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1404 | 1404.5279_arXiv.txt | We propose a mechanism for the damping of density oscillations in multicomponent compact stars. The mechanism is the periodic conversion between different phases, i.e.,~the movement of the interface between them, induced by pressure oscillations in the star. The damping grows nonlinearly with the amplitude of the oscillation. We study in detail the case of r-modes in a hybrid star with a sharp interface, and we find that this mechanism is powerful enough to saturate the r-mode at very low saturation amplitude, of order $10^{-10}$, and is therefore likely to be the dominant r-mode saturation mechanism in hybrid stars with a sharp interface. | The damping of mechanical oscillations of compact stars is a promising signature of the phases of dense matter in their interior. The damping of density perturbations, described locally by the bulk viscosity, is particularly important since it has been shown to vary greatly between different phases \cite{Sawyer:1989dp,Haensel:1992zz,Madsen:1992sx,Haensel:2000vz,Haensel:2001mw,Haensel:2001em,Jones:2001ya,Alford:2006gy,Manuel:2007pz,Alford:2007rw,Mannarelli:2009ia,Wang:2010ydb,Schwenzer:2012ga,Manuel:2013bwa}. In addition to the damping properties of bulk phases, the boundary between different phases can also be relevant for dissipation. A well-known example is Ekman layer damping due to shear forces at the boundary between a fluid and a solid phase \cite{Lindblom:2000gu}. Here we propose a dissipation mechanism that stems from the fact that pressure oscillations can cause the interface between two phases to move back and forth, as the two phases are periodically converted into each other. If the finite rate of this conversion produces a phase lag between the pressure oscillation and the position of the interface, energy will be dissipated in each cycle. We study the resultant damping for the case of a hybrid star with a sharp interface between the quark core and the hadronic mantle, where the dissipation is due to quark-hadron burning at the interface. However, the mechanism is generic and could be relevant for any star with an internal interface between phases of different energy density. Unstable global oscillation modes \cite{Friedman:1978hf} are of particular interest since they arise spontaneously and grow until stopped by some saturation (nonlinear damping) mechanism. For neutron stars, the most important example is r-modes, \cite{Andersson:1997xt,Andersson:2000mf} since they are unstable in typical millisecond pulsars unless sufficient damping is present. Several mechanisms for the saturation of the growth of unstable r-modes have been proposed \cite{Lindblom:2000az,Arras:2002dw,Bondarescu:2007jw,Alford:2011pi,Bondarescu:2013xwa,Haskell:2013hja}. Although bulk viscosity has a nonlinear ``suprathermal'' regime \cite{Madsen:1992sx,Alford:2010gw,Alford:2011df}, it has been found that this becomes relevant only at very high amplitudes, and is probably pre-empted by some other stronger mechanism \cite{Alford:2011pi}. In this paper we show that dissipation due to hadron-quark burning could well be the dominant r-mode saturation mechanism in hybrid stars. The dissipation is vanishingly small at infinitesimal amplitude, but becomes very strong as the amplitude increases. (For similar behavior in a different context, see Ref.~\cite{Haskell:2013hja}). This strong dissipation saturates unstable r-modes in compact stars with a sufficiently large core at amplitudes that are orders of magnitude below those provided by any other known saturation mechanism. We give a simple analytic prediction for the saturation amplitude, and find that it can be as low as $\alpha_{{\rm sat}}\lesssim10^{-10}$ for conditions present in observed pulsars. | \label{sec:conclusion} We have described how phase conversion in a multicomponent compact star provides a mechanism for damping density oscillations, via the phase lag in the response of the interface between components of different baryon densities to the applied pressure oscillation. The phase lag arises from the finite rate of interconversion between the phases, which limits the speed with which the interface can move. We studied the case where the two phases are separated by a sharp boundary (first-order phase transition) and analyzed the movement of the interface in the approximation of a steady state, neglecting additional acceleration effects and complicated hydrodynamic effects like turbulence. In particular, we studied the astrophysically interesting case of the damping of r-mode oscillations \cite{Andersson:1997xt,Andersson:2000mf} in a two-component star. We found that phase conversion dissipation does not affect the r-mode instability region, because it vanishes as $\al^3$ at low r-mode amplitude $\al$. However, depending on the values of relevant parameters, phase conversion dissipation can either saturate the r-mode at extremely low amplitudes, $\al_{\rm sat} \lesssim 10^{-10}$ in the explicit example of hadron-quark transformation at the sharp quark-hadron interface in a hybrid star, or be insufficient to saturate the r-mode at all. The reason for this behavior stems, analogously to the bulk visocity \cite{Alford:2010gw}, from the resonant character of the dissipation, which is relatively strong when the time scale of the dissipation matches the time scale of the external oscillation (see Fig.~\ref{fig:P_alpha_complete_HS0}). Whether saturation is possible depends therefore on the microscopic and astrophysical parameters, like in particular on the mass of the quark core, which should not be too small. Our main result is Eq.~\eqn{eqn:dW_dp}, which must be evaluated using numerical solutions of Eqs.~\eqn{eqn:dx_t_qm} and \eqn{eqn:dx_t_nm}. We also give the low-amplitude analytic expressions for the power dissipated [Eq.~\eqn{eqn:P_sub_approx}] and the saturation amplitude [Eq.~\eqn{eqn:alpha_sat_analytic}] which are valid when the dissipation is sufficiently strong, obeying Eq.~\eqn{eqn:ep_astro} with $\epsilon \ll 1$. Our results have significant implications for astrophysical signatures of exotic high-density phases of matter, such as quark matter. The observed data for millisecond pulsars is not consistent with the minimal model of pulsars as stars made of nuclear matter with damping of r-modes via bulk and shear viscosity \cite{Alford:2013pma}. Resolving this discrepancy requires either a new mechanism for stabilizing r-modes, or a new mechanism for saturating unstable r-modes at $\alpha_{\rm sat} \lesssim 10^{-8} \!\!-\!\!10^{-7}$ \cite{Mahmoodifar:2013quw,Alford:2013pma,Haskell:2012vg}. Previously proposed mechanisms have problems to achieve this. Suprathermal bulk viscosity and hydrodynamic oscillations both give $\al_{\rm sat}\sim 1$ \cite{Alford:2011pi,Lindblom:2000az}. The nonlinear coupling of the r-mode to viscously damped daughter modes could give $\alpha_{\rm sat} \sim 10^{-6}$ to $10^{-3}$ \cite{Brink:2004bg,Bondarescu:2013xwa}. The recently proposed vortex-fluxtube cutting mechanism \cite{Haskell:2013hja} might give sufficiently small saturation amplitudes but is present only at sufficiently low temperatures $T \ll T_{c}\lesssim 10^9$ K, which could be exceeded by the r-mode (and/or accretion) heating \cite{Alford:2013pma}. One of the main results of this paper is that phase conversion dissipation can provide saturation at the required amplitude to explain millisecond pulsar data. Second, due to the extremely low r-mode saturation amplitude of our proposed mechanism, hybrid stars would behave very differently from neutron or strange stars. As discussed in Ref.~\cite{Alford:2013pma}, if the known millisecond sources were hybrid stars then, for the low saturation amplitudes that we have found, they would have cooled out of the r-mode instability region quickly (in millions of years) so that they would have very low temperatures by now. In contrast, in neutron stars r-modes would be present and would provide such strong heating that the temperature of observed millisecond pulsars would be $T_\infty \sim O(10^5\!\!-\!\!10^6)$ K \cite{Alford:2013pma}. This prediction assumes a (so far unknown) saturation mechanism that would saturate the mode at a value $\alpha_{\rm sat} \lesssim 10^{-8}$ required by the pulsar data. This temperature is significantly higher than what standard cooling estimates suggest for such old sources. The same holds for strange quark stars where the enhanced viscous damping can explain the pulsar data, but even in this case the star would spin down along the boundary of the corresponding stability window which would keep it at similarly high temperatures. Measurements of or bounds on temperatures of isolated millisecond pulsars provide therefore a promising way to discriminate hybrid stars. Our analysis considered only strangeness-changing non-leptonic processes when we discussed the hadron-quark transformation as an example of phase conversion dissipation. However, there are also leptonic processes that equilibrate the non-strange neutron-proton or up-down ratio. For ordinary bulk viscosity in hadronic or quark matter these processes are only relevant at temperatures far above the temperature of a neutron star because their rate is parametrically smaller than the strangeness changing rate discussed here by a factor of $(T/\mu)^2$ \cite{Haensel:1992zz}. However, leptonic processes might play an important role in phase conversion dissipation because hadronic matter has more electrons and up quarks than quark matter, so, just as for strangeness, there will be a conversion region behind the moving boundary where conversion and diffusion of up-ness is occurring. Taking this into account could change the estimates given here and should be studied in more detail in the future. As well as the quark-hadron interface in a hybrid star, any first-order phase transition that leads to a sharp interface between two phases with different baryon densities could, via the mechanism discussed here, cause dissipation of global pressure oscillation modes. One possibility would be different phases of quark matter, perhaps with different Cooper pairing patterns, such as the color-flavor locked (CFL) phase, the two-flavor color superconductor (2SC), or various forms of inhomogeneous and asymmetric pairing \cite{Alford:2007xm}, which are all generally connected by first-order phase transitions. Because cross-flavor pairing induces shifts in the Fermi surfaces of the participating species, different color superconducting phases will often have different flavor fractions, so movement of the interface between them requires weak interactions, as in the case of the quark-hadron interface. The dissipation mechanism discussed here may therefore be expected to operate, albeit mildly suppressed by the smallness of the baryon number density differences between these phases. Our discussion was limited to the case of a sharp interface, which is the expected configuration if the surface tension is large enough. If the surface tension is small, there will instead be a mixed phase region where domains of charged hadronic and quark matter coexist \cite{Ravenhall:1983uh,Glendenning:1992vb}. We expect that the phase conversion dissipation mechanism will operate in this case too, as the domains expand and shrink in response to pressure oscillations. However, to estimate this contribution is far more complicated since it requires us to consider the dynamic formation, growth, and merging of these structures, taking into account the costs and gains due to surface tension and electric field energy. Such an analysis is far beyond the scope of this work, but we expect that the dissipation due to such transformations will be roughly comparable to the estimates given here. A similar mechanism should also be relevant for the ``nuclear pasta'' mixed phases in the inner crust of an ordinary neutron star. In this case in addition to the slow $\beta$-equilibration processes there may also be slow strong interaction equilibration processes, whose rate is suppressed by tunneling factors for the transition between geometric domains of different size. This could further enhance the dissipation. The phase conversion mechanism for damping relies on the transition between two phases being first order. If there is a crossover, then dissipation due to particle conversion is described by the standard bulk viscosity. Examples are the appearance of hyperons in the dense interior or the crossover from $npe$ to $npe\mu$ hadronic matter, where the conserved particle density is lepton number instead of baryon number \cite{Alford:2010jf}. The conversion is then not restricted to a thin transition region and partial conversion, giving rise to bulk viscosity dissipation taking place all over the relevant part of the star. The additional effect, that the size of the region where muons are present changes as well, is negligible, since the muon fraction continuously goes to zero. This is also reflected by the vanishing of the prefactor in the parenthesis of our general expressions Eq.~(\ref{eq:W1_W2}). In this work, we obtained a reasonable first estimate of the size of the damping by treating the movement of the phase boundary in the steady-state approximation \cite{Olinto:1986je}, assuming that it can accelerate arbitrarily fast and that it can move as fast as allowed by general thermodynamic constraints. In reality the acceleration of the phase boundary near the turning points of its motion might be further slowed down by the fact that the steady-state conversion region has to form, and if it therefore cannot accelerate fast enough there will be additional dissipation during this part of the cycle, even if the phase boundary is eventually fast enough to stay in chemical equilibrium near the equilibrium position. Our analysis showed that even being out of chemical equilibrium for only a small fraction of a cycle causes the system to dissipate a huge amount of energy, so it is possible that including these additional acceleration effects may yield an even lower r-mode saturation amplitude and saturate r-modes even in stars with small quark cores. Including the realistic acceleration of the phase boundary will require solving the full time-dependent evolution of the phase conversion front. Similarly, it is likely that turbulence plays a major role in the phase conversion, as found in several analyses \cite{Pagliara:2013tza, Herzog:2011sn, Niebergal:2010ds} of the one-time burning of a (meta-stable) neutron star. The inclusion of these complications is an interesting future project. \appendix | 14 | 4 | 1404.5279 |
1404 | 1404.4049_arXiv.txt | Prompted by the recent successful predictions of the internal dynamics of Andromeda's satellite galaxies, we revisit the classical Milky Way dwarf spheroidal satellites Draco, Sculptor, Sextans, Carina, and Fornax in the framework of Milgromian dynamics (MOND). We use for the first time a Poisson solver with adaptive mesh refinement (AMR) in order to account simultaneously for the gravitational influence of the Milky Way and its satellites. This allows us to rigorously model the important external field effect (EFE) of Milgromian dynamics, which can reduce the effective acceleration significantly. We make predictions on the dynamical mass-to-light ratio ($M_\text{dyn}/L$) expected to be measured by an observer who assumes Newtonian dynamics to be valid. We show that Milgromian dynamics predicts typical $M_\text{dyn}/L \approx 10$--$50 \,\Msun/\Lsun$. The results for the most luminous ones, Fornax and Sculptor, agree well with available velocity dispersion data. Moreover, the central power-law slopes of the dynamical masses agrees exceedingly well with values inferred observationally from velocity dispersion measurements. The results for Sextans, Carina and Draco are low compared to usually quoted observational estimates, as already pointed out by Angus. For Milgromian dynamics to survive further observational tests in these objects, one would thus need that either (a) previous observational findings based on velocity dispersion measurements have overestimated the dynamical mass due to, e.g., binaries and contaminant outliers, (b) the satellites are not in virial equilibrium due to the Milky Way tidal field, or (c) the specific theory used here does not describe the EFE correctly (e.g., the EFE could be practically negligible in some other theories), or a combination of (a)--(c). | \label{sect:intro} Data on large scale structures, when interpreted in terms of Einstein's field equations, point towards a Universe dominated by dark energy and dark matter. Dark energy is generally represented by a cosmological constant, $\Lambda$, and dark matter (DM) is most often assumed to be made of hitherto undetected massive elementary particles, the so-called cold dark matter (CDM). Models based on less massive particles, so-called warm dark matter (WDM) lead largely to the same results, apart from some mild differences in the minimum mass of DM haloes and the presence of small constant density cores at their centre \citep{Maccio12}. However, at galaxy scales, the observations are in disagreement with many predictions based on particle DM \citep[e.g.][]{Kroupa1,Kroupa2}, whilst the observation of a tight correlation between the distribution of baryonic and missing mass seems to indicate that the effective law of gravity is well-described by Milgromian dynamics particularly in rotationally supported galaxies (\citealp{Mil83}, see \citealp{FamMcgaugh} for a major review, and also \citealp{Hernandez2014}, \citealp{Trippe2014}), rather than Newtonian dynamics plus DM. The specific observed dynamics of spiral galaxies can be interpreted as becoming scale-invariant under transformations $(t,\boldsymbol x) \rightarrow (\lambda t,\lambda\boldsymbol x)$ with $\lambda \in \mathbb{R}$ when the accelerations fall well below the threshold acceleration $a_0 \approx 10^{-10}\,\mathrm{m}\,\mathrm{s}^{-2} \approx \Lambda^{1/2}$. This is mostly equivalent to stating that, in spherical symmetry, the gravitational attraction then approximately approaches $(g_\text{N} a_0)^{1/2}$, where $g_\text{N}$ is the classical Newtonian gravitational acceleration due to the baryonic matter. This prescription, known as Milgromian dynamics, leads to a large body of remarkable predictions in galaxies \citep{FamMcgaugh}. A general consequence of such dynamics is that, unlike Newtonian dynamics, it is nonlinear even in the nonrelativistic regime, meaning that it cannot satisfy the strong equivalence principle. For example, in the case of a satellite galaxy orbiting a more massive host galaxy, the satellite's internal dynamics is not independent from the acceleration it feels due to the external field of the host galaxy. The effect of this external acceleration on the internal dynamics of a system is known as the external field effect (EFE), and is very different from the tidal effect. For objects such as satellite galaxies, rigorously taking into account the EFE requires to account simultaneously for the gravitational influence of the host and the internal gravitational field of the satellites. In this work, we revisit the dynamics of dwarf spheroidal satellites of the Milky Way (MW) by making use of an advanced Poisson solver with adaptative mesh refinement (AMR). Such dwarf spheroidal galaxies orbiting around more massive hosts range from $10^3$ to $10^7\,\Lsun$ with half-light radii of about $500\unit{pc}$ to $1\unit{kpc}$. Two kinds of dwarf galaxies must exist in the framework of the standard cosmological model \citep[][and the references therein]{Kroupa2}: primordial dwarf galaxies (PDGs) and tidal dwarf galaxies (TDGs). PDGs formed early in the universe and are supposed to be embedded in small CDM haloes. Cosmological simulations have shown that a large number of PDGs as massive as $10^8\,\Msun$ and more should have formed as satellites orbiting the MW \citep{Klypin99,Moore99}. These primodial galaxies do not have preferred orbits and are thus roughly spherically distributed around the host, or only moderately flattened \citep{Wang2012}, and move in arbitrary directions. Even accretion from cold filaments has been demonstrated to not yield significant anisotropies \citep{Pawlowski2012b}. TDGs on the other hand are dwarf galaxies resulting from major encounters of galaxies. In such encounters, gas and stars are stripped off the galaxies through tidal forces and form large tidal debris tails within which dwarf galaxies can form. Contrary to PDGs, TDGs can have only little or no cold or WDM \citep{Barnes92,Bournaud2010} and are clearly correlated in phase-space if they originate from the same event. They typically form vast disc-like structures around their past-encounter hosts. Because the found dwarf spheroidal galaxies around the MW are observed to have extraordinary high dynamical mass-to-light ratios \citep[e.g.,][]{Mateo1991,Strigari2008,Walker2009,Walker2013,Battaglia2013}, they are generally thought to be PDGs enclosed in CDM subhaloes \citep[e.g.,][]{Belokurov2013}. There are, however, a number of problems with this interpretation. The oldest one is known as the missing satellite problem: while there should be more than 500 nearly isotropically distributed CDM subhaloes with bound masses of $\gtrsim 10^8\,\Msun$ with a tidally limited size of $\gtrsim 1\unit{kpc}$ \citep{Moore99}, only 11 bright satellites have been detected (and only about 26 are known in total). It has been subsequently assumed that gas had collapsed to form substantial stellar populations only in some `lucky' CDM subhaloes, whilst the others would have lost their baryons or had stellar formation quenched for a variety of reasons \citep[e.g.][]{Brooks2013}, ranging from stellar feedback to tidal forces and reionization. Nevertheless, even in semi-analytical models taking such effects into account, there remain problems at the low-mass and high-mass end \citep[e.g.,][]{Kroupa1}. For instance, the most massive subhaloes of the MW in CDM simulations are too dense to host any of its bright satellites \citep[this is known as the `too big to fail' problem;][]{2big2fail}, leaving as a mystery why these massive haloes failed to form galaxies. Moreover, a second and even more problematic observation is that the dwarf spheroidal satellite galaxies of the MW are arranged in a corotating, vast polar structure \citep[VPOS,][]{VPOS}, which is completely incompatible with the predictions from CDM simulations. The same problem arises in the Andromeda galaxy \citep{Ibata2013Andromeda} where half of the satellites are rotating in an extremely thin planar structure oriented towards the MW. The strong phase-space correlation of the satellites suggests that the observed satellites are not PDGs but TDGs. While this conclusion seems natural, it is in contradiction with CDM, because the dwarf satellites of the MW are observed to have very high dynamical mass-to-light ratios. The observations by \citet{Bournaud2007} also emphasize this conflict around external galaxies: they observe currently forming TDGs in the tidal debris of a galactic encounter, and these TDGs also possess a large amount of missing mass. This missing mass can, in the standard picture, only be explained by large amounts of unseen, presumably cold, molecular gas. The flat rotation curves of these dwarfs on the other hand are inconsistent with this expedient as they would require this baryonic DM to be distributed in an isothermal fashion. On the contrary, these rotation curves are well explained by Milgromian dynamics without any free parameters \citep{Gentile2007}. So, if the conclusion that the MW dSphs are of tidal origin is true, the observed high dynamical mass-to-light ratios would imply that these objects are either out of equilibrium \citep{Kroupa1997,KlessenKroupa1998,Casas2012} or that a modified gravity scheme, such as those based on Milgromian dynamics, applies, or both. In the latter case, only those galaxies that appear to be in dynamical equilibrium should be compared to the static predictions of Milgromian dynamics \citep{McGaughWolf}.\footnote{While the faintest dwarf spheroidals show clear sign of being out of equilibrium, this is not the case for the most massive ones.} In the view of Milgromian dynamics, the tidal scenario seems very natural. Timing arguments suggest that M31 and the MW must have had a close tidal encounter, likely 7--11\unit{Gyr} ago \citep{timing}. In the standard model, this simple tidal encounter scenario is not possible at all, because the dynamical friction between the CDM haloes of the two encountering galaxies would lead to a galactic merger. The formation of TDGs around the MW could however be explained by other scenarios, e.g. the one modelled by \citet{Hammer2013arxiv}, but it is still in contradiction to the observed high amount of missing matter in these objects. Since apparent high dynamical masses\footnote{The dynamical mass is the mass derived from the measured velocity dispersion under certain assumptions, e.g. dynamical equilibrium, while applying Newtonian dynamics.