ $\leq$ $L_{{\rm IR}}$ $<$ 10$^{12}$$L_{\odot}$) and ultraluminous ($L_{{\rm IR}}$ $>$ 10$^{12}$$L_{\odot}$) infrared (IR) galaxies (LIRGs and ULIRGs, respectively) actually dominates over the star formation seen in the ultraviolet (UV) and optical (e.g., Le Floc'h et al. 2005; Magnelli et al. 2009, 2011). Because of the observed concentration of star formation within the innermost nuclear regions (e.g., Soifer et al. 2001) high spatial resolution is crucial for detecting SNe in these environments. This can be achieved with observations from space, with ground-based adaptive optics (AO) imaging observations at near-IR wavelengths, or with interferometric radio imaging. High spatial resolution searches at near-IR wavelengths have already discovered several obscured SNe within a few hundred parsecs from LIRG nuclei (Mattila et al. 2007; Kankare et al. 2008, 2012). Furthermore, high spatial resolution searches at radio wavelengths have been able to reveal SN factories within the innermost $\sim$100 pc LIRG nuclear regions that have so far remained hidden at all other wavelengths (e.g. Lonsdale et al. 2006; P\'erez-Torres et al. 2009; Ulvestad 2009; Romero-Ca\~nizales et al. 2011, 2012; Bondi et al. 2012; Herrero-Illana et al. 2012). The effects of host galaxy extinction on the detectability of SNe are expected to increase with redshift since in general, shorter rest-frame wavelengths are observed at higher redshifts. Even more important, the fraction of the star formation hidden from optical searches in LIRGs and ULIRGs is expected to increase rapidly toward redshift $z$ $\sim$ 1 (P\'erez-Gonz\'alez et al. 2005; Le Floc'h et al. 2005; Caputi et al. 2007; Magnelli et al. 2009, 2011). Unless properly corrected for, errors in derived CCSN rates at $z$ $\sim$ 1 will be dominated by these effects (Mannucci et al. 2007; Dahlen et al. 2012; Melinder et al. 2012). Recent CCSN rate studies (e.g., Dahlen et al. 2004; Botticella et al. 2008; Bazin et al. 2009; Graur et al. 2011; Li et al. 2011a; Horiuchi et al. 2011) have indicated that the cosmic CCSN rate might not match the massive star formation rate (SFR) even in the local Universe. This could be caused by a population of SNe remaining undetected by the current optical searches either because they are intrinsically faint, or dark due to large host galaxy extinctions (e.g., Horiuchi et al. 2011). Also, SNe with lower extinctions but occurring within a few hundred parsecs of an LIRG nucleus would likely be detectable only by observations with a high spatial resolution (e.g., Kankare et al. 2012) typically not available for the current SN searches. More recently, Botticella et al. (2012) used a sample of 14 CCSNe within the 11 Mpc volume to derive a robust lower limit for the local CCSN rate. They found the volumetric CCSN rate to be consistent with that expected from the SFR derived from far-UV luminosities and higher than expected based on H$\alpha$ luminosities. This indicates that most of the intrinsically faint and/or dark events were detected in their local sample. The fraction of missing SNe as a function of redshift has been studied before by Mannucci et al. (2007). They compiled the star formation densities for different redshifts derived from UV and IR observations. They used these results together with their own estimates on how many SNe are lost due to obscuration by dust in local starburst galaxies, LIRGs and ULIRGs to derive a correction for SN rates at high redshifts. These estimates, however, were based on a very small number of SNe detected in such galaxies by that time (Maiolino et al. 2002; Mannucci et al. 2003). Also, at that time, very little was known about the nature of the high redshift LIRGs and ULIRGs. The assumption made in Mannucci et al. (2007) was that they were the same kind of systems as in the local universe, which was not an unreasonable assumption. However, later developments, in particular the recent results from $Spitzer$ and $Herschel$, have shown that the high-redshift U/LIRG population is dominated by disk galaxies forming stars in the 'normal' extended (the so called main sequence) mode rather than in compact starbursts as observed in the local U/LIRGs (e.g., Elbaz et al. 2011). In this investigation we use a somewhat similar approach to that of Mannucci et al. (2007) to estimate the corrections needed in order to account for CCSNe remaining undetected by optical surveys both locally and as a function of redshift. Our corrections consist of two parts. First, we estimate the fraction of CCSNe in normal galaxies with substantially higher host galaxy extinctions than predicted by simple models for the smooth dust distribution and the resulting inclination effects. Thereafter, we estimate the fraction of CCSNe missed in local U/LIRGs. For this we make use of the rich SN population of one of the nearest LIRGs, Arp 299. Assuming that the SNe with the highest host galaxy extinctions are missed by the optical searches and not compensated for by the standard extinction corrections, we can derive the fraction of SNe that remain missing and estimate the corrections needed to be applied when deriving CCSN rates. We then use this information together with the latest knowledge of the nature and evolution of high-$z$ U/LIRGs to calculate the fraction of CCSNe missed as a function of redshift. We assume H$_{0}$ = 70 km s$^{-1}$ Mpc$^{-1}$, $\Omega_{\Lambda}$ = 0.7, and $\Omega_{M}$ = 0.3 throughout the paper. | The SN events with high extinctions can have an important impact for SN statistics when estimating the {\it complete} CCSN rates including the optically obscured SNe. This is essential when using CCSNe as probes of the SFR at both low- and high-$z$ (e.g., Cappellaro et al. 1999; Dahlen et al. 2004, 2012; Botticella et al. 2008; Melinder et al. 2012) with the aim of providing a new independent measurement of the cosmic star formation history. Furthermore, accurate determination of the complete CCSN rates will be crucial for comparison with the diffuse SN neutrino background in the future (e.g., Lien et al. 2010). We have shown that a substantial fraction of CCSNe have remained undetected by current optical SN searches due to obscuration by large amounts of dust in their host galaxies. We find that there should be missing CCSNe in highly extinguished environments in both normal host galaxies (even with moderate inclination) by $\sim$5-36\% and in highly dust-enshrouded environments in U/LIRGs by up to $\sim$70-90\%. We note that our estimated missing SN fraction in normal galaxies is also consistent with the recent findings of Micha{\l}owski et al. (2012) for their sample of z $\lesssim$ 1 gamma-ray burst host galaxies. For a volume-limited rest-frame optical SN survey we find the missing SN fraction to increase from its average local value of $\sim$19\% to $\sim$38\% at $z$ $\sim$ 1.2 and then stay roughly constant up to $z$ = 2. Using a local sample of CCSNe discovered during the last 12 yr, we find a lower limit for the local CCSN rate of 1.5$^{+0.4}_{-0.3}\times 10^{-4}$ yr$^{-1}$ Mpc$^{-3}$ within the 6-15 Mpc volume, which is consistent with the CCSN rate estimate within 11 Mpc from Botticella et al (2012). Our estimated CCSN rate is significantly higher than the volumetric CCSN rate from the LOSS (Li et al. 2011a) of 0.84 $\pm$ 0.18 $\times 10^{-4}$ yr$^{-1}$ Mpc$^{-3}$ (scaled to correspond to $H_{0}$ = 70 km s$^{-1}$ Mpc$^{-1}$). If applying our newly derived missing SN fraction correction the volumetric rate of LOSS would become 1.04 $\pm$ 0.22 $\times 10^{-4}$~yr$^{-1}$~Mpc$^{-3}$ or 1.35 $\pm$ 0.29 $\times 10^{-4}$~yr$^{-1}$~Mpc$^{-3}$ if adopting the ``high missing fraction'' model. Therefore, within the uncertainties in the missing SN fraction correction, this is consistent with our CCSN rate estimate within 6-15 Mpc. We note that LOSS made use of their observed luminosity functions of SNe to compensate for the effects of host galaxy extinction for their derived SN rates. Their results indicated that the line-of-sight extinctions toward SNe in the highly inclined galaxies were not significantly higher than in the less inclined systems. However, they noted that this could still be a consequence of a small number of SNe. However, there are also a number of other possible contributing factors to the difference between the CCSN rate estimates, including the possibility of LOSS missing a larger fraction of the intrinsically faint events than our 15 Mpc sample. Also, we note that the volumetric CCSN rate of LOSS has been obtained by multiplying their estimated rates in units of galaxy $K$-band luminosities (SNuK) with the local $K$-band luminosity density introducing additional uncertainties. Our CCSN rate within 6-15 Mpc may also be elevated by cosmic variance. Assuming a Salpeter IMF between 0.1 and 125 $M_{\odot}$ and CCSN progenitor masses between 8 and 50 $M_{\odot}$, we find that our CCSN rate corresponds to an SFR 0.021$^{+0.006}_{-0.005}$ $M_{\odot}$ yr$^{-1}$ Mpc$^{-3}$. This is very similar to the local rate 0.019 $M_{\odot}$ yr$^{-1}$ Mpc$^{-3}$ of Horiuchi et al. (2011), where the latter rate is given for the cosmology adopted here. The SFR within 11 Mpc based on the HUGS program (Kennicutt et al. 2008; Bothwell et al. 2011) should, however, be similarly affected by cosmic variance, allowing a more direct comparison between rates. The SFR derived in Bothwell et al. 0.023$^{+0.002}_{-0.002}$ $M_{\odot}$ yr$^{-1}$ Mpc$^{-3}$~ (given for our adopted cosmology) is consistent with our rate within the error bars. This is also similar to the rate of Magnelli et al. (2009). We therefore conclude that our rate is consistent with what is expected from the SFR and there is no need to correct for SNe missed in our nearby sample. Horiuchi et al. (2011) and Melinder et al. (2012) discuss the choice of the IMF, and they show that the IMF dependence is mostly canceled out as long as the same IMF is used when originally scaling from the massive star SFR to the total SFR and when converting between the CCSN rate and the SFR. Here we have adopted the Salpeter IMF, which has also been used for deriving the SFRs. We also note that calculating the CCSN rate in the very nearby universe within a distance of $<6$~Mpc, we find a significant increase in the rate by a factor $\sim$5 compared to the rate found within 6-15 Mpc, caused by a few galaxies that have each hosted multiple SNe. This further supports the suggestion of a significant local overdensity in the SFR within $\sim$10 Mpc (e.g., Karachentsev et al. 2004). Horiuchi et al. (2011) note that local and low-redshift CCSN rates published before 2011, are lower compared to those expected from the SFR by a factor $\sim$2 at a 2$\sigma$~confidence. As a solution to this discrepancy, they suggested that there could be a population of faint CCSNe ($M \sim -15$) that are typically missed by SN surveys or that there could be a population of SNe hidden by dust, or a combination of these two effects. Using their sample of CCSNe a distance of within 11 Mpc, Botticella et al. (2012) did a detailed comparison with the local SFRs and found their CCSN rate to be consistent with that expected from the SFR derived from far-UV luminosities and higher than expected based on H$\alpha$ luminosities. In our CCSN sample within 12 Mpc, there are no CCSNe fainter than $M$ $\sim$ -15 and roughly 20\% fainter than $M$ $\sim$ -15.5. These intrinsically faint events are more likely to be missed in SN searches over a larger volume compared to our $<12$~Mpc sample and could therefore lead to underestimates of the CCSN rate. Even if such events at the peak would be above the magnitude limit of the survey, the time on the light curve they spend above the limiting magnitude of the search is shorter for this population and unless accounted for, will lead to an underestimate of the rates. Using our local sample of CCSNe, for which we were able to include SNe both with high extinctions and faint intrinsic magnitudes, we do not find any discrepancy with the expectations from the SFRs, even when taking the cosmic variance into account. Looking at the fraction of SNe missed in highly extinguished environments, we have found locally $f_{\rm missing}$=19$^{+19}_{-10}$\%, corresponding to a de-bias factor of $\sim$1.1-1.6. This is smaller than the factor $\sim$2 suggested by Horiuchi et al. (2011) but together with a realistic fraction of intrinsically faint events can account for the apparent discrepancy between some of the previous local CCSN rate estimates and the expectations from the SFRs. The effects of extinction correction on the CCSN rates at higher redshifts are presented and discussed thoroughly in Melinder et al. (2012) and Dahlen et al. (2012). We therefore conclude that correcting for the CCSNe missed due to very high dust extinctions in their host galaxies is crucial for deriving accurate CCSN rates. Taking these effects into account should lead to CCSN rates that are consistent with those expected from the SFRs. | 12 | 6 | 1206.1314 |
1206 | 1206.1064_arXiv.txt | We construct a photometrically calibrated catalog of non-variable sources from the Palomar Transient Factory (PTF) observations. The first version of this catalog presented here, the PTF photometric catalog 1.0, contains calibrated $R_{{\rm PTF}}$-filter magnitudes for $\approx2.1\times10^{7}$ sources brighter than magnitude 19, over an area of $\approx11233$\,deg$^{2}$. The magnitudes are provided in the PTF photometric system, and the color of a source is required in order to convert these magnitudes into other magnitude systems. We estimate that the magnitudes in this catalog have typical accuracy of about 0.02\,mag with respect to magnitudes from the Sloan Digital Sky Survey. The median repeatability of our catalog's magnitudes for stars between 15 and 16 mag, is about 0.01\,mag, and it is better than 0.03\,mag for 95\% of the sources in this magnitude range. The main goal of this catalog is to provide reference magnitudes for photometric calibration of visible light observations. Subsequent versions of this catalog, which will be published incrementally online, will be extended to a larger sky area and will also include $g_{{\rm PTF}}$-filter magnitudes, as well as variability and proper motion information. | \label{Introduction} All-sky photometrically-calibrated stellar catalogs are being used to measure the true apparent flux of astrophysical sources. Other approaches, like observing standard stars (e.g., Landolt 1992), are time consuming since they require additional observations (which are not of the source of interest) under photometric conditions. Therefore, it is desirable to have an all-sky catalog that contains calibrated stellar magnitudes. To date, the most widely used catalog for this purpose is probably the USNO-B1.0 (Monet et al. 2003), which provides the blue, red and near infra-red photographic plate magnitudes for about $10^{9}$ sources. Unfortunately, the photometric measurements in the USNO-B1 catalog show significant systematic variations in the magnitude zeropoint as a function of the position on the sky ($\sim0.5$\,mag), even at small angular scales (Sesar et al. 2006). The Sloan Digital Sky Survey (SDSS) is calibrated to an accuracy of better than 2\% (Adelman-McCarthy et al. 2008; Padmanabhan et al. 2008). However, SDSS Data Release 8 covers only about a third of the celestial sphere. Another possibility is to use bright Tycho-2 (H{\o}g et al. 2000) stars to photometrically calibrate images (Ofek 2008; Pickles \& Depagne 2010). However, this approach requires that the Tycho stars, brighter than magnitude $\approx12$, are not saturated in the images. The Palomar Transient Factory\footnote{http://www.astro.caltech.edu/ptf/} (PTF; Law et al. 2009; Rau et al. 2009) is a synoptic survey designed to explore the transient sky and to study stellar variability. The project utilizes the $48''$ Samuel Oschin Schmidt Telescope at Palomar Observatory. The telescope has a digital camera equipped with 11 active CCDs\footnote{The camera has 12 CCDs of which one is not functional.}, each 2K$\times$4K pixels (Rahmer et al. 2008), and has been surveying the northern sky since March 2009. Each PTF image covers 7.26\,deg$^{2}$ with a pixel scale of $1.01''$\,pix$^{-1}$. The median point-spread function full-width at half maximum is $\approx2''$ and it is uniform over the camera field of view (Law et al. 2010). The PTF main survey is currently performed in the $g$ band during dark time and in the Mould $R$ band during bright time, but most of the data taken prior to January 2011 were obtained using the $R$-band filter. In addition, a few nights around times of full Moon are used for surveying the sky with narrow-band H$\alpha$ filters. An overview of the PTF survey and its first-year performance is given in Law et al. (2010). The PTF data are reduced by pipelines running at Caltech's Infrared Processing and Analysis Center (IPAC). The processing includes astrometric and photometric calibration. Here we build on the PTF photometric calibration to construct a catalog of calibrated non-variable sources. This catalog can be used to photometrically calibrate other visible-light observations. The paper is organized as follows. In \S\ref{Calib}, we briefly discuss the PTF photometric calibration. The construction of the photometric catalog is described in \S\ref{Const}. The catalog is presented in \S\ref{Cat} and we discuss its accuracy and repeatability in \S\ref{Acc}. Finally we conclude in \S\ref{Conc}. | \label{Conc} To summarize, we present a catalog of calibrated PTF $R$-band magnitudes of sources extracted from PTF images. The catalog covers about 28\% of the celestial sphere, some of it outside the SDSS footprint. Conversion of PTF $R$-band magnitude to other magnitude systems requires knowledge of the source's color. We note that the scatter in colors of some populations of objects is small enough (e.g., RR~Lyr stars, asteroids) that their mean color can be used for conversion. We note that the current version of the catalog is designed as a photometric catalog, rather than astrometric catalog. Future versions of this catalog will also provide the $g$-band magnitudes, which will allow one to apply color corrections directly, with no assumptions. In future versions, we also plan to include more robust variability information, source morphology and proper motion measurements of individual sources. | 12 | 6 | 1206.1064 |
1206 | 1206.4688_arXiv.txt | We present Keck/NIRC2 $K_{s}$ band high-contrast coronagraphic imaging of the luminous debris disk around the nearby, young A star HD 32297 resolved at a projected separation of $r$ = 0.3--2.5\arcsec{} ($\approx$ 35--280 AU). The disk is highly warped to the north and exhibits a complex, ``wavy" surface brightness profile interior to $r$ $\approx$ 110 AU, where the peaks/plateaus in the profiles are shifted between the NE and SW disk lobes. The SW side of the disk is 50--100\% brighter at $r$ = 35--80 AU, and the location of its peak brightness roughly coincides with the disk's mm emission peak. Spectral energy distribution modeling suggests that HD 32297 has at least two dust populations that may originate from two separate belts likely at different locations, possibly at distances coinciding with the surface brightness peaks. A disk model for a single dust belt including a phase function with two components and a 5--10 AU pericenter offset explains the disk's warped structure and reproduces some of the surface brightness profile's shape (e.g. the overall ``wavy" profile, the SB peak/plateau shifts) but more poorly reproduces the disk's brightness asymmetry and the profile at wider separations ($r$ $>$ 110 AU). Although there may be alternate explanations, agreement between the SW disk brightness peak and disk's peak mm emission is consistent with an overdensity of very small, sub-blowout-sized dust and large, 0.1--1 mm-sized grains at $\approx$ 45 AU tracing the same parent population of planetesimals. New near-IR and submm observations may be able to clarify whether even more complex grain scattering properties or dynamical sculpting by an unseen planet are required to explain HD 32297's disk structure. | Debris disks are signposts of planets and planet formation \citep[e.g.][]{Wyatt2008,KenyonBromley2008}. Supporting this picture, the two stars with independently confirmed, directly imaged planetary systems HR 8799 and $\beta$ Pictoris \citep{Marois2008,Marois2010,Currie2011a,Lagrange2010} are surrounded by luminous debris disks \citep{Smith1984,Rhee2007,Su2009}. Similarly, Fomalhaut has a candidate planetary companion located just interior to the star's bright debris ring \citep{Kalas2008}. In the absence of a directly imaged planet, resolved imaging of debris disks may provide indirect evidence for a massive planet's existence, may help constrain the unseen planet's properties, and thus can help identify promising targets for future direct imaging \citep[e.g.][]{Wyatt1999}. For example, the inclined or ``warped" component of $\beta$ Pictoris's debris disk \citep{Heap2000,Golimowski2006} is likely due to the directly imaged planet \citep{Augereau2001,Dawson2011} and also provides an estimate for the planet's mass independent of planet cooling models \citep{Lagrange2010}. Dynamical sculpting by a planet/planets may explain the sharp inner edge and pericenter offset of Fomalhaut's debris ring \citep{Kalas2005a,Quillen2006,Kalas2008}. Other debris disk structures may be due to non-planet processes, in particular interactions with the interstellar medium or perturbations from a nearby star, as has been proposed to explain images of disks around HD 15115 and HD 61005 \citep[e.g.][]{Kalas2007,Hines2007}. The nearby \citep[$d = 112^{+12}_{-10}$ $pc$;][]{vanLeeuwen2007} A5 star HD 32297 is another example of a young star surrounded by a luminous, spatially-resolved, debris disk. At 30 Myr old \citep{Kalas2005a}, it is roughly coeval with HR 8799 and may probe debris disk evolution at a stage just after they are most collisionally active \citep{KenyonBromley2008,Currie2008,Currie2009}. Like $\beta$ Pic and HR 8799, HD 32297 has a large infrared (IR) excess emission due to circumstellar dust first identified from \textit{IRAS} data. \citet{Schneider2005} thus selected HD 32297 for \textit{Hubble Space Telescope}(\textit{HST}) NICMOS (F110W) coronagraphic imaging and resolved the disk out to an angular distance (from the star) of $\sim$ 3.3\arcsec{} ($\sim$ 400 AU). HD 32297 was subsequently resolved in the optical \citep{Kalas2005b}, near-IR \citep[1.6--2.2 $\mu m$,][]{Debes2009,Mawet2009}, thermal infrared \citep[10--20 $\mu m$,][]{Moerchen2007,Fitzgerald2007}, and millimeter \citep[1.3mm][]{Maness2008}. Previous work has claimed that HD 32297's disk structure is shaped by planet sculpting as well as non-planet processes. \citet{Debes2009} identified an asymmetry in the disk scattering efficiency between the northeast and southwest sides \citep[see also][]{Kalas2005b}. They argued that ISM sculpting explains this feature much like it explains some properties of the HD 15115 and HD 61005 disks. \citet{Schneider2005} identified a brightness asymmetry between the two disk sides, a feature consistent with sculpting by a massive planet \citep[see also][]{Maness2008}. The two mechanisms, ISM sculpting and planets, are not mutually exclusive. New images of the HD 15115 and HD 61005 disks reveal cleared inner regions and/or pericenter offsets, both of which are plausibly due to a planetary companion \citep{Rodigas2012, Buenzli2010}. Additionally, multiple debris belts, scaled analogues to the solar system's asteroid belt and Kuiper belt, are also likely planet signposts and may reside around HD 61005, HD 15115, and HD 32297 \citep{Fitzgerald2010, Maness2008,Rodigas2012}. To determine which mechanisms are responsible for shaping HD 32297's debris disk structure, we need new, high signal-to-noise images with which to derive precise disk properties. Although \citet{Schneider2005} identify a disk brightness asymmetry consistent with planet sculpting, they caution that the disk brightness measurements close to the coronagraphic spot (r $\sim$ 0.3--0.4\arcsec{}) which provide the basis for this asymmetry are highly uncertain. PSF subtraction errors due to the completely opaque NICMOS coronagraphic spot may limit our ability to conclusively identify disk structure at these small, speckle-dominated separations. Moreover, if the asymmetry identified a planet-induced density structure, it should align with the mm emission peak \citep{Maness2008}. However, it is not clear whether these asymmetries are aligned and thus whether they identify small and large grains originating from the same parent population. The Palomar/$K_{s}$ image from \citet{Mawet2009} has limited spatial resolution. While they did recover \citeauthor{Schneider2005}'s brightness asymmetry, higher spatial resolution observations could confirm and help clarify the physical origin of this and other features. For example, new data could identify breaks in the disk brightness profile that may reveal evidence for the multiple debris belts inferred from modeling unresolved IR data. To further clarify the nature of the HD 32297 debris disk, we present new coronagraphic imaging obtained at $K_{s}$ ($\sim$ 2 $\mu m$) with the Keck telescope on Mauna Kea, resolving the disk at angular separations of 0.3--2.5\arcsec{}. \S 2 describes our observations and extraction of the disk images. In \S 3, we investigate basic disk properties (position angle, full-width half-maximum, and surface brightness) as a function of angular separation from the star. We then combine imaging with new, unresolved broadband photometry from the \textit{Spitzer Space Telescope} and the \textit{WISE} satellite to constrain the disk structure and identify the location(s) of the disk emission (\S 4). Finally, we compare our analyses to those from previous work on HD 32297 (\S 5) and investigate the physical mechanisms responsible for sculpting the disk emission (\S 6). | 12 | 6 | 1206.4688 |
|
1206 | 1206.1778_arXiv.txt | \jmr{In the case of an initially conical jet, we study the relation \change{between} jet collimation by the external pressure and \pa{large-scale} morphology}. We first consider the important \jmr{length-}scales \jmr{in} the problem, and then carry out axisymmetric \jmr{hydrodynamic} simulations that include, for certain parameters, all the\jmr{se length-}scales. We find three important scales related to the collimation region: \jmr{(i)} where the sideways ram-pressure equals the external pressure, \jmr{(ii)} where the jet density equals the ambient density, and \jmr{(iii)} where the forward ram-pressure falls below the ambient pressure. These scales are set by the external Mach-number and opening angle \jmr{of the jet}. We demonstrate that the relative magnitude\jmr{s} of these scales determine \jmr{the} collimation, Mach-number, density and morphology of the large scale \mghk{jet. Based on analysis of the shock structure, we} reproduce successfully the morphology of Fanaroff-Riley (FR) class~I and ~II radio sources. \mghk{Within the framework of the model, an FR~I radio source must have a large intrinsic opening angle. Entrainment of ambient gas might also be important.} We also show that all FR~I sources with radio lobes or similar features must have had an earlier FR~II phase. | \label{sec:intro} Extragalactic radio \jmr{sources} are traditionally divided into two morphological classes \citep{FR74}: \jmr{those in} class~I \jmr{(FR~I) are} edge-darkened \jmr{and those in class~II} edge-brightened. \jmr{\citeauthor{FR74} found that t}he two classes differ in radio power, \jmr{ t}hose \jmr{with} 178~MHz \jmr{luminosities below} $2\times 10^{25}$~W~Hz$^{-1}$~sr$^{-1}$ \jmr{(Hubble's constant = 50 km s$^{-1}$ Mpc$^{-1}$)} \jmr{being} in class~I \jmr{and those above} in class~II. In subsequent studies, the critical power\jmr{, $P_\mathrm{crit}$,} was found to be correlated with the optical magnitude of the host galaxy \citep[$P_\mathrm{crit}\propto L_\mathrm{opt}^2$,][]{OL89,OW91,Owen93,LO96,GC01}. It is well known that brighter galaxies tend to have bigger central super-massive black holes \citep[e.g.][]{Guea09}, which are responsible for the jet production in the first place. Interestingly \jmr{however}, \citeauthor*{WLA07} (\citeyear{WLA07}) do not find a correlation of FR~class with the mass of the super-massive black hole in the host galaxy for a sample of 21~3CRR radio sources near the critical power. Thus, \change{in determining} the large scale morphology, the jet power is the most important \change{influence --} at least one other also plays a role, but \change{this factor} does not seem to be the black hole mass. FR~I radio sources often show narrow jets emanating from the core, which is usually thought to coincide with the AGN, and extending out to a bright flaring point. Beyond this flaring point, the flow widens and dims. These findings have been modeled as a transition from a laminar to a turbulent flow \citep[\mghk{e.g.}][]{Bick84,Bick86a,Bick86b,Kom90b,Kom90a,Kom90c,Wangea09}, which mixes turbulently with the entrained gas. This basic model has been confirmed by numerical simulations: \citet{Rossiea08} show that a jet that is forced to entrain may make the desired transition. \citet{PM07} find the transition in flow character after an induced strong expansion phase in the jet. The reason for such an expansion phase and why it should occur at low jet power only, remains however unclear. \citeauthor*{Hardea05} (\citeyear{Hardea05}) and \citeauthor{Jetea05} (\citeyear{Jetea05}) present studies of morphological features in three FR~I sources, focusing on the density structure in the ambient X-ray gas as observed by {\em Chandra} and {\em XMM-Newton}. They find the flaring point is located at a place where the ambient gas temperature rises steeply from the inner cool core to the hotter intra-cluster gas. This is accompanied by a local flattening of the density profile. In each case, the location is a few tens of kpc from the core. It is clear that observations suggest the FR~class of a radio source is significantly influenced by both \change{the} intrinsic jet properties and the properties of the environment. \jmr{The physics of} the structure and \jmr{evolution} of FR~II sources \jmr{has been studied in some detail}. Such sources often show evidence of a jet at various places from the core out to the edge of the source, which might be over a Megaparsec away (e.g. \citeauthor*{Mulea06} \citeyear{Mulea06}). There, they feature one or more hotspots. \jmr{A} diffuse, cylindrical ``cocoon'' \jmr{extends} from the hot spots \jmr{back} towards the radio core. Axis ratios of these cocoons vary between one and about six (e.g. \citeauthor{KA97} \citeyear{KA97}, and references therein, \citeauthor*{Mulea08} \citeyear{Mulea08}). This has inspired self-similar models of FR~II radio source growth \citep{Falle91,KA97}. These models are valid far away from the characteristic scales of the problem. An outer scale $L_2$ \citep{KF98}, \jmr{at around which the source comes into pressure equilibrium with its surroundings,} is given by \begin{eqnarray} L_2 &=& \left(\frac{Q_0}{\rho_\mathrm{x}\,c_\mathrm{x}^3} \right)^{1/2}\\ &=& 324 \,\mathrm{kpc}\, \nonumber \left(\frac{Q_0}{10^{39}\,\mathrm{W}}\right)^{1/2} \left(\frac{\rho_\mathrm{x}}{10^{-23}\,\mathrm{kg}\,\mathrm{m}^{-3}}\right) ^{-1/2}\\ &\,& \times \nonumber \left(\frac{c_\mathrm{x}}{1000\,\mathrm{km\,s^{-1}}}\right)^{-3/2} \, , \end{eqnarray} where $Q_0$ is the kinetic power of the source, $\rho_\mathrm{x}$ is the external density, and $c_\mathrm{x}$ is the external sound speed. \mghk{FR~II r}adio sources approaching $L_2$ have been studied analytically \cmt{[Paul wanted Alexander 2006 as reference, but I think there must be some misunderstanding and so I leave Alexander 2002]} \citep{Alex02} and numerically (e.g. \citeauthor{Krause2005b} \citeyear{Krause2005b}; \citeauthor*{Gaiblea09} \citeyear{Gaiblea09}). Up to $L_2$, the source is overpressured with respect to its environment, and \change{is} also expected to have a strong bow shock (weakening as the source approaches $L_2$). Observations of weak bow shocks in radio sources $\approx 100$~kpc in size \citep[e.g.][]{McNamea05,Nulsea05} may be simply understood in terms of them being close to $L_2$. Crucial to the existence of the self-similar solution is the self-confinement of the jet by the source's own cocoon pressure. This happens automatically in numerical models of the propagation of light jets (heavy jets show only \jmr{a rudimentary} cocoon). In such simulations, the overpressured cocoon drives a re-collimation shock into the beam as soon as the latter enters the computational domain, \jmr{regardless of whether the beam is initially conical or cylindrical \mghk{\citep[e.g.][]{KF98,mypap03a,HKA07}}.} An initially overdense, conical beam, may be collimated via a re-collimation shock. It occurs when the external pressure $p_\mathrm{x}$ becomes comparable to the sideways ram-pressure, $\rho_\mathrm{j} v_\mathrm{j}^2 \sin^2\theta$, where $\rho_\mathrm{j}$ is the jet density ($\propto r^{-2}$ in a conical jet, where r is the distance to the AGN), $v_\mathrm{j}$ the constant beam velocity, and $\theta$ the half opening angle (\citeauthor{Scheuer74}'s (\citeyear{Scheuer74}) model~B). This position is related to and occurs somewhat downstream of the inner scale $L_1$ \citep[e.g.][]{Alex06}, given by \begin{eqnarray} L_1 &=& 2 \sqrt{2}\left(\frac{Q_0}{\rho_\mathrm{x}\,v_\mathrm{j}^3} \right)^{1/2}\\ \frac{L_1}{\mathrm{pc}} &=& 56 \, \nonumber \left(\frac{Q_0}{10^{39}\,\mathrm{W}}\right)^{1/2} \left(\frac{\rho_\mathrm{x}}{10^{-22}\,\mathrm{kg}\,\mathrm{m}^{-3}}\right)^{-1/2} \left(\frac{v_\mathrm{j}}{c}\right)^{-3/2} \, . \end{eqnarray} On scales $L_1\ll L \ll L_2$, we expect self-similar behaviour. At $L_1$ the jet density becomes roughly comparable to the external density, and the mass of the swept-up gas becomes comparable to the mass that has gone through the jet channel. \jmr{The development of the} large-scale morphology of the radio source depends upon what happens around $L_1$. If a proper re-collimation shock \jmr{is driven} into the beam, an FR~II source \jmr{will develop}. \mghk{Otherwise, a morphology of the FR~I type might result.} Here, we present jet simulations on a spherical grid starting at a fraction of $L_1$ out to a few hundred times \mghk{$L_1$}. \jmr{We follow the approach of \citep{Alex06} in employing non-relativistic hydrodynamics, addressing the same scale, downstream of $L_1$.} This allows detailed studies of the re-collimation process and its relation to the large-scale morphology. We show that a proper re-collimation shock \jmr{only} occurs for small opening angles. We further discuss the important scales of the problem in Section~\ref{sec:scales}. Numerics and simulation setups are presented in Section~\ref{sec:sims}. The simulation results are shown in Section~\ref{sec:res}, and discussed in Section~\ref{sec:disc}. We conclude in Section~\ref{sec:conc}. | \label{sec:conc} We have shown that the \pa{large-scale} morphology of pressure collimated jets is determined by the processes near the region where the jet collimates due to the ambient pressure. We find that the main requirement to form a very underdense jet, and therefore a wide radio lobe is a high external Mach number. We find a clearly distinct shock structure for jets with initial half opening angles below and above \change{about} $24^\circ$, respectively. Jets with lower opening angles always have FR~II morphology, and we classify them accordingly by an appropriate FR-index based on the shock structure. Higher opening angle jets are found to transition from class~II to class~I. In the latter case, entrainment is identified as an important factor \change{in} the jet morphology. The initial opening angle \change{near the jet base} is much larger than the observed one. Predicting the observed opening angle from our simulations results in values which agree well with observations of M87 and Cygnus~A. | 12 | 6 | 1206.1778 |
1206 | 1206.2910_arXiv.txt | The effective interactions of dark matter with photons are fairly restricted. Yet both direct detection as well as monochromatic $\gamma$ ray signatures depend sensitively on the presence of such interactions. For a Dirac fermion, electromagnetic dipoles are possible, but are very constrained. For Majorana fermions, no such terms are allowed. We consider signals of an effective theory with a Majorana dark matter particle and its couplings to photons. In the presence of a nearby excited state, there is the possibility of a magnetic dipole transition (Magnetic inelastic Dark Matter or MiDM), which yields both direct and indirect detection signals, and, intriguingly, yields essentially the same size over a wide range of dipole strengths. Absent an excited state, the leading interaction of WIMPs is similar to the Rayleigh scattering of low energy photons from neutral atoms, which may be captured by an effective operator of dimension 7 of the form $\bar{\chi}\chi F_{\mu\nu}F^{\mu\nu}$. While it can be thought of as a phase of the Magnetic inelastic Dark Matter scenario where the excited state is much heavier than the ground state, it can arise from other theories as well. We study the resulting phenomenology of this scenario: gamma ray lines from the annihilation of WIMPs; nuclear recoils in direct detection; and direct production of the WIMP pair in high-energy colliders. Considering recent evidence in particular for a 130 GeV line from the galactic center, we discuss the detection prospects at upcoming experiments. | Weakly interacting massive particles (WIMPs) have long been studied as potential candidates for the cold dark matter observed in the Universe. The most well-motivated and deservedly most well-studied WIMPs are those that emerge in extensions of the Standard Model associated with the seemingly unrelated problems of the electroweak scale, such as supersymmetric extensions. An orthogonal line of inquiry is motivated by the deceptively elementary question of ``how dark is Dark Matter?'' Namely, what are the strongest constraints on the interaction of dark matter with the electromagnetic field? Numerous studies already exist and in particular the idea of electric and magnetic dipole interactions have recently attracted considerable attention~\cite{Bagnasco:1993st,Pospelov:2000bq,Sigurdson:2004zp,Gardner:2008yn, Masso:2009mu,Cho:2010br,An:2010kc,McDermott:2010pa,Chang:2010en,Banks:2010eh,DelNobile:2012tx}. In these models, single photon exchange provides a possible direct detection signal, while annihilation into two photons might provide an indirect detection signal (see e.g., \cite{Goodman:2010qn}). However, if dark matter is a Majorana fermion, then these single-photon couplings through electromagnetic dipoles do not exist - the dipole operator vanishes identically for Majorana fermions. For Dirac fermions, it is naturally off-diagonal~\cite{Dreiner:2008tw,Kopp:2009qt}. For pseudo-Dirac fermions, in which case the ground state is the dark matter candidate, the dipole interaction mediates transitions between this ground state $\chi$ and an excited state $\chi^*$. The authors of Ref.~\cite{Chang:2010en} exploited this possibility to build a model, dubbed Magnetic inelastic Dark Matter (MiDM), to explain the DAMA results through dipole-dipole dominated scattering. The interaction Lagrangian of MiDM is \be \label{eqn:MiDMInteraction} \mathcal{L}= \left(\frac{\mu_\chi}{2}\right)\bar \chi^* \sigma_{\mu\nu} B^{\mu\nu} \chi + c.c., \ee where $\mu_\chi$ is the dipole strength, $B^{\mu\nu}$ is the hypercharge field-strength tensor, and $\sigma_{\mu\nu} = i[\gamma_\mu,\gamma_\nu]/2$. This coupling contains within it the interaction with the electromagnetic field. We study the signatures of this model in the first part of this paper. In the limit that we take the excited state heavy, we are left with a Majorana fermion, and we can again ask the question ``how dark is Dark Matter?''. Starting with the MiDM Lagrangian above if the excited state, $\chi^*$, is much heavier than the energy available then it can be integrated out to yield the interactions \be \label{eqn:RDMInteraction} \mathcal{L} = \frac{\mu_\chi^2}{2\mXp} \left(\bar{\chi}\chi B_{\mu\nu}B^{\mu\nu} + i \bar{\chi}\gamma_5\chi B_{\mu\nu}\tilde{B}^{\mu\nu}\right), \ee where $ \tilde{B}^{\mu\nu} = \tfrac{1}{2}\epsilon^{\mu\nu\alpha\beta}B_{\alpha\beta}$ and $\epsilon^{\mu\nu\alpha\beta}$ is the Levi-Civita symbol. Motivated by this form, in the second part of this paper we will concentrate on the slightly more general case for the interaction of DM with the electroweak field strengths \be \label{eqn:RDMLagrangian} \mathcal{L} = &\frac{1}{4\LamR^3}&~\Big\{ \bar{\chi}\chi \left( \cos\thetaXS B_{\mu\nu}B^{\mu\nu} + \sin\thetaXS{\rm Tr} W_{\mu\nu}W^{\mu\nu} \right) \\\nonumber &+&\left. i~\bar{\chi}\gamma_5\chi \left( \cos\thetaXA B_{\mu\nu}\tilde{B}^{\mu\nu} + \sin\thetaXA{\rm Tr} W_{\mu\nu}\tilde{W}^{\mu\nu} \right)\right\}. \ee Here $\thetaX$ quantifies the relative coupling to the field strength of hypercharge in comparison to that of $\SUWeak$ and $\LamR$ is some high scale related to the cut-off scale of the theory. We will discuss UV realizations in a later section, but simple scenarios can arise either as a limit of MiDM, or for instance integrating out a dilaton (or axi-dilaton). The interactions of Eq.~(\ref{eqn:RDMLagrangian}) are akin to the familiar interactions of photons with neutral atoms at long wavelengths that lead to Rayleigh scattering. Hence we dub this scenario \textsl{Rayleigh Dark Matter} (RayDM). This could be the entirety of the DM interaction with the standard model, but it also serves as a reasonable form of the effective operators responsible for $\gamma$ lines in many models (even when they freeze out dominantly through other channels). The special form of this interaction, which necessitates at least two force mediators, requires a reconsideration of the basic processes by which we hope to detect dark matter and this constitutes a part of the current work. In this paper we set to explore these different possibilities for the interaction of Majorana WIMPS with light. The paper is organized as follows: In section~\ref{sec:MiDM} we discuss in detail the MiDM scenario including its signatures in gamma rays as well as the prospects for seeing it in direct detection experiments; In section~\ref{sec:RayDM} we explore the phenomenology of RayDM; Section~\ref{sec:collider} is devoted to the prospects of collider searches for both MiDM as well as RayDM; Finally, the main findings of this work are summarized in the conclusions, section~\ref{sec:conclusions}. We caution the reader that the clear separation between MiDM and RayDM is not always appropriate. As we shall discuss and emphasize below, there are certain aspects of the phenomenology where the two scenarios and the operators involved cannot be logically separated. | \label{sec:conclusions} The effective theory describing the interactions of a Majorana WIMP with photons is of critical importance, given that our best indirect detection searches come through monoenergetic $\gamma$-ray lines, and direct detection is clearly sensitive to scattering through a photon exchange. Interestingly, this effective theory is quite restricted: in the presence of a nearby excited state, there is the possibility of an interaction with electromagnetism via a dipole transition to the excited state (or Magnetic Inelastic Dark Matter or MiDM); in the absence of a nearby state, the leading operator comes in the form $\chi \chi W_{\mu\nu} W^{\mu\nu}$ or $\chi \chi B_{\mu\nu} B^{\mu\nu}$ or its the pseudoscalar and CP violating equivalents. These two scenarios have related, but distinct phenomenology. Remarkably, in the case of MiDM both the size of the signal in direct detection and $\gamma \gamma$+$\gamma Z$ signatures are independent of the size of the dipole, with the relic abundance suppression precisely canceling out against the enhanced scattering and annihilation cross sections. This offers a surprising concordance whereby the annihilation rates into $\gamma\gamma$ is in the range to explain the tentative excess in gamma rays at around $130\GeV$ and possibly explain the DAMA annual modulation. MiDM predicts a secondary line at around $114\GeV$ from $\gamma\ZZ$ with a relative rate of about $1:3$ compared with the $\gamma\gamma$ line at 130. Fermi should be able to test the $\gamma$ ray signature and, for small mass splitting $\mXp-\mX \approx 100\keV$, the MiDM scenario also predicts collision rates with nuclei that can now be tested at direct detection experiments. The production rates in colliders are below the current sensitivity of the LHC for thermal cross sections, but can exclude some regions of parameter space where this particle constitutes only a fraction of the total dark matter. The case of the thermal WIMP constituting all of the dark matter should be observable in the near future. We showed that given the scaling of the different quantities involved, the concordance is in fact independent of the dipole strength and is maintained even with an increased dipole strength where MiDM forms only a fraction of the total DM. Model-dependent corrections outside of the effective theory can change this result, however. Moreover, constraints from colliders place an ultimate limit on such an increase in the dipole to be no more than $\mathcal{O}(10)$. In the case of RayDM it is also possible to simultaneously achieve the right relic abundance as well as rates in the range now explored by gamma ray observations. But, in contrast with MiDM, it favors stronger coupling to the $\SUWeak$ vector-bosons than to hypercharge. If RayDm is describing only the interactions with photons, however, and freezes out through some other channel, coupling to hypercharge alone gives a good description of the data. RayDM predicts a ratio of $\gamma\ZZ$ to $\gamma\gamma$ of $1:5$ when coupling to hypercharge dominates, or about $5:2$ in the more likely case of dominant coupling to $\SUWeak$. Unfortunately, the direct detection prospects in this case are gloomy as the collision rates with nuclei due to two photon exchange are much too small. In contrast, this scenario offers interesting phenomenology in colliders including mono-photon, mono-Z, and mono-W signatures with rates that can now be probed at the LHC. There are a few interesting variations on the scenarios we have discussed. A particularly natural scenario is MiDM+RayDM, where the $\gamma \gamma$ signal is naturally boosted in an MiDM model by the presence of an additional hypercharge Rayleigh operator. Such an operator is generally present and would be expected to often dominate the $\gamma \gamma$ signal from these models. An alternative possibility is that some amount of hypercharge-dominated RayDM is just a {\em subdominant} component of the dark matter. Since the density scales as $\rho\sim \vev{\sigma v}_{ann}^{-1}$, the overall rate scales as $\rho^2 \vev{\sigma v}_{ann} \sim \vev{\sigma v}_{ann}^{-1}$. Thus, rather than having all dark matter annihilate to $\gamma \gamma$ with a cross section $\vev{\sigma v}_{ann} \sim 3 \times 10^{-27} {\rm cm^3 s^{-1}}$, we could have a cross section $\sim 10 \times \vev{\sigma v}_{thermal}$ and yield the claimed $\gamma \gamma$ signal from a subdominant component of dark matter. While a number of opportunities exist to distinguish the MiDM scenario from a RayDM scenario, there is another important difference: in RayDM, in particular when the dominant operator is $\chi \chi W_{\mu\nu}W^{\mu\nu}$, there is a sizable hadronic annihilation channel (via $W$'s and $Z$'s) compared to $\gamma \gamma$. In contrast, for MiDM, the $f \bar f$ channel is not present in the late universe as it is only present for $\chi^* \chi$ annihilations rather than $\chi \chi$. Limits on the continuum photon emissions such as those from dwarf galaxies \cite{GeringerSameth:2011iw,Ackermann:2011wa} or the galactic center \cite{Buchmuller:2012rc,Cohen:2012me,Cholis:2012fb} could potentially distinguish these scenarios. Ultimately, if a Majorana dark matter interacts significantly with light, there are a number of conclusions that can be drawn right away. While direct detection signals require a nearby state, collider signatures do not. The era of data - approaching dark matter with direct, indirect and collider experiments, may be on the verge of revealing its nature. | 12 | 6 | 1206.2910 |