} (deduced when using classical Newtonian dynamics) are a natural property of Milgromian dynamics for objects of low surface density \citep{FamMcgaugh}, it is thus of high interest to predict what should be expected for the MW dwarf satellites in this context. This was pioneered for the MW dwarf spheroidals by \citet{Milgrom1995}, \citet{BradaMilgrom2000}, \citet{Angus08} and \citet{Hernandez2010}, while predictions for the Andromeda dwarfs were made by \citet{McGMil1} and \citet{McGMil2}. Correct a priori predictions were for instance made for the velocity dispersions of AndXVII, AndXIX, AndXX, AndXXI, AndXXIII, AndXXV, AndXXVIII. Among these, some are seen as outliers from the mass--luminosity--radius relations within the CDM paradigm because of their large size and low velocity dispersions, for instance AndXIX, AndXXI and AndXXV. On the contrary, these low velocity dispersions were correctly predicted a priori in Milgromian dynamics thanks to the EFE \citep{McGMil2}. All these studies had the drawback of having to treat the EFE of Milgromian dynamics in a non-self-consistent manner. The external field indeed has a major influence on the predicted effective dynamical mass and has to be taken into account very carefully. This has recently been done properly in the work of \citet{Angus14} but without AMR, not allowing as much flexibility to study the various effects on vastly different scales. Here, we take advantage of the Milgromian Poisson solver with AMR, which we developed in the course of a larger project, in order to account simultaneously for the gravitational influence of the MW and its satellites. As a first application, we thus revisit the predictions for the brightest MW dwarfs, making predictions on the objects' dynamical mass-to-light ratios ($M_\text{dyn}/L$) expected to be measured when assuming Newtonian dynamics to be valid. | The problem of the nature and dynamics of the dwarf spheroidal satellite galaxies is a vivid one. As highlighted in numerous recent studies, their phase-space distribution around the MW and the Andromeda galaxy is not compatible with them being primordial galaxies embedded in CDM haloes \citep[e.g.,][]{Ibata2014,Pawlowski14prep}. On the contrary, if they are of tidal origin, they can contain only little or no DM. In this case, the observed high velocity dispersions conclude either that {\it all} these objects must be out of equilibrium, or that Newtonian dynamics fails on this scale and that a different theory of gravity must apply (e.g., Milgromian dynamics). In spiral galaxies, the correlation between the mass discrepancy and the gravitational acceleration has long been known to hold for orders of magnitude in mass, and can be interpreted as evidence for Milgromian dynamics. Such dynamics naturally predicts that the MW and Andromeda must have had a close tidal encounter, likely 7--11\unit{Gyr} ago \citep{timing}, leading to the formation of at least a significant fraction of today's satellites of the Local Group galaxies. Recent predictions of internal velocity dispersions of Andromeda's satellites within Milgromian dynamics have proven very successful \citep{McGMil1,McGMil2}. For the MW dwarfs, the situation is less clear. It has long been known that ultra-faint dwarfs cannot be accounted for in Milgromian dynamics if they are in dynamical equilibrium \citep{McGaughWolf}: these objects are close to fully filling their Milgromian tidal radii, and therefore are likely out of equilibrium. For classical dwarfs, we revisited the dynamics here (apart from UMi which also appears out of equilibrium), by taking advantage of the AMR Poisson solver to solve for the MW and the dwarf satellites simultaneously. We produced a table of predicted dynamical mass-to-light ratios which can be useful for observers (Table~\ref{tab:literature}). We find typical $M_\text{dyn}/L$ of $\approx 8$ to $50\,\Msun/\Lsun$ (depending on model parameters, particularly the stellar mass-to-light ratio). In the case of Sculptor and Fornax, these values agree well with observations. In the case of Draco, Sextans, and Carina, these values are low compared to todays observational findings. This is in accordance with what Angus~(2008) had found, and it can mean that \begin{enumerate} \item the satellites are not in virial equilibrium due to the MW tidal and external field, \item past observational findings are incorrect due to outliers and binary contamination, or \item that the specific modified gravity theory used\footnote{Note also that we implemented here only one particular $\nu$-function} is not the theory that describes the EFE correctly. For the latter case, we provide for each satellite upper limits of $M_\text{dyn}/L$ possible in Milgromian dynamics, in case the external field turns out to be negligible. \end{enumerate} It has already been argued in the past that the EFE might be an observational problem of Milgromian dynamics as formulated here, when confronting predictions to data \citep{Scarpa2006,Hernandez2010,Hernandez2012a,Hernandez2012b,Hernandez2013}. The argument is that, often, when the EFE starts playing a role, the agreement of Milgromian dynamics with observational data becomes marginal, while it remains good if the EFE is neglected: this might indeed be true for the dwarf spheroidals of the MW considered here. However, it is not necessarily the case in general. For instance, the escape speed from the MW can be determined from the EFE and agrees well with observations \citep{Famaey07}, and nearby open clusters having internal accelerations below $a_0$ do not exhibit large mass discrepancies. Also, in the CDM context, some dwarfs close to M31 have been pointed out as outliers because of their low velocity dispersions, while with Milgromian dynamics, such small velocity dispersions are naturally predicted \citep{McGMil2}: this prediction relies on the EFE being non-negligible as in this paper. Nevertheless, we should point out that, even though the EFE is a necessary consequence of Milgromian dynamics, in some implementations of the theory, it could be negligible in practice: this can be the case for instance in time-nonlocal modified inertia theories \citep{Milgrom2011}. Computations of, e.g., the escape speed from the MW would in this case become more complicated and many concepts such as the escape speed could have to be fully redefined. In view of the current inferences of dynamical masses of the MW dwarfs, this absence of EFE should certainly be kept as a possibility, as advocated in \citet{Scarpa2006,Hernandez2010,Hernandez2012b,Hernandez2013,Hernandez2012a}. \citet{Kroupa1997} has shown that it is possible to achieve high $M_\text{dyn}/L \approx 100$ even in DM-free dSphs by assuming purely classical Newtonian dynamics. The reason is that the satellites that were set up with spherical phase-space distribution functions evolve away from this state by losing particles from outer regions of phase-space due to the Galactic tides. The assumption made by the observer who assumes spherically symmetric equilibrium structures is then wrong, leading to very high apparent $M_\text{dyn}/L$ values, despite the models not having any DM. This finding also applies to Milgromian dynamics (and of course also to PDGs embedded in CDM haloes), although we expect that the effect is less strong \citep{Hernandez2012a}. That observational findings of the measured dynamical mass are not as correct as we think today is also one possibility which should not be excluded a priori. Dynamical masses are derived from the velocity dispersion, which is usually based on measurements that are very sensitive to effects that have not been taken into account yet, e.g. the number of binary stars, or plain outliers from the background. \citet{Serra10} have for instance shown that taking into account outliers was bringing Sextans back on the Milgromian prediction. A similar expectation can be made for Draco and Carina. Interestingly, it has recently been shown that the tidal effects are not significantly changing the predictions for Carina \citep{Angus14}. We note that the predictions of Milgromian dynamics are most accurate for the most luminous satellites, and least for the less luminous ones. The most luminous dwarf galaxies likely have had the highest star formation rates (SFRs) in the past. High SFRs result in high minimum embedded star cluster masses, making the embedded clusters denser and thus destroying binaries more efficiently \citep{Marks2011}. It is therefore likely that the velocity dispersion measurements of the less luminous dwarfs are more affected by unresolved binaries than those of the most massive dwarfs. If one finds that the dynamical masses computed here (which are predictions of Milgromian dynamics based on static equilibrium models, and taking into account the EFE) are compatible with future, more precise measurements of the velocity dispersions in these dwarf galaxies, this would strengthen the notion that the MW dSph satellite galaxies are TDGs that have been formed $7-11\unit{Gyr}$ ago as a consequence of a close encounter between M31 and the MW. In this case, $N$-body computations based on Milgromian dynamics of the MW--M31 encounter should further test this tidal scenario. If it however turns out that all measured velocity dispersions are correct and that the considered dwarf galaxies {\it are} in virial equilibrium, then the computed dynamical masses based on Milgromian dynamics tell us that the specific implementation used here can be excluded, and one has to consider other theories, such as modified inertia theories in which the EFE can be practically negligible \citep{Milgrom2011}. \subsection*{Acknowledgements} FL is supported by DFG grant \mbox{KR1635/16-1}. We thank the referee X. Hernandez for a careful reading of the manuscript and useful suggestions. | 14 | 4 | 1404.4049 |
1404 | 1404.0631_arXiv.txt | We study relevant cosmological topics in the framework of a certain vector-tensor theory of gravitation (hereafter VT). This theory is first compared with the so-called extended electromagnetism (EE). These theories have a notable resemblance and both explain the existence of a cosmological constant. It is shown that, in EE, a positive dark energy density requires a Lagrangian leading to quantum ghosts, whereas VT is free from these ghosts. On account of this fact, the remainder of the paper is devoted to study cosmology in the framework of VT. Initial conditions, at high redshift, are used to solve the evolution equations of all the VT scalar modes. In particular, a certain scalar mode characteristic of VT --which does not appear in general relativity (GR)-- is chosen in such a way that it evolves separately. In other words, the scalar modes of the standard model based on GR do not affect the evolution of the VT characteristic mode; however, this scalar mode influences the evolution of the standard GR ones. Some well known suitable codes (CMBFAST and COSMOMC) have been modified to include our VT initial conditions and evolution equations, which are fully general. One of the resulting codes --based on standard statistical methods-- has been used to fit VT predictions and observational evidences about both Ia supernovae and cosmic microwave background anisotropy. Seven free parameters are used in this fit. Six of them are often used in GR cosmology and the seventh one is characteristic of VT. From the statistical analysis it follows that VT seems to be advantageous against GR in order to explain cosmological observational evidences. | \label{sec:1} Extended electromagnetism (EE) was proposed in paper \cite{bm091}. The basic fields of this theory are the metric $g^{\mu \nu} $ and the electromagnetic field $A^{\mu} $. The fundamental symmetry is $A^{\mu} \rightarrow A^{\mu} + \nabla^{\mu} \Phi$, with $\nabla_{\mu} \nabla^{\mu} \Phi =0$; which is different from the standard U(1) gauge symmetry. Some cosmological applications of EE were discussed in various papers \citep{bm092,bm011,dal12}. In Dale \& S\'aez \cite{dal12}, the variational formulation of EE was revisited, and the cosmological linear perturbations were studied by using the well known Bardeen formalism \citep{bar80,huw97}. There is a vector-tensor (VT) theory of gravitation, studied in \cite{dal09}, which has a notable resemblance with EE. The post-Newtonian parametrized limit of VT is identical to that of general relativity (GR). Moreover, this theory was proved to be viable in \cite{bm093} (see below for more details). Here, the theories EE and VT are compared to conclude that, although they give the same results in cosmology, there are some problems with EE quantification. On account of these facts, our cosmological results are presented in the framework of VT. The initial conditions for the evolution of scalar perturbations are taken in the radiation dominated era, at redshift $z \sim 10^{8} $, when the perturbations of cosmological interest are outside the effective horizon (see paper \cite{mb95} for details). By using these initial conditions, the linear equations satisfied by the scalar perturbations are numerically solved, and the cosmic microwave background (CMB) anisotropy is estimated. Since all the scalar perturbations are evolved from the radiation dominated era, it may be seen how metric perturbations gradually deviate from the GR ones. Deviations arises at some redshift to be numerically estimated, without {\it a priori} assumptions about its possible value. There are well tested codes which are ready to do some calculations (evolution of scalar perturbations, CMB analysis, and so on) for standard cosmological models based on GR; e.g., CMBFAST \citep{seza96} and CAMB \citep{lew00}. These codes may be modified to work in the framework of VT (or EE). In spite of the fact that CMBFAST is not currently maintained, its last version is good enough for us and, moreover, its equations are essentially written by using the Bardeen formalism in the version of \cite{mb95}, which is the same formalism used to study VT along this paper. By this reason, we may easily modify CMBFAST to describe cosmological evolution in VT. The necessary modifications --based on references \cite{bar80}, \cite{mb95}, and \cite{dal12}-- are lengthy but straightforward. The code COSMOMC \citep{lew02} has been also modified for statistical analysis in VT; namely, to fit theoretical predictions and observations by using a set of parameters (see next sections for details). Our signature is (--,+,+,+). Greek (Latin) indices run from $0$ to $3$ (1 to 3). The symbol $\nabla $ ($\partial $) stands for a covariant (partial) derivative. The antisymmetric tensor $F_{\mu \nu} $ is defined by the relation $F_{\mu \nu} = \nabla_{\mu} A_{\nu } - \nabla_{\nu} A_{\mu }$, where $A^{\mu }$ is the vector field of the theory under consideration (EE or VT). Quantities $R_{\mu \nu}$, $R$, and $g$ are the covariant components of the Ricci tensor, the scalar curvature and the determinant of the matrix $g_{\mu \nu}$ formed by the covariant components of the metric, respectively. The gravitational constant is denoted $G$. Units are chosen in such a way that the speed of light is $c=1$. The scale factor is $a$. In flat universes, the present value of $a$ is arbitrary. We take a=1. The coordinate and conformal times are $t$ and $\tau $, respectively. Whatever quantity $D$ may be, $D_{B} $ stands for its background value and $\dot{D}$ is its derivative with respect to the conformal time. This paper is structured as follows. In Sec. \ref{sec:2}, some general aspects of VT and EE and the cosmological background equations of both theories are presented and compared. In Sec. \ref{sec:3}, the evolution equations of all the VT cosmological scalar modes and the initial conditions necessary to their numerical integration are found. Numerical results are obtained with our modified versions of CMBFAST and COSMOMC. These results are analyzed in Sec. \ref{sec:4} and, finally, Sec. \ref{sec:5} is a general discussion about methodology and conclusions. | \label{sec:5} It has been proved (see Sec. \ref{sec:2}) that, in EE and VT, the background energy density of the field $A^{\mu} $ plays the role of dark energy with $W=-1$; nevertheless, in order to have a positive dark energy, the coupling constant $\gamma $ must be positive (negative) in VT (EE). In Eqs.~(\ref{emtee}) and~(\ref{emtee_vt}), we see that the last terms of the right hand side have the same form but opposite signs. This fact has been justified with a detailed variational study. Since only these terms contribute to $\rho^{A}_{B}$ ($F^{\mu \nu} = 0$ in the background), this density appears to have opposite signs in Eqs.~(\ref{eqest}) and~(\ref{eqest_vt}), which correspond to EE and VT, respectively. From these equations and the condition $\rho^{A}_{B}>0$, the sign of $\gamma $ is fixed in both theories. Since the conservation equations~(\ref{conlaw}) have played a very relevant role in the Lagrangian formulation of EE, a few words about the conserved currents of VT and EE are worthwhile. As it follows from Eq.~(\ref{1.3}), the conserved current of EE is $J_{\mu} + J^{^{A}}_{\mu}$ [see Eq.~(\ref{conlaw})]. In the case $J^{\mu} =0$ (VT), the Lagrangian $- \frac {1}{4} F^{\mu \nu } F_{\mu \nu } +\gamma (\nabla_\mu A^{\mu})^{2}$ is invariant under the local gauge transformations $A^{\prime \mu} =A^{\mu} + \nabla^{\mu} \Phi$, with $\nabla_{\mu} \nabla^{\mu} \Phi =0$ and, consequently, the second Noether theorem may be applied to get the conserved current $J^{^{A}}_{\mu} $ [see Eq.~(\ref{confic}]. For $J^{\mu} \neq 0$ (EE), the Lagrangian is $- \frac {1}{4} F^{\mu \nu } F_{\mu \nu } +\gamma (\nabla_\mu A^{\mu})^{2} + J^{\mu}A_{\mu}$. It may be easily proved that this Lagrangian is also gauge invariant, under the above local gauge transformation, if $J^{\mu} $ is replaced by $\nabla^{\nu} F_{\mu \nu} - J^{^{A}}_{\mu}$, namely, if $J^{\mu} $ is constrained to satisfy the field equations (\ref{1.3}). From the resulting gauge invariant Lagrangian and the second Noether theorem, it follows that the conserved current is $J_{\mu} + J^{^{A}}_{\mu}$. In general, currents $J_{\mu} $ and $J^{^{A}}_{\mu}$ are not expected to be separately conserved, since we should not have two independent conserved currents associated to an unique group of local gauge transformations. We have verified that, in a neutral universe where the background current $J^{\mu} $ and its scalar perturbations vanish \citep{dal12}, EE and VT lead to the same cosmological conclusions in the study of both the background universe and the scalar perturbations; nevertheless, as a result of the negative $\gamma $ value involved in EE, which would lead to problems with quantification, our results are presented in the framework of VT. This theory is based on action (\ref{VT.2}), which has four terms. Deviations with respect to GR only can be produced by the second and third terms, which vanish for $\gamma=\varepsilon =0 $. In other words, for vanishing $\gamma $ and $\varepsilon $, action \ref{VT.2} reduces to the GR one and, consequently, for small enough values of $\gamma $ and $\varepsilon $, VT and GR would be indistinguishable. According to Eq.~(\ref{xib}), parameter $\gamma $ must satisfy the relation $\gamma (\nabla \cdot A)_{B}^{2} = \rho_{v} $. Furthermore, as it has been shown in previous sections (see also paper \cite{dal12}), there are no additional cosmological constraints to be satisfied by the constant quantities $\gamma $ and $(\nabla \cdot A)_{B} $. It is due to the fact that these quantities may be eliminated from the evolution equations of the scalar perturbations. Moreover, these equations do not involve the parameter $\varepsilon $ either. This means that, in cosmology, quantities $\gamma $ and $\varepsilon $ only must satisfy the inequality $2\varepsilon - \gamma > 0$. The strength of gravitation is fixed by the first term of action \ref{VT.2} (proportional to R). The second and third terms --related to gravitation in VT-- should involve small coupling constants compatible with the weak character of the gravitational interaction; namely, these constant must be compatible with the fact that the strength of the gravitational field is very low as compared to the strengths of electroweak and strong interactions. Appropriate values of the free constants $\gamma $ and $\varepsilon$ --which have not been fixed by cosmological considerations-- may be chosen (with the constraint $2\varepsilon - \gamma > 0$) to guaranty that the second and third terms of action \ref{VT.2} have nothing to do with strong and electroweak interactions, but with gravity. A general formalism to evolve the VT scalar modes from the redshift $z=10^{8} $ is developed. The evolution equations and the initial conditions for all the scalar modes are written in momentum space (Bardeen formalism) by using the synchronous gauge. Moreover, the scalar mode associated to the VT field $A^{\mu} $ is chosen in such a way that: (i) it evolves separately and, (ii) it is involved in the evolution equations for the scalar modes of GR cosmology (standard model). Our methodology is analogous to that used by Ma \& Bertschinger \cite{mb95}. Equations and initial conditions are fully general. Our calculations with VT-CMBFAST prove that some time derivatives of the metric modes $\eta $ and $h$ (which are involved in the evolution equations of the CMB photon distribution function) evolve in the same way --in both GR and VT-- until redshifts $\sim 10 $; then, the evolution of these derivatives starts to be different in both theories and, at redshifts $z \leq 5 $, they take on fully different values in VT and GR, except for very large spatial scales (see Sec. \ref{sec:4}). Deviations between VT and GR are oscillatory. They explain the differences between the CMB angular power spectra of both theories for $\ell \leq 250 $. By using the code VT-COSMOMC, WMAP7 and SNe Ia data have been adjusted to VT predictions by using seven parameters. In the standard GR model, either WMAP7 or WMAP9 and other data (supernovae, matter power spectrum and so on) are well fitted with a minimal model involving six parameters (see \cite{jar11,hin12}). We add the new parameter $D_{1}$ which is characteristic of VT to perform a fit based on seven parameters. In the best fit, the six common parameters of the GR and VT models are very similar, which means that VT works as well as GR; however, there are also good fits for $D_{1}$ values satisfying the condition $|D_{1}| < 3\times 10^{8} $ and, moreover, at 95\% confidence, the parameter $D_{1}$ satisfies the condition $|D_{1}| < 5.3\times 10^{8} $ (see Sec. \ref{sec:4}). The fact that we have found good fits for a wide range of $D_{1} $ values strongly suggests that VT models may explain cosmological observations better than GR. It is due to the existence of an additional degree of freedom (parameter $D_{1}$), which has a good behavior and helps us to get good fits. A new version of COSMOMC has been recently delivered. It includes PLANCK CMB spectra. We are trying to modify this version for future applications to VT. New fits based on the modified code would use better observational data and, moreover, these fits could involve more parameters, lensing, and other effects; nevertheless, the study of these general fits is beyond the paper scope. Here, we essentially point out that VT deserves attention, since it is a theory which explains: the existence of a cosmological constant, and recent CMB and SNe Ia observations (with a minimal model involving seven parameters). Moreover, parameter $D_{1} $ seems to be a help to fit predictions and observations in VT and, consequently, VT fits seem to be more promising than the GR ones. | 14 | 4 | 1404.0631 |
1404 | 1404.3542_arXiv.txt | \noindent The recent BICEP2 measurements of B-modes indicate a large tensor-to-scalar ratio in inflationary cosmology, which points towards trans-Planckian evolution of the inflaton. We propose possible string-theory realizations thereof. Schemes for natural and axion monodromy inflation are presented in the framework of the type IIB large volume scenario. The inflaton in both cases is given by the universal axion and its potential is generated by F-terms. Our models are shown to feature a natural mechanism for inflaton decay into predominantly Standard Model particles. | \label{sec:intro} The recent reports of the BICEP2 collaboration \cite{Ade:2014xna} indicate that for the first time there have been direct measurements of B-modes, which are CMB imprints of primordial gravity waves. Indeed, BICEP2 found the tensor-to-scalar ratio to be rather large, $r=0.2$. Realizing this value in slow-roll inflationary cosmology requires a motion of the inflaton over trans-Planckian distances in field space. This is difficult to achieve in a UV complete theory of quantum gravity, such as string theory, as one has to have control over many possible higher-order operators, which can spoil the slow-roll property. This is known as the $\eta$-problem, which is a challenge in general and becomes even stronger for trans-Planckian evolutions. As a matter of fact, most string or string-inspired models of inflation give much lower values of $r$ and would, if BICEP2 is confirmed, be ruled out. In order to achieve the required control over higher-order corrections, one can take advantage of the perturbative shift symmetry of axions, which is only broken non-perturbatively, by fluxes, or by the presence of branes. Interestingly, axions are ubiquitously present in string compactifications. In the prototype model, the inflationary potential takes the form $V(\theta)=\Lambda^4(1-\cos(\theta/f))$, where $f$ denotes the instanton decay constant of the axion $\theta$. In fact, this simple model is known to lead to a large tensor-to-scalar ratio, consistent with all other cosmological parameters, if $f>M_{\rm pl}$. It is a priori unclear whether in this regime the effective field-theory description is still trustable, however, this model of natural inflation \cite{Freese:1990rb,Adams:1992bn} fits the data amazingly well. Expanding the potential to quadratic order, it essentially reproduces Linde's model of chaotic inflation \cite{Linde:1983gd}, which in fact has been shown to be compatible with large field variations in \cite{Kaloper:2008fb,Kaloper:2011jz,Kaloper:2014zba}. In order to avoid the regime $f>M_{\rm pl}$, extensions of this simple axion model have been proposed. One is N-flation \cite{Kim:2004rp,Dimopoulos:2005ac}, where the collective evolution of $N$ axions in a sort of radial direction leads to the same predictions, but where each individual axion only travels over a sub-Planckian distance and has a decay constant $\sqrt{N}f_i>M_{\rm pl}$. A second variation is so-called axion monodromy inflation \cite{Silverstein:2008sg,McAllister:2008hb,Palti:2014kza}, where the shift symmetry is broken by the presence of a brane, inducing an approximately linear (or quadratic) potential for the axion. Thus, the former periodic axion is ``unwrapped'' and can now move over trans-Planckian distances, increasing the energy by a certain amount each time it goes around the period. It turns out that realizing N-flation in a concrete string-theory model is not an easy task \cite{Grimm:2007hs,Cicoli:2014sva}. One generic problem with N-flation is that for $N\gg 1$ a substantial renormalization of the Planck mass occurs. Another potential problem of many models is that at the end of the inflationary epoch, the inflaton is not guaranteed to predominantly decay into the visible sector, but the decay rates into a visible and a hidden sector degree of freedom tend to be of the same order (see e.g. \cite{Cicoli:2010ha, Cicoli:2010yj}). Clearly, in view of the BICEP2 results and its fairly constraining consequences, it is important to study what possibilities string theory can offer to realize such axion-inflation models. In this letter, we ignore the difficulties the regime $f>M_{\rm pl}$ causes and construct two models: a string-theory model of natural inflation, and a new type of monodromy inflation, where the shift symmetry of the axion is broken by fluxes instead of by the presence of branes. For concreteness, we focus on the LVS framework \cite{Balasubramanian:2005zx} and consider as the inflaton (a linear combination involving) the axionic component of the complex axio-dilaton field $S=C_0+i\exp(-\phi)$. Note that in most approaches before, this universal axion was considered to be fixed at high mass scale by background three-form fluxes. We argue that type IIB string theory has the necessary ingredients to construct successful models of inflation. In particular, \begin{itemize} \item{We assume that the (flux) landscape admits points where the masses of the saxions (including the dilaton) are hierarchically different from the mass of $C_0$. In particular, apart from the nearly massless axion of the big four-cycle in a LVS, $C_0$ can be the lightest closed-string modulus, making it a good candidate for the inflaton.} \item{For natural inflation, the potential of the axion is generated by non-perturbative effects from fluxed $E3$-instantons, whereas for axion monodromy inflation the axion $C_0$ can appear quadratically in the flux induced scalar potential.} \item{There exists a mechanism guaranteeing that inflaton decay at the end of inflation predominantly goes into standard model (SM) degrees of freedom.} \end{itemize} This last point is one of the very interesting aspects of the models considered in this letter. Note furthermore that the relevant axion potentials are F-terms in an effective spontaneously-broken supergravity theory, which is in the same spirit as \cite{Marchesano:2014mla}. Finally, note that an axion decay constant $f>M_{\rm pl}$ corresponds to the non-perturbative (F-theory) regime $g_s>1$ of the type IIB superstring. We collect some indications that the LVS scenario might be trustable even for string coupling constants slightly larger than one, but of course conclusive evidence requires the parametric control over infinitely many perturbative corrections to the K\"ahler potential. | In this letter we have proposed a type IIB, LVS-like string-realization of both natural inflation and axion monodromy inflation, where the role of the inflaton is played by the universal axion, whose scalar partner is the dilaton. Concerning natural inflation, under the assumption that the universal axion is not already fixed by a leading-order flux-induced potential, i.e. its shift symmetry is still intact, we have argued that a non-perturbative contribution to the superpotential coming from a magnetized $E3$-brane instanton gives rise to a leading-order potential. The resulting mass of the axion turned out to be smaller than that of the K\"ahler moduli and than the small-cycle axion. Concerning axion monodromy inflation, we have argued that shift-symmetry breaking fluxes can still allow for an axion of parametrically small mass. Interestingly, this shift-symmetry breaking potential could be quadratic in the axion, thus providing a string-derived candidate of chaotic inflation. In both cases, the big cycle axion was still massless at this stage and could still lead to dark radiation \cite{Cicoli:2012aq,Higaki:2012ar} via the large K\"ahler modulus decay. As one of main results, we have described a natural mechanism guaranteeing that at the end of inflation the inflaton predominantly decays into SM particles. This is achieved by having only the SM branes carry chirality-inducing gauge flux, which leads to a direct coupling of the inflaton to the SM degrees of freedom. Note that this mechanism works for both natural and axion monodromy inflation. The predictions of universal axion inflation could be met by choosing the overall volume $\mathcal V$ of the compactification space to be of the order $10^2-10^3$. This led to soft masses in the sequestered LVS of the order of $10^{12}$GeV, implying a high-scale susy breaking. The other moduli are very heavy in this model, so that there is no cosmological moduli problem. Having the axion decay constant larger than the Planck scale required the string coupling constant to be larger than one. We have presented one argument why this (F-theoretic) regime might still be under control in the LVS. This is of course the weakest point of our model; nevertheless, we think that it shows some new and interesting features. Moreover, in this letter we have simply assumed that the dilaton can be stabilized by either fluxes or no-scale breaking effects such that its mass is hierarchically bigger than the axion mass scale. However, the corresponding stabilization mechanism of the axio-dilaton deserves a closer technical investigation \cite{Blumenhagen:future}. \subsubsection* | 14 | 4 | 1404.3542 |