1206 | 1206.5537_arXiv.txt | For Leptogenesis based on the type-I seesaw mechanism, we present a systematic calculation of lepton-number violating and purely flavoured asymmetries within nonequilibrium Quantum Field Theory. We show that sterile neutrinos with non-degenerate masses in the GeV range can explain the baryon asymmetry of the Universe via flavoured Leptogenesis. This is possible due to the interplay of thermal and flavour effects. Our approach clarifies the relation between Leptogenesis from the oscillations of sterile neutrinos and the more commonly studied scenarios from decays and inverse decays. We explain why lower mass bounds for non-degenerate sterile neutrinos derived for Leptogenesis from out-of-equilibrium decays do not apply to flavoured Leptogenesis with GeV-scale neutrinos. | Right handed (RH) neutrinos can provide simple and elegant explanations for two pieces of observational evidence for Physics beyond the Standard Model (SM), namely neutrino oscillations and the baryon asymmetry of the universe (BAU). On one hand, they can generate neutrino masses via the seesaw mechanism~\cite{Minkowski:1977sc}. On the other hand, their $CP$-violating interactions in the early Universe can generate a matter-antimatter asymmetry amongst leptons, which can be transferred to the baryonic sector by sphalerons \cite{Kuzmin:1985mm}. This process is known as Leptogenesis~\cite{Fukugita:1986hr}. There exists a large number of Leptogenesis scenarios, see {\it e.g.}~\cite{DiBari:2012fz} for a recent review. One way to classify them is to distinguish how a deviation from thermal equilibrium, essential for baryogenesis~\cite{Sakharov:1967dj}, and the freeze out of the baryon asymmetry are realised. In most models studied to date, the asymmetry is generated in decays of RH neutrinos. The deviation from thermal equilibrium in this case is due to the expansion of the Universe, and Leptogenesis happens due to out-of-equilibrium decays at the time when the interaction rates of the RH neutrinos become Maxwell suppressed. These scenarios are known as thermal Leptogenesis. Another possibility is that the asymmetry is generated during the thermal production of right handed neutrinos by $CP$-violating oscillations amongst them~\cite{Akhmedov:1998qx}. Referring to its discoverers, this is sometimes referred to as Akhmedov-Rubakov-Smirnov (ARS) scenario. Both scenarios are based on the same Lagrangian terms \begin{align} \label{Lagrangian} {\cal L}=\frac{1}{2}\bar\psi_{Ni}({\rm i} \partial\!\!\!/-M_{ij}) \psi_{Nj} +\bar\psi_{\ell a}{\rm i}\partial\!\!\!/\psi_{\ell a} +(\partial^\mu\phi^\dagger)(\partial_\mu \phi) -Y_{ia}^*\bar\psi_{\ell a} \tilde\phi P_{\rm R}\psi_{Ni} -Y_{ia}\bar\psi_{Ni}P_{\rm L}\phi\psi_{\ell a}\,. \end{align} Here $\phi$ is the Higgs doublet, $\tilde\phi=(\epsilon\phi)^\dagger$ ($\epsilon$ is the antisymmetric rank two ${\rm SU}(2)_{\rm L}$ tensor). The Majorana spinors $\psi_{Ni}$ represent RH neutrinos, and $\psi_{\ell a}$ are the active leptons. We choose a flavour basis where the Majorana mass $M_{ij}$ and charged lepton Yukawa matrices are diagonal. Besides the Yukawa couplings $Y_{ia}$, interactions with active right-handed leptons are of importance, because these lead to the decoherence of off-diagonal correlations of $\ell_a$, with $a=e,\mu,\tau$. At the temperatures that the present work is concerned with, the decoherence can be assumed as complete~\cite{Endoh:2003mz,Pilaftsis:2005rv,Abada:2006fw,Nardi:2006fx}. For a discussion of the case of incomplete flavour decoherence, {\it cf.} Ref.~\cite{Beneke:2010dz}. Though flavour effects may be important~\cite{Endoh:2003mz,Pilaftsis:2005rv,Abada:2006fw,Nardi:2006fx,Blanchet:2006be}, the matter-antimatter asymmetry in thermal Leptogenesis is usually due to the violation of total lepton number by the Majorana masses $M_{ii}$ of the right handed neutrinos. Since lepton-number violation is strongly suppressed at low temperatures $T\ll M_{ii}$, the lepton asymmetry can be preserved from washout after the RH neutrino freeze-out though all other fields are in thermal equilibrium. An important phenomenological consequence for models of this type is that the mass of the lightest sterile neutrino should be larger than $10^9\,{\rm GeV}$~\cite{Davidson:2002qv,Buchmuller:2002rq}. Due account of the effects from active lepton flavours~\cite{Endoh:2003mz,Pilaftsis:2005rv,Abada:2006fw,Nardi:2006fx} leads to some changes in the details of the mass bound, including the possibility that the sterile neutrino whose decay leaves behind the lepton asymmetry is not necessarily the lightest~\cite{DiBari:2005st,Engelhard:2006yg,Antusch:2010ms}. They, however, have no qualitative impact on the mass bound, which remains far above the Electroweak scale. The large required Majorana masses, which make most model parameters inaccessible to laboratory experiments, are the main disadvantage of thermal Leptogenesis models. A popular way to evade the lower mass bound on $M_{ii}$ of $10^9\,{\rm GeV}$~\cite{Davidson:2002qv,Buchmuller:2002rq} within models specified by the Lagrangian~(\ref{Lagrangian}) is to introduce a symmetry or a tuning that implies a mass degeneracy \begin{align} \label{enhancement} \frac{M_{ii}M_{jj}}{|M_{ii}^2-M_{jj}^2|}\gg1\,. \end{align} This option is usually referred to as resonant Leptogenesis~\cite{Pilaftsis:2005rv,Covi:1996wh,Flanz:1996fb,Pilaftsis:1997dr,Pilaftsis:1997jf,Pilaftsis:2003gt}. The numerator above and correspondingly in the source for the lepton asymmetry, Eq.~(\ref{S:unflavoured}) below, occurs because the creation of a lepton asymmetry demands an insertion of a lepton-number violating (or, equivalently, helicity reversing) Majorana mass into the loop diagram that gives the main contribution to the decay asymmetry of the sterile neutrinos. In ARS models of Leptogenesis, on the other hand, it is essential that not all of the sterile RH neutrinos reach thermal equilibrium before the sphaleron freeze-out at $T= T_{\rm EW}\sim140$ GeV. Therefore, their Yukawa couplings must not be too large. This constrains the masses $M_{ii}$ from above, as these are related to the Yukawa couplings by the seesaw relation $m_\nu\sim Y^2v^2/(\sqrt 2 M)$. Here $v=246\,{\rm GeV}$ is the vacuum expectation value of the Higgs field and $m_\nu$ the active neutrino mass scale. As a result, the total lepton number violation in these models is tiny at $T\gtrsim T_{\rm EW}$ for $M_{ii}< T_{\rm EW}$. A non-zero baryon number can be generated even for vanishing total lepton number due to flavour effects and because sphalerons only couple to active neutrinos, which can carry a net asymmetry that is compensated for in the sterile sector. The smaller masses make it possible to search for the right handed neutrinos in collider experiments~\cite{Gorbunov:2007ak}. However, the small production rates for sterile neutrinos, essential to avoid their equilibration and washout of the asymmetries long before sphaleron freeze-out, also enter the source term for the asymmetries. Most studies of ARS-type models to date~\cite{Akhmedov:1998qx,Asaka:2005pn,Shaposhnikov:2008pf,Canetti:2010aw,Canetti:2012vf,Canetti:2012zc} require a mass degeneracy of the type~(\ref{enhancement}) to compensate for the resulting suppression. If not justified by a symmetry, this can be considered as tuning. In this work we show that, due to thermal effects, no mass degeneracy needs to be required to produce the observed BAU. While the total lepton number violation is always proportional to $M_{ii}$, and hence suppressed unless a degeneracy~(\ref{enhancement}) is imposed, there is no such suppression for the generation of asymmetries in individual flavours. This is a pure medium effect; in vacuum, Lorentz invariance and dimensional arguments imply that the purely flavoured asymmetry is proportional to the mass-square of the decaying sterile neutrino, which has been verified by explicit calculations~\cite{Covi:1996wh,Endoh:2003mz,Nardi:2006fx}. At temperatures $T\gg M_{ii}$ different medium effects are very important\footnote{The rest frame of the heat bath explicitly breaks Lorentz invariance, which generically leads to an enhancement of the numerator term. Moreover, kinematic cuts that contribute to the charge-parity ($CP$) asymmetry, which are suppressed or forbidden in the vacuum, can become important at finite temperature\cite{Garbrecht:2010sz}.}, and one can readily estimate the enhancement factor for the flavoured asymmetries to be \begin{equation} \label{enhancement:flavoured} \frac{T^2}{|M_{ii}^2-M_{jj}^2|}. \end{equation} We show explicitly that due to this effect, the flavoured asymmetries in ARS scenarios are largely enhanced compared to the total lepton asymmetry. This may be interpreted a way to circumvent the mass bounds~\cite{Davidson:2002qv,Buchmuller:2002rq}, that apply to the non-resonant creation of a lepton-number violating asymmetry. We derive simple analytic expressions for the flavoured asymmetries, that allow us to find parameters for which the observed BAU arises from sterile neutrinos with GeV masses and without the mass degeneracy~(\ref{enhancement}). The flavoured asymmetries are effectively converted into a baryon asymmetry due to sphaleron conversion, because for our parametric examples, the active lepton flavour $e$ is only weakly washed out before sphaleron freeze-out, while $\mu$ and $\tau$ suffer a strong washout. We expect that similar effects may also reduce the lower mass bound or required degree of mass degeneracy for flavoured scenarios in which the asymmetry is generated from heavy neutrino decays. The relevant temperature in the term~(\ref{enhancement:flavoured}) is determined by the time that is required to build up the off-diagonal correlations between the sterile neutrinos~\cite{Akhmedov:1998qx} (or, in other words, the oscillation time of the sterile neutrinos). For ${\rm GeV}$-scale neutrinos with mass-splittings of a similar size, it turns out that $T={\cal O}(10^6\,{\rm GeV})$. Further, we can estimate that the shorter Hubble time $H^{-1}\sim m_{\rm Pl}/T^2$ ($H$ is the Hubble rate and $m_{\rm Pl}=1.22\times 10^{19}\,{\rm GeV}$ is the Planck mass) suppresses the production of the flavoured asymmetries at high temperatures compared to the lepton-number violating asymmetry, that is mostly produced close to sphaleron freeze-out at $T\sim T_{\rm EW}$, by a factor of $T_{\rm EW}^2/T^2$. On the other hand, the production rate of sterile neutrinos with $M_{ii}\ll T$ is proportional to $T$, what leads to a relative enhancement $T/T_{\rm EW}$. Combining these enhancements and suppressions with the factor~(\ref{enhancement:flavoured}), one can therefore estimate that the flavoured asymmetries are enhanced by the large factor $T T_{\rm EW}/M_{ii}^2$ when compared to the unflavoured total lepton asymmetry. A similar enhancement mechanism, that relies on the ratio of the mass of a heavy sterile neutrino much above the Electroweak scale and the mass splitting between several Electroweak-scale Higgs doublets was recently proposed in Ref.~\cite{Garbrecht:2012qv}. Our results are inferred from the source term~(\ref{Source:flavoured:2}) that is a straightforward generalisation of the results of Ref.~\cite{Garbrecht:2011aw} ({\it cf.} also Ref.~\cite{Garny:2011hg}). The source term is calculated within the framework of nonequilibirum Quantum Field Theory, as described by the Schwinger-Keldysh or Closed-Time-Path (CTP) formalism \cite{Schwinger:1960qe}. Compared to calculations involving vacuum $S$-matrix elements~\cite{Pilaftsis:2005rv,Covi:1996wh,Flanz:1996fb,Pilaftsis:1997dr,Pilaftsis:1997jf,Pilaftsis:2003gt}, CTP methods~\cite{Beneke:2010dz,Garbrecht:2012qv,Garbrecht:2011aw,Garny:2011hg,Buchmuller:2000nd,De Simone:2007rw,Garny:2009rv,Garny:2009qn,Anisimov:2010aq,Garny:2010nj,Beneke:2010wd,Garny:2010nz,Garbrecht:2010sz,Anisimov:2010dk} allow to systematically include all medium effects in a well-controlled approximation scheme~\cite{Calzetta:1986cq,Prokopec:2003pj,Prokopec:2004ic,Cirigliano:2009yt,Herranen:2010mh,Drewes:2010pf,Cirigliano:2011di,Herranen:2011zg,Fidler:2011yq,Garbrecht:2011xw,Tulin:2012re,Drewes:2012qw}. It turns out~\cite{Garbrecht:2011aw} that the source term~(\ref{Source:flavoured:2}) corresponds to a sufficiently good approximation provided the sterile neutrinos have performed more than half of a flavour oscillation and when the mass splitting is larger than the width of the sterile neutrinos. Taking account of these limitations, the use of the source~(\ref{Source:flavoured:2}) allows for analytical estimates of the asymmetries that perhaps exhibit the relevant parametric dependences in a more direct manner than numerical studies based on the canonical time-evolution of a density matrix. Moreover, it clarifies the relation between the ARS mechanism and scenarios of thermal Leptogenesis. The plan of this paper is as follows: In Section~\ref{sec:source}, we generalise the result of Ref.~\cite{Garbrecht:2011aw} for the $CP$-violating source term to the case of flavoured Leptogenesis. Assuming ${\rm GeV}$-scale sterile neutrinos, we calculate the flavoured asymmetries present at the time of sphaleron freeze-out in Section~\ref{sec:ass}. The expression for the asymmetry is employed in Section~\ref{sec:par:examples} in order to identify points in parameter space that lead to successful Baryogenesis via Leptogenesis without imposing a mass degeneracy on the sterile neutrinos. In Section~\ref{sec:disc}, we summarise and indicate possible directions of future work. | \label{sec:disc} We have demonstrated that for ${\rm GeV}$-scale sterile neutrinos without a mass degeneracy, flavoured Leptogenesis can be a viable mechanism to generate the baryon asymmetry of the Universe. The simple analytic expression~(\ref{flavoured:asymmetries}) has been used to identify viable points in parameter space with no mass-degeneracy, which is in contrast to scenarios that have been discussed earlier and that rely on sterile neutrinos close to the Electroweak scale or below~\cite{Asaka:2005pn,Pilaftsis:2005rv,Shaposhnikov:2008pf,Canetti:2010aw}. The key ingredient to the variant of the ARS mechanism that is studied here is the fact that the flavoured asymmetry is for our parameters most effectively generated at $T_{\rm osc}\approx 5\times 10^5\,{\rm GeV}\gg M_{ii}$, where thermal effects can considerably enhance it. For higher temperatures, the mass difference is small compared to the Hubble rate and there is no time for the neutrinos to oscillate (or, in other words, for off-diagonal correlations to build up), what leads to a suppression. Compared to lower temperatures, the production at $T_{\rm osc}\approx 5\times 10^5{\rm GeV}$ is larger due to the resonant enhancement factor~(\ref{enhancement:flavoured}) and the neutrino production rate~(\ref{gamma:N}). On the other hand, an effective suppression results from the smaller time scale associated with $T_{\rm osc}$, $H^{-1}\sim m_{\rm Pl}^2/T_{\rm osc}$. The temperature $T_{\rm osc}$ has been identified earlier as a favourable instant for the creation of lepton asymmetries in Ref~\cite{Akhmedov:1998qx}. In Eq.~(\ref{Source:flavoured:2}), we have generalised the $CP$-violating source term of Refs.~\cite{Beneke:2010wd,Garbrecht:2011aw}, such that it includes the possibility of non-degenerate active lepton-flavours. Comparing the lepton-number violating with the purely flavoured contribution, we observe that the latter does not exhibit the suppression factor $M_{ii} M_{jj}$ that is associated with the lepton-number violating helicity flip. The Eqs.~(\ref{Sigma:T0}) and~(\ref{Sigma:Tlarge}) are a consistency check and further illustrate the importance of finite-temperature effects. In particular, they elucidate how the ARS scenario circumvents the mass bounds~\cite{Davidson:2002qv,Buchmuller:2002rq} that apply to the total lepton-number violation or when finite temperature effects are negligible. A similar type of enhancement of the flavoured asymmetries, that relies on the ratio between the square of the temperature and the difference of the squares of the masses of Higgs bosons has been proposed in Ref~\cite{Garbrecht:2012qv}. We have used here nonequilibrium Quantum Field Theory methods, in particular the CTP formalism, in order to calculate the asymmetries. In Refs.~\cite{Akhmedov:1998qx,Asaka:2005pn}, the canonical time-evolution of a density matrix is employed for this purpose. Our result for the flavoured asymmetry differs from Ref.~\cite{Akhmedov:1998qx}, but it parametrically agrees with Ref.~\cite{Asaka:2005pn}. Moreover, our flavoured asymmetries appear as a consistent generalisation of the results from Refs.~\cite{Covi:1996wh,Endoh:2003mz,Nardi:2006fx}, where the decay asymmetries are calculated from $S$-matrix elements. The present work therefore exhibits the close relation of the ARS mechanism to the more conventional scenarios of flavoured thermal Leptogenesis. Phenomenologically, we have demonstrated the viability of the mechanism with non-degenerate masses by calculating the lepton asymmetry for the parameters given in Table~\ref{table:scenarios}. That we do not need to require a mass degeneracy here is due to the fact that we find parameters, for which it is possible that the asymmetry in the flavour $e$ is only weakly washed out, while $\mu$ and $\tau$ already equilibrate with the sterile neutrinos above $T_{\rm EW}$. More systematic studies of the parameter space should however be of interest. The simple analytic formula~(\ref{flavoured:asymmetries}) for the asymmetry may be of particular use for such analyses. For the scenarios in Table~\ref{table:scenarios}, we find that the mass degeneracy of the sterile neutrinos can be completely alleviated or at least be largely relaxed compared to what is stated {\it e.g.} in Refs.~\cite{Asaka:2005pn,Pilaftsis:2005rv,Shaposhnikov:2008pf,Canetti:2010aw}. However, it should be noticed that the parameters $\omega_{ij}$ have no direct physical interpretation and that the moderately large values we consider correspond to cancellations of different contributions to the masses of active leptons. In other words, the Yukawa couplings are somewhat larger than for most of the points in parameter space for the seesaw mechanism. In the future, it will therefore be interesting to pursue possibilities that either do not require such cancellations or explain these: \begin{itemize} \item The estimate of $\Gamma^{\rm av}$, that is taken from Ref.~\cite{Besak:2012qm}, relies on the simple extrapolation of the Standard Model with additional sterile neutrinos to high temperatures, such that the main production channels for the sterile neutrinos are via scatterings of ${\rm SU}(2)_{\rm L}$ and ${\rm U}(1)_Y$ gauge bosons. In many extensions of the Standard Model, interactions with an extended Higgs sector, with the Dark Matter sector or larger couplings are encountered at higher energies. This would lead to an enhancement of $\Gamma^{\rm av}$ and would be of importance for the asymmetry, that, through the source term~(\ref{Source:flavoured:2}), depends quadratically on $\Gamma^{\rm av}$. \item Larger Yukawa couplings for fixed masses of the active neutrinos can be achieved in models with several Higgs doublets. In order to avoid flavour problems, an additional leptoholic Higgs, that exclusively couples to leptons, may be suitable. \item Models with an approximate lepton-number conservation can typically accommodate for largely enhanced Yukawa couplings~\cite{Branco:1988ex,GonzalezGarcia:1988rw,Pilaftsis:2004xx,Pilaftsis:2005rv,Shaposhnikov:2006nn,Asaka:2008bj,Blanchet:2009kk,Ibarra:2011xn,Racker:2012vw}. It would be interesting to study the implications of the thermal effects in the source term~(\ref{Source:flavoured:2}) for these scenarios. \item Sterile neutrinos with masses of a few GeV can in principle be found in laboratory experiments \cite{Gorbunov:2007ak}. It has been shown in \cite{Canetti:2010aw,Canetti:2012vf} that this possibility certainly exists when the BAU is generated from mass-degenerate sterile neutrinos. For the exemplary parts of the parameter space we study, the active-sterile mixing is too small to search for them in existing or near-future experimental facilities. Larger mixings are essentially forbidden because at least one active flavours must be out of chemical equilibrium at $\sim T_{EW}$ to avoid a complete washout of the flavour asymmetries. This is despite the fact that we consider a situation in which the mixings of two active flavours are large compared to the third one. It remains to be clarified in systematic scans of the higher-dimensional parameter-space for models with several right handed neutrinos whether there are regions in which this suppression is sufficiently strong such that sterile neutrinos without mass degeneracy that can explain the BAU may at the same time be directly experimentally accessible. \end{itemize} These are intriguing prospects, whether there is a Higgs sector as in Standard Model or in an extended form. Even with non-degenerate masses at the ${\rm GeV}$-scale, sterile neutrinos thus provide a plausible possible explanation for the baryon asymmetry of the Universe. \subsection*{Acknowledgements} We would like to thank Alejandro Ibarra for useful remarks on large imaginary parts of $\omega_{ij}$. This work is supported by the Gottfried Wilhelm Leibniz programme of the Deutsche Forschungsgemeinschaft. | 12 | 6 | 1206.5537 |
1206 | 1206.0306_arXiv.txt | To estimate the influence of the dark energy on the planetary orbits, we solve the general relativistic equations of motion of a test particle in the field of a point-like mass embedded in the cosmological background formed by the Lambda-term. It is found that under certain relations between three crucial parameters of the problem---the initial radius of the orbit, Schwarzschild and de~Sitter radii---a secular perturbation caused by the Lambda-term becomes significant, \textit{i.e.}\ can reach the rate of the standard Hubble flow. | 12 | 6 | 1206.0306 |
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1206 | 1206.3769_arXiv.txt | \lsi is one of the few GeV- and TeV-emitting X-ray binaries with a prominent, well-studied modulated radio and gamma-ray emission. Changes in its radio morphology suggested in the past the hypothesis of a precessing microquasar. In 2006, a set of VLBA observations performed all around the orbit and confirming the fast variation in morphology were not used to study the precession because the souce was explained in the context of the pulsar model, the alternative model for this system. However, a recent radio spectral index analysis over 6.7 years from Green Bank Interferometer data at 2.2 GHz and 8.3 GHz has well confirmed the predictions of the microquasar scenario in \lsp. At the light of these results we reanalysed the set of VLBA observations that constitutes a unique tool to determine the precession period and render a better understanding of the physical mechanism behind the precession. We improved the dynamic range of the images by a factor of four using self-calibration, and the self-calibrated maps reveal, in six out of ten images, a double-sided structure. The double-sided structure has variable position angle and switches at some epochs to a one-sided structure. These variations indicate a scenario where the precessing jet, inducing variable Doppler boosting, points close to our line of sight - a microblazar, the galactic version of the extra-galactic blazars. High energy observations of \lsi are consistent with the microblazar nature of this object. Moreover, we suggest in \lsi the first case of core shift effect observed in a microquasar. Because of this effect, well known in AGN, the cm-core of the jet is rather displaced from the system center. In \lsp, the cm-core of the jet traces a large ellipse, 7 times larger than the orbit, in a period of about 28~d. Our hypothesis is that this ellipse is the cross-section of the precession cone of the jet at the distance of the 3.6 cm-core, and its period is the precession period. | \lsi is a high-mass X-ray binary (HMXB) where the compact object travels through the dense equatorial wind of a rapidly rotating B0 Ve star. The nature of the compact object is still unknown due to its large mass range, 1.4\,$M_{\odot} < M < 3.8\,M_{\odot}$, which implies either a neutron star or a black hole. Two models have been proposed for this special HMXB, a strong and variable source at all wavelenghts of the electromagnetic spectrum, from radio to TeV. One model assumes that the compact object is a non-accreting young pulsar whose relativistic wind strongly interacts with the wind of the Be star. The second model instead proposes a microquasar, that is, an accreting object whose steady jet, perpendicular to the accretion disk, is occasionally travelled by shocks associated to transients. The peculiarity of \lsi is that, due to the eccentricity of the system, two episodes of a large mass accretion rate may occur along the orbit and consequently two transients may occur per orbital period (26.496 d) (see references in [1]). In 1993, VLBI observations of \lsi showed that the radio emission had a structure of milliarcsecond (mas) size corresponding to a few AU at the distance of 2.0~kpc \cite{massi93}. However, the complex morphology in successive VLBI observations \cite{peracaula98,paredes98,taylor00,massi01,massi04} made an interpretation in terms of a collimated ejection with a constant position angle difficult. The radio morphology not only changes position angle, but sometimes it is even one-sided while at other times two-sided. This fact suggested the hypothesis of \lsi being a precessing microblazar \citep{massi04}. A microblazar should be the galactic version of the extragalactic blazars, i.e., AGN with radio jets forming a small angle, $\theta$, with respect to the observer's line of sight. Doppler boosting enhances the radiation from material that is moving towards the observer, and attenuates it, if it moves in the opposite direction. For remarkable flux attenuation of the receding jet (i.e., attenuated to a level under the sensitivity of radio images) the structure will appear as a one-sided jet. A precession of the jet implies a variation of the angle and therefore variable Doppler boosting. The result is both, a continuous variation of the position angle of the radio emitting structure and of the flux density ratio between approaching and receding jet \citep{massi07}. In known precessing X-ray binaries, the timescale for tidally forced precession of the accretion disk around the compact object, induced by the companion star, lies within the range $8-22$\,times the orbital period \citep{larwood98, massizimmermann10}. In this context, the peculiarity of the variations of \lsi is their short timescale with respect to the predicted (8$-$22)$ \times 26.496$~d. In fact, MERLIN images revealed a surprising variation of 60\degr\, in position angle in only one day \citep{massi04}. Even if quantitatively the relationship between position angle in the image and the viewing angle $\theta$ is not straightforward, a fast variation in position angle implies nevertheless clearly a fast variation in $\theta$. The fast position angle variation measured with MERLIN was confirmed by VLBA observations \citep{dhawan06} measuring in VLBA images a rotation of the inner structure of roughly 5\degr$-$7\degr\, in 2.5 hrs, that is again almost 60{\degr}/day. In that work some one-sided structures were taken as evidence for the cometary tail of the pulsar model. If the compact object is a pulsar, the interaction between its relativistic wind and the equatorial wind of the Be star is predicted to create a bow-shock around the pulsar with a sort of cometary tail, i.e., a one-sided structure, extending away from the Be star \citep{dubus06}. However, recent analysis of the radio spectral index over 6.7 years from Green Bank Interferometer data at 2.2~GHz and 8.3~GHz discovered new characteristics in the radio emission of \lsi \cite{massikaufman09}. This analysis has proven