1404 | 1404.4012_arXiv.txt | We investigate the production and freeze-out of dark matter with a constant thermally averaged cross-section in a generic bouncing universe framework. Our result shows that, there is a novel avenue that dark matter is produced thermally and take a weakly freezing-out process, besides two previously known cases, the {\it thermally production \& strongly freezing-out} case and the {\it non-thermally production \& weakly freezing-out} case, in which the relic abundance of dark matter are inverse and proportional to its cross-section respectively. We calculated the relic abundance of dark matter for this new case, and find its relic abundance is independent of its cross-section. We also present the cosmological constraints on the cross-section and mass relation of dark matter for this new case. | To facilitate a model independent analysis of the dark matter production in a generic bouncing universe scenario, we divide the bounce schematically into three stages~\cite{Li:2014era, Cheung:2014nxi} as shown in~ Figure. \ref{fig:cosback.pdf} : \begin{itemize} \item{Phases I: {\it the pre-bounce contraction}, in which $H<0$ and $m_\chi< T < T_b$~;} \item{Phases II: {\it the post-bounce expansion}, in which $H>0$ and $m_\chi< T < T_b$~;} \item{Phases III: {\it the freeze-out phase}, in which $H>0$ and $m_\chi \, >\, T$~;} \end{itemize} and take a temperature-independent thermally averaged cross section $\langle \sigma v\rangle \propto T^0$, where $m_\chi$ is the mass of dark matter, $\chi$, and $H$ the Hubble parameters taking positive value in expansion and negative value in contraction. $T$ and $T_b$ are the temperatures of the cosmological background and of the bounce point, respectively. The bounce point, connecting Phases I and II with $T\sim T_b$, is highly model-dependent. The detailed modeling is sub-leading effect to our analysis of dark matter production as long as its time scale is short, and the bounce is assumed to be smooth and entropy conserved. \begin{figure}[htp!] \centering \includegraphics[width=0.48\textwidth]{cosback.pdf} \caption{The breakdown of the Big bounce period into a pre-bounce contraction (phase I), a post-bounce expansion (phase II), and the freeze-out of the dark matter particles (phase III). } \label{fig:cosback.pdf} \end{figure} Given that the entropy of universe is conserved around the bounce point~\cite{Cai:2011ci}, we, therefore, have a match condition for the relic abundance at the end of the pre-bounce contraction (denoted by $-$) and the initial abundance of the post-bounce expansion (denoted by $+$), \begin{equation} \label{eq:match} Y_- (x_b^-) = Y_+ (x_b^+)~, \quad Y\equiv\frac{n_\chi}{T^3}~, \quad x\equiv\frac{m_\chi}{T}~. \end{equation} where $n_\chi$ is the number density of dark matter particles. In the early stage before Phase I in the bouncing universe scenario, the temperature of background, $T\ll m_\chi$, is too low to produce dark matter particle efficiently, so the number density of dark matter particles can be set to zero at the onset of the pre-bounce contraction phase without of loss generality~\cite{Li:2014era}: \begin{equation} \label{eq:ini} Y_-(T \sim m_\chi)= 0. \end{equation} The evolution of dark matter in a bouncing universe is governed by the Boltzmann equation, \begin{equation} \label{eq:nsf} \frac{d(n_\chi a^3)}{a^3dt}=\langle\sigma v\rangle\left[\left(n_\chi^{(0)}\right)^2-n_\chi^2\right]~, \end{equation} where $n_\chi^{(0)}$ is the equilibrium number density of dark matter, $a$ the scale factor of the cosmological background, and $\langle\sigma v\rangle$ the thermally averaged cross section. In accordance with the generic bounce universe scenario, we model the pre-bounce contraction and the post-bounce expansion phases to be radiation-dominated, $H\propto a^{-4}$. Then, in the pre-bounce contraction phase, Eq.\ref{eq:nsf} is simplified to be, \begin{equation} \frac{dY_-}{dx}=-f\langle \sigma v\rangle m_\chi x^{-2}(1-\pi^4Y_-^2)~, \label{eq:hn} \end{equation} where $f$ is constant during the radiation-dominated era, $f\equiv \frac{m_\chi^2}{\pi^2} (|H|x^2)^{-1}=6.01\times 10^{26}~eV$, as constrained by observations. Consequently, in the post-bounce expansion phase, Eq.\ref{eq:nsf} also simplifies \begin{equation} \frac{dY_+}{dx}=f\langle \sigma v\rangle m_\chi x^{-2}(1-\pi^4Y_+^2)~, \label{eq:hp} \end{equation} which differs Eq.\ref{eq:hn} by an overall sign $\pm$ due to the signs of Hubble constant in either expansion or contraction. Solving Eq.\ref{eq:hn} and Eq.\ref{eq:hp} with the initial condition Eq.\ref{eq:ini} and Eq.\ref{eq:match} directly, we obtain the analytic solution of the dark matter abundance until the ending of the post-bounce expansion phase, \begin{equation} Y_+=\frac{1-e^{2\pi^2f\langle \sigma v\rangle m_\chi \left(\frac{1}{x}+\frac{x_b-2}{x_b}\right)}}{\left(1+e^{2\pi^2f\langle \sigma v\rangle m_\chi \left(\frac{1}{x}+\frac{x_b-2}{x_b}\right)}\right)\pi^2}~. \label{eq:yp} \end{equation} At the end of dark matter production, $T\sim m_\chi$, this complete solution can be categorized in two limits, {\it Thermal Production} and {\it Non-thermal Production} : \begin{equation} \label{eq:Yplus2} Y_+|_{x=1}= \left\{ \begin{array} {lr} {\displaystyle \pi^{-2}, \qquad\qquad\qquad 4\pi^2f\langle\sigma v\rangle m_\chi x^{-1}_b\gg 1} \\ {\displaystyle 2f\langle\sigma v\rangle m_\chi x^{-1}_b~, \quad~ 4\pi^2f\langle\sigma v\rangle m_\chi x^{-1}_b\ll 1} \\ \end{array} \right. . \end{equation} In {\it thermal production} case, the dark matter is produced swiftly to be in fully thermal equilibrium with primordial plasma due to its large cross-section, $4\pi^2f\langle\sigma v\rangle m_\chi x^{-1}_b\gg 1$. Then its abundance tracks the equilibrium values, $\pi^{-2}$, until freezing out, as depicted in~ Figure. \ref{fig:TriRelicEvolution.pdf}. And in the case of {\it non-thermal production}, the cross-section of dark matter is much smaller, $4\pi^2f\langle\sigma v\rangle m_\chi x^{-1}_b\ll 1$, so that the production of dark matter is insufficient to reach thermal equilibrium. Its abundance is proportional to $\langle\sigma v\rangle $, and the information of the cosmological evolution of the bouncing universe, the factor $2f x^{-1}_b~$, is carried on its outcome. Therefore, if such information can survive and be extracted after the freeze-out, it would become a signature of the bounce universe scenario. \begin{figure}[htp!] \centering \includegraphics[width=0.48\textwidth]{TriRelicEvolution.pdf} \caption{A schematic plot of the time evolution of dark matter in a generic bounce universe scenario. Three outcomes producing dark matter for satisfying current observations are illustrated. } \label{fig:TriRelicEvolution.pdf} \end{figure} | In this paper, we inverstigate the production and freeze-out of dark matter with a temperature-independent thermally averaged cross-section in a generic bouncing universe framework. We report a new avenue of the evolution of dark matter in big bounce, which the dark matter is produced {\it thermally} and freeze out {\it weakly}. This avenue predicts a novel characteristic relation between the relic density and cross-section of dark matter $\Omega\propto \langle\sigma v\rangle^0$ --in contrast to the well-known relation, $ \Omega_\chi\propto \langle \sigma v\rangle^{-1}$ for WIMP model in standard cosmology. By imposing the currently observed value of $\Omega_\chi$, the relation of $\langle\sigma v\rangle$ and $m_\chi$ satisfying the current observations is obtained, $m_\chi=216~eV~, \langle \sigma v\rangle\ll 1.68\times 10^{-28}eV^{-1}$, which serves as a falsifiable signature of the bounce universe scenario and opens up a new possibility of experimentlly testing the bounce universe scenario using dark matter detection. We also discuss the case in which dark matter is produced {\it non-thermally } and freeze out {\it weakly}. Its relic density is proportional to $\langle \sigma v\rangle x_b^{-1}$, and the cross-section and mass relation is ${\langle\sigma v\rangle}=1.82\times 10^{-26}m_\chi^{-2}x_b, ~ m_\chi\ge 432~eV$, which also serves as a falsifiable signature for the big bounce universe scenario with the property of dark matter particle. To summarize, if the value of $m_\chi$ and $\langle \sigma v\rangle$ determined in near future dark matter detection experiments~\cite{Aprile:2012nq, Akerib:2013tjd, Aalseth:2010vx, Bernabei:2010mq, Adriani:2013uda, Cheung:2014pea, Battiston:2014pqa, Aguilar:2014mma,Xiao:2014xyn} satisfy either relations for this two avenues, then it strongly indicates that bounce universe scenario are favorable. | 14 | 4 | 1404.4012 |
1404 | 1404.4823_arXiv.txt | We present the detection of 6,371 RR Lyrae (RRL) stars distributed across $\sim$14,000 deg$^2$ of the sky from the combined data of the Sloan Digital Sky Survey (SDSS), the Panoramic Survey Telescope and Rapid Response System 1 (PS1), and the second photometric catalogue from the Catalina Survey (CSDR2), out of these, $\sim$2,021 RRL stars ($\sim$572 RRab and 1,449 RRc) are new discoveries. The RRL stars have heliocentric distances in the 4--28 kpc distance range. RRL-like color cuts from the SDSS and variability cuts from the PS1 are used to cull our candidate list. We then use the CSDR2 multi-epoch data to refine our sample. Periods were measured using the Analysis of Variance technique while the classification process is performed with the Template Fitting Method in addition to the visual inspection of the light curves. A cross-match of our RRL star discoveries with previous published catalogs of RRL stars yield completeness levels of $\sim$50$\%$ for both RRab and RRc stars, and an efficiency of $\sim$99$\%$ and $\sim$87$\%$ for RRab and RRc stars, respectively. We show that our method for selecting RRL stars allows us to recover halo structures. The full lists of all the RRL stars are made publicly available. | Studying stars with ages approaching the age of the Universe is of a great importance since they can serve as tracers of the formation and early evolution of galaxies. In particular, they allow us to study the stellar halo which is mainly composed of old stars (e.g. \citealt{johnston2008,schlaufman2009}). It is believed from observations and simulations that mergers and accretions of smaller systems contributed to the formation of the outer halo (e.g. \citealt{bullock2001, bullock2005, carollo2007, mccarthy2012,beers2012}) while the inner halo is a result of accretion of a few massive systems in addition to in situ star formation processes (e.g. \citealt{yanny2003,juric2008,delucia2008,zolotov2010,font2011, schlaufman2012}). These accretion events and mergers leave signatures in the structure and kinematics of the stellar halo, usually in the form of stellar streams, substructures, and overdensities \citep{ibata1995,newberg2003,duffau2006,schlaufman2009,sesar2010}. It is easier to detect substructures and overdensities of stars at larger Galactocentric distances where the dynamical time scales are longer \citep{bullock2001,bell2008}. If the theoretical picture is correct, we expect an inhomogeneous outer halo that is full of streams and substructures from accreted systems (e.g. \citealt{johnston1998, johnston2008,cooper2010}). The absence of massive and luminous stars, the old main-sequence turn-offs, the prevalence of horizontal branch stars, and the low metallicities of the halo stars indicate that halo stars are predominantly old. However, it is still unclear whether these stars were mainly formed in situ during the early phase of the collapse of the Milky Way, or whether they were formed outside the Milky Way in satellite galaxies only to be accreted by the Milky Way at a later date (e.g. \citealt{vivas2004, carollo2007, bell2008}). Answers to such questions may be found by identifying and characterizing the streams that the satellite galaxies have left in the halo (e.g. \citealt{zolotov2010}) of the Milky Way where the contamination of foreground stars makes the mapping of stellar structures difficult. Additionally, these streams can serve as very sensitive probes to deduce the shape of the Milky Way's potential \citep{newberg2002,law2009}. \subsection{RR Lyrae stars as halo tracers} One way of finding streams is by identifying and mapping RR Lyrae (RRL) stars in the halo. RRL stars are low-mass, core helium burning pulsating stars that fall on the horizontal branch of a stellar population's color-magnitude diagram. RRL stars have a mean absolute $V$-band magnitude of $\langle M_{V} \rangle$ $=$ 0.6 $\pm$ 0.1 \citep{layden1996}, which makes them very good distance indicators. These variable stars are still bright enough to be detected at large distances such as in the halo \citep{ivezic2000}. They have been used as tracers of the chemical and dynamical properties of old stellar populations (e.g. \citealt{kinman2007, bernard2008,keller2008, morrison2009, kinman2009, haschke2012a}) and have served as test objects for theories of the evolution of low-mass stars and for theories of stellar pulsation \citep{smith1995}. Many of the substructures that were discovered in the Milky Way were re-confirmed using RRL stars (e.g. \citealt{duffau2006, kepley2007, watkins2009, sesar2010}). The best and most reliable way to detect RRL stars is by using multi-band time series observations of a sufficiently high cadence and over a sufficiently long period. RRL stars can be divided into fundamental-mode (RRab stars) and first-overtone (RRc stars) pulsators. Since RRL stars are short-period pulsating stars with typical mean periods of $\sim$ 0.57 and $\sim$ 0.34 days for RRab and RRc stars \citep{smith1995}, respectively, the time between observations is preferred to be short in order to sample the magnitudes of the stars at each phase. In addition to that, monitoring an RRL star over a long period of time will result in a more accurate and reliable classification and period determination. Over the past two decades, colors, variability, and light curve properties of RRL stars have been well studied and characterized (e.g. \citealt{smith1995,pojmanski2002, moody2003, vivas2006, wils2006,sesar2010}). \subsection{Our approach} In this paper, we use and combine data from different sky surveys out of which each survey has a distinctive advantage that helps in identifying RRL stars with high efficiency (fraction of true RRL stars in the candidate sample), completeness (the fraction of selected RRL stars), and reliability levels. First, we apply color cuts to the Sloan Digital Sky Survey (SDSS; \citealt{fukugita1996,york2000,abazajian2009}), 8th data release (DR8; \citealt{aihara2011}). Second, we apply variability cuts using data from the Panoramic Survey Telescope and Rapid Response System 1 3$\pi$ survey (hereafter PS1; \citealt{kaiser2002}) . Finally, we plot light curves and find the periods of the RRL stars using the second photometric catalogue from the Catalina Survey (CSDR2; \citealt{drake2009,drake2013a}) which is based on seven years of multi-epoch observations. Using one of the surveys without the others to find RRL stars results in low efficiency and completeness levels (see Section \ref{usedsurveys}). In order to define the SDSS color selection threshold limits and the PS1 and CSDR2 variability threshold limits, we use the color and variability properties of the Quasar Equatorial Survey Team (QUEST) RRL star catalogue (QRRL; \citealt{vivas2004,vivas2006}). To compute our efficiency and completeness levels, we compare our results with the RRL stars found in Stripe 82. Stripe 82 ($-50\,^{\circ} \textless $ R.A. $\textless 59\,^{\circ}$, $-1.25\,^{\circ} \textless$ Dec. $\textless 1.25\,^{\circ}$, where both right ascension (R.A.) and declination (Dec.) are given in decimal degrees) covers $\sim$ 270 deg$^2$ of the celestial equator and was observed $\sim$ 80 times by the SDSS. \citet{watkins2009} and \citet{sesar2007,sesar2010} independently searched for RRL stars in Stripe 82 using the SDSS data. Because \citeapos{sesar2010} catalog is 100$\%$ efficient and complete, we use it as a test catalog to compute the efficiency and completeness levels of our method. \subsubsection{Previous Studies} \citet{drake2013a} had full access to the first photometric catalogue of the Catalina Survey (CSDR1; \citealt{drake2009}), which allowed them to look for RRab stars in the whole $\sim$ 20,000 deg$^2$ area of the sky that was covered by the CSDR1. On the other hand, we had to manually do a multiple object cone search for at most 100 objects at a time as more is not permitted by the public data interface. The CSDR1 RRL star catalogue \citep{drake2013a} contains 12,227 RRab stars found in the CSDR1 \citep{drake2009} database and covers stars with heliocentric distances ($d_{h}$) up to 60 kpc. Because these authors were only interested in RRab stars and to avoid spurious detections, they removed all stars with periods outside the 0.43--0.95 days range. While our paper was nearing completion, \citet{drake2013b} announced the discovery of $\sim$ 2,700 additional RRab stars in a re-analyses of the CSDR1 photometry and using additional data from the CSDR2. In this paper, we use different variability statistics techniques than the ones used by \citet{drake2013a} and \citet{drake2013b} to find RRab stars. Unlike the latter two studies, we use template fitting techniques to help us in the classification process in addition to the visual inspection of all of the RRL candidate light curves. This allowed us to discover 646 additional RRab stars as compared to \citet{drake2013a} and \citet{drake2013b}. We also found 1,571 RRc stars, of which $\sim$ 1,449 stars are new discoveries. The properties of the different surveys used in this study are described in Section \ref{usedsurveys}. In Section \ref{identifyrrl}, we describe our method for selecting RRL candidates within the overlapping area between the PS1 and the SDSS. Using the QUEST RRL stars, we define and apply our SDSS color cuts in Section \ref{ColorBoxes} and our PS1 variability cuts in Section \ref{ps1variablity}. In Section \ref{lightcurves}, we use the multi-epoch data from the CSDR2 database to look for stellar variability. The method used to find the periods of the RRL stars is described in Section \ref{aov}. In Section \ref{tfm}, light curves are plotted and the methods used to distinguish RRL from contaminant (non-RRL) stars are described. Section \ref{results} summarizes our results and provides our catalogue of RRL stars. In Section \ref{comp_s82}, we compare our RRL star discoveries with the catalogue of RRL stars in Stripe 82 \citep{sesar2010} to compute the efficiency and completeness levels of our method and periods. The properties of the RRL stars that we missed are also described in the same section. In Section \ref{drake_csdr}, we compare our RRL star discoveries with the catalog of RRab stars from \citet{drake2013a} and \citet{drake2013b} and with the La Silla QUEST (LSQ) catalog of RRL stars \citep{zinn2014}. We discuss our newly discovered RRL stars in Section \ref{newrrs} and we compare them with stars found in the General Catalogue of Variable Stars (GCVS\footnote{Published in 2012 and available from VizieR via http://cdsarc.u-strasbg.fr/viz-bin/Cat?B/gcvs}; \citealt{samus2009}). In Section \ref{substructure}, we find the distances for our RRL stars and we use these distances to recover previously known halo substructures. The results of the paper are summarized in Section \ref{summary}. \begin{table*} \centering \begin{minipage}{900mm} \caption{The SDSS color cuts.} \begin{tabular}{@{}llrrrrlrlr@{}} \hline $(g-r)_{0}$ $\textless$ 0.4*$(u-g)_{0}$ $-$ 0.16\\ $(g-r)_{0}$ $\textgreater$ 0.4*$(u-g)_{0}$ $-$ 0.67\\ $(g-r)_{0}$ $\textless$ $-$2.5*$(u-g)_{0}$ $+$ 3.42\\ $(g-r)_{0}$ $\textgreater$ $-$2.5*$(u-g)_{0}$ $+$ 2.70\\ $-0.25$ $\textless$ $(g-r)_{0}$ $\textless$ $0.40$ \\ $-0.20$ $\textless$ $(r-i)_{0}$ $\textless$ $0.20$ \\ $-0.30$ $\textless$ $(i-z)_{0}$ $\textless$ $0.30$ \\ \hline \end{tabular} \label{colorcuts} \end{minipage} \end{table*} | \label{summary} We have combined data from different sky surveys (the SDSS, the PS1, and the Catalina Survey) to look for RRL stars in the Milky Way halo. The search resulted in the discovery of 6,371 RRL stars (4,800 RRab and 1,571 RRc) distributed around 14,000 deg$^2$ of the sky and with $d_{h}$ in the 4--28 kpc distance range. Around 2,021 ($\sim$ 572 RRab and 1,449 RRc) of these stars are new discoveries. In this paper, RRL stars were discovered using the SDSS color and the PS1 variability cuts in Section \ref{identifyrrl}. We define the threshold limits of these cuts using the QUEST catalogue of RRL stars \citep{vivas2006} rather than using the catalogue of RRL stars in Stripe 82 \citep{sesar2010} as we use the latter catalogue to test the efficiency and completeness levels of our method. Additional variability cuts were applied and light curves were plotted using the CSDR2 multi-epoch data. Periods were obtained using the AoV technique while the classification process was done by the TFM and by visual inspection. The comparison of our RRL star discoveries with the RRL stars in Stripe 82 from the SDSS shows that our completeness levels are $\sim$ 50$\%$ for RRab and RRc stars and that our efficiency levels are $\sim$ 99$\%$ and $\sim$ 87$\%$ for RRab and RRc stars, respectively. Additional comparison of our RRL star discoveries with the GCVS, the LSQ catalog of RRL stars, and the 14,500 RRab stars found previously in the Catalina Survey \citep{drake2009,drake2013b} suggests the reliability of our method. Additionally, the Virgo overdensity, Hercules\--Aquila cloud, and Sagittarius stream were recovered after plotting the number density distribution of our RRL stars in the Stripe 82 and Northern Galactic hemisphere areas. This indicates that our method is capable of identifying halo overdensities. In a forthcoming paper, we will present a more detailed analysis of halo substructure as traced by RRL stars. | 14 | 4 | 1404.4823 |
1404 | 1404.3632_arXiv.txt | Like a number of amateurs, I have been recording VLF signal strength using a home-made loop antenna, amplifier, and a computer sound-card. Having obtained a number of days data, it seemed to be an interesting exercise to fit the theoretically predicted $\log\sec$ variation with zenith angle of the reflection layer height in the ionosphere $D$-layer. This short papers attempts just that. I am no expert in radio astronomy, or radio engineering, or even of the physics involved, though I do have some background knowledge and expertise in mathematics and programming. So much of this short paper explains some of the theory I have learnt in the process of doing this work. I don't claim anything particularly new here, but some of the techniques I use may be of interest and my explanations of the background theory and description of the investigation here may be of interest to other VLF amateurs. There \textit{is} mathematics here, at the upper end of the current A-level standard, including some simple differential equations, but hopefully the presentation will be straightforward enough for readers at this level. It is quite reassuring that some quite significant results on the ionosphere and VLF needs nothing more complicated than this. | Fitting the Chapman model of diurnal variation can be done, and often seems successful except very close to the points of sunrise and sunset where the model (at least in the form given here) is not meaningful. However drawing conclusions from the model fitting has its difficulties, mainly because the mathematical mapping of reflection layer height (as predicted by the model) to phase difference (as measured) is many-to-one, hence different heights can results in fits that are or appear to be just as good. Any further experiments that exploit this model to obtain measurements of (for example) the scale height will have to resolve this problem and make very clear why the values for heights chosen are indeed the correct ones. Nevertheless, even if the actual numerical values obtained from the process are not believed, the technique can provide a source of evidence for ionospheric disturbances measured from VLF data near sunrise or sunset when no obvious traditional `SID pattern' is present in the data. In other words, these techniques can in principle be used to dramatically increase the sensitivity of a SID detector especially near sunrise/sunset. \nocite{*} | 14 | 4 | 1404.3632 |
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1404 | 1404.4224_arXiv.txt | \label{intro} \Aspects% \footnote{% Pronounced [asp$\varepsilonup$] in International Phonetic Alphabet transcription, not [{\ae}spekts], and preferentially written ``\!Aspects'' if small capitals are not available. ``\!\Aspects'' is a French acronym for ``\!\emph{\souligne{As}sociation \souligne{p}ositionnell\souligne{e}/% \souligne{p}robabilist\souligne{e} de \souligne{c}a\souligne{t}alogues de \souligne{s}ources}'' (``Positional/\allowbreak proba\-bilistic association of catalogs of sources'' in English). The French word ``\!\emph{Aspect}'' (pluralized in the acronym) has the same general meaning as the corresponding English word; interestingly, it signifies in particular the relative position of heavenly bodies\textellipsis{} } is a code for the probabilistic cross-identification of astrophysical sources. Version~2.0\footnote{% The current version is in fact v2.0.2. The only differences with respect to v2.0.1 are in the documentation (introduction of hyperlinks, exact reference for the main paper). Version v2.0.1 differed from v2.0[.0] by a few minor changes in the formatting of outputs produced by \Fichier{example\_read.f90} and by subroutine \Info{write\_prob} of \Fichier{mod\_output\_prob.f90}. } of the code fully supersedes the version~1.0 described in \citet{article_Aspects_v1}% \footnote{The latter provided biased probabilities (and therefore also biased values of the likelihood and of estimators of unknown parameters) under assumption $H_\oto$ (\cf~\S~\ref{purpose}).} and is an implementation in Fortran~95 of the relations established in \citet{article_Aspects_v2}% \footnote{Available as file \Fichier{paper.pdf} in directory \Fichier{v2.0/} (see below). References to sections or equations of this paper are preceded by ``\paper''. A basic presentation of \Aspects is also given in \citet{seminaire_Aspects} (file \Fichier{IAP\_seminar.pdf}).}. Its source files are freely% \footnote{The \emph{Numerical Recipes} routines in Fortran~90 \citep{NR} mentionned in \citet{article_Aspects_v2} have been replaced by free equivalents.} available at \begin{center} \Fichier{\href{http://www2.iap.fr/users/fioc/Aspects/}{http://www2.iap.fr/users/fioc/Aspects/}} \end{center} in tar file \Fichier{Aspects\_v2.0.tar}. Type \Info{tar xvf Aspects\_v2.0.tar} to extract them in \Fichier{Aspects\_v2.0/}. | 14 | 4 | 1404.4224 |
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1404 | 1404.2222_arXiv.txt | The scale invariant scalar and tensor perturbations, which are predicted from inflation, are eigenmodes in the conformal coordinates. The 'out' observer in the de Sitter space observes a thermal spectrum with a Gibbons-Hawking temperature $H/2\pi$ of these 'Bunch-Davies' particles. The tensor power spectrum observed in experiments can have an imprint of the Gibbons-Hawking thermal distribution due to the mode mixing between 'in' state conformal coordinates and the coordinate frame of the observer. We find that the the Bunch-Davies modes appear as thermal modes to the asymptotic Minkowski observer in the future and the power spectrum of the gravitational waves is blue-tilted with a spectral index $n_T \sim 1$ even in the standard slow-roll inflation. On the other hand if the coordinate frame of the observer is taken to be static coordinates, the tensor spectrum is red-tilted with $n_T\sim -1$. A likelihood analysis shows and find the best fit values of the slow-roll parameters for both cases. We find that the blue-tilted tensor gives a better fit and reconciles the PLANCK upper bound on the tensor-to-scalar ratio, $r <0.11$ with BICEP2 measurement of $r=0.2$. This supports the idea of particle production due to the mode mixing between the initial Bunch-Davies vacuum modes and the asymptotic Minkowski vacuum of the post-inflation universe. | The prediction of a scale invariant scalar and tensor perturbations \cite{scalar, grw} from inflation \cite{Inflation} rest on the assumption of a Bunch-Davies initial state in conformal coordinates of de Sitter space \cite{Mukhanov:2007zz}. An observer in a different coordinate system, for instance an inertial observer in the static coordinates, will see the same perturbations as a thermal distribution with a Gibbons-Hawking temperature $T=H/2\pi$ \cite{Gibbons:1977mu} due to mode-mixing between the Bunch-Davies modes and eigenmodes of the static coordinates \cite{Lapedes:1977ip,Mishima:1987uj,Brandenberger:1982xi,Mottola:1984ar,Allen:1987tz,Spradlin:2001pw,Greene,Agullo:2008ka} . Another way by which the scale invariant perturbations produced during inflation can appear as a thermal distribution is when one considers the mode mixing due to the change in observer between the conformal observer during inflation and the asymptotic Minkowski observer in future which measure the perturbations \cite{Polyakov:2012uc,Anderson:2013ila,Singh:2013dia}. Variations of the standard Bunch-Davies state can be of phenomenological interest as a way of reconciling the large value of the tensor-to-scalar ratio implied by the B-mode polarization measurement by the BICEP2 collaboration with the lower upper bound established by PLANCK from the temperature anisotropy \cite{Ashoorioon:2014nta}. The BICEP2 collaboration \cite{Ade:2014xna} reported a tensor-to-scalar ratio $r={0.2}^{+0.07}_{-0.05}$ by the measurement of the B-mode polarization \cite{Seljak:1996gy}, which is in apparent contradiction with the upper bound $r<0.11$ (at $95\%$ CL) placed by PLANCK \cite{Ade:2013uln} from the measurement of the TT spectrum. There is no direct contradiction between these two measurements as BICEP2 is most sensitive at $l\sim 150$ corresponding to a hub of $k=0.01 Mpc^{-1}$ while the PLANCK 2013 measurement uses the hub $k=0.002 Mpc^{-1}$ which corresponds to $l\sim 30$. However explaining the two measurements in a model of inflation would require (1) a blue tilted tensor spectrum with spectral index $n_T \sim 1 $ \cite{Gerbino:2014eqa,Smith:2014kka,Wang:2014kqa} or (2) a running of the scalar spectrum $d \ln n_s/d \ln k = -0.02 $ \cite{Ade:2013uln}. Either of the possible ways to explain the PLANCK-2013 and BICEP2 data simultaneously would require going beyond the single field inflation with Bunch-Davies initial state. Subsequently the dust popularization measurement reported by PLANCK-2014 \cite{Adam:2014bub} has diminished the statistical significance of the BICEP2 measurement but not ruled it out \cite{Mortonson:2014bja}. There is a possibility that the measurement of the B-mode polarization in other experiments (like KECK, SPTpol etc ) may result in a value of the tensor-to-scalar ratio which still calls for a non-standard interpretation of the inflationary power spectrum to evade the standard consistency relation $n_T= r /8$ of the standard single field inflation. In this paper we show that if we assume a mode mixing between the Bunch-Davies initial vacuum and the post-inflation final vacuum and the Bogoliubov coefficients $\alpha$ and $\beta$ of the mode-mixing is of the thermal form $|\beta|^2=\frac{1}{e^{\beta\omega}-1}$ with the Gibbons-Hawking temperature $T=\beta^{-1}=H/2\pi$, then the spectral index of tensor modes will be blue-tilted with $n_T=1-2\epsilon $. On the other hand if we assume that the 'out' observer is the one with the static coordinates, then the Bogoliubov coefficients again give the same thermal distribution with identical $ |\beta|^2$, however, the spectral index in this case is red-tilted $n_T=-1-2\epsilon$. The difference in the spectral tilt between the two cases is due to the fact that when we transform the initial state from the conformal to static coordinates we have $\alpha \beta^* <0$ while the transformation between the conformal coordinates and the asymptotic Minkowski coordinates of the late time observer gives $ \alpha \beta^*>0$. The difference in sign of $\alpha \beta^*$ with the same $|\beta|^2$ results in a different spectral tilt. In order to avoid the successful prediction of the scale invariant scalar power spectrum, we will assume that the slow roll parameter $\eta$ of the scalar potential is negative so that the scalar modes are tachyonic and the Hawking radiation of scalar modes is suppressed \cite{Epstein:2014jaa}. We do a likelihood analysis for the values of the tensor-to-scalar ratio for the case of red and blue tilted spectra and determine the slow roll parameters of the model which would be reconcile the B-mode and TT anisotropy data. We conclude that mode mixing between the Bunch-Davies vacuum and the vacuum state of the observer, may resolve the tension between the PLANCK-2013 bound and BICEP2 measurement and the accurate experimental measurement of the spectral index can determine the nature of the initial state of the inflation generated perturbations. | The combined data from B-mode measurement by BICEP2 \cite{Ade:2014xna} with the temperature anisotropy measurement from PLANK-2013 \cite{Ade:2013uln} implies that the slow roll inflation consistency relation $n_T\sim r/8$ is violated. It is well known that assuming a different initial state compared to the Bunch-Davies one can modify the relation between the slow-roll $\epsilon$ parameter derived from the potential and the observed tensor spectral index $n_T$ \cite{Hui:2001ce,Ashoorioon:2014nta}. In this paper we examine the modification to the tensor spectrum due to mode mixing between a Bunch-Davies 'in' vacuum and the 'out' vacuum of the (a) static coordinate observer and (b) the post inflation asymptotic Minkowski observer. Both the scenarios result in a Gibbons-Hawking thermal distribution as observed w.r.t the 'out' vacuum. The relative phases of the Bogoliubov coefficients are different in the two cases and these lead to quite different predictions for the tensor spectral index. The combined BICEP2 and PLANCK-2013 data gives a better fit for a blue-tilted tensor spectrum which supports the post-inflation particle production scenario. The Hawking-Gibbons temperature unlike temperature of perturbation form a possible pre-inflation radiation era does not go down exponentially during the course of inflation so the effect is not diluted after a few e-foldings \cite{Bhattacharya:2005wn, Bhattacharya:2006dm}. Measurements of the B-mode in future experiments may give a signature of the Gibbons-Hawking temperature. | 14 | 4 | 1404.2222 |
1404 | 1404.1841.txt | We present very high energy (VHE) imaging of MGRO~J2019$+37$ obtained with the VERITAS observatory. The bright extended ($\sim2^{\circ}$) unidentified Milagro source is located towards the rich star formation region Cygnus-X. MGRO~J2019$+37$ is resolved into two VERITAS sources. The faint point-like source VER~J2016$+$371 overlaps CTB~87, a filled-center remnant (SNR) with no evidence of a supernova remnant shell at the present time. Its spectrum is well fit in the $0.65 - 10$~TeV energy range by a power-law model with photon index $2.3\pm0.4$. VER~J2019$+$368 is a bright extended ($\sim1^{\circ}$) source, that likely accounts for the bulk of the Milagro emission and is notably coincident with PSR~J2021$+$3651 and the star formation region Sh~2$-$104. Its spectrum in the range $1-30$~TeV is well fit with a power-law model of photon index $1.75\pm0.3$, among the hardest values measured in the VHE band, comparable to that observed near Vela-X. We explore the unusual spectrum and morphology in the radio and X-ray bands to constrain possible emission mechanisms for this source. | High-mass star formation (and death) has long been associated with the acceleration of very high energy (VHE; $>$100 GeV) particles~\citep{ginzburg64} and gamma-ray emission \citep{montmerle79,kaaret96}. There is clear evidence of VHE particle acceleration in the products of stellar death such as pulsars, supernova remnant (SNR) shells and pulsar wind nebulae (PWNe). Star-forming regions produce copious kinetic power in other forms, such as winds from Wolf-Rayet and OB stars. Regions with stellar winds, from single, binary, or collections of stars, have been suggested as possible VHE gamma-ray emitting sites, but as of today,~observational evidence of this is still very scarce~\citep{lemoinegoumard11}. The Cygnus-X region is one of the richest known regions of star formation in the Galaxy. It is also close by (at only ~1.4 kpc) and is, therefore, an excellent laboratory to study high-energy particle acceleration related to high-mass star formation and death. Because there are several spiral arms in the same direction, care must be exercised in relating any individual source to Cygnus-X. The Milagro sky survey identified several bright and extended VHE gamma-ray sources in the general direction of Cygnus~\citep{abdo07b}. However, each Milagro source has multiple possible counterparts at lower energies which complicates unambiguous associations. %%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%% \begin{figure*}[t] \epsscale{0.8} \plotone{fig1.pdf} \caption{VHE gamma-ray excess map of the MGRO J2019+37 region as observed by VERITAS above 600 GeV. The color bar indicates the number of excess events within a search radius of 0$^{\circ}$.23, which corresponds to the extended source search analysis described in the text. The shift between red and blue color scale occurs at the 3$\sigma$ level. Regions used for spectral analysis of VER J2016+371 and J2019+368 are defined by white dashed circles. The locations of possible counterparts are marked using different colors. The contour of significance 9$\sigma$ of MGRO J2019+37 is overlaid in white. \label{fig1}} \end{figure*} %%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure*}[t] \epsscale{0.8} \plotone{fig2.pdf} \caption{ Slices in the uncorrelated excess maps of the new VHE sources. The width of the slice is indicated on each panel. The slices are centered on the best fit position of each VHE source. The direction of the slices follows right ascension. The top panels show the slices for VER J2016+371 and the peak position of the 1420 MHz emission of CTB 87~\citep{kothes03} is indicated with a dashed line. The bottom panels correspond to VER J2019+368 and the dashed line shows the position of the pulsar PSR J2021+3651. \label{fig2}} \end{figure*} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% MGRO J2019+37, with a measured flux of about 80\% of the Crab Nebula flux at 20 TeV~\citep{abdo07b}, is the brightest Milagro source in the region. Since its discovery, the nature of MGRO J2019+37 has been the subject of studies and speculation, yet it remains unknown. Its bright inner region has an extent of about 1$^{\circ}$ and overlaps with several SNRs, H{\sc ii} regions, Wolf-Rayet stars, high-energy gamma-ray (HE; $>$100 MeV) sources, and a hard X-ray transient. A tentative association with the young energetic radio and gamma-ray pulsar PSR J2021+3651 and its nebula, SNR G75.1+0.2, has been suggested~\citep{abdo07b}. There is extended X-ray and radio emission associated with the pulsar, but the size (less than $10'$, \citet{roberts08}) is significantly smaller than the VHE source measured with Milagro. \cite{paredes09} suggested that this pulsar alone is not able to power the whole emission of MGRO J2019+37 because the time required for the electrons to diffuse and to fill a region of 1$^{\circ}$ (at an uncertain distance of 2 to 10 kpc) is larger than their cooling time. The same authors performed deep radio and near-infrared surveys to find other potential counterparts and proposed the massive star-forming region associated with the H{\sc ii} region Sharpless 104 (Sh 2-104) as a possible contributor to the VHE emission through wind collisions or interactions of protostar jets with the surrounding medium (e.g.\ \cite{torres04}). Particle acceleration in shocks driven by the winds from the Wolf-Rayet stars in the young cluster Ber 87 in the Cyg OB1 association has also been proposed as an origin of the VHE gamma rays \citep{bednarek07}. %Since its discovery, the nature of MGRO J2019+37 has been subject of studies and speculation, yet it remains unknown. Several VHE instruments have reported results on the region near MGRO J2019+37 at energies below 10~TeV. Relatively short observations with the imaging atmospheric Cherenkov telescopes (IACTs) MAGIC and VERITAS led to upper limits consistent with the Milagro source being extended and hard \citep{bartko08, kieda08}. \citet{bartoli12} recently reported a non-detection based on data from the air-shower array ARGO-YBJ and concluded that the source could be variable. Only the Tibet Air Shower array has confirmed the detection of an extended VHE source from the same direction, with a statistical significance of 5.8 standard deviations (5.8$\sigma$)~\citep{amenomori08}. In this paper we report on new and deeper observations of the region around MGRO J2019+37 made with VERITAS. The new observations provide much better angular resolution than Milagro and better sensitivity than any of the previous VHE measurements. These observations enable us to map the VHE emission in an attempt to better understand its physical origin. The instrument and observations are described in \S~2, while analysis and results can be found in \S~3. A multi-wavelength analysis of the possible counterparts to this emission and a general discussion are presented in \S~4. A short summary and conclusions are drawn in \S~5. % | We have carried out a deep VHE observation in the region of MGRO J2019+37 with VERITAS, confirming this to be a very gamma-ray rich area of the Galactic Plane with emission detected also with {\sl Fermi}-LAT and Milagro, and, thus, covering the full range of the high energy spectrum. The new VHE image spatially resolves, for the first time, one Milagro extended source into at least two clearly separate sources. The angular resolution is good enough to exclude some scenarios that were proposed for MGRO J2019+37. The most likely counterpart of the new source VER J2016+371 is the PWN in the SNR CTB 87. The co-location, the VHE extent and the X-ray/VHE luminosity ratio argue in favor of this. More complicated is the multi-wavelength emission from VER J2019+368, as there are a few possible explanations for its physical origin. The young and energetic pulsar PSR J2021+3651 and its PWN, proposed by many before, seems a likely contributor to VER J2019+368, and therefore MGRO J2019+37. The extended VHE morphology in the direction of the X-ray and radio nebula favors this possibility. The very hard spectrum of the source, $\Gamma=1.75\pm0.08_{stat}\pm0.3_{sys}$, which resembles that of Vela X~\citep{aharonian06}, another PWN system, also favors this scenario. However, the picture might be more complex as non-thermal X-ray emission coincident with Sh 2-104 and also an unassociated {\sl Fermi}-LAT source are also in physical association with this large VHE emission. Follow-up multi-wavelength observations of the region, including VHE data, will certainly help clarify which scenario or scenarios are in fact originating VER J2019+368. %The other newly discovered source, VER J2019+368 is a very extended and hard source with $\Gamma=1.75\pm0.08_{stat}\pm0.3_{sys}$. VER J2019+368 contributes the major part of emission of MGRO J2019+37. From the spectrum comparison and centroid location, they are likely sharing the counterparts. While the presence of the young and energetic pulsar PSR J2021+3651 in the vicinity and uncommonly hard spectral index resembles what was observed in Vela X~\citep{aharonian06}, multiwavelength studies suggest a more complicated picture, in which other sources could be involved. More sensitive observations of the field at all wavelengths and improvements on the estimation of the distance to the pulsar should shed more light into the origin of VER J2019+368. | 14 | 4 | 1404.1841 |
1404 | 1404.4297_arXiv.txt | The majority of massive stars are formed in binary systems. It is hence reasonable to expect that most core-collapse supernovae (CCSNe) take place in binaries and the existence of a companion star may leave some imprints in observed features. Having this in mind, we have conducted two-dimensional hydrodynamical simulations of the collisions of CCSNe ejecta with the companion star in an almost-equal-mass ($\sim 10{\rm \msun}$) binary to find out possible consequences of such events. In particular we pay attention to the amount of mass removed and its dependence on the binary separation. In contrast to the previous surmise, we find that the companion mass is stripped not by momentum transfer but by shock heating. Up to $25\%$ of the original mass can be removed for the closest separations and the removed mass decreases as $M_{\rm ub} \propto a^{-4.3}$ with the binary separation $a$. By performing some experimental computations with artificially-modified densities of incident ejecta, we show that if the velocity of ejecta is fixed, the density of incident ejecta is the single important parameter that actually determines the removed mass as $M_{\rm ub} \propto \rho_{\rm ej} ^{1.4} $. On the other hand, another set of simulations with modified velocities of incident ejecta demonstrate that the strength of the forward shock, which heats up the stellar material and causes the mass loss of the companion star, is actually the key parameter for the removed mass. | It is known observationally that about half of the observed stars are members of binary or higher order multiple systems \cite[]{rag10,duc13}. The fraction increases with the primary star mass and reaches up to 69\% for O stars \cite[]{san12}. These massive stars are supposed to end up exploding as core-collapse supernovae (CCSNe). It is hence natural to expect that the majority of CCSNe should take place in binaries. Binary interactions may be crucially important for the evolution leading to core-collapse \cite[]{pod04}. In particular, mass transfer will be essential to the spectral type of the supernova (SN) explosion. In fact, it is argued that type Ib and Ic SNe mainly occur in interacting binaries \cite[]{smi11}. It has also recently been reported that the late time photometry of iPTF 13bvn, a type Ib SN, cannot be reproduced by single star progenitors, but can naturally be explained by binary progenitor models \cite[]{fre14,ber14}. This may indicate that type Ib SNe are actually occurring in binaries although we had better wait for direct observations of the surviving companions in the future. The aftermath of the explosion could be no less important for the evolution of the binary system itself as well as of the companion star. It is well known that the binary system is disrupted if more than half of the total mass is expelled. This criterion is easily fulfilled when the primary star explodes unless it has lost most of its mass before explosion. Even if the amount of mass expelled is less than half the total mass, the system may still be disrupted due to neutron star kicks. The companion star will then carry on its life as a single star. If the binary survives the SN explosion, it will have a highly eccentric orbit \cite[]{pij12}. Some observational facts of a high mass companion actually surviving the SN explosion are known \cite[]{sew12,gel80}. Most high mass X-ray binaries (HMXBs) and low mass X-ray binaries must have undergone SN at some time in their formation, which means a certain fraction of binaries need to survive from explosion. Collisions of the supernova ejecta (SNE) with the companion star may also affect the evolution of the latter if the binary separation is small enough. \cite{wlm75} were the first to estimate the mass removed from the companion star by the impact. They considered momentum conservation in a simple analytical model to express the amount of mass removed with a single parameter and estimated that up to 15$\%$ of the companion mass will be ejected. Numerical computations were also carried out by \cite{frx81}, confirming the results by \cite{wlm75}. Their two-dimensional computational grid of $32\times32$ was rather coarse by the current standard. They also assumed a planar shell as a model of SNE, which may not be a good approximation for small binary separations, where the spherical geometry of SNE is not negligible. \cite{liv92} followed, assuming a red giant companion of 1 $\msun$. They treated SNE as a spherical shell and used a finer mesh, enough to describe the envelope with fine zoning (typically 107 $\times$ 65). They found that almost all the envelope of the red giants were stripped off by SNE. The result may be applied not only to type Ib SNe but also to type Ia SNe. The impact of SNE on companion stars have been better studied for type Ia SNe \cite[]{mar00,pan13,liu13,kas10} in the single degenerate (SD) scenario, where a carbon-oxygen white dwarf accretes mass from its low-mass binary companion \cite[]{nom82}. Carrying out numerical calculations with high resolutions, these authors placed strong constraints on the structure of companion stars in the SD scenario. In this paper, we perform similar simulations, but assuming more massive stars for both the primary and secondary stars, which will be appropriate for CCSNe. Unlike for type Ia SNe in the low-mass binary, there is no standard model for CCSNe. In fact, the masses and structures of the primary and secondary stars as well as the binary separation are almost free parameters, since there are not many observational constraints. We pay particular attention to the mass removed from the massive companion and its dependence on separation. For the analyses of the results, we perform additional simulations of experimental nature, modifying the density and/or velocity of SNE artificially. It turns out that these are indeed helpful to pin down which physical quantity is most essential in determining the amount of removed mass. This paper is structured as follows: In Section 2, we describe the models and numerical method we used. The main results are shown in Section 3, and discussions are given in Section 4. Finally, we summarize our results in Section 5. | As an attempt to understand the value of the parameter $m_{ab}$, we conducted several experimental calculations varying several physical parameters of SNE. As mentioned already, the quantities that change with the binary separation are the solid angle of the companion, the density and pressure of SNE, and the time until the bulk of SNE flows past the companion star. The mass and energy contained in the solid angle also vary as a result of these changes. Since kinetic energy dominates in SNE, we ignore the dependence on the incident pressure and internal energy in the following. We first pay attention to the incident density. As the binary separation increases, it decreases as $a^{-3}$. Since the solid angle of the companion also decreases as $a^{-2}$, the mass and total energy contained in the solid angle would be reduced even if the density were unchanged, which could have a big impact on the mass loss. In order to see the dependence of the removed mass on the incident density alone, though, we artificially amplified the density of the SNE by a factor of 1.2, 1.5, 1.8 and 2.0, without changing other physical values including separation. Note that this modification still increases the kinetic energy as well as the momentum of the SNE that collide with the companion. These experiments were carried out for models with separations of $(1.0, 1.3, 1.5, 1.8, 2.0) \times a_{\rm min}$. Their results are shown in Figure \ref{dendep}, in which the removed masses are plotted against $(C_{\rm amp}(a/a_{\rm min})^{-3}) \propto\rho_{\rm ej}$, where $C_{\rm amp}$ is the amplification factor of density and the last factor $(a/a_{\rm min})^{-3}$ accounts for the decline in density according to expansion of the SNE. It can be seen that almost all models lie on a single line in the $\log-\log$ plot, which has a power law index of $1.4$. This suggests that the removed mass depends solely on $\rho_{\rm ej}$ irrespective of separation as \begin{equation} M_{\rm ub}\propto \rho_{\rm ej}^{1.4}. \label{eq:mub_den_relation} \end{equation} This means that the mass and/or total energy injected into the solid angle of the companion star are not very important. These results seem to be at odds with the analytical estimates $M_{\rm ub} \propto M_{\rm SN}a^{-2}$ by \cite{wlm75}, in which $M_{\rm SN}$ is the total ejecta mass and corresponds to $C_{\rm amp}$ in our case. Models with the highest $\rho_{\rm ej}$ start to depart from the power law. This is because the removed mass becomes comparable to the remaining mass, thus modifying the escape velocity significantly. \begin{figure} \plotone{dendep.pdf} \caption{Removed mass vs. incident density of SNE. Plots with the same colour are the results of models with the same separation. The dashed line shows a power law with a power-law index of $1.4$.\label{dendep}} \end{figure} Next we artificially multiplied $v^2$ by a factor of $1.2, 1.5, 1.8, 2.0$ as we did with density. The binary separation was fixed to $a = 1.3 \times a_{\rm min}$ this time, implying that the solid angle of the companion and hence the density of SNE are unchanged but the incident kinetic energy is still increased, which is expected to have a similar effect to the enhancement of density. We also tried different combinations of these two effects so that the kinetic energy of the entire SNE would be fixed. \begin{table} \centering \caption{Results for the Experimental Computations\label{phystests}} \begin{tabular}{ccccc} \hline\hline model & $\rho_{\rm ej}$\tablenotemark{a} & $v^2_{\rm ej}$ \tablenotemark{a}& $E_{\rm ej}$\tablenotemark{a} & $M_{\rm ub}(\msun)$\\ \hline base & 1.00 & 1.00 & 1.00 & 0.866 \\ dd1.2 & 1.20 & 1.00 & 1.20 & 1.107 \\ dd1.5 & 1.50 & 1.00 & 1.50 & 1.578 \\ dd1.8 & 1.80 & 1.00 & 1.80 & 2.069 \\ dd2.0 & 2.00 & 1.00 & 2.00 & 2.404 \\ vd1.2 & 1.00 & 1.20 & 1.20 & 1.136 \\ vd1.5 & 1.00 & 1.50 & 1.50 & 1.659 \\ vd1.8 & 1.00 & 1.80 & 1.80 & 2.212 \\ vd2.0 & 1.00 & 2.00 & 2.00 & 2.592 \\ ef1.2 & 1.20 & 0.83 & 1.00 & 0.798 \\ ef1.5 & 1.50 & 0.67 & 1.00 & 0.770 \\ ef1.8 & 1.80 & 0.56 & 1.00 & 0.746 \\ ef2.0 & 2.00 & 0.50 & 1.00 & 0.731 \\ \hline \end{tabular} \footnotetext{$\rho_{\rm ej},v^2_{\rm ej}$ and $E_{\rm ej}$ are the values of the SNE normalized by the values of the base model but with $a=1.3\times a_{\rm min}$.