that in \lsi occurs the typical characteristic of microquasars of an optically thin outburst after an interval of optically thick emission. In microquasars, the so called transient jet, associated to the large optically thin outburst, is related to shocks travelling in a pre-existing steady jet, that is a slow moving continuous conical outflow with a composite flat/inverted radio spectrum (i.e., optically thick emission) \citep{fender04, massi11}. The remarkable fact in \lsi is that, during the maximum of the long-term radio periodicity (4.6 yr) present in this source, the alternance, optically thick/thin emission, occurs twice along the orbit, first around periastron and then again, shifted almost 0.3$-$0.4 in orbital phase towards apastron (i.e, (0.3$-$0.4)$\times$ 26.496~d = (8$-$11)~d after periastron) \citep{massikaufman09}. This agrees qualitatively and quantitatively with the well known ``two peak accretion/ejection model'', applied by several authors in \lsp, predicting for large mass accretion rate, $\dot{M}$, two events: one event around periastron and the second one shifted about 0.3 in orbital phase towards apastron \citep{taylor92, martiparedes95, boschramon06, romero07}. As a matter of fact, the radio spectral index data corroborate the microquasar model for \lsp. Then, the open issue is what would produce the observed fast precession. The basis for such a study is to establish the precessional period. This important parameter could be derived by the re-analysis of the VLBA observations performed every 3 days over 30 consecutive days, towards the minimum of the long-term radio periodicity \citep{dhawan06}. We present here preliminary results of our analysis \citep{massi12}. | \lsi is one of the few established massive X-ray binaries that emit in the high and very high energy range. It is formed by a compact object of unknown nature (black hole or neutron star) travelling with a period of 26.496 d around a Be star. Two models have been proposed in the past: a millisecond pulsar and a microquasar model. Recent analysis of the radio spectral index has proven in \lsi the typical characteristic of microquasars of an optically thin outburst after an interval of optically thick emission twice along the orbit, as predicted by the two peak microquasar model. The results of our re-analysis of VLBA observations of \lsi presented here are that the radio emission has in several images a double-sided structure (see. Fig. 1). The astrometry show that the peaks of the images trace a well defined ellipse in (27$-$28) d (see Fig. 2). The pulsar model explains neither the double-sided morphology nor the observed change from double sided to a one-sided structure. The microquasar model can explain them with variable Doppler boosting, i.e., with a precessing jet. The cm-core of a precessing steady jet pointing close to our line of sight, as in a microblazar, is expected to describe an ellipse during the precession. During the transient jet phase there will be an additional shift due to the approaching jet component. We conclude therefore that the precession period is the time of (27$-$28)~d necessary to complete the ellipse. A precession period of (27$-$28) d for the accretion disk in \lsi induced by tidal forces of the Be star \citep{massizimmermann10} would require the unrealistic value for the size of the accretion disk of $0.5-0.8 \times 10^{13}$~cm, i.e., nearly the semi-major axis, and can therefore be ruled out. On the contrary, for a slow rotating compact object, a precession period of 28 d induced by Lense-Thirring effect (i.e., frame dragging produced by the rotation of the compact object) could be compatible \cite{massizimmermann10}. High energy observations of \lsi are consistent with the microblazar nature of this object. Simultaneous X-ray and VHE observations during an outburst of \lsi resulted in a correlation, indicating a simultaneity in the emission processes \citep{Anderhub09}. In particular, with respect to the comparison with blazars, it has been noticed \citep{massizimmermann10} as the two fluxes result in $F_{\rm VHE}\propto F_{\rm X}^{\eta}$ with $\eta=0.99$ in agreement with the correlation observed in blazars \citep{Katarzynski2010}. In addition, the respective values of the photon indices seem to be comparable. During a bright flaring event of the blazar 1ES 2344+514, VERITAS measured a photon index of $\Gamma=2.43 \pm$ 0.22, whereas for the X-ray emission, RXTE and Swift-XRT measured a hard photon index of $\sim$1.9 \citep{Acciari2011}. For \lsp: MAGIC had a $\Gamma=2.7$ and the X-ray emission detected by \textit{XMM-Newton} and Swift-XRT a harder photon index of 1.5-1.8 \citep{Anderhub09}. In blazars the X-ray emission is due to synchrotron, and VHE is synchrotron self-Compton (SSC) \citep{Katarzynski2005}. As discussed in \citep{zimmermannmassi12}, several authors have in fact explained the X-ray excess around apastron in \lsi with synchrotron and the VHE with either external inverse Compton (EIC) or SSC emission \citep{Gupta2006,Zabalza2011}. In particular, the X-ray/VHE correlation in \lsi \citep{Anderhub09} is compatible with a one zone leptonic particle population producing the emission \citep{Anderhub09,Zabalza2011}. Concerning high energy emission in the GeV range, detected e.g., with \textit{Fermi}-LAT, GeV emission is seen all along the orbit. In fact, electrons from the steady jet can always upscatter stellar UV photons to GeV energies (i.e., EIC see \citep{boschramon06}). Nevertheless, more energetic particles from the transient jet could in addition also produce GeV emission via EIC and SSC. Intriguingly, the spectrum measured by \textit{Fermi}-LAT shows, in addition to a power law with a cut-off around 6 GeV, upper limits possibly compatible with the spectrum measured with MAGIC and VERITAS (see e.g., Figs. 2 and 3 in \citep{Hadasch2010} and discussion in \citep{zimmermannmassi12}). As a matter of fact, there is an interesting increase in the overall flux level observed with \textit{Fermi}-LAT after March 2009 together with a broadening of the peak shape \citep{Hadasch2010}. The up to now observed \textit{Fermi}-LAT variations are therefore consistent with a long term variation. Similarly, strong variations are observed at very high energies. With VERITAS the source went from being detected around apastron to becoming quiescent between 2008 and 2010 \citep{acciari11}. With respect to the long-term, 4.6 yr, radio periodicity mentioned in Sect. 1, the insufficient temporal coverage at high energy, evident in Fig. 1 of \citep{zimmermannmassi12}, does not allow at the moment a more closer comparison. However, a different trend with respect to the 4.6 yr radio periodicity is expected. In fact, the high energy emission is indeed related to the steady jet but its peak seems to occur during the transient jet and not during the steady one (Fig. 4 in \citep{massi11}). As a matter of fact the steady jet, related to the radio periodicity, is not always followed by the transient one. A timing analysis of the transient jet is in progress. | 12 | 6 | 1206.3769 |
1206 | 1206.1888_arXiv.txt | Unlike Trojans, horseshoe coorbitals are not generally considered to be long-term stable \citep{der81a, md99}. As the lifetime of Earth's and Venus's horseshoe coorbitals is expected to be about a Gyr, we investigated the possible contribution of late-escaping inner planet coorbitals to the lunar Late Heavy Bombardment. Contrary to analytical estimates, we do not find many horseshoe objects escaping after the first 100 Myr. In order to understand this behaviour, we ran a second set of simulations featuring idealized planets on circular orbits with a range of masses. We find that horseshoe coorbitals are generally long lived (and potentially stable) for systems with primary-to-secondary mass ratios larger than about 1200. This is consistent with the results of \citet{lau02} for equal-mass pairs of coorbital planets and the instability of Jupiter's horseshoe companions \citep{sta08}. Horseshoe orbits at smaller mass ratios are unstable because they must approach within 5 Hill radii of the secondary. In contrast, tadpole orbits are more robust and can remain stable even when approaching within 4 Hill radii of the secondary. | A horseshoe orbit is a type of coorbital motion where two bodies maintain the same average distance from the central object, while librating around points $180^{\circ}$ apart in longitude. If one body is much more massive than the other, the smaller object's trajectory resembles a horseshoe when plotted in the frame rotating with the bodies' average mean motion. Horseshoe orbits were a little-known theoretical prediction \citep{bro11, rab61} until it was realized that Saturn's moons Janus and Epimetheus actually follow such paths \citep{smi80}. The most detailed theoretical exploration of horseshoe orbits was undertaken by \citet{der81a, der81b}, and the same treatment is featured in the textbook by \citet{md99}. Using an analytical approach, \citet{der81a} could not confirm that successive horseshoe loops repeat exactly, even in the restricted problem. Instead, they derived an estimate of possible drift during one horseshoe cycle, and extrapolated the lifetime of the horseshoe configuration assuming that these drifts over long periods of time behave like a random walk. With this approach, \citet{der81a} derived the following formula for the horseshoe lifetime \begin{equation} \tau \lesssim T / \mu^{5/3}, \label{tau} \end{equation} where $T$ the orbital period and $\mu$ is the secondary-to-primary mass ratio. While this formula was originally derived as a first-order estimate of how long the horseshoe motion may last (S. Dermott, 2010, personal communication), it was later presented as a relatively firm upper limit on the lifetime of such configurations \citep[e.g.][] {md99, sta08, chr11}. Note that this relation indicates that the observed horseshoe coorbitals Janus and Epimetheus can last longer than 10 Gyr, while Jovian horseshoes should be unstable on Myr timescales \citep[as confirmed numerically by ][]{sta08}. Given that this relation is based on a relatively simple extrapolation, the ultimate intrinsic stability of horseshoe orbits must be explored using direct integrations which were not possible in the Voyager era. \begin{figure*} \begin{minipage}{2.8truein} \centering (a)\includegraphics[scale=.5, angle=270]{fig1a.eps} \label{10Myr} \end{minipage} \hspace{0.1truein} \begin{minipage}{3.3truein} \centering (b)\includegraphics[scale=0.5, angle=270]{fig1b.eps} \label{100Myr} \end{minipage} \begin{minipage}{2.8truein} \centering (c)\includegraphics[scale=0.5, angle=270]{fig1c.eps} \label{300Myr} \end{minipage} \hspace{0.1truein} \begin{minipage}{3.3truein} \centering (d)\includegraphics[scale=0.5, angle=270]{fig1d.eps} \label{700Myr} \end{minipage} \centering \caption{Remaining stable Trojans (squares) and horseshoe coorbitals (circles) of Earth after (a) 10 Myr, (b) 100 Myr, (c) 300 Myr and (d) 700 Myr. Pluses indicate unstable particles. At t=0, all orbits had e=0.05 and the same longitude of the node and pericenter as Earth.} \label{earth} \end{figure*} The initial motivation for this study was the question of the source of late lunar impactors, usually termed the Late Heavy Bombardment \citep{ccg07}. The formation of the Moon's giant Imbrium basin 3.85 Gyr ago, accompanied by many other smaller impacts, indicates that a population of impactors was present in near-Earth space about 700 Myr after the formation of the planets. While non-coorbital inner Solar System planetesimals should have been mostly cleared out by then \citep{bot07}, Eq. \ref{tau} indicates that horseshoe coorbitals may linger for a Gyr or so. Eq. \ref{tau} gives the horseshoe lifetimes of 1.6 Gyr for Earth and 0.7 Gyr for Venus, the right order of magnitude to explain the Late Heavy Bombardment \citep[and consistent with previous numerical results;][]{tab00}. Furthermore, \citet{sch05} found that Venus Trojans\footnote{Here we use "Trojan" to mean a tadpole coorbital of any celestial body.} may be also unstable on Gyr timescales. While the question of late impactors on the Moon has motivated our original numerical experiments (Section 2), our study was eventually broadened to address the intrinsic stability of horseshoe coorbitals in general (Section 3). | Using direct numerical integrations, we find that a substantial number of horseshoe coorbitals of Earth and Venus appear to be long-term stable. Some of the low-inclination Trojans of these two planets are also stable over 1 Gyr, but the escapes from the stable region continue throughout the simulations, likely due to secular interactions with the planets \citep{bra02, sch05}. More work is needed to ascertain if any of the Trojans of Earth and Venus are stable over the Solar System's lifetime, and if not, what are the timescales and exact mechanisms of their instability. In any case, the lack of observed primordial coorbitals of Earth or Venus, together with our finding of their relative stability, indicate that these objects were not an important contribution to late bombardment on Earth and the Moon. We also integrated a number of horseshoe coorbitals in planar, circular one-planet systems. We find that only planets smaller than about one Jupiter mass ($\mu=1/1200$ or smaller) can have stable horseshoe coorbitals. The main reason for this stability boundary is that the horns of the horseshoe approach too close to the planet (in terms of the planet's Hill radii) for more massive planets. This result is in agreement with the work of \citet{lau02} on equal-mass planet pairs, the known instability of Jupiter horseshoes, and the long-term stability of the only observed horseshoe pair, Janus and Epimetheus. | 12 | 6 | 1206.1888 |
1206 | 1206.2352.txt | {In this work we confront dark matter models to constraints that may be derived from radio synchrotron radiation from the Galaxy, taking into account the astrophysical uncertainties and we compare these to bounds set by {accelerator and complementary indirect dark matter searches}%nearby dwarf spheroidal galaxies and accelerator searches . Specifically we apply our analysis to three popular particle physics models. First, a generic effective operator approach, in which case we set bounds on the corresponding mass scale, and then, two specific UV completions, the $Z^\prime$ and Higgs portals. We show that for many candidates, the radio synchrotron limits are competitive with the other searches, and could even give the strongest constraints (as of today) with some reasonable assumptions regarding the astrophysical uncertainties.} %In this work, we compare the constraints on dark matter derived from {radio} synchrotron radiation measurements %to the bounds obtained by other type of indirect detection experiments and accelerator searches. %Taking into account astrophysical uncertainties, we then apply the analysis to several popular particle physics model: %Meffective couplings approach, Higgs portal and Z'-portal. We show that in many cases, the synchrotron limits %can be as competitive as other searches and can even give the strongest constraints with some reasonable %astrophysical assumptions. {We also show the future reach of radio constraints as a function of accuracy in modeling of the standard astrophysical backgrounds.} | \label{sec:intro} Dark Matter (DM) is one of the most important issues in particle physics and cosmology and understanding its nature will likely play an essential r\^ole in our comprehension of both fundamental interactions and the structure of the Universe. Over the years, a Weakly Interacting Massive Particle (WIMP) has emerged as one of the favourite candidates, in part due to the natural explanation of its cosmological abundance through thermal freeze-out (see e.g. \cite{Bergstrom:2000pn,Bertone:2004pz,Bertone:2010zz}). %The possibility for DM to be made by WIMPs [ref] has became popular since the last \red{20?} years and has openned new directions of research in which a lot of effort has been done (see [] and references therein). While, as of today, we have no other evidence for DM than through its gravitational manifestations, %, that would enable us to make predictions about signals being searched in present and future experiments. the alleged weak interaction of WIMPs have open the possibility to actually observe DM experimentally. Several strategies have been proposed, and are actively pursued, to search for WIMPs. Direct detection experiments, such as CDMS \cite{Ahmed:2010wy} and XENON100 \cite{Moon:2010wq}, are dedicated to the search of DM in the vicinity of the solar system. These are supplemented by multi-purpose particle physics experiments at colliders, most notably the LHC, where DM is expected to be produced, and to manifest itself as missing energy, in collisions. In particular, analysis of single-photon or mono-jet events with missing energy have recently proved to give very pertinent constraints on WIMP mass and interactions \cite{Goodman:2010ku,Bai:2010hh,Fox:2011fx,Fox:2011pm,Chatrchyan:2012te}. A radically different, and a complementary approach is to search for indirect detection of WIMPs, through the remnants of their annihilation (or decays) in astrophysical environments, like the Galactic Centre (GC) of the Milky Way, nearby dwarf spheroidal galaxies (dSphs) or in general any dense region of the Universe. The possible remnants, or messengers, are high energy neutrinos, anti-matter in cosmic rays (CR), and gamma-rays, or more generally an injection of energy of charged particles in the early universe. %In particular, analysis of nearby dSphs by the {\it Fermi} LAT\footnote{\small{http://www-glast.slac.stanford.edu/software/IS/glast\_lat\_performance.htm.}} collaboration \cite{Ackermann:2011wa}, %a gamma-ray space detector, has allowed to put strong indirect constraints on the annihilation cross-sections of WIMPs. %Important collaborations like that of FERMI-LAT [Ref], Atmospheric Cerenkov detectors (ref HESS, MAGIC, VERITAS), PAMELA [ref], Ice Cube etc... %provided us with bounds on DM annihilation from the study of astrophysical signals. It is clear that a possible DM signal will have to be confirmed in these three complementary search techniques and that only together they can form a complete picture of underlying physical mechanisms. %electron/positron fluxes arriving to the Earth, as well as photon fluxes%which are studied in a wide range of frequencies, from synchrotron to gamma-rays %, when looking at particular directions across the entire sky. \red{Unfortunately, the two approaches are usually disconnected from each other, and the communities are not always aware of the results coming from their counterparts. Remove?} %\red{Add some background to the field here: combination of colliders with direct detection or anti-proton constraints, ... ref ibarra? } %In particular, recently there has been an increase of interest in light ($\lsi 10$ GeV) DM candidates inspired both by hints in indirect detection searches (ref Dan) and direct detection experiments (ref Dan and all). In \cite{Mambrini:2011pw} some of us analysed bounds on effective couplings between dark matter and SM particles from single-photon and mono-jet signals, at LEP and the LHC respectively. Such studies are usually compared to exclusion limits set by direct detection experiments (see also {\em e.g.} \cite{Bai:2010hh,Fox:2011pm,Chatrchyan:2012te}). In general terms, the colliders data are comparatively more constraining for low mass dark matter candidates, in particular below the threshold of direct detection experiments, while the latter are more constraining at higher masses, where dark matter production at colliders is impeded. Interestingly, indirect searches tend also to be most constraining for low mass dark matter candidates. This is essentially because the flux of particles produced by dark matter annihilation (gamma-rays, etc.) is proportional to the inverse DM mass to the square. In particular, interesting constraints have been set on the annihilation cross section of DM based on the measured synchrotron radiation from the inner regions of the Milky Way. {While synchrotron radiation constraints on DM have already been much studied in the literature (e.g. in \cite{Bergstrom:2008ag,Bringmann:2009ca,Borriello:2008gy,Boehm:2010kg,Fornengo:2011iq}), to our knowledge no analysis of specific particle physics models implications have been made so far}. Concretely in the present work we confront the constraints from synchrotron radiation in the Galaxy at radio frequencies to those set by colliders data. In particular we study to which extend they are complementary. Our analysis is based both on an effective operator approach (so we put limits on energy scales) and on two specific DM models, the so-called $Z^\prime$ and Higgs portals. We also show how colliders and radio synchrotron radiation limits compare to bounds set by {\it Fermi} LAT based on dSphs \cite{Ackermann:2011wa}, and to constraints imposed on DM annihilations from the effect on the CMB anisotropies \cite{Galli:2011rz}. %, and on the other hand, on bounds coming from mono-photon and mono-jet signals studied at LEP and LHC %, which we believe is something not been addressed so far. %The residuals in the synchrotron data at higher ($\gsi$ 22 GHz) frequencies ('WMAP haze') has been in fact considered as a hint for a DM signal [ref Dan...]. While tens of GHz are potentially more sensitive to hard electron produced in DM annihilations $\gsi$100 GeV, it was shown in [ref] that lower frequencies are more constraining for lower masses which will be in our focus in this work. The constraints from colliders and those from indirect searches do not quite stand on the same footing. In particular, although the radio data are potentially strongly constraining for rather light DM candidates -- as we show also in this work -- the modelling of DM induced radio fluxes suffers from several sources of astrophysical uncertainties. %, and in this work we do not explicitly take this systematic uncertainty into account in our limits. %we explore its impact, by i) exploring the impact on the limits varying the magnitude of the mag field in our region of interest, ii) We explore those by using both a semi-analytic approach, which allows to control, for instance, the dependence of the radio flux on the magnitude of the magnetic fields in our region of interest, and a full numerical calculation as implemented in the \texttt{GALPROP}\footnote{http://galprop.stanford.edu/webrun.php} code \cite{Porter:2008ve,Vladimirov:2010aq} which allows to explore the full set of CR propagation parameters and up-to-date energy losses, thus cross checking the semi-analytic method and calibrating its parameters. To gauge the impact of CR propagation parameters on synchrotron signals, we sample a range of CR propagation parameters sets using both those derived to probe uncertainty in the local CR fluxes, and used traditionally to bracket this type of uncertainty (MIN, MED, MAX set of parameters \cite{Donato:2003xg}), and CR propagation sets which were recently shown to give a good description of the gamma-ray \cite{FermiLAT:2012aa,Trotta:2010mx} and radio \cite{Strong:2011wd} data and which are therefore suited to test electron propagation parameters in the inner regions of our galaxy. We present our results as a function of the systematic uncertainties on the modelling of the backgrounds due to standard astrophysics, illustrating potential future improvements of the limits based on radio data. %XXXX ? \textcolor{red}{While systematic uncertainty due to the modelling of a DM signal is not explicitly included in the limits we derive here}, XXXX we compare our findings to the limits taken from the stacked analysis of 10 satellite dwarf Galaxies, as performed by the Fermi-LAT collaboration \red{[ref]}, which has most of the systematics marginalized over. The paper is organised as follows. In section \ref{sec:synchrotron} we review the formalism of the semi-analytical approach used in this work, and also present the setup for the full numerical study. In Section \ref{sec:astro} we discuss at lengths the astrophysical framework. In part \ref{sec:astroU} we discuss the astrophysical uncertainties, while in part \ref{sec:cross} we discuss our cross-check between semi-analytical and numerical approaches. In part \ref{sec:DMprofiles} we show the dependence of the synchrotron flux with different choices of Dark Matter profile, and Part \ref{sec:CRpars} is devoted to study, numerically, the impact of different choices of CR diffusion and propagation parameters to the synchrotron signal. Part \ref{sec:magn} is a semi-analytical (cross-checked by numerical) study of the dependence of the synchrotron flux on the magnetic field normalisation. Then, section \ref{sec:models} is devoted to the discussion of synchrotron constraints on particle physics models. In part \ref{sec:effectiveOperators} we adopt a generic, also known as model-independent, approach based on effective operators. There we confront the synchrotron constraints we derive with other indirect searches and colliders constraints. In parts \ref{sec:HiggsPortal} and \ref{sec:ZpPortal} we consider two specific UV completions, the Higgs and Z$^\prime$ portal, to which we apply the synchrotron constraints. While the conclusions bear some resemblance, the constraints are quite distinct for the two models. Finally we give our conclusion and prospects in \ref{sec:conclusion}. | \label{sec:conclusion} \noindent