} \end{table} The results for these tests are summarized in Table \ref{phystests}. It is evident from the vd-series, in which only the velocity was changed, that the removed mass increases as the velocity rises just as expected. Interestingly, the comparison between the vd-series and the dd-series, in which we varied density alone, reveals that if the change in kinetic energy is the same, changing velocity has a slightly larger effect on the amount of removed mass than changing density. This is also vindicated by the ef-series, in which both density and velocity were modified but the kinetic energy was fixed. The latter result may imply that increase in the incident momentum decreases removed mass as long as the incident kinetic energy is identical. Now we know how the density and/or velocity of SNE affect the removed mass, our next question will be -- why? We have observed that direct mass stripping was extremely inefficient in our models because the SNE is directed away from the companion star once the bow shock is formed. Most of the mass loss occurs instead by ablation owing to the shock heating of stellar matter. This means that the energy, not the momentum, imparted to the companion star is most important. Then the shock strength will be the physical parameter that we should look into, since it determines how much the star will be heated. To see how the shock strength depends on the incident density, we consider a Riemann problem as presented in Figure \ref{riemannillu}. This is meant to be a very crude approximation to the collision of SNE against the companion star. The left side of the initial discontinuity represents the SNE, taking typical values of pressure and velocity from our simulation ($p_1=1\times 10^{-2}, v_1=3\times 10^8$). We vary $\rho_1$ to see how this affects the strength of the forward shock produced by collision. For the right state approximating the envelope of the companion star, we use average values of density and pressure from our companion model: $\rho_2=1\times 10^{-8},p_2=1\times 10^6,v_2=0$. Here CGS units are adopted. We assume that the companion star is at rest. We employ the same assumption as in \cite{che74} to determine the maximum value of $\rho_1$: the ejecta mass is distributed in a uniform shell with a thickness of $\frac{1}{3}$ the shock radius. This gives us the maximum density as a reference: \begin{eqnarray} \rho_{\rm ej}^{max}=\rho_{\rm ej}(a_{\rm min})=\frac{27}{19}\frac{3M_{\rm ej}}{4\pi a_{\rm min}^3}, \end{eqnarray} where $M_{\rm ej}$ is the mass of SNE. \begin{figure} \centering \begin{picture}(200,60) \put(100,0){\line(0,1){60}} \put( 50,50){Ejecta} \put(125,50){Star} \put( 10,35){$\rho_1$:variable} \put( 10,20){$p_1=1\times 10^{-2}$erg/cm$^3$} \put( 10, 5){$v_1=3\times 10^8$cm/s} \put(110,35){$\rho_2=1\times 10^{-8}{\rm g/cm^3}$} \put(110,20){$p_2=1\times 10^6$erg/cm$^3$} \put(110, 5){$v_2=0$ cm/s} \end{picture} \caption{Illustration of the Riemann problem.} \label{riemannillu} \end{figure} The solutions of the Riemann problem are given in Figure \ref{riemannevo}. The left panels show the pressure distributions and the right panels show the density counter part. Each row hold results for different initial conditions, i.e. $\rho_1=\rho_{\rm ej}^{max}$ for the top panels, $\rho_1=\rho_{\rm ej}^{max}/1.5$ for the middle panels, and $\rho_1=\rho_{\rm ej}^{max}/2.0$ for the bottom panels. The different colours of lines correspond to different times. We can see jumps in density and pressure at the positions of the forward shock propagating through the companion star and sweeping up mass. There is also a reverse shock propagating away from the companion into the SNE, which tries to push it back toward the star. A contact surface divides the SNE from the companion and density but not pressure has a jump there. The region between the forward and reverse shocks corresponds to the matter heated by one of these shocks. Figure \ref{riemanndep} shows the pressure divided by the post-shock density $\rho_{sh}$, a measure of the shock strength, as a function of $\rho_1$. We again find a power law, whose exponent is rather sensitive to the value of $\rho_2$. \begin{figure} \centering \plotone{riemann.pdf} \caption{Solutions of the Riemann problem given in Figure \ref{riemannillu}. Left panels show distributions of pressure while right panels display those of density. {\it Top} : results for $\rho_1=\rho_{\rm ej}^{max}$, {\it Middle} : $\rho_1=\rho_{\rm ej}^{max}/1.5$ and {\it Bottom} : $\rho_1=\rho_{\rm ej}^{max}/2.0$. Different lines correspond to different times.\label{riemannevo}} \end{figure} \begin{figure} \plotone{riemanndep.pdf} \caption{Pressure of the shock-heated region as a function of $\rho_1$.\label{riemanndep}} \end{figure} In our simulations, the forward shock initially has a rather flat front perpendicular to the symmetry axis. It maintains a nearly constant speed until the reverse shock starts to expand toward the primary star. This launch of the reverse shock is accompanied by the generation of a rarefaction wave, which in turn propagates towards the forward shock. It eventually catches up and sucks the energy that would otherwise be injected to the shock. It is hence natural to expect that the total energy given to the companion is determined at this point. Based on the above observation, we estimate the removed mass as follows. Figure \ref{mheat} displays a schematic picture that gives the idea and notations we use here. Assuming that the shock front is a plane perpendicular to the symmetry axis, we approximate the shock-heated portion of the companion star by the shaded region in the picture. $X$ is the distance from the stellar surface to the shock front and $M_{heat}$ is the mass contained in this shocked region. We show in Figure \ref{slicemass} $M_{heat}$ as a function of $X$ calculated as \begin{eqnarray} M_{heat}(X)=\int_{r\cos\theta>X}\rho(r)dV. \end{eqnarray} It is probably by coincidence that this function can be fit by a simple power law very well, which allows us to approximate $M_{heat}$ as \begin{eqnarray} M_{heated}\propto X^3. \end{eqnarray} If we assume that the shock propagates at a constant velocity, we have $X=v_{sh}t$, in which $t$ is the time after collision. As argued earlier, the main shock heating stops at $t=t_{heat}$, when the reverse shock starts to expand outwards. We find in our models that $t_{heat}$ roughly corresponds to the time, at which the instantaneous unbound mass reaches the maximum (see Figure \ref{timemub}), and that this time does not differ so much among models. Hence assuming that $t_{heat}$ is constant, we obtain $M_{heat}\propto v_{sh}^3$ at $t=t_{heat}$. The total energy, $E_{heat}$, deposited by the forward shock is estimated as follows, \begin{eqnarray} E_{heat} &=& \epsilon_{sh}\cdot M_{heat}, \nonumber\\ &\propto&\rho_{\rm ej}^{0.6}\cdot v_{sh}^3, \nonumber\\ &\propto&\rho_{\rm ej}^{0.6}\cdot (\rho_{\rm ej}^{0.3})^3, \nonumber\\ &\propto&\rho_{\rm ej}^{1.5}, \end{eqnarray} where $\epsilon_{sh}$ is the specific internal energy and is assumed to be proportional to $p_1/\rho_{\rm sh}$; in the second line we employed the relations $M_{heat}\propto v_{sh}^3$ just obtained and $p_1/\rho_{\rm sh} \propto \rho_{\rm ej}^{0.6}$ in Figure \ref{riemanndep}. In the third line, on the other hand, we made use of the approximation $v_{sh}^2 \propto p_1/\rho_{\rm sh}$. This energy is redistributed in the removed mass via hydrodynamical interactions. It is hence natural to assume that the removed mass is proportional to $E_{heat}$. This hypothesis finally leads us to the relation $M_{\rm ub} \propto \rho_{\rm ej}^{1.5}$, which is pretty close to the power law with $m_{ab} \sim1.4$ (see Eq.(\ref{eq:mub_den_relation})) obtained in the simulations. \begin{figure} \plotone{mheat.pdf} \caption{Schematic picture of shock propagation through the companion star. The shaded region is the shock-heated material, whose mass is referred to as $M_{heat}$. The distance from the shock front to the stellar surface is denoted by $X$.\label{mheat}} \end{figure} \begin{figure} \plotone{slicemass.pdf} \caption{$M_{heat}$ as a function of $X$ (red line). The green line is a power law $X^3$.\label{slicemass}} \end{figure} In our simulations, we cut out the central core of the companion star. Although this makes it difficult to accurately estimate the kick velocity imparted by the SNE, it is still possible to make rough estimations on this so called ``rocket effect'' \cite[]{che74}. We calculate the imbalance between the total momentum that flows in from the ejecta side and the momentum that flows out of the other side and find that it is $\sim2\times10^{38} {\rm g\cdot km s^{-1}}$ for the base model with $a=a_{\rm min}$. This should be equal to the momentum deposited to the remnant of the companion star. The kick velocity obtained this way is $v_{kick}\sim2\times10^{38}/(M_2-M_{\rm ub})\sim100$ km s$^{-1}$, which is comparable to the orbital velocity $\sim 50$ km s$^{-1}$ and could destroy the binary system. Note, however, this will be an upper limit, and it decreases as $\propto a^{-2}$ with the binary separation according to the solid angle of the companion. | 14 | 4 | 1404.4297 |
1404 | 1404.4404_arXiv.txt | {Numerical simulations have explored the possibility to form molecular clouds through either a quasi-static, self-gravitating mechanism or the collision of gas streams or lower-density clouds. They also quantitatively predict the distribution of matter at the transition from atomic to molecular gases.} {We aim to observationally test these models by studying the environment of W43, a molecular cloud complex recently identified near the tip of the Galactic long bar.} {Using Galaxy-wide \ion{H}{I} and $^{12}$CO 1--0 surveys we searched for gas flowing toward the W43 molecular cloud complex. We also estimated the \ion{H}{I} and H$_{2}$ mass surface densities to constrain the transition from atomic to molecular gas around and within W43.} {We found three cloud ensembles within the position-velocity diagrams of $^{12}$CO and \ion{H}{I} gases. They are separated by $\sim$20~$\kms$ along the line of sight and extend into the $^{13}$CO velocity structure of W43. Since their velocity gradients are consistent with free-fall, they could be nearby clouds attracted by, and streaming toward, the W43 $\sim$10$^7~\msun$ potential well. We show that the \ion{H}{I} surface density, $\Sigma_{\ion{H}{I}} = 45-85~\msun\,$pc$^{-2}$, does not reach any threshold level but increases when entering the 130\,pc-wide molecular complex previously defined. This suggests that an equilibrium between H$_2$ formation and photodissociation has not yet been reached. The H$_2$-to-\ion{H}{I} ratio measured over the W43 region and its surroundings, $R_{{\rm H_{2}}}\sim3.5\pm_{2}^{3}$, is high, indicating that most of the gas is already in molecular form in W43 and in structures several hundreds of parsecs downstream along the Scutum-Centaurus arm.} {The W43 molecular cloud complex may have formed, and in fact may still be accreting mass from the agglomeration of clouds. Already in the molecular-dominated regime, most of these clouds are streaming from the Scutum-Centaurus arm. This is in clear disagreement with quasi-static and steady-state models of molecular cloud formation.} | The term `converging flows', although applicable to all mechanisms of cloud formation, generally refers to the convergence of \ion{H}{I} streams that can naturally be driven by local instabilities in the disk such as those due to gravity, supernova explosions, or spiral shocks \citep[e.g.][]{KoIn00,heitsch05,vazquez07}. For the past decade, numerical models have investigated the capability of such colliding flows (Warm Neutral Medium, $\sim$$6 000$~K) to form cold structures (Cold Neutral Medium, $\sim$70~K) through shocks \citep[e.g.][]{vazquez96,HePe99,ballesteros99}. However, it is only recently that 3D models have simulated the thermal transition from the atomic to the molecular phase (\ion{H}{I} $\rightarrow$ H$_2$) with realistic heating and cooling functions \citep[e.g.][]{AuHe05,GlML07}. Several groups aim at studying in detail the formation of molecular clouds with sufficient resolution to model star formation. Recent 3D numerical simulations now include gravity, magnetic fields, thermal and dynamical instabilities \citep[e.g.][]{banerjee09, hartmann12} and in some cases treat the chemical evolution of the gas \citep{HeHa08, clark12, InIn12}. Massive giant molecular clouds, or cloud complexes, may alternatively form from the collision/agglomeration of clouds \citep[e.g.][]{BlSh80,dobbs08}. Clouds are higher density and more structured media than diffuse \ion{H}{I} streams, and so they are mainly composed of cold \ion{H}{I} and H$_2$ gas. Cloud-cloud collisions are expected to be the dominant phenomenon in high-density regions of galaxies \citep[e.g.][]{dobbs08} as well as during the late-stage evolution of molecular clouds formed through \ion{H}{I} converging flows \citep[e.g.][]{vazquez10}. Several groups are studying the formation, evolution, and disruption of massive clouds by spiral waves, bar potentials, and satellite galaxies with hydrodynamic simulations of galaxies able to resolve molecular clouds \citep[e.g.][]{bournaud10, DP13}. Both colliding flows and cloud-cloud collisions naturally explain the observed rapid onset of star formation once the cloud has formed, which has proven problematic in the past \citep[$<$$3-10 \times 10^6$~yr,][]{ballesteros99,hartmann01,roman09}. In these scenarios, molecular clouds are never in a kinematic equilibrium state, as part of the cloud collapses while part of it disperses. A few models have described the formation of molecular clouds by assuming equilibrium between the formation of H$_2$ molecules and their photodissociation \citep[e.g.][]{AnWa93,krumholz09}. In short, these authors applied a simplified version of the chemical modeling of photodissociation regions \citep[e.g.][]{vDiBl86} to a spherical geometry. However, such an equilibrium may never be reached since its timescale should be $1-3\times 10^7$~yr or even longer \citep{MLG12}. Non steady-state models have been developed using turbulence and/or colliding streams to enhance and accelerate the formation of H$_2$ molecules behind shocks \citep[e.g.][]{heitsch08,hennebelle08,KoIn00,clark12}. These two families of models make different predictions, for the conversion of \ion{H}{I} into H$_2$, especially in terms of the lifetime of the process and the mixing of the H$_2$ and \ion{H}{I} gases. Indeed, steady-state models assume that an equilibrium between the \ion{H}{I} and H$_2$ formation/destruction is rapidly reached. The \ion{H}{I} and H$_2$ gases are also assumed to be mutually exclusive, with a sharp transition from \ion{H}{I} to H$_2$-dominated media when entering the cloud \citep[e.g][]{krumholz09}. As a consequence, equilibrium models predict the existence of a threshold for the atomic gas surface density, at $\Sigma_{\ion{H}{I}} \simeq 10~\msun\,$pc$^{-2}$ for solar metallicity gas according to \cite{krumholz09}. In contrast, non-steady state models start with an accumulation of \ion{H}{I} gas that translates into a mass surface density above this classical threshold. The H$_2$ formation rate, high at the beginning of the molecular cloud formation process, continuously slows down as the cloud becomes fully molecular \citep[e.g.][]{clark12}. The \ion{H}{I} surface density thus decreases over time, first sharply, then slower and slower, eventually reaching this equilibrium state. W43 should be a perfect testbed to investigate the formation of molecular clouds and star formation in the framework of dynamical scenarios. At only 5.5~kpc from us, W43 is among the most extreme molecular cloud complexes of the Milky Way \citep{nguyen11b,zhang14}. It is massive, $M_{\mbox{\tiny total}}\sim 6\times 10^6~\msun$\footnote{ The mass and diameter values given in \cite{nguyen11b} have been recalculated to account for the refinement of W43 distance, from 6~kpc to 5.5~kpc, by \cite{zhang14}.} within an equivalent diameter of $\sim$130~pc, and is highly concentrated into dense star-forming sites \citep{nguyen11b}. Despite a velocity dispersion FWHM of $\sim$$22.3~\kms$, the W43 molecular cloud complex is a coherent and gravitationally bound ensemble of clouds. Moreover, W43 has the potential to form starburst clusters in the near future \citep[SFR$\, \sim 0.1~\msun\, \mbox{yr}^{-1}$,][]{nguyen11b,louvet14}. Its densest parts correspond to the Galactic mini-starburst cloud W43-Main \citep{motte03} recently mapped by the \emph{Herschel}/Hi-GAL and HOBYS key programs \citep{molinari10,motte10}. \citet{nguyen13} identified within W43-Main two dense filamentary clouds categorized as ridges following the definition of \citet{hill11} and \citet{hennemann12}. In short, ridges are elongated clouds with very high column density, \Nhtwo$\,>10^{23}~\cmd$, over several squared parsecs \citep[see also][]{nguyen11a,motte12}. \citet{nguyen13} proposed and \cite{louvet14} showed that the W43-MM1 and W43-MM2 ridges are progenitors of young massive clusters. W43 is located near the meeting point of the Scutum-Centaurus (or Scutum-Crux) Galactic arm and the Galactic long bar, a dynamically complex region where collisions are expected \citep{nguyen11b, carlhoff13}. Several massive stellar associations, called red supergiant clusters, have also been identified in the $1\degr-6\degr$ neighborhood of W43 \citep[see][and references therein]{gonz12}. In this paper, we attempt to trace back the formation of molecular clouds in the W43 complex. Employing the database described in Sect.~\ref{s:obs}, we look for gas streams and cloud ensembles at the outskirts of the atomic and molecular complex and characterize its atomic envelope (see Sect.~\ref{s:results}). Section~\ref{s:discu} follows the transition from atomic to molecular media and discusses the collision probability of gas streams and clouds. Finally, Sect.~\ref{s:conc} concludes that the equilibrium relations of the \ion{H}{I} into H$_2$ transition do not apply in W43 and that this extreme cloud complex may have been created by the collision of molecular clouds. | \label{s:conc} In order to improve our knowledge of molecular cloud formation, we have initiated an investigation into W43, an extreme molecular cloud and star-forming complex located at a dynamical place within the Milky Way, 5.5~kpc from the Sun. We used an \ion{H}{I} and $^{12}$CO 1--0 database allowing us to trace back the formation of molecular clouds on 10~pc to 400~pc scales for this region. Our main findings can be summarized as follows: \begin{enumerate} \item We detected an \ion{H}{I} envelope around the W43 molecular cloud (see Fig.~\ref{fig:co_hi_intmap}), confirming the work of \citet{nguyen11b}. It has an aspect ratio of 3:2 (with the larger axis along the Galactic longitude), an equivalent diameter of $\sim$270~pc, and a mass of $\sim$$3\times 10^6~\msun$. Interestingly, such a well-defined and symmetrical envelope is rarely seen around star-forming regions. \item Three cloud ensembles of \ion{H}{I} and $^{12}$CO gas develop along hundreds of parsecs, at the outskirts of and within the atomic envelope (see Figs.~\ref{fig:co_hi_pvdiag1}-\ref{fig:co_hi_pvdiag3}). The velocity gradients of these cloud ensembles are used to position them in the W43 region. Cloud ensemble \#1 may fall from the high-latitude part of the Galactic disk, \#2 seems to originate from the Scutum-Centaurus arm, and \#3 may be at the very tip of the long bar. This picture is consistent with W43 being in front of the long bar, a region with crowded orbits known to be efficient in accumulating gas. \item These three (mostly) molecular ensemble of clouds are separated by $\sim$20--40~$\kms$ along the line of sight and converge on the location of W43. The measured velocity gradients extend within the W43 complex as velocity structures, are consistent with free-fall velocities, and display $\sim$20~$\kms$ velocity jumps where they merge. The cloud ensembles \#1--\#3 could thus be streams that are accreted onto the central W43 region, which has a total mass of $\sim$10$^7~\msun$, driven by gravity rather than forced by converging flows of atomic gas. \item The \ion{H}{I} surface density measured throughout the W43 complex is high when compared to the values usually quoted in the literature: $\Sigma_{\ion{H}{I}} \sim 65\pm20~\msun\,$pc$^{-2}$ instead of $7-15~\msun$\,pc$^{-2}$. The \ion{H}{I} surface density does not show a saturated behavior but rather increases when entering the molecular complex (see Fig.~\ref{fig:gasratio1}). This suggests that W43 is a heterogeneous structure of mixed H$_2$ and \ion{H}{I} gas and that equilibrium between H$_2$ formation and photodissociation is not reached. These results thus argue in favor of a non steady-state formation of molecular clouds in W43. \item The H$_2$-to-\ion{H}{I} ratio measured over the complete W43 region is high, $R_{{\rm H_{2}}}\sim3.5\pm_{2}^{3}$, proving that most of the gas is already in molecular form before reaching W43 (see Fig.~\ref{fig:gasratio2}). High-density regions of galaxies, such as the W43 molecular cloud complex, located in what was previously called the molecular ring of the Milky Way, obviously cannot provide constraints on the transition from atomic to molecular material. The formation of such molecular cloud entities is therefore weakly related to the efficiency of turning \ion{H}{I} atoms into H$_2$ molecules. \item We conclude that the W43 molecular cloud complex most probably formed through a dynamical process such as the collision of several clouds, already in a molecular-dominated regime. The geometry and strength of this collision, as well as the molecular ratio and structure of the clouds, should be used to customize colliding cloud models. This is one of the goals of the W43-HERO IRAM large program which uses the IRAM 30~m telescope to determine the diagnostics of colliding clouds and explain the extreme characteristics of the W43 molecular cloud star-forming region. \end{enumerate} | 14 | 4 | 1404.4404 |
1404 | 1404.1221_arXiv.txt | Calibrating the absolute energy scale of air showers initiated by ultra-high energy cosmic rays is an important experimental issue. Currently, the corresponding systematic uncertainty amounts to 14-21\% using the fluorescence technique. Here we describe a new, independent method which can be applied if ultra-high energy photons are observed. While such photon-initiated showers have not yet been identified, the capabilities of present and future cosmic-ray detectors may allow their discovery. The method makes use of the geomagnetic conversion of UHE photons (preshower effect), which significantly affects the subsequent longitudinal shower development. The conversion probability depends on photon energy and can be calculated accurately by QED. The comparison of the observed fraction of converted photon events to the expected one allows the determination of the absolute energy scale of the observed photon air showers and, thus, an energy calibration of the air shower experiment. We provide details of the method and estimate the accuracy that can be reached as a function of the number of observed photon showers. Already a very small number of UHE photons may help to test and fix the absolute energy scale. | 14 | 4 | 1404.1221 |
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1404 | 1404.4632_arXiv.txt | The redshift-dependent fraction of color-selected galaxies revealing Lyman alpha emission, \xlya\ has become the most valuable constraint on the evolving neutrality of the early intergalactic medium. However, in addition to resonant scattering by neutral gas, the visibility of Lyman alpha is also dependent on the intrinsic properties of the host galaxy, including its stellar population, dust content and the nature of outflowing gas. Taking advantage of significant progress we have made in determining the line emitting properties of $z \simeq 4-6$ galaxies, we propose an improved method, based on using the measured slopes of the rest-frame ultraviolet continua of galaxies, to interpret the growing body of near-infrared spectra of $z>7$ galaxies in order to take into account these host galaxy dependencies. In a first application of our new method, we demonstrate its potential via a new spectroscopic survey of $7<z<8$ galaxies undertaken with the Keck MOSFIRE spectrograph. Together with earlier published data our data provides improved estimates of the evolving visibility of Lyman alpha, particularly at redshift $z\simeq 8$. As a byproduct, we also present a new line emitting galaxy at a redshift $z=7.62$ which supersedes an earlier redshift record. We discuss the improving constraints on the evolving neutral fraction over $6<z<8$ and the implications for cosmic reionization. | \label{sec:intro} The transition from a neutral intergalactic medium (IGM) to one that is ionized, and therefore transparent to ultraviolet photons, represents the latest frontier in our overall understanding of cosmic history. In addition to determining when this `cosmic reionization' occurred, a key question is the role of star-forming galaxies in governing the process. Structure in the polarization of the cosmic microwave background suggests the reionization process occurred within the redshift interval $6<z<20$ \citep{Hinshaw2013a} and deep infrared imaging with Hubble Space Telescope has provided the first opportunity to conduct a census of galaxies during the latter half of this period \citep{Ellis2013a, Oesch2013a}. Recent progress in this area has been reviewed by \cite{Robertson2013a} and \citet{Bromm2013a}. In the absence of significant numbers of high redshift QSOs or gamma ray bursts, the most immediately available probe of the evolving neutrality of the IGM beyond $z \simeq 6-7$ is the visibility of the Lyman alpha (\lya) emission line in controlled samples of color-selected galaxies. Although a prominent line in star-forming galaxies at $z \leq 6$, as Ly$\alpha$ is a resonant transition, it is readily suppressed by neutral gas, both in the host galaxy and, if present, in the surrounding IGM. First proposed as a practical experiment using Lyman break galaxies (LBGs) by \citet{Stark2010a}, the idea followed earlier theoretical work by \citet{Miralda-Escude2000a}, \citet{Santos2004a} and others. Ground-based near-infrared spectroscopic surveys have now targeted various samples of color-selected Lyman break galaxies over $6<z<8$ allowing the construction of a redshift-dependent \lya\ fraction, \xlya , which falls sharply from a value of $\simeq$ 50\% at $z\simeq 6$ \citep{Stark2010a} to less than 10\% at and beyond $z\simeq 7$ \citep{Pentericci2011a,Schenker2012a, Ono2012a, Treu2012a,Pentericci2014a}. Although converting this downturn in the visibility of the line into the volume fraction of neutral hydrogen, \xhi, is uncertain \citep{Bolton2013a}, the prospects for improving the statistics of this test are promising given the arrival of multi-object instruments such as MOSFIRE on the Keck 1 telescope \citep{McLean2012a}. So far, this important measure of late reionization has been applied by adopting an empirical description of the demographics of Ly$\alpha$ emission in LBGs, parameterized according to the equivalent width (EW) distribution for various UV luminosities over the redshift range $3<z<6$ when the Universe is fully ionized. The trend is then extrapolated to higher redshifts in the form of a `no evolution' prediction with the aim of rejecting this prediction at some level of significance (e.g. \citealt{Schenker2012a}). As we discuss here, this method, now widely used, has several disadvantages. Recognizing these and noting the spectroscopic and optical and near-infrared imaging data of LBGs over $3<z<6$ has improved in scope and quality, in this paper we adopt a more physically-based approach to the visibility of Ly$\alpha$ in the vicinity of the host galaxy. Our new approach aims to predict its visibility in a high redshift galaxy on the basis of its measured UV continuum slope that, in turn, contains information on the dust content, and stellar population, which both directly influence the strength of any Ly$\alpha$ emission. This approach has the distinct advantage that, for the new $z>7$ samples being studied with MOSFIRE and other spectrographs, composite UV slopes for the population are usually available so that unnecessary extrapolation can be avoided. The present paper is concerned with describing this improved Ly$\alpha$ fraction test and applying it to the first comprehensive set of spectroscopic data emerging from MOSFIRE. In addition to incorporating the earlier surveys conducted with Keck \citep{Schenker2012a,Ono2012a,Treu2012a}, and FORS2 on the VLT \citep{Pentericci2011a}, we present the first results from a survey of high quality Ultra Deep Field (UDF) targets which provides a valuable extension of the aforementioned studies. As part of this survey, we demonstrate a new Ly$\alpha$-emitting galaxy at a redshift $z$=7.62 extending once again the frontier of spectroscopically-confirmed HST sources. A plan of the paper follows. In Section 2, we introduce our new method for the Lyman alpha fraction test. Section 3 introduces the new compilation of $3<z<6$ data drawn from our now completed Keck spectroscopic survey \citep{Stark2014a}, and Section 4 contains an analysis of this data in the context of our new method. In Section 5 we introduce our new MOSFIRE data and apply our new method to both this data and that obtained earlier. | Using our sample of 451 $3 < z < 6$ spectroscopically followed-up Lyman break galaxies, we demonstrate an improved correlation between the ultraviolet continuum slope of a galaxy, $\beta$, and its \lya\ emission strength. Given the availability of deep WFC3 photometry for both the GOODS-N and S fields, this progress follows measurements for many individual galaxies in this redshift range, rather than via stacked or averaged UV slopes, as in earlier work \citep{Shapley2003a,Stark2010a}. We demonstrate that this correlation with the presence of \lya\ is stronger and more physically-motivated than that based on the UV luminosity and thus provides a natural basis for an improved model for the \lya\ fraction test, now widely used to measure the evolving neutrality of the $z > 6.5$ IGM. We demonstrate the benefits of this new model using a new MOSFIRE spectroscopic survey of $7<z<8$ targets from the Ultra Deep Field 2012 catalog and CLASH lensing survey, and combine this with data at these redshifts already published in the literature. As a result we present the implications of the most comprehensive search for \lya\ emission at $z \simeq 8$ to date, confirming once again important evidence that cosmic reionization ended at redshifts $z \simeq 6.5$. As a byproduct we also present the $4.0\sigma$ confirmation of \lya\ in a galaxy at $z = 7.62$, likely the most distant spectroscopically-confirmed galaxy. | 14 | 4 | 1404.4632 |