In this work, we derived the constraints on synchrotron emission from the secondary products of dark matter annihilation in our Galaxy, based on the radio 45 MHz data. We expanded upon the current literature in several aspects: a) by using both a semi-analytical approach to model the particle propagation in the intergalactic medium \cite{Baltz:1998xv,Delahaye:2007fr}, and a full numerical analysis based on the \texttt{GALPROP} code \cite{Porter:2008ve,Vladimirov:2010aq}, benefiting from the strengths of both in particular aspects of the work, b) considering intermediate Galactic latitudes, where the DM profiles are more robustly constrained, and c) taking into account the large astrophysical uncertainties on the magnetic fields. We have shown that synchrotron emissions can give very pertinent bounds on DM annihilation cross section, confirming previous results \cite{Bergstrom:2008ag,Borriello:2008gy,Boehm:2010kg,Fornengo:2011iq}. \noindent %After a brief introduction to synchrotron radiation \ref{sec:synchrotron}, The discussion of the astrophysical propagation setup, %which is the object of Section \ref{sec:astro}, occupies a large fraction of this work. %We have in particular carefully assessed the impact of propagation parameters. Together with a usual set of CR propagation parameters used previously to gauge uncertainties of the astrophysical conditions on the radio signals, (MIN, MED and MAX models of propagation \cite{Donato:2003xg}), we have considered several other sets of CR parameters, which are shown to be consistent with CR, gamma ray and/or synchrotron data \cite{FermiLAT:2012aa,Trotta:2010mx,Strong:2011wd}. %, and found that they in general predict lower synchrotron fluxes in our region of interest (ROI) and frequency of interest. We have also explored the impact of the magnitude of the magnetic field in our ROI and found that it is generally mild, ranging a factor of 3--4 for magnetic fields in the inner Galaxy in the range between 1--100~$\mu$G. One of the purpose of our work is to put in perspective various indirect bounds on dark matter models, complemented with collider constraints. Although the scope of our results is broader, this was in part motivated by the fact that both colliders and indirect searches are supposed to put very relevant limits on relatively light dark matter candidates, $m_{DM} \lsim 10$ GeV, for which direct detection limits are weaker, or altogether inexistent. In this spirit, %in Section \ref{section:dwarfs} we have briefly reviewed (and applied to particle physics models in question, including forecasts) the constraints from {\it Fermi} LAT observations of nearby dwarf spheroidal galaxies \cite{Ackermann:2011wa}, as well as the limits set by CMB anisotropies \cite{Galli:2011rz}. Both of these observations give stringent indirect limits on dark matter annihilation cross sections and treat targets different than the one we focus on to derive the radio DM constraints, providing therefore independent probes of DM self-annihilation signatures. %In Section \ref{sec:models} We have applied our results to various DM particle models, starting with a generic approach based on effective operators. There, we have shown that, for reasonable values of parameters, and for a conservatively chosen ROI, synchrotron searches for DM could be comparable to those of colliders, and sometimes even do better. In particular, in the case of effective couplings to leptons, we have shown that, even for very conservative setups, where we supposed that all the radio data are saturated by the synchrotron radiation produced by DM annihilation, the limits obtained are already competitive with those based on LEP measurements (photon+missing energy). In this case too, radio constraints can even be better than the ones derived from CMB, depending on the uncertainty on the astrophysical modelling. Concretely, allowing that DM contribute to 5\% the background signal could give the best limit obtained by current indirect detection signals. For effective couplings to quarks, the synchrotron have a strong potential too, but due to huge uncertainties in the prediction of this signal, one cannot robustly claim that the most conservative synchrotron constraints can improve over the collider bounds. As expected, if DM couples to hadrons, dwarf constraint generally perform better. %\blue{On the long run, the collider limits should give the strongest bound, in particular on light dark matter candidates.} The effective approach is powerful, but reaches its limits when resonance effects become relevant. To assess such effects, and for the own sake of a more microscopic approach to DM phenomenology, we have considered the constraints set by radio synchrotron radiation on two specific DM models: the so-called Higgs and $Z'$ portals. This is motivated by the fact that these models are among the simplest extensions of the SM with DM candidates. Moreover, each of these models provide fully self-consistent UV completions of the effective operator approach, and thus provide complementary, albeit model dependent, information. We have shown that radio data may put severe constraints on these models, but at some price. Provided the uncertainty on the background could be assessed at the $5\%$ level, and assuming a cuspy profile (NFW), and a large magnetic field, most of the Higgs portal parameter space is excluded, except near resonance (the Higgs pole), or close the threshold for $W^+W^-$ annihilation, which is impeded in the Galaxy (by construction both these effects are inexistent in an effective operator approach). We have also shown a very good complementarity between synchrotron bounds and the last XENON100 bounds when considering the exclusion of the parameter space of the model. For the case of the $Z^\prime$ portal, because of substantial annihilation into leptons, the constraints are stronger, or alternatively, the astrophysical setup may be more conservative (smaller magnetic field, less cuspy profile), but some control of the background is also required to exclude (most of) the parameter space. This work illustrates again, if necessary, that a multi-signal approach provides very complementary information on DM phenomenology. If on the long run, DM production at colliders is likely to give the strongest constraints, one should keep in mind that missing energy may not be directly related to the actual DM that is supposedly present in our Galaxy. Our results present (part of) the state of art in confronting indirect searches, with a particular emphasis on synchrotron radio data, a very promising signal for dark matter, provided some control may be gained on the mundane, astrophysical background, a fascinating challenge for both future observations and theoretical works. To pave the road, in the near future, PLANCK will be able to study Galactic emission in the frequency range where it is dominated by the dust emission, mapping with unprecedented precision dust (and therefore indirectly gas) content of our Galaxy. Together with improvements in measurement of the charge cosmic ray spectra we will soon be getting from AMS--02\footnote{http://ams.cern.ch/} and measurement of diffuse emission in gamma rays of such CR population, with the {\it Fermi} LAT, models of propagation and energy losses of CR are expected to advance significantly over the next 5-10 year period. Finally, the future radio telescope facilities, like the LOFAR and SKA, will provide further leverage on the possible radio synchrotron signal from DM particles, in particular for lighter candidates. | 12 | 6 | 1206.2352 |
1206 | 1206.3305_arXiv.txt | Characterizing the level of primordial non-Gaussianity (PNG) in the initial conditions for structure formation is one of the most promising ways to test inflation and differentiate among different scenarios. The scale-dependent imprint of PNG on the large-scale clustering of galaxies and quasars has already been used to place significant constraints on the level of PNG in our observed Universe. Such measurements depend upon an accurate and robust theory of how PNG affects the bias of galactic halos relative to the underlying matter density field. We improve upon previous work by employing a more general analytical method - the path-integral extension of the excursion set formalism - which is able to account for the non-Markovianity caused by PNG in the random-walk model used to identify halos in the initial density field. This non-Markovianity encodes information about environmental effects on halo formation which have so far not been taken into account in analytical bias calculations. We compute both scale-dependent and -independent corrections to the halo bias, along the way presenting an expression for the conditional collapsed fraction for the first time, and a new expression for the conditional halo mass function. To leading order in our perturbative calculation, we recover the halo bias results of Desjacques et. al. (2011), including the new scale-dependent correction reported there. However, we show that the non-Markovian dynamics from PNG can lead to marked differences in halo bias when next-to-leading order terms are included. We quantify these differences here. We find that the next-to-leading order corrections suppress the amplitudes of both the scale-dependent and -independent bias by $\sim5-10\%$ for massive halos with $M\sim 10^{15} \Msun/h$, and $\sim30-40\%$ for halos with $M\sim 10^{14} \Msun/h$. The corrections appear to be more significant as the halo mass is lowered, though we caution that the apparently large effects we observe in the low-mass regime likely signal a breakdown of the perturbative approach taken here. | The inflationary paradigm provides a robust framework for explaining key aspects of our observable Universe such as its geometric flatness, features of the cosmic microwave background, and the initial conditions for structure formation. Despite these remarkable successes, we still know very little about the physics behind it, and currently cannot distinguish among a wide variety of viable inflationary models. One of the most promising ways to differentiate among these models is to probe the statistics of the initial density fluctuations \citep[see][and references therein]{2010CQGra..27l4011D}. While the simplest scenarios - the canonical single-field slow-roll models - predict an almost perfectly Gaussian distribution of initial fluctuations, more general inflationary models predict significant deviations from Gaussianity that observations might yet be sensitive enough to detect. There is therefore great interest in developing ways to measure primordial non-Gaussianity (PNG) since its detection would have profound implications for inflationary theory. There are presently two methods that have so far been applied with some success to place significant constraints on the level of PNG in our observed Universe. The first is the statistical imprint of PNG in the temperature anisotropies of the cosmic microwave background (CMB), which directly probe the initial fluctuations while they are still in the linear regime \citep[e.g.][]{2010CQGra..27l4010K}. The second is the imprint on the large-scale structure that develops as the initial fluctuations grow to the highly non-linear point of forming galaxies, which serve as tracers of the underlying matter. In general, non-linear growth can complicate the interpretation of the observed structure, both because density fluctuations develop non-Gaussianity even when the initial conditions are purely Gaussian, and because the theoretical predictions in this regime ultimately depend upon N-body simulations. On large enough scales, however, the density fluctuations filtered on these scales are still linear, and the problem reduces to the theory of how well galaxies trace the large-scale mass distribution - the so-called ``bias." The prospect of probing PNG with large-scale structure improved dramatically when it was discovered that the mode coupling effects of PNG induce a scale-dependent signature in the power spectrum of biased tracers (such as galactic halos) on large scales \citep{2008PhRvD..77l3514D, 2008ApJ...677L..77M,2008PhRvD..78l3507A}. The first and best studied example of this signature involves the local-quadratic model of PNG, in which the primordial Bardeen potential fluctuation in the matter-dominated epoch, $\Phi_{\mathrm{NG}}(\boldsymbol{x})$, is obtained from a quadratic transformation of the local Gaussian fluctuation field, $\phi_{\mathrm{G}}(\boldsymbol{x})$, according to \begin{equation} \Phi_{\mathrm{NG}}(\boldsymbol{x}) = \phi_{\mathrm{G}}(\boldsymbol{x}) + \fNL \left[ \phi_{\mathrm{G}}(\boldsymbol{x})^2 - \langle \phi_{\mathrm{G}}^2(\boldsymbol{x}) \rangle \right], \label{EQ:localquadratic} \end{equation} where $\fNL$ is the so-called non-linearity parameter \citep{1990PhRvD..42.3936S,2001PhRvD..63f3002K}. In this case, while the Gaussian field is entirely characterized by its power spectrum, $P_{\Phi}(k)$, information about higher-order correlations, for example through the bispectrum, is required to characterize the statistics of the non-Gaussian potential. To first order in $\fNL$, equation (\ref{EQ:localquadratic}) gives a bispectrum with the form\footnote{The bispectrum in equation (\ref{EQ:localquadraticbispectrum}) is more general than equation (\ref{EQ:localquadratic}), as it can be generated in number of different models that do not involve the latter \citep[see footnote 34 in][for example]{2011ApJS..192...18K}. It is nonetheless customary to refer to this form for the bispectrum as the local template. }, \begin{align} B^{\mathrm{local}}_{\Phi}(k_1,k_2,k_3) = 2 \fNL [ P_{\Phi}(k_1)P_{\Phi}(k_2) + P_{\Phi}(k_1)P_{\Phi}(k_3) + P_{\Phi}(k_2)P_{\Phi}(k_3) ]. \label{EQ:localquadraticbispectrum} \end{align} Observational constraints have been placed on this form of the bispectrum by finding the range of allowed amplitudes, expressed in terms of $\fNL$. For example, the CMB anisotropy measurements by the Wilkinson Microwave Anisotropy Probe seven-year data analysis (WMAP7) find a $95\%$ limit of $-10 < \fNL < 74$ \citep{2011ApJS..192...18K}. The bispectrum in equation (\ref{EQ:localquadraticbispectrum}) is important in the phenomenology of PNG because a detection of non-zero $\fNL$ would rule out standard single-field inflation \citep{2004JCAP...10..006C,2005JCAP...06..003S,2007JCAP...01..002C,2008JCAP...02..021C}. In order to constrain equation (\ref{EQ:localquadraticbispectrum}) from observations of large-scale structure, it is necessary to consider the expected halo bias for this model, i.e. the ratio of the fractional halo number density to the fractional matter density. In Fourier space, this ratio has been found to depart from the Gaussian expectation by a correction term, $\Delta b(k)$, containing two parts: one that depends on the wavenumber (scale-dependent) and one that does not (scale-independent). In the limit of small wavenumber, the correction approaches the form $\Delta b(k) \propto \fNL (b_{\mathrm{G}} - 1) / k^2$, where $b_{\mathrm{G}}$ is the expected Gaussian bias \citep{2008PhRvD..77l3514D, 2008ApJ...677L..77M,2008PhRvD..78l3507A}. Based upon this assumed $k^{-2}$ scale-dependence, \citet{2008JCAP...08..031S} have already constrained $\fNL$ to be in the range $-31 < \fNL < 70$ ($95\%$ limit) using the clustering of massive galaxies and quasars in the Sloan Digital Sky Survey; a result that is competitive with the WMAP7 constraints. There is naturally a great interest in this method as future large-scale structure surveys of ever-increasing volume utilizing both the galaxy power spectrum and bispectrum may surpass the CMB measurements in constraining $\fNL$ \citep{2004PhRvD..69j3513S,2009ApJ...703.1230J,2010JCAP...07..002N,2011JCAP...04..006B,2012MNRAS.422.2854G}. Numerical N-body methods have confirmed that the halo bias scales as $k^{-2}$ in the small-$k$ limit in the local-quadratic model, with a redshift dependence inversely proportional to the linear perturbation growth factor, $D(z)$, as predicted by the analytical theory \citep{2008PhRvD..77l3514D,2009MNRAS.396...85D,2010MNRAS.402..191P,2009MNRAS.398..321G,2010JCAP...07..002N,2011JCAP...11..009S}. However, the amplitude of the bias is still somewhat uncertain, as the N-body simulations so far produce a range of values differing at the $10-20\%$ level \citep{2010AdAst2010E..89D}. On the other hand, the analytical predictions disagree significantly with results from N-body simulations in models beyond the local-quadratic case \citep{2010PhRvD..81b3006D,2011JCAP...03..017S,2012JCAP...03..002W}. This motivated \citet{2011PhRvD..84f3512D} to re-examine three analytical derivations of the bias \citep[see also][]{2012JCAP...03..032S}: 1) An approach based on the statistics of thresholded regions in the density field \citep{2008ApJ...677L..77M}. 2) A peak-background split (PBS) approach based on the separation of uncorrelated long- and short-wavelength contributions to the \emph{Gaussian} perturbations \citep{2008PhRvD..77l3514D,2008JCAP...08..031S,2010PhRvD..82j3002S}. 3) A second PBS approach \citep{2010PhRvD..82j3529D} using the conditional halo mass function, which they derive by an extension of the \citet{1974ApJ...187..425P} method to non-Gaussian initial conditions \citep[also see][]{Matarrese:2000pb,Lo-Verde:2008rt}. This approach is conceptually different from the previous one because it does not involve a separation of scales in the Gaussian perturbations, but instead considers through the conditional mass function how the local halo-abundance depends on the large-scale \emph{non-Gaussian} density contrast. In addition to showing that the thresholding method cannot be reconciled with N-body simulations, \citet{2011PhRvD..84f3512D} use the last two approaches to derive a new scale-dependent contribution to the bias that was previously overlooked in the literature. In a companion paper \citep{2011PhRvD..84f1301D}, they showed that the new term is critical for improving the analytical predictions that were previously discrepant with N-body simulations. It is important to confirm the above findings with more general methods. Here, we consider an independent analytical approach to the halo bias - the excursion set formalism \citep{Bond:1991sf,1993MNRAS.262..627L}. Until recently, the excursion set method had been analytically tractable only in the case with Gaussian initial conditions and, even then, only when a sharp k-space filter was used. In this case, the dynamics in the excursion-set random-walk model for identifying halos in the initial density field are Markovian. \citet{2010ApJ...711..907M,2010ApJ...717..515M,2010ApJ...717..526M} recently showed how to extend the excursion set model to include non-Markovian dynamics by formulating it with a path integral. This breakthrough opens the door to non-Gaussian initial conditions and/or more general filter functions \citep[for a different approach to non-Markovian dynamics, see][]{2012MNRAS.419..132P,2012MNRAS.420.1429P,2012MNRAS.420..369M,2012MNRAS.tmpL.449M,2012arXiv1205.3401M}. The path-integral approach has been successfully applied in a number of contexts involving PNG \citep{2010ApJ...717..526M,2011JCAP...02..001D,2011MNRAS.412.2587D,2011PhRvD..83b3521D,2011MNRAS.415.1913D,2011MNRAS.418.2403D}. However, it has not yet been used to derive the scale-dependent correction to the halo bias. In what follows, we use the path-integral excursion set method to derive expressions for the conditional collapsed fraction and conditional mass function for non-Gaussian models with general bispectra. We then use these expressions to compute both scale-dependent and -independent corrections to the halo bias. In comparison with the results of \citet{2011PhRvD..84f3512D}, our results will come closest to the conclusions of their third approach described above. In the process of deriving our result, we will be able to investigate more specifically under what circumstances their result is valid. In particular, the excursion-set approach shows through the non-Markovian dynamics that environmental effects on halo formation can lead to marked differences in halo bias. We will also quantify these differences here by a perturbative calculation, applied for illustrative purposes to the familiar local-quadratic model, as well as a second example - the so-called orthogonal template. The remainder of this paper is organized as follows. In $\S$ \ref{SEC:statofdensityfield}, we review statistics of the linear density field and define the bispectrum templates used in this work for plotting purposes. In $\S$ \ref{SEC:PNGpathintegral}, we outline the path-integral excursion set method of \citet{2010ApJ...711..907M,2010ApJ...717..515M,2010ApJ...717..526M}. In $\S$ \ref{SEC:collapsefraction}, we use the formalism to calculate the conditional collapsed fraction to leading-order, and also compute the next-to-leading order environmental corrections. We then use the collapsed fraction to obtain expressions for the conditional mass function in $\S$ \ref{SEC:condmassfunc}. From the conditional mass function, we obtain scale-dependent and -independent linear bias parameters in $\S$ \ref{SEC:halobias}. Finally, we summarize our results and offer concluding remarks in $\S$ \ref{SEC:conclusion}. When plotting our results, we use a fiducial $\Lambda$CDM cosmology with parameters $\Omega_m=0.27$, $\Omega_{\Lambda} = 0.73$, $\Omega_b = 0.046$, $H_0 = 100 h~\mathrm{km~s^{-1}~Mpc^{-1}}$ (with $h=0.7$), $n_s=0.97$ and $\sigma_8=0.82$, consistent with WMAP7 constraints \citep{2011ApJS..192...18K}. We also employ the linear matter power spectrum of \citet{1999ApJ...511....5E}. | \label{SEC:conclusion} We have used the path-integral formulation of the excursion set method with constant barrier and sharp $k$-space filter to calculate the conditional collapsed fraction, conditional mass function, and linear halo bias, including both scale-dependent and -independent contributions, in the case of non-Gaussian initial conditions with general bispectra. Our main results are summarized as follows: \begin{itemize} \item{ Equations (\ref{EQ:fcollform}) and (\ref{EQ:fcoll}) give the collapsed fraction to leading order in the expansion of the three-point connected correlator in equation (\ref{EQ:sysexpansion}). In addition to being useful for other applications, this expression serves as a starting point for deriving the leading-order conditional mass function and linear halo bias.} \item{The next-to-leading order term of the collapsed fraction is given by equation (\ref{EQ:f_coll_2}). When combined with the leading-order contribution, this term more accurately accounts for the hierarchy of three-point correlators appearing in the excursion-set random-walk distribution function, equation (\ref{EQ:PIgen}). } \item{Our expression for the leading-order conditional mass function is equation (\ref{EQ:nm_cond}). We note that this equation recovers the \citet{Lo-Verde:2008rt} mass function in the limit where the environmental density filtering radius is arbitrarily large. Next-to-leading order corrections in the large-scale environment limit of the conditional mass function can be obtained from equations (\ref{EQ:dfcolldS_1storder}) and (\ref{EQ:dfcolldS_2lsl}). } \item{ The leading-order scale-independent and -dependent linear bias parameters are given by equation (\ref{EQ:SI_bias_1}) and (\ref{EQ:sd_bias_1storder}) respectively. The path-integral excursion set method to leading order recovers equations (115) and (118) of \citet{2011PhRvD..84f3512D} for $N=3$. Notably, we reproduce the additional scale-dependent term involving a derivative of the form factor, which was only recently pointed out by \citet{2011PhRvD..84f3512D}. While this term is negligible for the local template in the large-scale regime, it is important in other templates, where neglecting it significantly degrades the accuracy when compared to the bias measured from N-body simulations \citep{2011PhRvD..84f1301D}.} \item{The scale-independent and -dependent bias up to next-to-leading order in (\ref{EQ:sysexpansion}) are given by equations (\ref{EQ:si_bias_2ndorder}) and (\ref{EQ:2ndorderSDbias}) respectively. For cluster-halo masses ($M\sim10^{15}\Msun/h)$, the next-to-leading order terms suppress the amplitude of both contributions to the bias by $\sim5-10\%$. In both cases, the relative effects of the next-to-leading order corrections grow as the mass is decreased. However, we caution that such large effects in the low-mass regime (see Figures \ref{FIG:sd_bias_local} and \ref{FIG:sd_bias_orthogonal} for example) may signal the breakdown of the expansion in (\ref{EQ:sysexpansion}). We note that even the amplitude of the scale-dependent bias of the local template in the low-$k$ limit is modified in the excursion set prediction, thus altering a well-known result (see equation (\ref{EQ:local_lowk_2ndorder})). } \end{itemize} For the bispectrum templates tested in this work, the next-to-leading order terms become similar to the leading-order terms for masses as large as $M\sim5\times10^{13}\Msun/h$ (for which $\sqrt{S} / \delta_c = 0.62$). This calls into question the validity of the expansion (\ref{EQ:sysexpansion}) at those masses and below. On the other hand, galaxy surveys aiming to constrain PNG will require predictions that are applicable for galactic halos, whose masses are typically lower. Corrections to the bias due to environment and formation history may be important if non-Gaussianity is detected, because they could affect the value of $\fNL$ that is extracted. Our findings therefore motivate more work towards understanding the range of validity of (\ref{EQ:sysexpansion}), and possible alternatives to extend the excursion set method to galactic mass-scales \citep{2011JCAP...02..001D,2011arXiv1108.5512S,2012MNRAS.420..369M}. Note that we have quantified the environmental effects only due to PNG, for simplicity neglecting additional effects within the model that arise from non-Markovianity introduced by the filter function. Extensions of this work should focus on the full effects of the environment on halo formation in the context of the halo bias with non-Gaussian initial conditions. In addition to resolving the potential issues above, future effort should be devoted to testing the excursion set model against the bias as measured in N-body simulations, along with the numerous analytical predictions in the literature. We note that some authors have required a ``fudge factor" applied to the analytical predictions in order to reduce their amplitude by $\sim10-25\%$ and improve agreement with simulations \citep[e.g.][]{2009MNRAS.398..321G,2010PhRvD..81f3530G,2010MNRAS.402..191P,2012JCAP...03..002W}. Though this fudge factor has sometimes been attributed to non-spherical collapse, \cite{2010ApJ...711..907M,2010ApJ...717..515M,2010ApJ...717..526M} note that a similar factor naturally arises within the excursion set model from the stochasticity of the collapse barrier \citep[see also][]{Robertson:2008ad}. We point out that the next-to-leading order corrections that we derived here also act to diminish the amplitude of the scale-dependent bias (i.e by $\lesssim 40 \%$ for $M > 10^{14}\Msun/h$). Though it is difficult to draw conclusions at this time, it is possible that the ``memory" effects encapsulated in these terms, in combination with other effects (see below), may play a role in the reconciliation of analytical predictions with the lower amplitudes observed in simulations by some authors. In comparing the excursion set bias to N-body simulations, it is important to take into account the full range of physical effects accessible to the model: 1) The effects of environment and formation history encoded in the non-Markovianity from both non-Gaussianity \citep[][and the current work]{2010ApJ...717..526M,2011MNRAS.415.1913D,2011MNRAS.418.2403D} and the filter function \citep{2010ApJ...711..907M,2011MNRAS.411.2644M}. 2) The stochasticity of the collapse barrier to parameterize the complex nature of halo collapse \citep{Robertson:2008ad,2010ApJ...717..515M}, and 3) Non-spherical collapse characterized by a dependence of the collapse barrier on the filtering scale \citep{2002MNRAS.329...61S,Zhang:2006ek,2011MNRAS.412.2587D,2011MNRAS.418.2403D,Adshead2012}. With regards to an improved treatment of the collapse barrier, we became aware of a calculation by \citet{Adshead2012} during the preparation of this manuscript. While they consider only leading order terms in the expansion, (\ref{EQ:sysexpansion}), they add corrections to the scale-dependent bias due to a moving barrier. We note that they also recover the $N=3$ case of equation (118) in \citet{2011PhRvD..84f3512D} by setting the barrier to a constant, in agreement with our findings. The combination of a higher-order treatment of the connected three-point correlators with their moving barrier analysis would be a natural extension to this work. | 12 | 6 | 1206.3305 |
1206 | 1206.1907_arXiv.txt | Filamentary structures are ubiquitously seen in the interstellar medium. The concentrated molecular mass in the filaments allows fragmentation to occur in a shorter timescale than the timescale of the global collapse. Such hierarchical fragmentation may further assist the dissipation of excessive angular momentum. It is crucial to resolve the morphology and the internal velocity structures of the molecular filaments observationally. We perform 0$''$.5--2$''$.5 angular resolution interferometric observations toward the nearly face--on OB cluster forming region G33.92+0.11. Observations of various spectral lines as well as the millimeter dust continuum emission, consistently trace several $\sim$1 pc scale, clumpy molecular arms. Some of the molecular arms geometrically merge to an inner 3.0$^{\mbox{\scriptsize{+2.8}}}_{\mbox{-\scriptsize{1.4}}}\cdot$10$^{3}$\,$M_{\odot}$, 0.6 pc scale central molecular clump, and may directly channel the molecular gas to the warm ($\sim$50 K) molecular gas immediately surrounding the centrally embedded OB stars. The NH$_{3}$ spectra suggest a medium turbulence line width of FWHM$\lesssim$2\,km\,s$^{-1}$ in the central molecular clump, implying a $\gtrsim$10 times larger molecular mass than the virial mass. Feedbacks from shocks and the centrally embedded OB stars and localized (proto)stellar clusters, likely play a key role in the heating of molecular gas and could lead to the observed chemical stratification. Although (proto)stellar feedbacks are already present, G33.92+0.11 chemically appears to be at an early evolutionary stage given by the low abundance limit of SO$_{2}$ observed in this region. | \label{chap_introduction} Analyses of visual and infrared extinction (Rathborne et al. 2006; Butler \& Tan 2009; Schneider et al. 2011), and the Herschel Space Telescope observations of thermal dust emission (Andr{\'e} et al. 2010; Henning et al. 2010; Men'shchikov et al.2010; Molinari et al. 2010) unveiled overall filamentary and clumpy morphology of the molecular interstellar medium (ISM). How the densest molecular clumps/cores as well as the subsequent stellar clusters will form, are of fundamental interest in the evolution of molecular filaments (c.f. Klessen \& Burkert 2000; Klessen \& Burkert 2001; Bonnell \& Bate 2002; Bate et al. 2003; Padoan et al. 2007; V{\'a}zquez-Semadeni et al. 2007; Myers 2011). Observational case studies in nearby low--mass star forming regions have been reviewed by Myers (2009). At further distances of the Orion cloud and the Cygnus--X region, which form high--mass stars (e.g. $\ge$8 $M_{\odot}$), parsec scale molecular filaments are well known (e.g. Orion: Megzer 1990; Dutrey et al. 1993; Tatematsu et al. 1993, 1998; Chini et al. 1997; Buckle et al. 2010; Shimajiri et al. 2011; Cygnus--X: Chandler et al. 1993; Bontemps et al. 2010; Schneider et al. 2010), including the NH$_{3}$ emission filaments which radiate from the Orion--KL massive star forming core (Wiseman \& Ho 1996, 1998). As the majority of massive OB cluster forming molecular clouds are located at the typical distances of a few kpc, their filamentary structures and kinematics are only now being explored with high angular resolution observations. Interferometric observations of the NH$_{3}$ emission on Infrared Dark Clouds (IRDCs) G28.34+0.06 and G30.88+00.13 (Wang et al. 2008; Zhang \& Wang 2011), and the submillimeter bolometer observations on IRDC G304.74+01.32 (Miettinen \& Harju 2010), unveiled systems of parsec scale massive molecular filaments. High angular resolution observations of the millimeter and submillimeter thermal dust continuum emission on IRDC G28.34+0.06 (Zhang et al. 2009) and G030.88+00.13 (Swift 2009; Zhang \& Wang 2011) have demonstrated that fragmentation takes place within parsec scale molecular filaments, which leads to the formation of regularly spaced 10$^{1}$--10$^{2}$\,$M_{\odot}$ molecular cores embedded in multiple distinct condensations or clumps (Wang et al. 2011). Stability and chemical evolution of filamentary IRDCs have been addressed in observational studies of G29.96--0.02, G35.20--1.74 (Pillai et al. 2011) and IRAS 20293+3952 (Busquet et al. 2010). By combining single dish and interferometric observations of the thermal dust continuum emission obtained toward the massive molecular \textit{Hub--Filament System (HFS)} G10.6-0.4, Liu et al. (2012) reported hierarchical fragmentation at $\sim$10 pc scales within this region, which suggests a scenario of OB cluster formation via hierarchical contraction. In the meantime, by analyzing the kinematics in the W33A region, Galv{\'a}n-Madrid et al. (2010) proposed that the collision of molecular filaments is conducive to the formation of massive stars. Evidence for filament--filament collisions has recently been reported by Jim{\'e}nez-Serra et al. (2010) and Csengeri et al. (2011a) toward the IRDC G035.39-00.33 and DR21 region, respectively, via the detection of widespread SiO and weak and extended CH$_{3}$CN emission. Despite all this progress, it still remains unclear how the parsec scale molecular filaments connect with the $\lesssim$0.1 pc scale OB star--forming cores. Is the molecular gas funneled into the ultracompact (UC) H\textsc{ii} regions via molecular filaments? This question can be addressed by case studies of morphologies of dense molecular clouds. The majority of previous high angular resolution observations in high--mass star forming molecular clumps/cores focuses on the dynamically broadened systems, for the purposes of detecting rotation in massive disks, or global infall motions (e.g. Beltr{\'a}n et al. 2011; Galv{\'a}n-Madrid et al. 2009; Keto et al. 1987; Liu et al. 2010a, 2011; Sandell \& Wright 2010; Zapata et al. 2010; Zhang et al. 1997). In these cases, the dense molecular gas usually concentrates to a flattened plane due to rotation or the magnetic support. This geometrical flattening causes the structure to be blended along the line--of--sight, which is adverse for resolving the morphology. With the still limited angular resolution of the current instruments, we need to look for nearly face--on systems to avoid blending. Since the face--on orientation of the flattened accretion flows implies that the dominant motion is perpendicular to the line--of--sight, we expect line widths to be much smaller than the kinematically broadened line widths of edge--on systems, which are typically several km\,s$^{-1}$. To select the face--on flattened accretion flows, we have searched for narrow line systems among NRAO\footnote{The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.} Very Large Array (VLA) archived molecular line data. Our target sources were selected from a VLA D--array NH$_{3}$ line dataset of OB cluster forming regions. Part of our NH$_{3}$ database was obtained for the thesis work of Sollins (2005). Among the 7 samples in our database ( G10.6-0.4 (or G10.62-0.38), G20.08-0.14N, G28.20-0.05, G28.29-0.36, G33.92+0.11, G35.58-0.03, G43.80-0.13; Galv{\'a}n-Madrid et al. 2009; Keto et al, 1987,1988; Liu et al. 2010a; Sollins 2005), the target G33.92+0.11 shows a line width of $\lesssim$2.5\,km\,s$^{-1}$, which is much narrower than those of rest of the targets, and is the only source where the kinematic broadening does not cause the main and the satellite hyperfine inversion lines of the NH$_{3}$ (J,K)=(1,1) transitions to be blended. The UC H\textsc{ii} region G33.92+0.11 may represent an OB cluster forming region in a face--on configuration, providing an excellent opportunity to investigate the morphology, possible gravitational instability, and chemical stratification. G33.92+0.11, at a distance of 7.1$^{+1.2}_{-1.3}$ kpc (Fish et al. 2003) has a bolometric luminosity of 2.5$\times$10$^{5}$ L$_{\odot}$. Its strong free--free continuum emission at the centimeter bands ($\lambda$=3.6 cm: 1.1 Jy; $\lambda$=1.05 cm: 0.79 Jy), indicates the already existing embedded OB cluster. Berkeley Illinois Maryland Array (BIMA) observations (10$''$ resolution) of $^{13}$CO/C$^{18}$O 1--0 reveal two associated massive molecular clumps, G33.92+0.11 A and G33.92+0.11 B. The estimated H$_{2}$ mass (based on C$^{18}$O emission) of these two molecular clumps are 5100 $M_{\odot}$ and 3200 $M_{\odot}$, respectively. These values of H$_{2}$ mass are 10 times larger than the virial masses (G33.92+0.11 A: 520 $M_{\odot}$; G33.92+0.11 B: 270 $M_{\odot}$) estimated from the C$^{18}$O line width (Watt \& Mundy 1999). This could be due either to the existence of unusually strong support that counters the accretion flow, or to the fact that the majority of motions are perpendicular to the line--of--sight, yielding minimal blueshifted and redshifted velocities (see also Peretto 2006; Schneider et al. 2010; Smith et al. 2012). To our knowledge, we do not see any observational evidence for such unusually strong support, and thereby favor the later scenario. To resolve whether and how the molecular accretion flow continues from the external parsec scale filaments to the embedded UC H\textsc{ii} region, we carried out mosaic observations of the thermal dust continuum and molecular line emission toward G33.92+0.11 using the Submillimeter Array (SMA; Ho, Moran, \& Lo 2004)\footnote{The Submillimeter Array is a joint project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy and Astrophysics, and is funded by the Smithsonian Institution and the Academia Sinica.}, at (sub--)arcsecond resolution. The primary goals of the present paper are to demonstrate the context of the filamentary structures, and to address the internal fragmentation of the molecular filaments that leads to local intermediate-- or high--mass star formation. Details of our observations are summarized in Table \ref{chap_obs}. Observational results of G33.92+0.11 are presented in Section \ref{chap_result}. In Section \ref{chap_discussion}, we discuss the possible interpretations of the G33.92+0.11 data, and the physical implication. A summary is provided in Section \ref{chap_summary}. | \label{chap_discussion} In this section, we discuss physical implications of our observational results. In Section \ref{sub_g33pv}, we argue a small inclination angle of the target source G33.92+0.11 based on the detected kinematics. In Section \ref{sub_fragmentation}, we discuss the evolutionary context of OB cluster forming molecular clumps, based on the resolved geometry/morphology and kinematics in G33.92+0.11. In Section \ref{sub_angular momentum}, we address how the asymmetrical matter distribution in G33.92+0.11 alleviates the angular momentum problem in the accretion process. The resolved chemical diversities in G33.92+0.11 are discussed in Section \ref{sub_diversity}. \subsection{G33.92+0.11 as a Nearly Face--On Spinning--Up Massive Molecular Clump?} \label{sub_g33pv} With a $\sim$1.6--5.8$\cdot$10$^{3}$\,$M_{\odot}$ embedded molecular gas (see Section \ref{chap_ch0}), the expected rotational velocity ($\sim\sqrt{GM/r}$) at a 0.3 pc radius around G33.92+0.11 A should be 4.6--8.8\,km\,s$^{-1}$, while the expected free infall velocity ($\sim\sqrt{2GM/r}$) is 6.5--12\,km\,s$^{-1}$. Further in, i.e. at a radius of 0.05\,pc, the expected rotational or infall velocities around G33.92+0.11 A1 and A2 cores are $\gtrsim\pm$2.8 km\,s$^{-1}$. These velocities are large compared to the previously reported C$^{18}$O 1--0 line width of 2.5--3.2 km\,s$^{-1}$ (Watt \& Mundy 1999), and our NH$_{3}$ observations constrain the systematic motion of the dense gas to be within a velocity range of [$v_{lsr}$$-$1.6 km\,s$^{-1}$, $v_{lsr}$$+$1.0 km\,s$^{-1}$] toward G33.92+0.11 A (Section \ref{sub_moleculark}). The detected small velocities in G33.92+0.11 A can be explained by planar motions with an inclination angle much smaller than $\sim$30$^{\circ}$. Assuming that all OB cluster--forming massive molecular clumps are flattened either due to rotation or due to the magnetic support, and considering that their rotation axes do not have preferential orientations, the probability that the inclination angle (i.e. the angle between the rotational axis and the line of sight) of a target is smaller than 30$^{\circ}$ is about 13\%. Among the 7 targets in our database of VLA NH$_{3}$ observations (Section \ref{chap_introduction}), the probability to find at least one such highly inclined object can be estimated by $P$ = $1-(1-13\%)^{7}$ = $62.3\%$. As addressed in Section \ref{sub_moleculark}, the resolved motion in G33.92+0.11 A, B resembles an inclined disk--like structure as well. If G33.92+0.11 A, B are face--on massive molecular clumps, the global systematic rotation/infall will minimally contribute to the measured NH$_{3}$ line widths (e.g. by $\ll$1.4\,km\,s$^{-1}$). In the NE and SW regions which are less affected by these dynamical broadening (see also Section \ref{sub_moleculark}), as well as the G33.92+0.11 B, the detected NH$_{3}$ (1,1) line widths are FHWM$\sim$2\,km\,s$^{-1}$. At linear scales of $\sim$0.1\,pc, the detected $\sim$50\,$M_{\odot}$ localized dense molecular cores (Table \ref{table_cores}) have virial velocities of 1.4\,km\,s$^{-1}$, although they are expected to contribute to only $\sim$30\% of the measured flux in the case of optically thin emission (e.g. the NH$_{3}$ (1,1) satellite hyperfine lines). We suggest that the detected 2\,km\,s$^{-1}$ NH$_{3}$ (1,1) line width is mainly caused by turbulence in the bulk of the molecular gas. The NH$_{3}$ (3,3) line preferentially traces warmer and broader heated components, either associated with the central warm cores A1 and A2, or shocks. High angular resolution observations of NH$_{3}$ can help constrain the broadening by the kinematics of the known localized cores as well as the protostellar outflows, and provide a more accurate measure of turbulent velocity. We note that the previous observations on a similar type of object G10.6-0.4 have found high rotational/infall velocities of 3--4 km\,s$^{-1}$, and a turnover radius r$_{T}\sim$0.3\,pc within which specific angular momentum experiences a significant loss (Liu et al. 2010a; see Figure \ref{fig_ch0} and Figure \ref{fig_ocs} for a sense of structures at the 0.3\,pc radius in G33.92+0.11). Still, the smaller redshifted and blueshifted velocities detected in G33.92+0.11 are not conclusive evidence that G33.92+0.11 is a face--on system. Our new observations on G33.92+0.11 do not rule out the possibility that any support mechanism (e.g. turbulent, magnetic or thermal support) retards the molecular accretion flow. However, strong turbulence cannot be the dominant mechanism to support the molecular gas because turbulence itself also leads to the same level of spectral line broadening, which is discount by the observed narrow NH$_{3}$ lines. The evidence of strong magnetic support so far is absent. Thermal support is most unlikely since it also leads to the spectral line broadening, and is contradictory to the modest NH$_{3}$ and CH$_{3}$CN excitation temperature of 30--50\,K measured from this region (Section \ref{chap_ch3cn}, \ref{chap_nh3}). Additionally, strong thermal support is adverse to fragmentation, which is contradictory to the detection of rich localized structures in the 1.3 mm continuum images (Figure \ref{fig_ch0}). \subsection{The Evolutionary Context of the Hub--Filament System} \label{sub_fragmentation} The resolved geometry in G33.92+0.11 resembles a $\sim$1 pc scale, molecular \textit{Hub--Filament System} (c.f. \textit{HFS}: Myers et al. 2009, 2011). This system is embedded with a close pair of high--mass cores (Section \ref{chap_ch0}) in the central 0.1 pc region. The extended filaments in this system show numerous localized cores, and the \textit{in situ} intermediate-- or high--mass star formation which exerts (proto)stellar feedback. Over the observed area, the abundance of the late type molecule SO$_{2}$ is very low, implying that both the centrally embedded high--mass cores, and the intermediate-- or high--mass star forming cores located in the $\lesssim$1 pc scale molecular filaments (\textit{satellite cores} hereafter), are at an early evolutionary stage (see Section \ref{sub_diversity}). Recalling the observational facts that: \begin{itemize} \item[1.] We do not detect evidence of energetic massive molecular jets emanating from the central massive cores. \item[2.] From the observations of H30$\alpha$ emission, it seems that the UV photon illumination or the expansion of the ionized gas mostly affects the molecular gas southeast and northeast of the central massive cores. \item[3.] The high angular resolution observations of the thermal dust continuum emission show organized filamentary structures, rather than irregular fragments. Fine structures with small size scale can exist, even near the central OB cluster. For example, we see mini arms east of the core A2. This may indicate that either the feedback from the central OB cluster is not yet strong enough to significantly affect or sweep up the structure; or that the majority of molecular gas is (self--)shielded. \item[4.] Kinematically, the detected linewidths of the molecular gas toward G33.92+0.11 are small. The kinematics of the dense molecular gas appears to be still organized, without showing expansion signatures which typically have velocities of several km\,s$^{-1}$. These seem to be in contradiction to the expected strong influence by the central OB cluster. \end{itemize} We think that not all those satellite cores are secondary clumpy structures, whose formation is related to the influence of the strong feedback exerted from the central OB cluster (reference to Section \ref{chap_rrl} for the definition of the central OB cluster). Instead, they may form around the same time. We hypothesize that filamentary molecular structures already exist in a much early evolutionary stage (i.e. the time before the formation of the centralized massive cores and the satellite cores), and contribute to the accretion of molecular gas into the central hub (see below). The matter concentration in the initial Hub--Filament configuration leads to a shorter local free--fall timescale than the timescale of the global contraction, which allows the simultaneous formation of the satellite cores and the centralized massive cores. While dense molecular cores evolve in a much quicker dynamical timescale and form (proto)stellar objects (see also the discussion in Section \ref{sub_diversity}), the geometry of extended molecular filaments remains similar to their initial geometrical configuration. Given/assuming the comparable ages, the fact that the molecular mass of each of the central massive cores is several times higher than the molecular mass of the satellite cores (Table \ref{table_cores}) requires the centralized molecular cores to accrete more efficiently. This requirement can be realized because of two unique properties of the central region: (1) the deeper gravitational potential well in the center yields higher infall velocities, and (2) with the HFS configuration, molecular gas is channelled to the central region more efficiently through the detected molecular filaments. The fossil record of this continuous accretion onto the central molecular clump would be the detection of broad line emission from typical shock tracers such as SiO, OCS or CH$_{3}$CN (Bachiller \& Perez Gutierrez 1997; Jimenez-Serra et al. 2005; 2010; Csengeri et al. 2011a). Even with comparable accretion velocities, the more adequate molecular gas reservoir for the central region will allow higher accretion rate than the satellite cores that are embedded in isolated, single molecular filaments. The molecular filaments may persist until later evolutionary stages. As an example, toward G10.6-0.4 a centralized 175 $M_{\odot}$ OB cluster (Sollins \& Ho 2005), few expanding UC H\textsc{ii} regions (Liu, Zhang \& Ho. 2011), and many satellite high--mass stars (Liu et al. 2010b) are already present. However, its central $\sim$2 pc scale massive molecular clump still keeps the geometrical configuration that looks similar to the Hub--Filament configuration in G33.92+0.11 (Liu et al. 2011b). Since filamentary structures seen toward G10.6-0.4 have small cross sections, gas infall can overcome the strong feedback from the central OB cluster, helping the gas accretion onto it. This scenario is supported by advanced numerical MHD simulations (Smith et al. 2009; Wang et al. 2010), which show that in the \textit{clump-fed} configuration, the luminous O--type stars are fed by the extended ($\gg$0.1 pc) dense filaments connected to the parsec scale, central massive clump. The relevant recent analytical framework can be found in Hartmann et al. (2011), Myers et al. (2009), (2011), Pon et al. (2011), Toal{\'a} et al. (2011), and therein. \subsection{The Angular Momentum Issue} \label{sub_angular momentum} In addition to how the accretion flow overcomes the stellar feedback, another fundamental issue for the OB star formation is how to propagate angular momentum out, or how to redistribute the angular momentum. The angular momentum problem becomes important even before stellar feedback comes into play. The angular momentum is a conserved quantity that persistently affects the dynamical evolution, and may limit the mass of the massive core as well as the subsequently formed OB stars. Earlier analytical work suggested that strong (e.g. a few mG), organized magnetic field may play some role of dissipate the angular momentum (e.g. Keto et al. 1987). With high angular resolution observations of the polarized thermal dust emission and observations of multiple molecular lines on OB cluster forming region G31.41+0.31, Girart et al. (2009) reported the decrease of the specific angular momentum toward the center of the system, and the competitively strong organized magnetic field that helps propagate out the angular momentum. Contrary to the case of G31.41+0.31, deeper observations of polarized thermal dust emission on OB cluster forming region G10.6-0.4 yields a null detection, implying that either the magnetic field is weak, the orientation of the magnetic field lines are random, or inefficient grain alignment (Liu et al. 2011b). The molecular