1404 | 1404.1832_arXiv.txt | \noindent Supersymmetric hybrid inflation is an exquisite framework to connect inflationary cosmology to particle physics at the scale of grand unification. Ending in a phase transition associated with spontaneous symmetry breaking, it can naturally explain the generation of entropy, matter and dark matter. Coupling F-term hybrid inflation to soft supersymmetry breaking distorts the rotational invariance in the complex inflaton plane---an important fact, which has been neglected in all previous studies. Based on the $\delta N$ formalism, we analyze the cosmological perturbations for the first time in the full two-field model, also taking into account the fast-roll dynamics at and after the end of inflation. As a consequence of the two-field nature of hybrid inflation, the predictions for the primordial fluctuations depend not only on the parameters of the Lagrangian, but are eventually fixed by the choice of the inflationary trajectory. Recognizing hybrid inflation as a two-field model resolves two shortcomings often times attributed to it: The fine-tuning problem of the initial conditions is greatly relaxed and a spectral index in accordance with the PLANCK data can be achieved in a large part of the parameter space without the aid of supergravity corrections. Our analysis can be easily generalized to other (including large-field) scenarios of inflation in which soft supersymmetry breaking transforms an initially single-field model into a multi-field model. | Supersymmetric hybrid inflation is a promising framework for describing the very early universe. Not only does it account for a phase of accelerated expansion; it also provides a detailed picture of the subsequent transition to the radiation dominated phase. Different versions are F-term~\cite{Dvali:1994ms,Copeland:1994vg}, D-term~\cite{Binetruy:1996xj,Halyo:1996pp} and P-term~\cite{Kallosh:2003ux} inflation, with supersymmetry during the inflationary phase being broken by an F-term, a D-term or a mixture of both, respectively. Hybrid inflation is very attractive for a number of reasons. It can be naturally embedded into grand unification, and the GUT scale $M_{\rm GUT}$ yields the correct order of magnitude for the amplitude of the primordial scalar fluctuations~\cite{Dvali:1994ms}. Moreover, supergravity corrections are typically small, since during inflation the value of the inflaton field is $\mathcal{O}(M_{\rm GUT})$, i.e.\ much smaller than the Planck scale. Hybrid inflation ends by tachyonic preheating, a rapid `waterfall' phase transition in the course of which a global or local symmetry is spontaneously broken~\cite{Felder:2000hj}. Pre- and reheating have recently been studied in detail for the case where this symmetry is $B$$-$$L$, the difference between baryon and lepton number. The decays of heavy $B$$-$$L$ Higgs bosons and heavy Majorana neutrinos can naturally explain the primordial entropy, the observed baryon asymmetry and the dark matter abundance~\cite{Buchmuller:2010yy,Buchmuller:2011mw,Buchmuller:2012wn}.% \footnote{For related earlier work, cf.\ Refs.~\cite{Asaka:1999yd,Senoguz:2005bc}.} Finally, inflation, preheating and the formation of cosmic strings are all accompanied by the generation of gravitational waves that can be probed with forthcoming gravitational wave detectors~\cite{Shafi:2010jr,GarciaBellido:2007dg,Dufaux:2008dn, Hindmarsh:2011qj, Buchmuller:2013lra}. The supersymmetric extension of the Standard Model with local $B$$-$$L$ symmetry is described by the superpotential \begin{align} \label{eq_W} W = \lambda \Phi \left(\frac{v^2}{2} - S_1 S_2 \right) + \frac{1}{\sqrt{2}} h_i^n n_i^c n_i^c S_1 + h^{\nu}_{ij} \textbf{5}^*_i n_j^c H_u + W_{\text{MSSM}} \,. \end{align} The first term is precisely the superpotential of F-term hybrid inflation, with the singlet superfield $\Phi$ containing the inflaton $\phi$ and the waterfall superfields $S_1$ and $S_2$ containing the Higgs field $\chi$ responsible for breaking $B$$-$$L$ at the scale $v$. The next two terms involve the singlet superfields $n^c_i$ whose fermionic components represent the charge conjugates of the three generations of right-handed neutrinos. These two terms endow the singlet neutrinos with a Majorana mass term and a Yukawa coupling to the MSSM Higgs and lepton doublets, denoted here by $H_u$ and $\textbf{5}^*$ in $SU(5)$ notation. $\lambda$ and $h$ are coupling constants. In a universe with an (almost) vanishing cosmological constant, F-term supersymmetry breaking leads to a constant term in the superpotential, \begin{align} W_0 = \alpha \, \mG\Mp^2 \,, \label{eq_W0} \end{align} where $\mG$ is the vacuum gravitino mass at low energies and $\alpha$ a model-dependent $\mathcal{O}(1)$ parameter. In the Polonyi model, one has $\alpha = \exp{(\sqrt{3}-2)}$~\cite{Polonyi:1977pj}. For definiteness, we choose $\alpha \equiv 1$ in the following. We assume that the supersymmetry breaking field is located in its minimum and that its dynamics can be neglected during inflation. Together with the non-vanishing F-term of the inflaton field during inflation, $F_\Phi = -\lambda \,v^2 / 2$, this constant term in the superpotential induces a term linear in the real part of the inflaton field in the scalar potential~\cite{Buchmuller:2000zm}, \begin{align} V(\phi) \supset -\left[3\,W(\phi) + F_\Phi^* \,\phi \right]\frac{W_0^*}{M_{\textrm{Pl}}^2} + \textrm{h.c.} \supset -4 \, \alpha \, m_{3/2}\,\textrm{Re}\left\{-F_\Phi^* \, \phi\right\} \,, \quad W(\Phi) = -F_\Phi^* \Phi + ... \,. \label{eq:Vlinear} \end{align} The real and the imaginary part of the inflaton field are thus governed by different equations of motion, requiring an analysis of the inflationary dynamics in the complex inflaton plane. As a consequence, all of the inflationary observables are sensitive to the choice of the inflationary trajectory. In this sense, the measured values of these quantities do not point to a particular Lagrangian or specific values of the fundamental model parameters. To large extent, they are the outcome of a random selection among different initial conditions which has no deeper meaning within the model itself. We emphasize that these conclusions apply in general to every inflationary model in which inflation is driven by one or several large F-terms. In the presence of soft supersymmetry breaking, these F-terms will always couple to the constant in the superpotential and thus induce linear terms in the scalar potential of exactly the same form as in Eq.~\eqref{eq:Vlinear}. The analysis in this paper can hence be easily generalized to other models of inflation, in particular also to models of the large-field type. Taking the two-field nature of hybrid inflation into account, we find that the initial conditions problem of hybrid inflation is significantly relaxed and we can obtain successful inflation in accordance with the PLANCK data~\cite{Ade:2013uln} without running into problems due to cosmic strings~\cite{Ade:2013xla}. First results of this two-field analysis were presented in Ref.~\cite{Buchmuller:2013dja}. Non-supersymmetric multi-field hybrid inflation, commonly referred to as `multi-brid' inflation, has been studied in Refs.~\cite{Sasaki:2008uc,Naruko:2008sq}. The model investigated here differs from multi-brid inflation in two regards: (i) we embed inflation into a realistic model of particle physics and (ii) we study inflation in the context of softly broken supersymmetry. Furthermore, we note that, during the final stages of preparing this paper, evidence for a potentially primordial B-mode signal in the polarization of the cosmic microwave background (CMB) radiation was announced by the BICEP2 Collaboration~\cite{Ade:2014xna}. In App.~\ref{app-bicep2}, we discuss the implications of this very recent development on F-term hybrid inflation. Our discussion is organized as follows. In Sec.~\ref{sec_2}, we analyze the connection between $W_0$ and the spectral index analytically for inflation along the real axis. In Sec.~\ref{sec_complex_plane}, we then turn to the generic situation of arbitrary inflationary trajectories in the complex plane. We perform a full numerical scan of the parameter space, based on a customized version of the $\delta N$ formalism, in order to determine the inflationary observables and again reconstruct our results analytically. Sec.~\ref{sec:inicon} demonstrates how these results relax the initial conditions problem of F-term hybrid inflation and Sec.~\ref{sec_gravitino_mass} is dedicated to an investigation of the allowed range for the gravitino mass. Finally, we conclude in Sec.~\ref{sec_conclusion}. As a supplement, we derive in App.~\ref{app:index} simple analytical expressions that allow to estimate the scalar amplitude as well as the scalar spectral tilt in general multi-field models of inflation in the limit of negligible effects due to isocurvature perturbations. | } Supersymmetric hybrid inflation models typically feature a true vacuum in which supersymmetry is fully restored. A simple and straightforward way to accommodate soft low-energy supersymmetry breaking in this Minkowski vacuum is to assume that supersymmetry is spontaneously broken by non-vanishing F-terms in a hidden sector, whose dynamics are already completely fixed during inflation. This effectively results in a constant term in the superpotential proportional to the vacuum gravitino mass. Since the mass scale of the gravitino is typically expected to be much smaller than the energy scale of inflation, the effect of this term on the inflationary dynamics has been widely neglected. However, since the inclusion of this term breaks the rotational invariance of the scalar potential in the complex inflaton plane, its effects can be very important even for small gravitino masses. F-term hybrid inflation is consequently a two-field model of inflation, such that its predictions for the observables related to the primordial fluctuations depend not only on the parameters of the scalar potential, but in particular also on the choice of the inflationary trajectory. This puts the measured values of the amplitude of the scalar power spectrum, the scalar spectral index and the amplitude of the local bispectrum into new light: their precise values are no longer dictated by the fundamental model parameters, but are rather strongly influenced by a selection process at very early times that appears to be random within the model itself. As these insights only rely on the presence of a large F-term driving inflation and the assumption of soft symmetry breaking in a hidden sector at very high scales, similar conclusions should apply in comparable inflationary scenarios. We expect that our study and in particular our analysis of the linear term in the scalar potential can be easily generalized to other models of inflation, including large-field models, in which supersymmetry breaking turns an originally single-field model into a multi-field model. In this paper, we analyzed the inflationary dynamics of F-term hybrid inflation in the complex plane based on the $\delta N$ formalism. After extending the method presented in Refs.~\cite{Yokoyama:2007uu,Yokoyama:2007dw} so as to explicitly take into account the contributions to the curvature perturbation spectrum produced after the end of slow-roll inflation, we calculated the inflationary observables related to the scalar power spectrum and the local bispectrum as functions of the symmetry breaking scale $v$, the superpotential coupling $\lambda$, the gravitino mass $\mG$ and the choice of the inflationary trajectory, labeled by the final inflaton phase $\theta_f$. We found that the predictions for the scalar power spectrum are well described in an effective single-field approximation, whereas the bispectrum can obtain large contributions from the inherently multi-field dynamics. In ordinary single-field slow-roll inflation, we would expect the primordial non-Gaussianities to be suppressed by the slow-roll parameters. By contrast, in hybrid inflation in the complex plane, we partly obtained $f_{\textrm{NL}}^{\textrm{local}}$ values roughly as large as $0.5$. We cross-checked the results of our numerical analysis by means of analytical calculations, which provided us with accurate analytical formulas for the hill-top regime on the real axis as well as with semi-analytical formulas for the two-field case. The results of our analysis demonstrate that F-term hybrid inflation is in much better shape than widely believed in two important points. First, the fine-tuning in the initial conditions necessary to obtain successful inflation is greatly reduced. Second, the measured scalar spectral index can be reproduced in a significant part of the parameter space without resorting to a non-canonical K\"ahler potential. Roughly speaking, a correct spectral index is obtained when the contributions to the slope of the scalar potential from one-loop corrections and from supersymmetry breaking have opposite sign, but are of comparable size. This is typically accomplished along trajectories in the complex plane corresponding to $\theta_f \lesssim \pi/4$, i.e.\ trajectories which pass through the vicinity of the hill-top region on the real axis. Taking into account the effect of supersymmetry breaking hence links the CMB observables to the mass scale of soft supersymmetry breaking. The resulting mass range for the gravitino mass turns out to lie in a region which is very interesting, including the mass range relevant for supersymmetric electroweak symmetry breaking, for gravitino LSP dark matter as well as for nonthermal dark matter production through the decay of heavy gravitinos. A crucial further development which will have an important impact on F-term hybrid inflation is the ongoing search for primordial B-mode polarization of the CMB radiation. If the recent results of the BICEP2 experiment are confirmed, an explanation within the framework of small-field inflation will be challenging. \subsubsection*{Acknowledgements} The authors thank A.~Hebecker, V.~Mukhanov, T.~Suyama, T.~Takahashi, A.~Westphal, M.~Yamaguchi, T.~Yanagida and S.~Yokoyama for helpful discussions and comments. This work has been supported in part by the German Science Foundation (DFG) within the Collaborative Research Center 676 ``Particles, Strings and the Early Universe'' (W.B.), by the European Union FP7-ITN INVISIBLES (Marie Curie Action PITAN-GA-2011-289442-INVISIBLES) (V.D.), by the JSPS Postdoctoral Fellowships for Research Abroad (K.K.) and by the World Premier International Research Center Initiative (WPI Initiative) of the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan (K.S.). \begin{appendix} | 14 | 4 | 1404.1832 |
1404 | 1404.1003_arXiv.txt | \noindent We present a {\em fully} flavour-covariant formalism for transport phenomena, by deriving Markovian master equations that describe the time-evolution of particle number densities in a statistical ensemble with arbitrary flavour content. As an application of this general formalism, we study flavour effects in a scenario of resonant leptogenesis~(RL) and obtain the flavour-covariant evolution equations for heavy-neutrino and lepton number densities. This provides a complete and unified description of RL, capturing three {\em distinct} physical phenomena: (i) the resonant mixing between the heavy-neutrino states, (ii) coherent oscillations between different heavy-neutrino flavours, and (iii) quantum decoherence effects in the charged-lepton sector. To illustrate the importance of this formalism, we numerically solve the flavour-covariant rate equations for a minimal RL model and show that the total lepton asymmetry can be enhanced by up to one order of magnitude, as compared to that obtained from flavour-diagonal or partially flavour off-diagonal rate equations. Thus, the viable RL model parameter space is enlarged, thereby enhancing further the prospects of probing a common origin of neutrino masses and the baryon asymmetry in the Universe at the LHC, as well as in low-energy experiments searching for lepton flavour and number violation. The key new ingredients in our flavour-covariant formalism are rank-4 rate tensors, which are required for the consistency of our flavour-mixing treatment, as shown by an explicit calculation of the relevant transition amplitudes by generalizing the optical theorem. We also provide a geometric and physical interpretation of the heavy-neutrino degeneracy limits in the minimal RL scenario. Finally, we comment on the consistency of various suggested forms for the heavy-neutrino self-energy regulator in the lepton-number conserving limit. | \label{sec:1} The observed matter-antimatter asymmetry in the Universe and the observation of non-zero neutrino masses and mixing (for a review, see~\cite{pdg}) provide two of the strongest pieces of experimental evidence for physics beyond the Standard Model (SM). Leptogenesis~\cite{Fukugita:1986hr} is an elegant framework that satisfies the basic Sakharov conditions~\cite{Sakharov:1967}, dynamically generating the observed matter-antimatter asymmetry. According to the standard paradigm of leptogenesis (for reviews, see e.g.~\cite{Pilaftsis:1998pd, Buchmuller:2005eh, Davidson:2008bu, Blanchet:2012bk}), there exist heavy Majorana neutrinos in minimal extensions of the SM, whose out-of-equilibrium decays in an expanding Universe create a net excess of lepton number ($L$), which is reprocessed into the observed baryon number ($B$) through the equilibrated $(B+L)$-violating electroweak sphaleron interactions~\cite{Kuzmin:1985mm}. In addition, these heavy SM-singlet Majorana neutrinos $N_\alpha$ (with $\alpha = 1,...,\mathcal{N}_N$) could explain the observed smallness of the light neutrino masses by the seesaw mechanism~\cite{seesaw1, seesaw2, seesaw4, seesaw5, seesaw6}. Hence, leptogenesis can be regarded as a cosmological consequence of the seesaw mechanism, thus providing an attractive link between two seemingly disparate pieces of evidence for new physics at or above the electroweak scale. In the original scenario of thermal leptogenesis~\cite{Fukugita:1986hr}, the heavy Majorana neutrino masses are typically close to the Grand Unified Theory (GUT) scale, $M_{\rm GUT} \sim 10^{16}$ GeV, as suggested by natural GUT embedding of the seesaw mechanism~\cite{seesaw2, seesaw4, seesaw5}. In a `vanilla' leptogenesis scenario~\cite{Buchmuller:2004nz}, where the heavy neutrino masses are hierarchical ($m_{N_1} \ll m_{N_{2}} < m_{N_{3}}$), the solar and atmospheric neutrino oscillation data impose a {\it lower} limit on $m_{N_1} \gsim 10^9$ GeV~\cite{Davidson:2002qv, Buchmuller:2002rq, Hambye:2003rt, Branco:2006ce}. As a consequence, such leptogenesis models are difficult to test in foreseeable laboratory experiments. Moreover, these high-scale thermal leptogenesis scenarios, when embedded within supergravity models of inflation, could potentially lead to a conflict with the upper bound on the reheating temperature of the Universe, $T_R \lsim 10^6$--$10^9$ GeV, required to avoid overproduction of gravitinos whose late decays may otherwise spoil the success of Big Bang Nucleosynthesis~\cite{Khlopov:1984pf, Ellis:1984eq, Ellis:1984er, Kawasaki:1994af, Cyburt:2002uv, Kawasaki:2004qu, Kawasaki:2008qe}. In general, it is difficult to build a {\it testable} low-scale model of leptogenesis, with a hierarchical heavy neutrino mass spectrum~\cite{Pilaftsis:1998pd, Hambye:2001eu}. A potentially interesting solution to the aforementioned problems may be obtained within the framework of resonant leptogenesis (RL)~\cite{Pilaftsis:1997dr, Pilaftsis:1997jf, Pilaftsis:2003gt}. The key aspect of RL is that the heavy Majorana neutrino self-energy effects~\cite{Liu:1993tg} on the leptonic $ \CP$-asymmetry become dominant~\cite{Flanz:1994yx, Covi:1996wh} and get resonantly enhanced, even up to order one~\cite{Pilaftsis:1997dr, Pilaftsis:1997jf}, when at least two of the heavy neutrinos have a small mass difference comparable to their decay widths. As a consequence of thermal RL, the heavy Majorana neutrino mass scale can be as low as the electroweak scale~\cite{Pilaftsis:2005rv}, while maintaining complete agreement with the neutrino oscillation data~\cite{pdg}. A crucial model-building aspect of RL is the {\it quasi-degeneracy} of the heavy neutrino mass spectrum, which could be obtained as a natural consequence of the approximate breaking of some symmetry in the leptonic sector. In minimal extensions of the SM, there is no theoretically or phenomenologically compelling reason that prevents the singlet neutrino sector from possessing such a symmetry and, in fact, in realistic ultraviolet-complete extensions of the SM, such a symmetry can often be realized naturally. For instance, the RL model discussed in~\cite{Pilaftsis:1997dr, Pilaftsis:1997jf} was based on a $U(1)_L$ lepton symmetry in the heavy neutrino sector, motivated by superstring-inspired $E_6$ GUTs~\cite{Mohapatra:1986aw, Nandi:1985uh, Mohapatra:1986bd}. The small mass splitting between the heavy neutrinos was generated by approximate breaking of this lepton symmetry via GUT- and/or Planck-scale-suppressed higher-dimensional operators. The RL model discussed in~\cite{Pilaftsis:2003gt} was based on the Froggatt-Nielsen (FN) mechanism~\cite{Froggatt:1978nt} in which two of the heavy Majorana neutrinos, having opposite charges under $U(1)_{\rm FN}$, naturally had a mass difference comparable to their decay widths. There is a vast literature on other viable constructions of RL models, e.g.~within minimal extensions of the SM~\cite{Xing:2006ms, Hambye:2006zn, Blanchet:2009bu, Iso:2010mv, Okada:2012fs, Haba:2013pca}, with approximate flavour symmetries~\cite{Ellis:2002eh, Araki:2005ec, Cirigliano:2006nu, Chun:2007vh, Babu:2007zm, Branco:2009by}, with variations of the minimal type-I seesaw~\cite{Ma:1998dx, Albright:2003xb, Hambye:2003rt, Hambye:2000ui, Asaka:2008bj, Blanchet:2009kk}, within $SO(10)$ GUTs~\cite{Akhmedov:2003dg, Albright:2004ws, Majee:2007uv, Blanchet:2010kw}, within the context of supersymmetric theories~\cite{Dar:2003cr, Allahverdi:2004ix, Hambye:2004jf, West:2004me, West:2006fs}, and in extra-dimensional theories~\cite{Pilaftsis:1999jk, Gherghetta:2007au, Eisele:2007ws, Gu:2010ye, Bechinger:2009qk}. There also exist other variants of the RL scenario, such as radiative RL~\cite{Felipe:2003fi, Turzynski:2004xy, Branco:2005ye, Branco:2006hz} and soft RL~\cite{Grossman:2003jv, D'Ambrosio:2003wy}. In another important variant of RL, a {\it single} lepton-flavour asymmetry is resonantly produced by out-of-equilibrium decays of heavy Majorana neutrinos of a particular family type~\cite{ Pilaftsis:2004xx, Deppisch:2010fr}. This mechanism uses the fact that the sphaleron processes preserve, in addition to $B-L$, the individual quantum numbers $X_i = {B}/3 - {L}_i$~\cite{Khlebnikov:1988sr, Harvey:1990qw, Dreiner:1992vm, Cline:1993vv,Laine:1999wv}, where $i = 1, 2, 3$ is the SM family index and $L_i$ is the lepton asymmetry in the $i$th family. Therefore, it is important to estimate the net baryon number $B$ created by sphalerons just before they freeze out. In particular, a generated baryon asymmetry can be protected from potentially large washout effects due to sphalerons if an individual lepton flavour $\ell$ is out of equilibrium. We refer to such scenarios of RL as {\it resonant $\ell$-genesis} (RL$_\ell$). In this case, the heavy Majorana neutrinos could be as light as the electroweak scale~\cite{Pilaftsis:2005rv} and still have sizable couplings to other charged-lepton flavours $\ell' \neq \ell$. This enables the modelling of minimal RL$_\ell$ scenarios~\cite{Deppisch:2010fr} with electroweak-scale heavy Majorana neutrinos that could be {\it tested} at the LHC~\cite{Dev:2013wba}, while being consistent with the indirect constraints from various low-energy experiments at the intensity frontier~\cite{deGouvea:2013zba}. Flavour effects play an important role in determining the final lepton asymmetry in RL models. There are two kinds of flavour effects, which are usually ignored in vanilla leptogenesis scenarios, namely: (i) heavy neutrino flavour effects, assuming that the final asymmetry is produced dominantly by the out-of-equilibrium decay of only one (usually the lightest) heavy neutrino, with negligible contributions from heavier species; and (ii) charged-lepton flavour effects, assuming that the flavour composition of the lepton quantum states produced by (or producing) the heavy neutrinos can be neglected and all leptons can be treated as having the same flavour. Neglecting (i) can be justified in `vanilla' scenarios, because the $\CP$ asymmetries due to the heavier Majorana neutrinos are usually suppressed in the hierarchical limit $m_{N_1} \ll m_{N_{2,3}}$. Moreover, even if a sizable asymmetry is produced by these effects, it is washed out by the processes involving the lightest heavy neutrino~\cite{Buchmuller:2004nz}.\footnote{There is an exception to this case depending on the flavour structure of the neutrino Yukawa couplings, when the contribution from the next-to-lightest heavy neutrino decay could be dominant~\cite{DiBari:2005st, Vives:2005ra}.} However, for quasi-degenerate heavy neutrinos, as in the RL case, the flavour effects due to the neutrino Yukawa couplings do play an important role~\cite{Pilaftsis:2004xx, Endoh:2003mz}. In fact, a sizable lepton asymmetry can be generated through $\CP$-violating oscillations of sterile neutrinos~\cite{Akhmedov:1998qx, Asaka:2005, Shaposhnikov:2008pf, Canetti:2012kh, Drewes:2012ma}, which is then communicated to the SM lepton sector through their Yukawa couplings. On the other hand, the lepton flavour effects, as identified in (ii) above, are related to the interactions mediated by charged-lepton Yukawa couplings~\cite{Barbieri:1999ma}. Depending on whether these interactions are in or out of thermal equilibrium at the leptogenesis scale, the predicted value for the baryon asymmetry could get significantly modified, as already shown by various partially flavour-dependent treatments~\cite{Abada:2006ea, Abada:2006fw, Nardi:2006fx, Blanchet:2006be, De Simone:2006dd, Pascoli:2006ie}.\footnote{Similar partial flavour effects have also been considered for other variants of leptogenesis models, e.g.~with type-II seesaw~\cite{Abada:2008gs, Felipe:2013kk, Sierra:2014tqa} and soft leptogenesis~\cite{Fong:2008mu}.} The lepton flavour effects can be neglected only when the heavy neutrino mass scale $m_{N_\alpha} \gsim 10^{12}$ GeV, in which case all the charged-lepton Yukawa interactions are out-of-equilibrium and the quantum states of all charged-lepton flavours evolve {\it coherently}, i.e.~effectively as a single lepton flavour, between their production from $N_\alpha \to L_l \Phi$ and subsequent inverse decay $L_l \Phi \to N_\alpha$. Here, $L_l = (\begin{array}{cc}\nu_{lL} & l_L\end{array})^{\sf T}$ is the $SU(2)_L$ lepton doublet (with flavour index $l = e, \mu, \tau$) and $\Phi$ is the SM Higgs doublet. For $10^9 \lsim m_{N_\alpha} \lsim 10^{12}$ GeV, the $\tau$-lepton Yukawa interactions are in thermal equilibrium, and hence, the lepton quantum states are an incoherent mixture of $\tau$-lepton and a coherent superposition of electron and muon. Finally, for $m_{N_\alpha} \lsim 10^9$ GeV, since the muon and electron Yukawa interactions are also in equilibrium, their impact on the final lepton asymmetry must be taken into account in low-scale RL models. Note that flavour effects also play an important role in the collision terms describing $\Delta L = 1$ scatterings that involve Yukawa and gauge interactions, as well as $\Delta L = 0$ and $\Delta L = 2$ scatterings mediated by heavy neutrinos~\cite{Pilaftsis:2005rv}. Therefore, a {\it flavour-covariant} formalism is required, in order to consistently capture all the flavour effects, including flavour mixing, oscillations and (de)coherence. These intrinsically quantum effects can be accounted for by extending the classical Boltzmann equations for number densities of individual flavour species to a semi-classical evolution equation containing a matrix of number densities, analogous to the formalism presented in~\cite{Sigl:1993} for light neutrinos. Following this approach, a matrix Boltzmann equation in the lepton flavour space was obtained in~\cite{Abada:2006fw, De Simone:2006dd}. Similar considerations were made in~\cite{Blanchet:2011xq} to include heavy neutrino flavour effects in a hierarchical scenario. However, in RL scenarios, the interplay between heavy-neutrino and lepton flavour effects are important. With these observations, a {\it fully} flavour-covariant treatment of the quantum statistical evolution of all relevant number densities, including their off-diagonal coherences, is entirely necessary. This is the main objective of this long article. To this end, we derive a set of general flavour-covariant transport equations for the number densities of any population of lepton and heavy-neutrino flavours in a quantum-statistical ensemble. This set of transport equations are obtained from a set of master equations for number density matrices derived in the Markovian approximation, in which quantum `memory' effects are ignored (see e.g.~\cite{Bellac}). We demonstrate the necessary appearance of rank-4 tensor rates in flavour space that properly account for the statistical evolution of off-diagonal flavour coherences. This novel formalism enables us to capture three important flavour effects pertinent to RL: (i) the resonant mixing of heavy neutrinos, (ii) the coherent oscillations between heavy neutrino flavours, and (iii) quantum (de)coherence effects in the charged-lepton sector. In addition, we describe the structure of generalized flavour-covariant discrete symmetry transformations $C$, $P$ and $T$, ensuring definite transformation properties of the transport equations and the generated lepton asymmetries in arbitrary flavour bases. Subsequently, we obtain a simplified version of the general transport equations in the heavy-neutrino mass eigenbasis, but retaining {\it all} the flavour effects. We further check that these rate equations reduce to the well-known Boltzmann equations in the flavour-diagonal limit. To illustrate the importance of the effects captured {\it only} in this flavour-covariant treatment, we consider a minimal low-scale RL scenario in which the baryon asymmetry is generated from and protected in a {\it single} lepton flavour~\cite{Pilaftsis:2004xx}. As a concrete example, we consider a minimal model of resonant $\tau$-genesis (RL$_\tau$)~\cite{Pilaftsis:2004xx}, involving three quasi-degenerate heavy neutrinos, at or above the electroweak scale, with sizable couplings to the electron and muon, while satisfying all the current experimental constraints. We show that the final lepton asymmetry obtained in our flavour-covariant formalism can be significantly enhanced (by roughly one order of magnitude), as compared to the partially flavour-dependent limits. We should emphasize that our flavour-covariant formalism is rather general, and its applicability is not limited only to the RL phenomenon. The flavour-covariant transport equations presented here provide a complete description of the leptogenesis mechanism in all relevant temperature regimes. In addition, this formalism can be used to study other physical phenomena, in which flavour effects may be important, such as the evolution of multiple jet flavours in a dense QCD medium in the quark-gluon plasma (see e.g.~\cite{Blaizot:2013vha}), the evolution of neutrino flavours in a supernova core collapse (see e.g.~\cite{Zhang:2013lka}), or the scenario of $\CP T$-violation induced by the propagation of neutrinos in gravitational backgrounds~\cite{Mavromatos:2012ii}. We have also developed a flavour-covariant generalization of the helicity amplitude technique, and a generalized optical theorem in the presence of a non-homogeneous background ensemble, which may find applications in non-equilibrium Quantum Field Theory (QFT). It is worth mentioning here that there have been a number of studies (see e.g.~\cite{Buchmuller:2000nd, De Simone:2007rw, De Simone:2007pa, Cirigliano:2007hb, Garny:2009qn, Cirigliano:2009yt, Beneke:2010dz, Anisimov:2010dk, Garbrecht:2011aw, Garny:2011hg, Frossard:2012pc, Iso:2013lba}), aspiring to go beyond the semi-classical approach to Boltzmann equations in order to understand the transport phenomena from `first principles' within the framework of non-equilibrium QFT. Such approaches are commonly based on the Schwinger-Keldysh Closed Time Path (CTP) formalism~\cite{Schwinger:1961, Keldysh:1964}. This real-time framework allows one to derive quantum field-theoretic analogues of the Boltzmann equations, known as Kadanoff-Baym equations~\cite{Kadanoff:1962}, obtained from the CTP Schwinger-Dyson equation and describing the non-equilibrium time-evolution of the two-point correlation functions. The Kadanoff-Baym equations are manifestly non-Markovian, accounting for the so-called `memory' effects that depend on the history of the system. These equations can, in principle, account consistently for all flavour and thermal effects. However, one should note that in order to define particle number densities and solve the Kadanoff-Baym equations for their out-of-equilibrium evolution (as e.g.~in the context of leptogenesis), particular approximations are often made. These specifically include quasi-particle approximation and gradient expansion in time derivatives~\cite{Bornath:1996zz}. Moreover, the loopwise perturbative expansion of non-equilibrium propagators are normally spoiled by the so-called pinch singularities~\cite{Altherr:1994fx}, which are mathematical pathologies arising from ill-defined products of delta functions with identical arguments. Recently, a new formalism was developed for a perturbative non-equilibrium thermal field theory~\cite{Millington:2012pf}, which makes use of physically meaningful particle number densities that are directly derivable from the Noether charge. This approach allows the loopwise truncation of the resulting transport equations without the appearance of pinch singularities, while maintaining all orders in gradients, thereby capturing more accurately the early-time non-Markovian regime of the non-equilibrium dynamics. An application of this approach to study the impact of thermal effects on the flavour-covariant RL formalism presented here lies beyond the scope of this article. The rest of the paper is organized as follows: in Section~\ref{sec:2}, we review the main features of the flavour-diagonal Boltzmann equations. In Section~\ref{sec:3}, we derive a set of general flavour-covariant transport equations in the Markovian regime. In Section~\ref{sec:4}, we apply the formalism developed in Section~\ref{sec:3} to a generic RL scenario and derive the relevant flavour-covariant evolution equations for the heavy-neutrino and lepton-doublet number densities. In Section~\ref{sec:5}, we present a geometric understanding of the degeneracy limit in minimal RL scenarios and also discuss an explicit model of RL$_\tau$. In Section~\ref{sec:6}, we present numerical results for three benchmark points, which illustrate the impact of flavour off-diagonal effects on the final lepton asymmetry. We summarize our conclusions in Section~\ref{sec:7}. In~\ref{app:cp}, we comment on different forms of the self-energy regulator used in the literature to calculate the leptonic $\CP$-asymmetry in RL models and check their consistency in the $L$-conserving limit. In~\ref{app:propagator}, we develop a flavour-covariant generalization of the helicity amplitude formalism and describe the flavour-covariant quantization of spinorial fields in the presence of time-dependent and spatially-inhomogeneous backgrounds. In~\ref{app:optical}, we justify the tensorial flavour structure of the transport equations introduced in Section~\ref{sec:3}, by means of a generalization of the optical theorem. Finally, in \ref{app:loop}, we exhibit the form factors relevant for the lepton flavour violating decay rates discussed in Section~\ref{sec:6}. | \label{sec:7} We have presented a {\it fully} flavour-covariant formalism for transport phenomena, in which we have derived Markovian master equations describing the time-evolution of particle number densities in a quantum-statistical ensemble with arbitrary flavour degrees of freedom. In particular, we have obtained a flavour-covariant generalization of the semi-classical flavour-diagonal Boltzmann equations. In order to explicitly demonstrate the importance of the effects captured {\it only} in the flavour-covariant formalism, we have discussed a particular application to the phenomenon of resonant leptogenesis (RL). It is known that the RL scenario offers a unique opportunity for testing the connection between the origin of neutrino mass and matter-antimatter asymmetry by the ongoing LHC experiments as well as by various low-energy experiments probing lepton flavour and number violation. For this reason, it is essential to capture all the flavour effects due to the heavy neutrinos as well as SM leptons {\it in a consistent manner}, in order to obtain a more accurate prediction for the baryon asymmetry in this scenario. As we have shown in this paper, including {\it all} flavour off-diagonal effects could enhance the predicted lepton asymmetry as much as one order of magnitude in certain RL models, as compared to predictions obtained from partially flavour-dependent treatments. Thus, our flavour-covariant formalism allows us to access an enlarged parameter space of the RL models, which could be tested in ongoing and planned experiments at both the high energy and intensity frontiers. The main {\it new} results of our fully flavour-covariant formalism for RL scenarios, as contained in the final rate equations~\eqref{eq:evofinal2}--\eqref{eq:evofinal1}, are the following: \begin{itemize} \item[(i)] The appearance of new rank-4 tensors in flavour space in transport equations (see Section~\ref{sec:3.4}). These are necessary to describe the time-evolution of the number density matrices for leptons and heavy neutrinos in a flavour-covariant manner. One can extend this formalism, by introducing even higher rank rate tensors, to describe sub-dominant processes, such as $LN\leftrightarrow Le_R$, involving more flavour degrees of freedom. The existence of the tensorial structure in the rate equations is firmly supported by an explicit calculation of the transition matrix elements, by virtue of a generalization of the optical theorem (see~\ref{app:optical}). To further elucidate the consistency of our treatment, we develop a flavour-covariant generalization of the helicity amplitude technique, applied to spinorial fields in the presence of time-dependent and spatially-inhomogeneous backgrounds (see~\ref{app:propagator}). \item[(ii)] A systematic treatment of two intrinsically quantum effects, i.e. oscillations between different heavy neutrino flavours (see Section~\ref{sec:4.2}) and quantum decoherence between the charged-lepton flavours (see Section~\ref{sec:4.3}). Numerical studies for a particular RL$_\tau$ model reveal that these flavour off-diagonal effects could enhance the total lepton asymmetry by up to one order of magnitude, as compared to the flavour-diagonal case (see Figures~\ref{fig5}--\ref{fig7}). \item[(iii)] The approximate analytic solutions (see Section~\ref{sec:5.3}) to the fully flavour-covariant transport equations, which capture the two relevant flavour effects discussed above. Taking this into account in the strong washout regime, the total lepton asymmetry at $z\gsim 1$ may be estimated by the sum of the contributions from flavour mixing, oscillation and decoherence effects: \begin{eqnarray} \delta \eta^L_{\rm tot} \ \simeq \ \delta \eta^L_{\rm mix} \: + \: \delta \eta^L_{\rm osc} \: + \: \delta \eta^L_{\rm dec} \; , \end{eqnarray} as given by \eqref{eq:anal_diag}, \eqref{eq:delta_eta_L_osc_anal} and \eqref{eq:eta_L_attr_anal}, respectively. The quantitative predictions obtained from the analytic solutions for all our benchmark points agree well with the exact numerical results obtained from the full flavour-covariant transport equations. The analytic expressions are presented with the aim to facilitate phenomenological studies for a given model, without necessarily having to solve the full flavour-covariant rate equations. \end{itemize} Aside from these main results specific to the flavour-covariant formalism, we have also given a geometric and physical understanding of the degeneracy limit in the heavy neutrino parameter space (see Section~\ref{sec:5.1}) for the minimal RL scenario in which the quasi-degeneracy of the heavy neutrino masses at low scale can be naturally explained as a small deviation from the $O({\cal N_N})$-symmetric limit at some high scale through RG effects. We also point out that the role of RG effects in lifting the degeneracies encountered here is reminiscent of the role of time-independent perturbations in the degenerate perturbation theory of ordinary Quantum Mechanics. We also comment on the various existing forms of the self-energy regulator used to calculate the $\varepsilon$-type $\CP$-asymmetry and make a comparative study in a simple toy model, in order to demonstrate their behaviour in certain lepton number conserving limits (see~\ref{app:cp}). We find that only the regulator given by \eqref{fpu} gives a valid and well-defined $\CP$-asymmetry in the entire parameter space possessing the correct $L$-conserving limit, whereas the other regulators are not well-defined in certain regions of the parameter space. In conclusion, our flavour-covariant formalism provides a complete and unified description of transport phenomena in RL models, capturing three relevant physical phenomena: (i)~the resonant mixing between the heavy neutrino states, (ii)~coherent oscillations between different heavy neutrino flavours, and (iii)~quantum decoherence effects in the charged-lepton sector. The formalism developed here is rather general and may also find applications in various other transport phenomena involving flavour effects. | 14 | 4 | 1404.1003 |
1404 | 1404.6286_arXiv.txt | Type I X-ray Bursts (XRBs) are thermonuclear explosions of accreted material on the surfaces of a neutron stars in low mass X-ray binaries. Prior to the ignition of a subsonic burning front, runaway burning at the base of the accreted layer drives convection that mixes fuel and heavy-element ashes. In this second paper in a series, we explore the behavior of this low Mach number convection in mixed hydrogen/helium layers on the surface of a neutron star using two-dimensional simulations with the Maestro code. Maestro takes advantage of the highly subsonic flow field by filtering dynamically unimportant sound waves while retaining local compressibility effects, such as those due to stratification and energy release from nuclear reactions. In these preliminary calculations, we find that the rp-process approximate network creates a convective region that is split into two layers. While this splitting appears artificial due to the approximations of the network regarding nuclear flow out of the breakout reaction \isot{Ne}{18}\ap\isot{Na}{21}, these calculations hint at further simplifications and improvements of the burning treatement for use in subsequent calculations in three dimensions for a future paper. | \label{Sec:Introduction} An accreting neutron star can only build up a thin ($\sim 10$~m) surface layer of H/He before the immense gravitational acceleration compresses this fuel to the point of ignition. The ensuing thermonuclear runaway is short lived (10--100~s) but releases an enormous flux of X-rays (total energy $\sim10^{40}$ ergs)---a transient event we detect and classify as a Type I X-ray Burst (XRB) (see \citealt{lewin81,lewin93,BILDSTEN00,strohmayerbildsten2003,intZand2011} for reviews). Once the explosion subsides, the accretion builds up a fresh layer of fuel in a matter of hours to days, and a new outburst occurs. An XRB lightcurve shows a sharp rise---about an order of magnitude increase during $\sim 1~\mathrm{s}$ --- in the X-ray luminosity followed by an extended ($\sim 10~\mathrm{s}$) decay. Some ultra-compact systems are thought to accrete pure \isot{He}{4} (4U 1820-30, for example; \citealt{CUMMING_03}). The most common systems, however, likely accrete a mixture of H/He from an evolved companion star (see, for example, the compilation of bursts in \citealt{galloway:2008}). Depending on the local accretion rate, the \isot{H}{1} accreted in these systems may either 1) burn stably to form a pure \isot{He}{4} layer, which then experiences a thin-shell instability resulting in an outburst, or 2) become unstable itself in the presence of helium resulting in a mixed outburst \citep{fujimoto1981,FL87_XRB,CUMMING_BILDSTEN_00,BILDSTEN00}. Mixed bursts typically have longer lightcurves due to the waiting points in the weak nuclear reactions (see \citealt{strohmayerbildsten2003} for an overview). Mixed H/He XRBs are important sites of explosive hydrogen burning via the rp-process~\citep{wallacewoosley:1981,rpprocess,parikh:2014}. The nuclear physics of the rp-process nuclei is a focus of the U.S. Department of Energy proposed Facility for Rare Isotope Beams. Understanding the conditions that exist in XRBs is critical to accurately modeling the nucleosynthesis, which may then alter the lightcurve. Furthermore, the subset of XRBs exhibiting so-called Photospheric Radius Expansion (PRE) burst phenomena --- whereby the burst's luminosity is large enough to lift the photosphere to larger radii (lower effective temperature) before settling back down to the neutron star surface---can yield information about neutron star masses and radii (see for example~\citealt{bhattacharyya:2010,ozel:2010,steiner:2010}). Most of our theoretical understanding on XRBs comes from one-dimensional studies with stellar evolution codes, assuming spherical symmetry. These one-dimensional calculations are able to roughly reproduce the observed energies, durations, and recurrence timescales for XRBs \citep{taam1980,TAAM_ETAL93,taamwoosleylamb1996,woosley-xrb,fisker:2008}. Due to their one-dimensional nature, these simulations can use larger reaction networks than multi-dimensional studies to predict the nucleosynthetic yields from advanced burning stages, like the rp-process, and explore the nucleosynthesis in detail~\citep{schatz:rp1999,rpprocess,woosley-xrb,fisker:2008,jose:2010,parikh:2013}. However, the one-dimensional nature prevents the simulations from directly modeling the convection, and simplified models like mixing length theory (see, for example~\citealt{KipWei}) are needed. Recent multi-dimensional simulations have questioned the validity of mixing length theory, and emphasized the role of turbulence~\citep{meakin:2007,arnett:2009}. If the convection is not modeled properly, then the wrong temperature/pressure history for a fluid element will be obtained, affecting the nucleosynthesis and lightcurve. Simulations of the vertical structure of reacting flow on neutron stars are rare. Several models of detonations \citep{FRY_WOOS_DETONATION_82,ZINGALE_ETAL01,simonenko:2012} have been done, but these sample density regimes that are not typical of an XRB. \citet{Lin:2006} used a low Mach number algorithm to model pure helium bursts in two-dimensions, following the rise in temperature and watching the development of convection. \citet{cavecchi:2012} used a simplified hydrodynamic model (the vertical direction was treated as hydrostatic) to model flame propagation across the neutron star on length and timescales appropriate to an XRB, but the numerical technique does not allow for a detailed understanding of the dynamics at the front, including mixing and turbulence. It is also important to understand whether the convection can bring ashes up to the photosphere~\citep{intZand:2010,bhattacharyya:2010}, altering our interpretation of the radiation. In paper~I~\citep{xrb} we explored the convective dynamics of a pure helium XRB using our low Mach number simulation code, Maestro. Our results differed from those of \citet{Lin:2006} in that we found that a much higher resolution is needed to resolve the He burning peak and to properly capture the convective dynamics. Here we extend the low Mach number methodology to the case of mixed H/He bursts with an extended network that captures the hydrogen burning. Our ultimate goal in this series of papers is to evolve the convective region to the point where we can see a nonlinear rise in the temperature, and to assess how the convection impacts the nucleosynthesis. | \label{Sec:Conclusion} We presented the first multidimensional calculations of convective flow in the context of mixed H/He X-ray bursts using realistic hydrodynamics and an approximate reaction network for H/He-burning. We demonstrated convergence of our results and explored the behavior of the nucleosynthesis and convection. The approximate network we utilized assumed some reaction chains occurred faster than what would happen in a larger network. In addition, the approximate network utilized here resulted in the developement of two layers of convection as a result of the existence of a secondary peak in energy gernation rate, which eventually dominated the total energy output. We traced the cause of this secondary peak in energy generation rate to the critical rp-process breakout branching ratio, $\lambda_1$, which measures the ratio of the $\beta^+$-decay rate versus $\alpha$-capture rate of \isot{Ne}{18}. With our particular initial conditions, this branching ratio sharply transitions between zero and one midway through our atmosphere. The secondary peak in energy generation rate becomes comparable to the primary peak around $t\sim0.1$ s (see Figure \ref{fig:enuclate}). The split of the convective region lags behind the growth of the energy generation rate peak. Indeed, the two layered structure is not well defined until about $t\sim0.14$ s. A small entropy jump between the two layers prevents material from crossing between each layer. This causes a quenching of the mixing of isotopes, and alters the burning. Coincidentally, Figure \ref{fig:resstudy} shows that the rate of increase of the peak temperature changes around the time of layer formation. We note that we artificially boosted the temperature and density at the base of our accreted layer to give prodigous burning (see the discussion in \ref{Sec:Initial Model}). Simple Kepler calculations show that in order to reproduce a model with characteristics similar to our base density, the initial metallicity of the accreted material has to be turned down significantly, $Z\sim 10^{-4}$, making such a system perhaps rare in nature. Continuing these calculations in one-dimension, the full network in Kepler showed a very slight non-monotonicity of the energy generation rate in a region containing composition profiles qualitatively similar to what we see near the development of our secondary peak in energy generation rate. However, this minor bump in Kepler's energy generation rate was transient and certainly never dominated the burning as we see in our calculations with the approximate network. The development of layered convective regions in our simulations is likely artificial and due to the approximations used in the reaction network. These calculations are a starting point for more realistic calculations of H/He X-ray bursts. Future work will focus on improving the nuclear physics, moving to three dimensions, and considering larger domains. We note that very little hydrogen and helium were processed during the short duration of our simulations---and similar Kepler calculations show very little change in energy generation rate profiles on this timescale. This suggests that even further (and possibly more accurate) simplifications can be made to the network for use on the short timescales amenable to multidimensional simulations. Indeed, the original approximate network of \citet{wallacewoosley:1981} was designed (in part) to model the full burst cycle where copious amounts of heavy elements were produced. Improvements to the nuclear physics and approximations therein are work for a future paper. In addition, one path that will enable larger simulations is to develop a subgrid model for the burning, and using more realistic initial models (perhaps following the methodology from \citealt{CUMMING_BILDSTEN_00}, or better mapping techniques between Kepler models and Maestro models). It seems that we can capture the convective behavior on a moderate-resolution grid, but the steep temperature dependence in the reactions requires fine resolution where the energy generation peaks. This was much more extreme in the case of pure He bursts (Paper~I) than in the calculations here, however, a potential path forward is to use subgrid resolution for the burning and average the resulting energetics and compositions back to the hydrodynamic grid. Ultimately, we would like to model a laterally propagating burning front with realistic nuclear physics. In the context of Maestro, this will require support for lateral gradients instead of a single base state. This development will be explored in tandem with the follow-on simulations described above. | 14 | 4 | 1404.6286 |