filaments around G10.6-0.4 have radiative orientations, which contradictory to the flattened structure expected for a strongly magnetized system with an organized B field. Observations of multiple spectral lines consistently indicate a significant decrease of the specific angular momentum toward the center of G10.6-0.4 (Liu et al. 2010a). Other than the scenario of dissipating angular momentum via magnetic field braking, Liu et al. (2010a) suggested fragmentation can help resolve this angular momentum issue. Theoretical studies further suggested that in strongly self--gravitational systems, molecular arms help propagate out the angular momentum (Lodato \& Rice 2005). In turbulent systems that have local distribution of velocity and specific angular momentum, the accretion can also take place in a diffusive manner, for which only the gas with lower specific angular momentum trickles in. The possibilities of redistributing angular momentum via fragmentation, or propagating out the angular momentum via molecular arms, are now being explored with our higher angular observations. If the comparably massive core A1 and A2 are orbiting with respect to each other, the gas accreting into the individual cores A1 and A2 only needs to lose excess specific angular momentum relative to that in the orbits of A1 and A2. Our results of the H30$\alpha$ line observations and the 1.3 mm continuum emission suggest that the core A1 itself may show multiplicity (Section \ref{chap_rrl}; Figure \ref{fig_h30a}, right). The subsequent fragmentation in core A1 may alleviate the angular momentum issue at scales $\ll$0.1 pc. On the other hand, we suspect that the aforementioned diffusive accretion process is not efficient enough at this 0.1--0.2 pc scale. The molecular arm in the north of core A2 (Figure \ref{fig_345ch0}) as well as the more extended ($\sim$1 pc) arm--S1 and arm--S2 may also help propagate out the angular momentum. At 1 pc scale, the size and curvature of the cavity wall have the evolutionary timescales of 10$^{4}$--10$^{5}$ years (Liu, Zhang, \& Ho 2011), which may be also sufficiently long for the SO$_{2}$ abundance to be enriched and become abundant in the gas phase (see Section$\,$\ref{sub_diversity}). However, we cannot rule out the possibility that some of the apparent parsec scale molecular arms are in fact curved cavity walls of the H\textsc{ii} region (e.g. arm--N), not the trailing arms that may form in a rotating system. \subsection{The Chemical Diversity and Its Origin} \label{sub_diversity} Our SMA images of different molecular tracers toward G33.92+0.11 suggest the presence of different chemical regimes across this high-mass star forming region. Within the central $\sim$0.1$\,$pc of G33.92+0.11, cores A1 and A2 present bright CH$_3$CN J=12-11 K=0,1 line emission, suggestive of hot-core chemistry (bright CH$_3$CN lines are typically found toward high-mass hot cores such as W3(H$_{2}$O), NGC7538 IRS1 or G24.78; see Chen et al. 2006; Bisschop et al. 2007; Galvan-Madrid et al. 2010). Other hot--core molecules (e.g. H$_2$S and SO) are also found toward the inner $<$15$''$ of G33.92+0.11 (see Section \ref{chap_s}), supporting the idea that cores A1 and A2 are hot--core--like objects where the molecular gas has been chemically enriched by the evaporation of the grain mantles by the heating from the central OB stars. The lack of detection of SO$_2$ (a late-type product of the sulfur chemistry), however, indicates that the time-scales involved in the formation of cores A1 and A2 are only some 10$^4$ yr (Charnley et al. 1997; Viti et al. 2004; Wakelam et al. 2004). This implies that cores A1 and A2 are likely young. This hypothesis is consistent with the moderate CH$_3$CN temperatures measured toward cores A1 and A2 (of $\sim$50$\,$K), and suggests that these cores could be at an intermediate evolutionary stage for which the central OB star cluster has not had enough time to heat up the surrounding molecular gas to the gas temperatures of $\sim$100-300 K typically found toward more evolved hot cores (see e.g. van der Tak et al. 2000). We note that the more evolved OB cluster forming clump G10.6-0.4 (a system with similar physical properties to those of G33.92+0.11, but seen at a different viewing angle), shows strong SO$_{2}$ emission lines (Liu et al. 2010a), supporting the idea that G33.92+0.11 is at an early stage in its evolution. Finally, toward cores A1 and A2, we do not find any line emission from SiO or OCS that could be associated with outflowing activity from the central OB star cluster (Section 3.1.4). At distances of $\sim$0.3-0.4 pc from the central cores A1 and A2, the SMA images reveal localized emission from typical shock tracers such as SiO and OCS (Martin-Pintado et al. 1992; Jimenez-Serra et al. 2005), showing broad line profiles (linewidths from $\sim$5-20$\,$km$\,$s$^{-1}$). As shown in Section 3.1.4, the regions where SiO and OCS have been enhanced tend to be located near the conjunctions of the massive molecular clump G33.92+0.11 and the external molecular arms/filaments. NH$_{3}$ is also significantly enhanced around the SiO emission peaks SiO--1,2 and toward the region where arm--S1,S2 continue into G33.92+0.11 A, indicating that a significant amount of molecular gas has been injected into the gas phase from dust grains. Since the NH$_3$ inversion lines reveal a temperature gradient as one moves inward the central clump in G33.92+0.11, we propose that the SiO, OCS and NH$_3$ enhancement found at distances of 0.3-0.4 pc from the central OB cluster, is due to gas accretion shocks at the regions where the external molecular arms/filaments are entering the massive molecular clump G33.92+0.11 A. We note that weaker CH$_3$CN emission is also detected toward these regions, suggesting that this emission could be associated with low-velocity shocks as found toward DR21(OH) by Csengeri et al. (2011a) and NGC 7538 S (Sandell \& Wright 2010). Alternatively, gas shock compression could increase the gas density and pressure toward these localized regions, accelerating their collapse and subsequently leading to the formation of new protostars. The molecular outflows driven by these new objects would interact with the surrounding medium within the central G33.92+0.11 clump, sputtering dust grains and injecting large amounts of molecular material into the gas phase (Caselli et al. 1997; Jimenez-Serra et al. 2008; Gusdorf et al. 2008). At even larger spatial scales from the central G33.92+0.11 A core (i.e. at $\sim$0.7 pc), our SMA data show that the large-scale filaments/arms present emission from sulfur-bearing species such as $^{13}$CS and SO. In particular, from Figures 4 and 6 there seems to be a systematic spatial shift between the 8$\,$$\mu$m emission (associated with PAH emission and found closer in to the central OB star cluster) and the $^{13}$CS, $^{13}$CO and SO lines. This chemical stratification has also been observed toward typical PDR regions such as the Orion bar, the Horse-Head Nebula or MonR2 (see respectively van der Wiel et al. 2009; Goicoechea et al. 2006; Bern\'{e} et al. 2009). Therefore, it is possible that the strong UV field arising from the central cluster of OB stars is escaping the dense gas of the central molecular clump, and illuminates the closer walls of the molecular filaments/arms leading to the formation of a typical PDR. Indeed, the H\textsc{ii} region detected toward G33.92+0.11 shows a cometary morphology, with the less-density gas (and therefore easier to escape from) toward the east (see Figure 9). The scenario where G33.92+0.11 shows multiple chemical regimes, will be tested in the near future with a deep and broad bandwidth molecular line survey toward the hot cores in G33.92+0.11 A, toward the shocked regions at the confluence of the molecular arms with the central clump, and toward the PDR found in arm-E. We performed high angular resolution observations in the 1.3 mm lines and the dust continuum emission using the SMA, of the UC H\textsc{ii} region G33.92+0.11. In addition, we observed the NH$_{3}$ (J, K) = (1,1), (2,2) and (3,3) lines with higher velocity resolution ($\le$0.6 km\,s$^{-1}$) using the VLA D--array. A total of 19 spectral lines are selected for detailed inspection and analysis. We compare these new observations with observations of another UC H\textsc{ii} region G10.6-0.4, which has comparable molecular mass, size, bolometric luminosity, and is located at a comparable distance. Each of these two targets may represent respectively, examples of highly inclined and face--on, rotationally flattened massive molecular clumps. Our main conclusions are summarized as follows: \begin{itemize} \item[1.] From $\ge$1 pc to $\le$0.1 pc scale, the molecular gas in G33.92+0.11 has a morphological configuration resembling a \textit{Hub--Filament System}. The UC H\textsc{ii} region is embedded in the center of the \textit{hub} (i.e. G33.92+0.11 A). The molecular gas appears to be heated by the UC H\textsc{ii} region and the embedded OB stars. Observations of NH$_{3}$ transitions show higher rotational temperature ($\gtrsim$35 K) close to the center of G33.92+0.11 A. Observations of CH$_{3}$CN J=12--11 transitions show the rotational temperature of 49.3 K at the center of G33.92+0.11 A. \item[2.] The brightest component of the UC H\textsc{ii} region has an elongated shape. We marginally resolve the blueshifted and redshfited motion of the ionized gas in this elongated region. The velocity scale of the motion is $\sim\pm$10 km\,s$^{-1}$, which can be explained by the thermal expansion of the ionized gas, or a collimated, low velocity ionized jet. \item[3.] Numerous satellite dense cores are embedded in the resolved molecular filaments. In the center of the \textit{hub} G33.92+0.11 A, a pair of centralized massive cores show several times higher molecular mass than the rest of the satellite dense cores. The centralized massive cores account for 11\% of the total molecular mass in the G33.92+0.11 A region (including arm--S1, S2). Together with the satellite dense cores, the resolved compact cores account for 24.3 \% of the total molecular mass in the G33.92+0.11 A region. \item[4.] We suggest (hierarchical) fragmentation is a plausible mechanism to resolve the angular momentum issue of the core/(proto)stellar accretion. \item[5.] Cores embedded in the G33.92+0.11 A region appear to be chemically young as suggested by the low upper limit of the SO$_{2}$ abundance measured toward this source. This is in contrast with the bright SO$_{2}$ emission found toward the target G10.6-0.4 (Liu et al. 2010a). The abundance X(SO$_{2}$) is constrained to be less than 3$\times$10$^{-9}$. \item[6.] An overall north--south (or northeast--southwest) velocity gradient is seen in molecular gas in G33.92+0.11. At a parsec scale radius, the velocity gradient is about 0.96 km\,s$^{-1}$\,pc$^{-1}$. A higher velocity gradient of 4.6 km\,s$^{-1}$\,pc$^{-1}$ may be seen in the central $\pm$10$''$ (i.e. $\pm$0.344 pc) area in G33.92+0.11 A. The velocity profile is asymmetrical in the central 0.6 pc area in G33.92+0.11 A, and show higher blueshifted velocity than the redshifted velocity. The intrinsic spatial and velocity asymmetries appear to be essential in such strongly self--gravitating OB cluster forming molecular clumps. The asymmetry of the velocity profile in the target G10.6-0.4 is reported in Liu et al. (2010a). \item[7.] We resolved zones that show chemical diversities. The molecular line emission in the central 0.1--0.2 region in G33.92+0.11 A can be characterized by a hot core chemistry. We do not see signatures of strong shocks in this central region. In diameters of 0.2--0.5 pc in G33.92+0.11 A, several places show strong SiO and OCS emission, which are consistent with the shock enrichment of these species. In more extended areas, stratifications of the 8 $\mu$m emission, the $^{13}$CO/C$^{18}$O emission, the SO emission, and the $^{13}$CS emission resembles a PDR chemistry induced by the illumination from the central OB cluster. Follow up observations on this target may improve our understanding of the chemical evolution in the OB cluster forming massive molecular envelope. \end{itemize} We emphasize that our main focus is the formation of an overall OB cluster. Studies of accretion of individual OB stars cannot be addressed because of the still insufficient angular resolution. ALMA observations in the future will provide much better angular/velocity resolution and sensitivity, to systematically survey other similar targets, or fainter objects with lower masses or lower temperatures. | 12 | 6 | 1206.1907 |
1206 | 1206.2653_arXiv.txt | Most of the successful physical theories rely on the constancy of a few fundamental quantities such as the fine structure constant, $\alpha=e^2/\hbar c$, the proton-to-electron mass ratio, $\mu$, etc. Some modern theories of high energy physics that try to unify the fundamental interactions predict the variation of these dimensionless fundamental constants over cosmological scales \citep[see] [and references therein for more details]{Uzan03}. Current laboratory constraints exclude any significant variation of these constants over solar system scales and on geological time scales \citep[see][]{Olive04,Petrov06,Rosenband08}. It is not observationally/experimentally excluded however that they could vary over cosmological scales. Therefore, constraining time and spatial variations of fundamental constants of physics will have a great impact on understanding the true behavior of the nature. \citet{Savedoff56} first pointed out the possibility of using redshifted atomic lines from distant objects to test the evolution of dimensionless physical constants. Initial attempts in this field mainly used the Alkali-Doublet (AD) method to constrain $\alpha$ variation \citep{Savedoff56,Bahcall67b,Wolfe76,Levshakov94,Varshalovich96,Cowie95,Varshalovich00,Murphy01, Chand05}. While the AD method is simple, and least affected by systematics related to ionization and chemical inhomogeneities, the limits achieved on $\Delta\alpha/\alpha$ $\equiv(\alpha_{\rm z}-\alpha_{0})/\alpha_{0}$ are not usually stringent \footnote{Here $\alpha_{\rm z}$ and $\alpha_0$ are the measured values of $\alpha$ at any redshift, $z$, and in the laboratory on Earth}. The most precise value reported to date using this method being $\Delta\alpha/\alpha =-(0.02\pm0.55)\times10^{-5}$ \citep{Chand05} over a redshift range of 1.59$\le z\le$ 2.92. \citet{Dzuba99a,Dzuba99b} and \citet{Webb99} introduced the Many-Multiplet (MM) method as a generalization of the AD method, in which one correlates different multiplets from different ions simultaneously. Applying this method on a sample of 128 absorbers observed at high spectral resolution with the Keck telescope, \citet{Murphy03} claimed a detection, $\Delta\alpha$/$\alpha$=$-(0.57\pm0.10)\times10^{-5}$, over the redshift range 0.2$\le z \le$3.7. However, this result was not confirmed by \citet{Srianand04} and \citet{Chand04} who used higher signal-to-noise ratio (SNR~$\sim$~70 per pixel), high spectral resolution ($R\ge$45000) UVES/VLT data of 23 \MgII\ systems detected towards 18 quasars in the redshift range $0.4\le z\le 2.3$ and found ${ \Delta\alpha/\alpha}$~=~${ (-0.06\pm0.06)\times10^{-5}}$. This analysis was criticized by \citet{Murphy07prl}. However, from the reanalysis of the UVES data, using the Voigt profile fitting code VPFIT\footnote{http://www.ast.cam.ac.uk/~rfc/vpfit.html}, \citet{Srianand07b} confirmed the null result albeit with larger error bars (i.e ${ \Delta\alpha/\alpha}$~=~${ (0.01\pm0.15)\times10^{-5}}$). Other analysis using only \FeII\ transitions in two particularly well suited absorption systems at $z = 1.15$ and $z = 1.84$ failed to confirm any variation in $\alpha$ \citep{Quast04, Levshakov06, Chand06, Levshakov07}. Recently, \citet{Webb11} have reported the results of the analysis of 153 systems present in quasar spectra observed with VLT/UVES. They find that $\alpha$ increases with increasing cosmological distance from the Earth. Moreover for $z<1.8$, they confirm the results by \citet{Srianand07b}, ${\Delta\alpha/\alpha}$~=~$-(0.6\pm1.6)\times10^{-6}$. However combining their new VLT measurements with their previous Keck measurements they suggest the possibility for a spatial variation of $\alpha$ and speculate on the existence of an $\alpha-$dipole. If true, this dipole is very difficult to explain theoretically \citep{Olive11}. While the MM-method provides improved precision, it is affected by systematics related to ionization, chemical inhomogeneities and isotopic composition. The effects of inhomogeneities can be canceled using a large sample of absorption systems but the effects of isotopic composition will likely to remain an issue. Most of the existing theories predict that the proton-to-electron mass ratio $\mu$ should vary much more than $\alpha$ \citep[for example see][and references therein]{Olive02,Dent03,Dine03} though some predicts the reverse \citep[][]{Dent08}. The variations of $\mu$ can be probed using H$_2$ Lyman and Werner band absorption lines \citep{Varshalovich93}. H$_2$ molecules are occasionally detected in high redshift damped Lyman-$\alpha$ systems \citep{Petitjean00,ledoux03,noterdaeme08,Srianand12} with only a handful of them being suitable for probing the variation of $\mu$. No clear indication of any variation in $\mu$ in excess of 1 part in 10$^5$ is seen in the existing data for $z\ge2$ \citep{Ivanchik05, Reinhold06, King08,Thompson09b, Wendt11, vanWeerdenburg11}. By comparing inversion line transitions of NH$_3$ with the rotational transitions of other molecules, a strong constraint on $\Delta \mu/\mu$ can be obtained \citep{Murphy08}. At present such an exercise is possible for only two gravitationally lensed systems at $z<1$ \citep{Henkel05, Henkel08}. The best reported constraint is $\Delta \mu/\mu \le 3.6\times 10^{-7} (3\sigma)$ at $z$ = 0.685 by \citet{Kanekar11}. Detecting more NH$_3$ absorption towards normal quasars is required to reduce systematics related to the usage of lensed quasars (See \citet{Henkel08} for discussions on various other systematics). As the energy of the 21-cm transition is proportional to, $x\equiv\alpha^2 g_{\rm p}/ \mu$, high resolution optical spectra and 21-cm spectra can be used together to probe the combined variation of these constants \citep{Wolfe76}. Constraints of the order of $\sigma (\Delta x/x) \lesssim 10^{-5}$ were obtained towards individual systems \citep{Cowie95,Kanekar06,Srianand10}. \citet{Tzanavaris07} derived ${\Delta x/ x} = (0.63\pm0.99)\times 10^{-5}$ for a sample of nine 21-cm absorbers with $0.23~ <~ z~ <~ 2.35$. The majority of the 21-cm spectra used in this study were digitally scanned from the printed literature and the UV-optical data were obtained mainly with VLT/UVES. Better constraints can be derived from higher quality spectra in the radio and optical wavelength ranges of a well selected sample of 21-cm absorbers. This is possible now thanks to systematic surveys for 21-cm absorption towards strong Mg~{\sc ii} absorbers \citep[e.g.][]{Gupta09}. This work has resulted in the detection of 9 new 21-cm absorption systems over a narrow redshift range (i.e 1.05$\le z\le$1.45) that can be used for constraining $\Delta x/x$. While this technique is very powerful there are two issues that introduce systematic uncertainties in the measurements. These are: (i) the identification of the optical component corresponding to the gas that produces the 21-cm absorption and (ii) the fact that the radio and optical sources could probe different volumes of the absorbing gas as the radio emitting region in quasars is in general extended compared to the UV emitting region. It has been suggested that the gas detected by their \CI\ and/or $\rm H_2$ absorption is closely associated with the 21-cm gas \citep[][]{Cowie95,Srianand10}. However, only few 21-cm absorbers show detectable \CI\ and $\rm H_2$ absorption and even in these cases velocity offsets up to 1-2 \kms\ are noticed \citep[][]{Srianand12}. All these indicate \CI/$\rm H_2$ and 21-cm absorption need not originate from the same physical region. Another option is to connect 21-cm absorption to absorption from singly ionized species that trace \HI\ gas. For example \citet{Tzanavaris07} have associated the pixel with strongest absorption in the UV with the pixel with the strongest 21-cm absorption. As neighboring pixels are correlated in optical spectra, the redshift of the strongest metal absorption component will be better defined by using simultaneous Voigt profile fits to the absorption lines. This is the method we adopt in the analysis presented here. The second uncertainty discussed above can be minimized by selecting absorbers towards quasars that are compact at milliarcsec scales. While individual measurements may not be completely free of these systematics, even after careful consideration of the specific properties of the system, it should be possible to minimize them and get a statistically reliable measurement using large sample of absorbers. As different methods used for constraining the fundamental constants suffer from different systematic effects it is important to increase the number of measurements based on each method to address the time and space variation of different constants. Here we provide new measurements of \dxx\ using a new sample of 21-cm absorbers. We have selected 5 systems from the literature [4 from \citet{Gupta09} and one from \citet{Kanekar09}] previously known to be associated with narrow 21-cm absorption lines towards radio sources that are compact at arcsecond scales. We have obtained high resolution UV and radio data of the quasars together with high resolution Very Large Baseline Array (VLBA) images. We report here the analysis of this dataset. This paper is organized as following. In Section 2, we present details of optical and radio observations and data reduction. In Sections 3 and 4 we provide details of Gaussian fits to the 21-cm absorption lines and Voigt profile fitting of the UV lines. In Section 5, we summarize our $\Delta x/x$ measurements in individual systems and discuss the associated systematic errors. In Section 6 we discuss the results and conclude. We use simultaneous Voigt profile fits to identify the redshift of the strongest UV component closest to the 21-cm absorption. We also discuss the results if we adopt the method used by \citet{Tzanavaris07}. \begin{table*} \caption{Log of the optical spectroscopic observation with VLT/UVES} \begin{center} \begin{tabular}{cccccccc} \hline \hline Source name & Exposure name &Date & Starting & Exposure & Setting & Seeing & Airmass\\ & & & Time (UT) & (sec) & &(arcsec)& \\ ~~~~~~~~(1)& (2) & (3) & (4) & (5) & (6) & (7) & (8)\\ \hline J0108$-$0037& EXP1 &2008-11-21 &01:15:02 & 3700 & 390+580 &0.64 &1.11 \\ & EXP2 &2008-11-23 &02:41:45 & 3700 & 390+580 &0.77 &1.13 \\ & EXP3 &2008-11-25 &01:52:08 & 3700 & 390+580 &0.89 &1.10 \\ & EXP4 &2008-12-03 &01:11:20 & 3690 & 390+580 &0.71 &1.10 \\ J1623+0718 & EXP1 &2010-05-08 &05:48:49 & 3340 & 390+580 &1.33 &1.18 \\ & EXP2 &2010-08-07 &01:08:41 & 3340 & 390+580 &0.82 &1.23 \\ & EXP3 &2010-08-08 &00:45:37 & 3340 & 390+580 &0.86 &1.20 \\ & EXP4 &2010-08-09 &00:56:50 & 3340 & 390+580 &0.70 &1.22 \\ J2340$-$0053& EXP1 &2008-10-02 &02:39:30 & 4500 & 390+580 &0.88 &1.13 \\ & EXP2 &2008-10-05 &02:01:02 & 4500 & 390+580 &0.82 &1.17 \\ & EXP3 &2008-10-05 &03:25:10 & 4500 & 390+580 &0.88 &1.09 \\ & EXP4 &2008-10-06 &00:28:59 & 4500 & 390+580 &0.90 &1.50 \\ & EXP5 &2008-10-06 &01:55:32 & 4500 & 390+580 &0.79 &1.18 \\ & EXP6 &2008-10-28 &04:41:03 & 4500 & 390+580 &0.79 &1.45 \\ J2358$-$1020& EXP1 &2010-08-04 &06:27:07 & 3340 & 390+580 &0.75 &1.10 \\ & EXP2 &2010-08-06 &04:43:45 & 3340 & 390+580 &0.69 &1.40 \\ & EXP3 &2010-08-06 &05:50:01 & 3340 & 390+580 &0.71 &1.16 \\ & EXP4 &2010-08-06 &06:55:07 & 3340 & 390+580 &0.64 &1.05 \\ & EXP5 &2010-08-06 &08:00:14 & 3340 & 390+580 &0.65 &1.04 \\ & EXP6 &2010-08-06 &09:05:21 & 3340 & 390+580 &0.77 &1.10 \\ & EXP7 &2010-08-07 &04:53:34 & 3340 & 390+580 &0.78 &1.34 \\ J0501$-$0159& EXP1 &2000-10-21 &06:13:17 & 3600 & 437+750 &0.61 &1.17 \\ & EXP2 &2000-10-23 &04:08:46 & 3600 & 346+580 &0.53 &1.73 \\ & EXP3 &2001-10-16 &07:20:51 & 5400 & 346+570 &0.46 &1.10 \\ & EXP4 &2004-10-21 &04:38:08 & 4500 & 390+564 &0.63 &1.25 \\ & EXP5 &2004-10-21 &05:42:38 & 5400 & 390+564 &0.79 &1.56 \\ & EXP6 &2004-10-21 &07:05:51 & 3600 & 437+860 &1.17 &1.10 \\ & EXP7 &2004-10-22 &04:38:08 & 3600 & 437+860 &0.84 &1.29 \\ & EXP8 &2004-10-22 &05:42:42 & 4500 & 390+564 &0.89 &1.12 \\ & EXP9 &2004-10-22 &07:05:55 & 4500 & 390+564 &0.59 &1.81 \\ & EXP10&2004-10-22 &08:04:58 & 3360 & 437+860 &1.00 &1.09 \\ \hline \end{tabular} \end{center} \begin{flushleft} Column 1: Source name; Column 2: Assigned name for the exposure. Column 3: Date of observation; Column 4: Starting time of exposure; Column 5: Exposure time; Column 6: Spectrograph settings; Column 7: Seeing in arcsec; Column 8: Airmass at the beginning of the exposures. \end{flushleft} \label{MgIIslist} \end{table*} | In Table~\ref{tab_dxx_all} we summarize the \dxx\ measurements in individual systems. We recollect that the values are obtained under the assumption that the strongest UV and 21-cm absorption are produced by the same gas. The final errors in \dxx\ for our VLT/UVES measurements given in column (8) are the quadratic sum of the statistical and systematic errors. We find the simple mean of \dxx\ regardless of the associated errors in individual measurements to be $ $(0.0$\pm$1.5)$\times 10^{-6}$ with an rms of 3.0$\times 10^{-6}$ around the mean. A constant \dxx\ of $ $0.0$\times 10^{-6}$ has a reduced $\chi^2$ of 1.0 for our four UVES measurements that shows the estimated errors in \dxx\ are not underestimated. If we apply the standard procedure of weighting the data points by their inverse square errors (given in column (8) of Table~\ref{tab_dxx_all}), we get $-(0.1\pm1.3)\times 10^{-6}$. \begin{figure} \centering \includegraphics[width=0.75\hsize,bb=18 18 594 774,clip=,angle=90]{dx_other_1.ps} \caption{Comparison of our \dxx\ measurements with three other measurements in the literature. Filled circles are our measurements and the filled square is from \citet{Srianand10} using a 21-cm absorber at $z \sim$ 3.174 along the line of sight of J1337$+$3152. The dashed-dotted box corresponds to the standard deviation of our four measurements The 1$\sigma$ error around the mean is shown as a solid box. The dashed line and long-dashed box are the \dxx\ and its error measured by \citet{Tzanavaris07}. The filled and empty stars are respectively from \citet{Kanekar10} and \citet{Kanekar06}. } \label{fig_dx_all} \end{figure} Our VLBA images suggest that two of the quasars in the sample (i.e J1623$+$0718 and J0501$-$0159) may have resolved structures at milliarcsec scale containing more than 50\% of the flux. This may imply that if the absorbing gas is extended then some additional 21-cm absorption can originate from the gas that is not probed by the optical sight lines. However in the remaining two quasars this is not the case as most of the flux is recovered in the unresolved VLBA component. If we only use these two cases we derive \dxx\ = $+(0.2\pm1.6)\times10^{-6}$. This is very much consistent with what we find using all the four systems. Therefore the analysis presented here does not find any statistically significant variation in $x$ and this null result may not be related to systematics due to radio structure. There are two quasars for which we have spectra from both VLT and Keck. As can be seen from Table~\ref{tab_dxx_all} in both cases the VLT and Keck measurements are consistent with each other with Keck measurements having larger statistical uncertainties. The mean \dxx\ from VLT/UVES data of $ $(0.0$\pm$1.5)$\times 10^{-6}$ is consistent with \dxx\ = $+$(1.8$\pm$2.8)$\times 10^{-6}$ from Keck/HIRES data where we could not include the systematic error. This is also the case for the weighted means. In Fig. \ref{fig_dx_all} we compare our \dxx\ results with other \dxx\ measurements from the literature. Filled circles are our measurements. The dashed-dotted rectangular box indicates the mean and standard deviation of our measurements. The solid rectangular box gives the mean and final error on it when combining the 4 measurements. The green box with the dashed line gives the weighted mean and 1$\sigma$ found by \citet{Tzanavaris07}. The two filled stars are from \citet{Kanekar10} and the empty star is from \citet{Kanekar06}. The data point at $z\sim 3.174$ is from \citet{Srianand10}. The better accuracy reached in our study is mainly due to the following reasons: (1) Systems are chosen to have narrow 21-cm absorption components. (2) Three of the quasars have high resolution (R$\sim$45000) and high SNR UV-optical spectra obtained specifically for constraining \dxx\ with attached ThAr calibration lamps for each spectrum. This minimizes the systematic error of wavelength calibration. (3) Very high ($\sim$1 \kms per channel) or high ($2-4$ \kms per channel) resolution 21-cm spectra are used. (4) As we could get repeated observations for 21-cm absorptions we are able to identify the RFI related problems in the absorption profiles. (5) We also estimate \dxx\ by using only absorbers for which the background sources are unresolved even at milliarcsec scale in VLBA images. \begin{figure} \centering \includegraphics[width=0.75\hsize,bb=18 18 594 774,clip=,angle=90]{dalpha.ps} \caption{Comparison of \daa\ estimated in this work with other measurements in literature. The dashed dotted line and the surrounded solid box show our measured \daa\ and its error and the filled square is the one from \citet{Srianand10} based on the same method and assuming $\mu$ and $g_{\rm p}$ are not changing with time.} \label{fig_alpha_all} \end{figure} \begin{figure} \centering \includegraphics[width=0.75\hsize,bb=18 18 594 774,clip=,angle=90]{dmu.ps} \caption{Comparison of \dmm\ estimated in this work with other measurements in literature. The dashed dotted line and the surrounded solid box show our measured \dmm\ and its error based on our \dxx\ measurements and assuming $\alpha$ and $g_p$ do not vary. Apart from the filled square at $z$$\sim$3.2 which is calculated from \dxx\ of \citet{Srianand10} with the assumption of non-variation of other constants, the rest of the measurements for $z > 2$ are based on the analysis of $\rm H_2$ electronic transitions. The empty triangle towards up is from \citet{King11}, empty star from \citet{Malec10}, empty square with a large bar from \citet{vanWeerdenburg11}, empty circle with a large bar from \citet{Wendt11}, filled triangles towards down from \citet{Thompson09b}, and filled triangles towards up from \citet{Reinhold06}. The two measurements at $z \le 1$ are based on the molecular inversion and rotational transitions. The filled and empty squares are from \citet{Henkel08} and \citet{Murphy08} respectively.} \label{fig_dmu_all} \end{figure} Although tight constraints on the variation of fundamental constants are obtained by comparing 21-cm and UV-optical redshifts, the method is not exempt of systematics as all other methods in this field. As it is has already been discussed, the main source of uncertainty on \dxx\ is related to the assumption used to associate one of the several UV-optical components to the 21-cm absorption. By choosing absorbers with compact background radio sources at mas scale one can minimize the uncertainties related to the possibility that optical and radio sightlines are different. Different methods have been implemented to associate the UV-optical component to the 21-cm one. \citet{Tzanavaris07} associated the pixel with strongest UV-optical optical depth to the pixel with strongest 21-cm optical depth. In this work we follow the same idea but using components of simultaneous Voigt profile fitting models. Using the same method as \citet{Tzanavaris07}, we find \dxx\ = $(3.6\pm3.1)\times10^{-6}$. Keeping this in mind we will now discuss the implication of our constraint on \dxx\ on the variation of individual constants that constitute $x$. As $x = g_{\rm p} \alpha^2/\mu$, its variation can be related to the variation of $g_{\rm p}$, $\alpha$, and/or $\mu$ via $\Delta x/x = \Delta g_{\rm p}/g_{\rm p} + 2\times \Delta \alpha/\alpha-\Delta \mu/\mu$. Therefore the constancy of $x$ can be related either to the constancy of all the three constants, $g_{\rm p}$, $\alpha$ and $\mu$, or to some complicated combination of variations of these constants with an overall null effect on $x$. Assuming $\mu$ and $g_{\rm p}$ are constants then our measured \dxx\ translates to \daa\ = $\left(0.0\pm0.8\right)\times 10^{-6}$ which is one of the most stringent constraint on the variation of $\alpha$. In Fig~\ref{fig_alpha_all} we summarize the available constraints on \daa\ from the literature. It is clear that our measurements are consistent with \daa = $(0.1\pm1.5)\times10^{-6}$ (and a factor 2 better than that) found by \citet{Srianand07b} and with the results of \citet{Webb11} for $z\le 1.8$ UVES data. Even if we use the conservative approach of \citet{Tzanavaris07} we get \daa\ = $(1.8\pm1.5)\times10^{-6}$ which is as good as the results from the MM method. \citet{Webb11} used a combined set of absorbers observed with VLT/UVES and Keck/HIRES to conjecture about the possible presence of a spatial dipole pattern in the variation of $\alpha$. Their best fitted model indicates a spatial dipole in the direction with right ascension 17.5$\pm$0.9 h and declination $-58 \pm 9$ deg, significant at the 4.2$\sigma$ level with \daa\ = $A r \cos(\Theta)$, where $A = (1.1\pm0.25)\times10^{-6}\rm GLyr^{-1}$, $r(z)=ct(z)$, $c$ being the speed of light and $t(z)$ the look back time, and $\Theta$ is the angle on the sky between the quasar sight line and the best fit dipole position. We calculated the prediction of this model for our sample using the same cosmology as \citet{Webb11}. We also calculated the error on \daa\ using \begin{equation} \sigma(\frac{\Delta\alpha}{\alpha}) = \sqrt{\left(\frac{\Delta\alpha/\alpha}{A}\right)^2\sigma_{A}^2+\left(\frac{\Delta\alpha/\alpha}{\cos(\Theta)}\right)^2\sigma_{\cos(\Theta)}^2}. \end{equation} The measured $\Theta$ and accordingly the predicted values for \daa\ are presented in columns 11 and 12 of Table~\ref{tab_dxx_all}. Last column of Table~\ref{tab_dxx_all} shows the difference of \daa\ between the dipole and our measurement and its error. For the sight lines towards J1623$+$0718 and J0501$-$0159 the dipole predicts a variation of $\alpha$ at, respectively, the $\sim$2.4$\sigma$ and 2.9$\sigma$ level. In both cases, our null results on the $\alpha$-variation are inconsistent with this dipole prediction at more than 90\% confidence level. For the other two sight lines towards J2340$-$0053 and J2358$-$1020 our measurements are consistent with null variation as also predicted by the dipole. In the case of J1337$+$3152 \citet{Srianand10} measured \dxx\ = $-(1.7\pm1.7)\times10^{-6}$ for the absorber at \zabs\ = 3.174 which translates to \daa\ = $-(0.9\pm0.9)\times10^{-6}$. The dipole prediction in this case is \daa\ = $-(2.70\pm1.9)\times10^{-6}$ with a difference of $-(1.80\pm2.1)\times10^{-6}$ with the measurement. The difference between these five measurements and the dipole predictions results in a $\chi^2$ of 14.5. The probability of $\chi^2$ $>$ 14.5 is $\sim$ 1\% which implies that the existence of a dipole is not favored by our measurements. More independent measurements especially towards systems where the dipole predicts large variations will be useful to confirm/refute the existence of the $\alpha-$dipole at higher significant level. Assuming that $\alpha$ and $g_{\rm p}$ have been constant we derive \dmm\ = $\left(0.0 \pm1.5 \right)\times 10^{-6}$. Fig. \ref{fig_dmu_all} compares our results with other direct measurements of \dmm\ obtained either using rotational transitions of $\rm H_2$ and HD molecules (for $z \ge 2.0$) or based on the comparison of NH$_3$ inversion transitions with some rotational transition lines (e.g. CO, CS, $\rm HC_3 N$; for $z \le 1.0$). While the constraints we get are not as good as the one obtained using NH$_3$ they are very stringent compared to those based on H$_2$ at $z\ge2$. What is more interesting is that our measurements fill the redshift gap between NH$_3$ and H$_2$ based measurements (see Fig.~\ref{fig_dmu_all}). If we use the 1$\sigma$ constraints on \daa\ found for $z\le1.8$ absorbers \citep[from][]{Srianand07b, Webb11} and \dmm\ estimated at $z\sim0.7$ using NH$_3$ \citep{Kanekar11}, considering they are valid at $z\sim1.3$, we get $\Delta g_{\rm p}/g_{\rm p} \le 3.5 \times10^{-6} (1\sigma)$ from our \dxx\ measurements. In summary, using 21-cm and metal UV absorption lines we are able to derive stringent constraints on the variation of $\alpha$, $\mu$, and $g_{\rm p}$. As discussed before the best estimate on \dmm\ at z $\le$1 is obtained by comparing the frequencies of NH$_3$ inversion transitions with rotational transitions of other molecules. The existing two measurements are towards the line of sight of two well known gravitationally lensed BL Lacs (B~0218+357 and PKS~1830$-$211) that show complex radio morphologies. As different transitions occur at different frequencies the dependence of the background radio structure on frequency is an important source of systematic error \citep[see][]{Murphy08,Kanekar11}. Therefore detecting NH$_3$ and other molecules towards unlensed compact radio sources is important to constrain \dmm. Unlike NH$_3$ and other complex heavy molecules, 21-cm absorption is more frequently detected towards normal radio sources covering a wide redshift range. The main source of systematics in this method is related to how accurately the 21-cm absorption component is associated to the corresponding metal line component. More measurements towards compact radio sources are needed to address this issue adequately. Future blind searches for 21-cm absorption using the upcoming Square Kilometer Array (SKA) path finders hopefully will provide a large number of suitable targets to perform such measurements. | 12 | 6 | 1206.2653 |
|
1206 | 1206.0656_arXiv.txt | We introduce the first $g$-mode pulsator found to reside on the classical blue horizontal branch. One year of \kep\ observations of \target\ reveals a rich spectrum of low-amplitude modes with periods between one and twelve hours, most of which follow a regular spacing of \val{276.3}{s}. This mode structure strongly resembles that of the \sdbg\ pulsators, with only a slight shift towards longer periods. Our spectroscopy, however, reveals \target\ to be quite distinct from the sdB stars that show \sdbg\ pulsations, which all have surface gravities higher than \grav{5.1} and helium abundances depleted by at least an order of magnitude relative to the solar composition. We find that \target\ has \temp{22\,100}, \grav{4.72}, and a super-solar helium abundance (\helium{--0.45}). This places it well above the extreme horizontal branch, and rather on the very blue end of the classical horizontal branch, where shell hydrogen burning is present. We conclude that \target\ must have suffered extreme mass loss during its first giant stage, but not sufficient to reach the extreme horizontal branch. | The \kep\ spacecraft is monitoring a 105 deg$^2$ field in the Cygnus--Lyrae region, primarily to detect transiting planets \citep{borucki11}. As a bycatch, pulsating stars are observed, and these high-quality datasets are a treasure trove for asteroseismology studies \citep{gilliland10a}. In the first four quarters of the \kepmi\ a survey for pulsating stars was made, and a total of 113 compact-pulsator candidates were checked for variability \citep{ostensen10b,ostensen11b}. The survey was extremely successful with respect to subdwarf-B (sdB) pulsators, with discoveries including one clear \sdbv\ pulsator \citep{kawaler10a}, a total of thirteen \sdbg\ stars \citep{reed10a,kawaler10b,baran11b,2m1938}. Preselection of \kep\ targets based on their photometric and spectroscopic properties has provided us with the most outstanding photometric lightcurves in the history of astronomy for a host of known pulsator types. In addition, the large archive of \kep\ data\footnote{http://archive.stsci.edu/kepler/.}, mostly obtained for detecting exoplanets, provides an inexhaustible source of spectacular lightcurves of all kinds of variable stars, and unlimited opportunities for exciting new discoveries. Here we present one such. It was included in the color-selected sample of white-dwarf-pulsator candidates that provided the only V777\,Her pulsator in the \kep\ field \citep[KIC\,8626021][]{ostensen11c}. However, the spectrum obtained in that survey placed it well outside of the known pulsator ranges, and it was not considered further. By chance, it was observed by {\em Kepler} as an exoplanet target, permitting serendipity to trump our otherwise pinpoint-precision survey strategy. Our spectrum shows that \target\ is technically a hot subdwarf of the sdB type, as it appears as a B-type star with a rather high surface gravity, placing it below the main sequence in the Hertzsprung-Russell diagram. However, its surface gravity is lower and its helium abundance is much higher than the majority of the sdBs, making it quite unusual. After ascending the red-giant branch (RGB) most stars with main-sequence masses less than \sval{\sim}{2}{\msol} will undergo a core-helium flash and end up by the red clump, where they spend \sval{\sim}{100}{Myr} burning helium in the core, before ascending the asymptotic-giant branch (AGB). If such stars suffer significant mass loss, then they will appear bluer after helium ignition while still having roughly the same luminosity. This produces the distinctive feature seen in color-magnitude diagrams of globular clusters, known as the horizontal branch (HB). HB stars possess a hydrogen-burning shell, whenever the hydrogen envelope contains \sval{>}{0.02}{\msol}. Stars with thinner envelopes will reside on the extreme horizontal branch (EHB) \citep{heber86}. Other HB stars are often designated as either red or blue, with RHB stars encompassing the red clump and the notable class of RR\,Lyrae pulsators. These are classical radial pulsators excited by the same heat mechanism acting in the partial ionization zone of He$^+$/He$^{2+}$ that also drives pulsations in Cepheids and $\delta$\,Scuti stars \citep{christy66}. The BHB stars include all stars of spectral type A and B up to the start of the EHB at \grav{5}. The distribution of stars along the HB is a convoluted function of mass loss on the RGB, overall metallicity, and interactions with a close companion. \begin{figure*}[t!]$ \begin{array}{cc} \parbox[b]{0.5\hsize}{ \includegraphics[width=0.97\hsize]{spek.eps} \includegraphics[width=0.94\hsize]{sed.eps}} & \includegraphics[width=0.498\hsize]{fit.eps} \end{array}$ \put(-527,155){\bf a} \put(-527,-8){\bf b} \put(-260,155){\bf c} \caption{ a:~The discovery spectrum of \target. b:~SED fit to broad-band photometry. c:~Line-profile fit to the WHT spectrum.} \label{fig:sp} \end{figure*} The process that produces the EHB stars is thought to include a large contribution from binaries that underwent mass transfer and drastic mass loss in either common-envelope or Roche-lobe-overfilling configurations on the RGB \citep{han02,han03}. Whereas the majority of the sdB stars on the EHB are members of short-period binaries \citep[][and references therein]{ostensen09}, such short-period binaries are hard to find on the classical horizontal branch \citep{prsa08}. Since the discovery of short-period pulsations by \citet{kilkenny97}, the sdB stars have been extensively studied. The $p$-mode pulsators are known as \sdbv\ stars after the prototype, and constitute $\sim$10\%\ of sdBs with temperatures between \sval{\sim}{28000}{K} and \val{36000}{K} \citep{sdbnot}. \citet{green03} discovered longer-period pulsations in 75\%\ of stars between \sval{\sim}{22000}{K} and \val{30000}{K}; the \sdbg\ stars. Here we present the first discovery of a star that exhibits long-period pulsations similar to the \sdbg\ stars on the EHB, but is located on the BHB instead. | We have shown that \target\ is spectroscopically an intermediate-helium-sdB star, most likely associated with the BHB. Photometric data of extremely high precision and coverage obtained with \kep\ have revealed a pulsation spectrum with a clear period spacing of \val{276.3}{s}, indicative of a core-helium burning star similar to the \sdbg\ pulsators. There is no reason to believe that the driving mechanism responsible for exciting the pulsations in \target\ is any other than the same $\kappa$-mechanism that drives the pulsations in the \sdbg\ and \sdbv\ stars \citep{fontaine03}. The red edge of the \sdbg\ instability strip has never been firmly established, due to the sharp drop in the number of observed EHB stars at around \val{24\,000}{K}. \sdbg\ pulsations in stars at the blue tip of the BHB should not really come as a big surprise, as early models for these stars predicted pulsations at the cool end of the EHB and beyond \citep{jeffery06a}. \target\ must have suffered extreme mass loss during its evolution in order to reach its present configuration. While our SED fit displays no sign of any main-sequence companion, a white-dwarf companion is not excluded. The \kep\ photometry rules out any close object, since a period of \val{10}{d} or less would be readily detected from Doppler beaming in the light curve, unless the orbit is seen face on \citep{telting12b}. White-dwarf companions with orbits \sval{\sim}{30}{d} are harder to detect with \kep\ due to the monthly data-download cycle, and the reacquisition of the field after each such manoeuvre introduces trends in the data that must be filtered out. Spectroscopic follow-up observations are being undertaken, but have not yet provided any stronger limits than can be determined from photometry. We conclude that we have observed $g$-mode pulsations in a star at the blue end of the classical horizontal branch that are driven by the same $\kappa$-mechanism as in the \sdbg\ pulsators and slowly-pulsating main-sequence-B stars. The pulsations are of longer period and lower maximum amplitude than has been observed in any of the \kep\ \sdbg\ targets, making this type of pulsator practically undetectable with ground-based observations. In analogy with the naming sdBV for the group consisting of \sdbv\ and \sdbg\ pulsators, we propose to call \target\ and similar BHB variables for BHBV stars. The rarity of BHB stars at similar temperatures will make it hard to find other examples of such pulsators in the limited field-of-view of \kep. However, the question of how far towards the red along the BHB $g$-mode pulsations may extend remains a question to be explored. | 12 | 6 | 1206.0656 |
1206 | 1206.3978_arXiv.txt | We report on a detailed spectral analysis of all the available XMM-Newton data of \rxj , the brightest and most extensively observed nearby, thermally emitting neutron star. Very small variations ($\sim$1-2\%) in the single-blackbody temperature are detected, but are probably due to an instrumental effect, since they correlate with the position of the source on the detector. Restricting the analysis to a homogeneous subset of observations, with the source at the same detector position, we place strong limits on possible spectral or flux variations from March 2005 to present-day. A slightly higher temperature (kT$\sim$61.5 eV, compared to the average value kT$\sim$61 eV) was instead measured in April 2002. If this difference is not of instrumental origin, it implies a rate of variation of about 0.15 eV yr$^{-1}$ between April 2002 and March 2005. The high-statistics spectrum from the selected observations is well fit by the sum of two blackbody models, which extrapolate to an optical flux level in agreement with the observed value. | The X-ray Dim Isolated Neutron Stars (XDINSs, see \citet{tur09} for a review) are a small group of nearby, $d\lesssim300\,\rm pc$, thermally-emitting neutron stars, characterized by temperatures $kT^\infty\sim50-100\,\rm eV$, luminosities $L_X\sim10^{31}-10^{32}\,\rm erg\,s^{-1}$, and spin periods in the 3--12 s range. They are radio-quiet and have very faint optical/UV counterparts, $m_V\sim26-27$. Their spin-down rates ($\sim10^{-14}-10^{-13}\,\rm s\,s^{-1}$) imply magnetic fields $B\sim10^{13}-10^{14}\, \rm G$, in good agreement with those inferred from the broad spectral features observed in some of these sources. Only one of the XDINSs, RX J0720.4$-$3125, showed significant long term spectral and flux variations \citep{dev04,hoh12a}, for which several interpretations were proposed, including precession of the neutron star and changes induced by a glitch \citep{hab06,van07}. No evidence of variability has been reported in the other six members of this class, but most of them have not been observed very frequently and have lower fluxes than RX J0720.4$-$3125, therefore the derived limits are not very constraining. On the other hand, \rxj\ is the brightest XDINS and it has been routinely observed, almost twice per year since 2002 for calibration purposes, by the XMM-Newton X-ray satellite. The resulting large amount of data allows us to investigate its spectral evolution on time scales from months to $\sim$10 years, but a reliable interpretation of these data requires to carefully consider the stability of the detectors and any calibration issue that might affect the results. \begin{figure*}[bht!] \begin{center} \includegraphics[width=0.75\textwidth,angle=0]{cooling.ps} \caption{Long term evolution of the BB temperature from a set of homogeneous observations with the source at the same position on the EPIC pn detector. The dotted line is a linear fit to all the points. The dashed line represents a linear fit excluding the first point (April 2002).} \label{fig-kt} \end{center} \end{figure*} \begin{figure*}[bht!] \begin{center} \includegraphics[width=0.7\textwidth,angle=-90]{composite-spec.ps} \caption{Spectrum of \rxj\ extracted from a homogenous set of observations yielding a total exposure time of $\sim254$ ks. The upper panel shows the best fit with two blackbodies. The features in the residuals (lower panel) have a width smaller than the pn energy resolution and are most likely due to non perfect instrumental calibrations.} \label{fig-sp} \end{center} \end{figure*} | We have carried out a detailed analysis to investigate the long term spectral variability of the brightest XDINS, reaching the limit set by the current uncertainties in the instrumental calibration, and without finding evidence for relative variations larger than a few percent during the last decade. We stress that the absolute values of the spectral parameters derived with XMM-Newton for \rxj\ (and also for other very soft X-ray sources) must be taken with caution since they can be affected by systematics errors at the level of few percent. | 12 | 6 | 1206.3978 |
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