1404 | 1404.1373_arXiv.txt | Thermal relic dark matter particles with a mass of 31-40 GeV and that dominantly annihilate to bottom quarks have been shown to provide an excellent description of the excess gamma rays observed from the center of the Milky Way. Flavored dark matter provides a well-motivated framework in which the dark matter can dominantly couple to bottom quarks in a flavor-safe manner. We propose a phenomenologically viable model of bottom flavored dark matter that can account for the spectral shape and normalization of the gamma-ray excess while naturally suppressing the elastic scattering cross sections probed by direct detection experiments. This model will be definitively tested with increased exposure at LUX and with data from the upcoming high-energy run of the Large Hadron Collider (LHC). | 14 | 4 | 1404.1373 |
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1404 | 1404.4760_arXiv.txt | Nuclear matter under the conditions of a supernova explosion unfolds into a rich variety of spatially structured phases, called nuclear pasta. We investigate the role of periodic network-like structures with negatively curved interfaces in nuclear pasta structures, by static and dynamic Hartree-Fock simulations in periodic lattices. As the most prominent result, we identify for the first time the {\it single gyroid} network structure of cubic chiral $I4_123$ symmetry, a well known configuration in nanostructured soft-matter systems, both as a dynamical state and as a cooled static solution. Single gyroid structures form spontaneously in the course of the dynamical simulations. Most of them are isomeric states. The very small energy differences to the ground state indicate its relevance for structures in nuclear pasta. | Nuclear matter, although not observable in laboratories on earth, plays a crucial role in astrophysical scenarios such as neutron stars or core-collapse supernovae \cite{Bethe,Suzuki}. Near equilibrium density, nuclear matter is a homogeneous quantum liquid, somewhat trivial from a structure perspective. However, an exciting world of various geometrical profiles develops at lower densities covering ensembles of rods, slabs, tubes, or bubbles \cite{Ravenhall,Hashimoto,Pais,Watanabe2001,Schuetrumpf2013a}. Most of these phases can be considered as manifestations of liquid crystals \cite{Pethick1998} and the geometrical analogy to spaghetti, lasagna etc. has led to summarize these under the notion of a nuclear ``pasta''. Their complex shapes and topologies can be classified by integral curvature measures \cite{Nakazato2009,Nakazato2011,Schuetrumpf2013a}, developed in the realm of soft matter physics and known as Minkowski functionals~\cite{Mecke:1998,MeckeStoyan:2000,SchroederTurketal:2010,SchroederTurk:2013}. \begin{figure}[tb] \centering \vspace*{0.55cm} \includegraphics[width=\linewidth]{pasta_gyroid_3d}% \rput(-5.8,5.5){\large Pasta Matter}% \rput(-1.9,5.46){\large Single Gyroid}% \rput(-2.02,0.2){$22\,\mathrm{fm}$}% \caption{(Color online) Gyroidal pasta shape: the green structure on the left hand represents the density distribution of the gyroidal state of nuclear pasta matter computed with TDHF for an average density of $0.06{\rm\,fm^{-3}}$ and box length $a=22\,\mathrm{fm}$. Shown is the Gibbs dividing surface with a corresponding threshold density. The solid volume representing densities above this value and the void representing densities below this value. The blue structure on the right hand side shows the nodal approximation \eqref{eq:gyroid} of a single gyroid CMC surface at the same volume fraction. Also shown by orange bars is a gyroid network in the void phase of both the pasta shape and the nodal approximation, showing that they are indeed homotopic. Black frames are guides to the eye, of size $1.25\,a$ the cubic lattice parameter.} \label{fig:basic} \end{figure} A particularly intricate structure amongst the pasta phases is the gyroid, a triply-periodic geometry consisting of two inter-grown network domains separated by a periodic manifold-like surface which is (at least on average) saddle-shaped and with negative Gaussian curvature (cf. Fig.~\ref{fig:basic}). In soft-matter systems, these periodic saddle-shaped surfaces have been found in solid biological systems \cite{MichielsenStavenga:2008, SaranathanOsujiMochrieNohNarayananSandyDufresnePrum:2010, SchroederTurkWickhamAverdunkBrinkFitzGeraldPoladianLargeHyde:2011, GalushaRicheyGardnerChaBartler:2008,Pouya:11,Wilts2012,Nissen:1969}, in the so-called 'core-shell' gyroid phase of di-block copolymers \cite{HajdukHarperGrunerHonekerKimThomasFetters:1994} and in inverse bicontinuous phases in lipid-water systems \cite{Larsson:1989}. Gyroid-like geometries can also be expected in nuclear pasta, due to a balance between the nuclear and Coulomb forces \cite{Nakazato2009,Nakazato2011}. Similar kinds of periodic bicontinuous structures are discussed in supernova cores and neutron star crusts \cite{Pethick,Mat06a}. It is generally accepted that liquid crystalline phases, i.e., pasta phases, occur in supernova cores in the form of slabs, rods and tubes \cite{Ravenhall,Hashimoto,Pais,Watanabe2001}. The search for elaborate structures in astro-physical matter with self-consistent nuclear models has a long history, starting from the first full Skyrme-Hartree-Fock (SHF) simulation of \cite{Bonche}. With continued refinement of the calculations, more and more intricate structures had been discovered. For example, the possible occurrence of periodic bicontinuous structures was found by stationary Hartree-Fock calculations \cite{Goe01aR,Mag02,Goe07a,NewtonStone,Pais}, later on in dynamical simulations of supernova matter using time-dependent Hartree-Fock (TDHF) calculations for supernova matter \cite{Sebille,Sebille2011} and also in a quantum molecular dynamics approach \cite{Sonoda2008}. Gyroids were examined so far only within a liquid-drop model \cite{Nakazato2009,Nakazato2011} where double gyroids were found to be energetically close to the ground state. (Note the important difference between single and double Gyroid geometries, see Fig.~\ref{fig:gyroids}.) If realized in supernova matter, the network-like percolating nature of the gyroid could greatly affect neutrino transport during the collapse of a massive star's core and the subsequent core bounce. It is the aim of this paper to investigate gyroid structures on the basis of fully quantum-mechanical Hartree-Fock and TDHF simulations. To that end, we employ the well established Skyrme-Hartree-Fock (SHF) energy functional which provides a reliable description of nuclei and nuclear dynamics over the entire nuclear landscape \cite{Bender03} and also in astro-physical systems \cite{Stone2007}. Figure~\ref{fig:basic} provides a graphical demonstration of the key result of this article, namely the occurrence of a meta-stable gyroid phase in nuclear pasta. It shows the Gibbs diving surface (see section \ref{eq:cmc}) and draws the liquid phase as filled, the gas phase as void (although in practice filled with some neutron dust). The network-like domain on the left-hand side of the figure represents the liquid (or high density) domain in full SHF calculations whose shape and topology match closely those of one of the gyroid network domains (shown on the left hand side of the figure). The remaining void space (the gas phase) forms a complementary network-like domain with the same topology, albeit of different volume fraction. | We have investigated the appearance of non-homogeneous structures in nuclear matter under astro-physical conditions, paying particular attention to structures with network-like geometry and topology, amongst them as particularly appealing shape the single Gyroid (G). To that end, we used static optimization as well as dynamical simulations within a self-consistent nuclear mean-field model (Skyrme-Hartree-Fock). The emerging structures have been characterized by Minkowski measures. To uniquely identify a G, an additional subsequent graphical analysis has been performed. We have shown that single gyroid (G) structures indeed emerge in static and dynamical simulations. We have looked at further CMC surfaces and find close competition with the primitive (P) surface and the slab (S) while the diamond seem to play no role. The static calculations show that G and P are mostly metastable while the S usually provides the ground state, however, with only slightly larger binding energies. G and P, being triply periodic saddle surfaces, have maxima for the binding energies as function of box length, for P at $a\approx22{\rm\,fm}$ and for G predicted at $a\approx27{\rm\,fm}$, assuming that the Bonnet transformation is applicable in this system. Dynamical simulations at high excitation energy produce several cases where these structures appear again. This indicates that these network-like geometries are rather robust in nuclear matter. We also find some static G structures with deformations which may be due to the fact that the surface energy is rather small under the given conditions thus easily allowing deformed G isomers. The large expense of these microscopic calculations limits presently the size of the affordable numerical box. This inhibits so far a unambiguous assessment by studying the trends with box size in larger ranges. The present results are, however, strong indicators for the appearance of CMC and particularly G structures which call for further studies. | 14 | 4 | 1404.4760 |
1404 | 1404.6079_arXiv.txt | We consider the problem of convergence in stratified isothermal shearing boxes with zero net magnetic flux. We present results with the highest resolution to-date--up to 200 grid-point per pressure scale height--that show no clear evidence of convergence. Rather, the Maxwell stresses continue to decrease with increasing resolution. We propose some possible scenarios to explain the lack of convergence based on multi-layer dynamo systems. | The magneto-rotational instability (MRI) and magneto-rotational turbulence (MRT) provide an elegant framework to study the origin of enhanced angular momentum transport in accretion discs. Much effort has been devoted to understanding the nonlinear development of the MRI and the processes that control the saturation amplitude of the instability, since, ultimately this controls the transport efficiency. Because of the difficulties inherent in approaching a strongly nonlinear problem analytically, much of the work on MRT has relied on numerical simulations with all their attendant idealizations and approximations. By far the most popular is the shearing-box approximation in which the computational domain is restricted to a region of small radial extent at a large radius in the disc. Under reasonable assumptions this can be mapped into a Cartesian layer with shearing-periodic boundary conditions in the radial direction. Because the shearing-box approximation conserves vertical magnetic flux it is important to distinguish two types of simulations: those with finite initial (vertical) flux and those with zero initial flux. If the flux is finite there is a linear instability with a well defined growth rate and wavelength of maximum growth whose values are determined by the amount of flux \citep{Balbus91}. In the nonlinear regime the amplitude of the Maxwell stresses--primarily responsible for angular momentum transport--is controlled by the amount of magnetic flux, and most crucially, remains finite in the ideal limit of vanishing dissipation. If, on the other hand, the initial flux is zero, the domain could in principle de-magnetize completely and relax to a state of uniform shear. If after a long time it does not, it must be because the magnetic field is being regenerated by turbulent motions. In this case, the MRI does not manifest itself as an exponentially growing linear instability, rather it is a subcritical dynamo process. In this case, the spatial scales of the dominant magnetic structures and the efficiency of the angular momentum transport are determined by the dynamo itself. Two questions naturally arise: what kind of dynamo action can be sustained in a shearing-box, namely small-scale or large-scale, and what happens to the dynamo when the diffusivity, numerical or otherwise, becomes vanishingly small. Addressing these issues has turned out to be a major and complex undertaking, even within the idealized framework of the shearing-box approximation. The first question is not specific to MRI driven dynamos but to dynamos in general. Under what circumstances does a dynamo generate substantial amount of magnetic flux has been a long standing problem in astrophysical dynamo theory. Large-scale dynamos are often associated with flows lacking reflectional symmetry, or incorporating large scale shear, or a net flux of magnetic helicity through the boundaries, or any combination of the above. The second question was originally posed by \citet{Fromang07} within the framework of unstratified, homogeneous shearing boxes and it has since become known as the problem of convergence. Simply stated, a family of solutions of the MRI equations does {\it not} converge if the Maxwell stresses tend to zero as the dissipation tends to zero. Although, superficially, the convergence problem might seem mostly a matter of numerics, and indeed originally it was framed that way, actually it is not. Understanding why some shearing-box models converge and some do not is a fundamental question about nonlinear dynamo action in centrifugally stable systems. It is now commonly accepted that homogeneous, unstratified shearing boxes without explicit dissipation--these were the cases originally considered by \citet{Fromang07} do not converge \citep[for recent reviews, see ][]{Fromang13, Turner14}. The reason for the lack of convergence may be related to the small-scale nature of the dynamo operating in these systems, or to the lack of a characteristic outer scale or to a combination of these two factors \citep{Bodo11}. All other cases are not as clear. In the present paper we address the problem of convergence, or lack thereof, in the stratified isothermal case without explicit dissipation. This is the simplest shearing-box model with nontrivial stratification. Despite the simplicity of the models, the dynamo that operates in these systems is far from simple. In an isothermal atmosphere with linear gravity reversing in the middle, hydrostatic balance gives rise to a density stratification with an approximately Gaussian profile and most of the mass concentrated near the mid-plane. A seemingly turbulent dynamo operates in this dense, central region while propagating wavelike magnetic activity patterns are observed in the tenuous overlying layers \citep{Gressel10}. A resolution study by \citet{Davis10} with resolution up to 128 grid-points per scale height concluded that there was strong evidence for convergence. This led several authors to declare this case as settled in favor of convergence \citep{Gammie12, Fromang13, Turner14}. Here, we extend this study to 200 grid-points with a similar, but not identical, setup and numerics to that of \citet{Davis10} and find {\it no} evidence for convergence, at least up to these resolutions. Our conclusion is, therefore, that the problem of convergence for stratified, isothermal shearing-boxes is very much still an open issue. | \label{conclusions} We have revisited the problem of MRI driven turbulence in isothermal, stratified shearing boxes with zero net (vertical) magnetic flux and no explicit dissipation. We have extended our study to the highest resolution to date and find that, contrary to previously made claims based on lower resolution studies, the solutions do not converge, or at any rate, there is no convincing evidence of convergence. The average Maxwell stresses, principally responsible for the angular momentum transport, continue to decrease with increasing resolution. This conclusion can be further elaborated in terms of simple models of the types discussed by \citet{Blackman04} and \citet{ Gressel10} consisting of coupled dynamo systems operating in different regions. One dynamo system is confined to the mid-plane where most of the mass is concentrated and gravity reverses, the other operating in the tenuous overlying regions. The second dynamo is assumed to be of the mean-field type and be responsible for the generation of the magnetic structures that appear in the form of upward propagating dynamo waves. As for the nature of the mid-plane dynamo system two possibilities readily come to mind. One is that the motions in the mid-plane are driven by small-scale dynamo action similar to that observed in unstratified shearing-boxes. The justification for this assumption is that gravity is weak near the mid-plane. In this scenario the overlying mean-field dynamos are driven by the magneto-rotational turbulence in the mid-plane. The source of the turbulence is a subcritical dynamo instability. The other possibility is that the mean-field dynamos generate enough mean toroidal field in the mid-plane to drive an azimuthal MRI whose non-linear development drives the turbulence that, in turn, drives the mean-field dynamos. Although the outward manifestation of these two scenarios is the same, the reason for the apparent non-convergence is different. In the first scenario, the lack of convergence of the overall system follows from the non-convergence of the small-scale dynamo operating in the mid-plane, which can plausibly be reconstructed to the non-convergence of the unstratified homogeneous cases. If this analysis is the correct one, in the isothermal case, because most of the mass is concentrated in a region where there is practically no gravity, stratification does not help to resolve the convergence problem. It is useful to note that the above argument reduces the convergence issue for the stratified case to the convergence issue for the homogeneous case. In other words, the former does not converge because the latter does not converge. Contrariwise, it could be argued that if the homogeneous case were to converge so would the stratified one. At present, there is convincing numerical evidence from several different groups that in the absence of explicit dissipation the unstratified, homogeneous case does not converge \citep{Fromang07, Pessah07, Guan09, Simon09, Bodo11}. The case in which dissipation is included explicitly is not so clear cut \citep[see, for instance, the comments in][]{Turner14}. Although it is often asserted that the homogeneous case with explicit dissipation converges \citep{Fromang13, Gammie12}, as far as we can tell, all the numerical evidence supporting these assertions originates from a single paper, namely that of \citet{Fromang10}. And although the simulations described therein remain an impressive numerical tour de force, we would argue that they are not such as to settle the issue of convergence unequivocally. We hope however that in the near future other attempt will be made to settle the issue of convergence in the presence of explicit dissipation conclusively. In the second scenario the non-convergence derives from the inability of the mean-field dynamo to operate at high magnetic Reynolds numbers--be they real or numerical. This is a well known effect that has received much attention and goes back to the original works by \citet{Cattaneo92, Kulsrud92} and \citet{Gruzinov94}. In this case as the dissipation decreases so does the generated mean toroidal field needed to destabilize the azimuthal MRI in the mid-plane regions. Eventually the mean toroidal field is so weak that the system become indistinguishable from the one in the first scenario with all its attendant limitations. Should this analysis turn out to be correct it is interesting that it applies to a case with boundary conditions that allow a net flux of magnetic helicity. Undoubtedly other scenarios can be constructed that agree with the numerical evidence, provide an explanation for the non-convergence and highlight the role of other physical processes. However, to quote from one of the authors' favorite poems ``whatever the reason his heart or his shoes" \citep{Seuss57} the stratified isothermal shearing-box appears not to converge. | 14 | 4 | 1404.6079 |
1404 | 1404.3189_arXiv.txt | {As the nearest known AGB star ($d = 64$\,pc) and one of the brightest ($m_K \approx -2$), L$_2$ Pup is a particularly interesting benchmark object to monitor the final stages of stellar evolution. We report new serendipitous imaging observations of this star with the VLT/NACO adaptive optics system in twelve narrow-band filters covering the $1.0-4.0\,\mu$m wavelength range. These diffraction-limited images reveal an extended circumstellar dust lane in front of the star that exhibits a high opacity in the $J$ band and becomes translucent in the $H$ and $K$ bands. In the $L$ band, extended thermal emission from the dust is detected. We reproduced these observations using Monte Carlo radiative transfer modeling of a dust disk with the RADMC-3D code. We also present new interferometric observations with the VLTI/VINCI and MIDI instruments. We measured in the $K$ band an upper limit to the limb-darkened angular diameter of $\theta_\mathrm{LD} = 17.9 \pm 1.6$\,mas, converting to a maximum linear radius of $R = 123 \pm 14\,R_\odot$. Considering the geometry of the extended $K$ band emission in the NACO images, this upper limit is probably close to the actual angular diameter of the star. The position of L$_2$\,Pup in the Hertzsprung-Russell diagram indicates that this star has a mass of about $2\,M_\odot$ and is probably experiencing an early stage of the asymptotic giant branch. We did not detect any stellar companion of L$_2$\,Pup in our adaptive optics and interferometric observations, and we attribute its apparent astrometric wobble in the \emph{Hipparcos} data to variable lighting effects on its circumstellar material. However, we do not exclude the presence of a binary companion, because the large loop structure extending to more than 10\,AU to the northeast of the disk in our $L$ -band images may be the result of interaction between the stellar wind of L$_2$\,Pup and a hidden secondary object. The geometric configuration that we propose, with a large dust disk seen almost edge-on, appears particularly favorable to test and develop our understanding of the formation of bipolar nebulae. } | Evolved stars are important contributors to the enrichment of heavy elements in the interstellar medium, and more generally to the chemical evolution of the Universe. L$_2$\,Puppis (\object{HD 56096}, \object{HIP 34922}, \object{HR 2748}) is an asymptotic giant branch (AGB) semiregular variable. Its variability was discovered by Gould as early as 1872 \citepads{1907AnHar..55....1C}. Its M5III spectral type corresponds to an approximate effective temperature of $T_\mathrm{eff} = 3500$\,K, which is what we considered here. Its proximity \citepads[$\pi = 15.61 \pm 0.99$\,mas,][]{2007A&A...474..653V} makes it the closest AGB star and one of the brightest stars in the infrared sky. \citetads{2007ApJS..173..137G} identified a periodic shift in the \emph{Hipparcos} astrometric position of L$_2$\,Pup with a 141-day period and a semimajor axis of 9.5\,mas. They attributed this displacement to the orbital reflex motion of the AGB star due to an unresolved companion. The corresponding orbital period is almost identical to the photometric variation period (140.6\,days) as listed in the General Catalogue of Variable Stars \citepads{2009yCat....102025S}. \citetads{2002MNRAS.337...79B} explained the long-term (over decades) variability of the brightness of L$_2$\,Pup as the consequence of the obscuration of the star by circumstellar dust. These authors also pointed out that the period of L$_2$\,Pup has been remarkably stable over 75\,years of photometric observations, making it a semiregular variable of the SRa type (i.e. with a well-defined period), closely related to Miras. \citetads{2005A&A...431..623L} obtained six radial velocity measurements spread around the maximum and minimum light phases, and estimated a radial velocity amplitude of 12 km.s$^{-1}$. The binarity hypothesis was discussed (and dismissed) by \citetads{2009A&A...498..489J}, based in particular on geometrical arguments on the linear size of the giant star. \citetads{2013ApJ...774...21M} recently discovered a 139-day periodic velocity centroid variation from SiO maser emission. They concluded that this variability points at the presence of differential illumination, or an asymmetric distribution of the circumstellar material around L$_2$\,Pup. Alternatively, \citetads{2009MNRAS.394...51G} predicted that the centroid of SiO emission would shift in velocity according to the stage in the stellar cycle, as a consequence of the shock behavior and because the SiO maser region is located in a compact region, within a few stellar radii of the central object. \citetads{2014A&A...561A..47O} recently observed L$_2$\,Pup in the thermal infrared domain ($N$ band) using the high spectral resolution mode of VISIR, and concluded that its spectrum cannot be reproduced satisfactorily using MARCS atmosphere models. However, this author considered a temperature of 2800\,K for the central star, which may be underestimated (see Sect.~\ref{photom}). We present in Sect.~\ref{observations} our new NACO, VINCI and MIDI observations of L$_2$\,Pup, and in Sect.~\ref{radmc} the RADMC-3D radiative transfer model we propose to reproduce these observations. This model consists of a central star surrounded by an edge-on circumstellar disk. Section~\ref{discussion} is dedicated to a discussion of the evolutionary status, mass loss geometry, and possible binarity of L$_2$\,Pup. | The NACO observations we presented in Sect.~\ref{nacoobs} show that L$_2$\,Pup is veiled by a large dust band. Its morphology appears consistent with a circumstellar dust disk seen almost edge-on. Its aspect changes significantly from 1.0 to 4.0\,$\mu$m. At shorter wavelengths ($J$ band), the scattering by dust grains is very efficient, resulting in a high opacity and the presence of a dark band obscuring the stellar light. In the $L$ band, the dust scattering is much less efficient, and the thermal emission from the inner edge of the disk becomes dominant. In the intermediate near-infrared bands ($HK$), the disk is translucent and the central star becomes progressively more visible as the wavelength increases. Our simulations using the RADMC-3D radiative transfer code strengthened this interpretation because the model we developed reproduced both the aspect of the NACO images as a function of wavelength and the observed spectral energy distribution. If we consider that the dust density is inhomogenous in the disk, the variable dust obscuration scenario proposed by \citetads{2002MNRAS.337...79B} to explain the long-term variability of L$_2$\,Pup is consistent with the proposed edge-on configuration. In this framework, the long minimum flux phase observed since $\approx 1995$ would result from the transit of a dense part of the dust disk in front of the star, creating the morphology observed in the NACO images. A simple evolutionary analysis shows that L$_2$\,Pup is probably in an early phase of the AGB, with a mass of approximately $2\,M_\odot$, and an age of about 1.5\,Gyr. Its physical properties are very similar to those of the short-period Mira star R\,Vir, and its luminosity is consistent with the period-luminosity relation of this class of stars. We propose that L$_2$\,Pup should be classified as a short-period Mira star instead of a semiregular variable. We did not detect any stellar companion to L$_2$\,Pup in our NACO images or in our VINCI interferometric observations. We propose that the astrometric wobble observed by \citetads{2007ApJS..173..137G} is caused by time-variable lighting effects on L$_2$\,Pup's circumstellar nebula and not by an orbiting companion. The measured radial velocity amplitude is also consistent with the pulsation of the central star, without the need to invoke a secondary object. We stress, however, that we do not exclude the possibility that a companion is present, particularly if its orbital period is significantly longer than the pulsation period of L$_2$\,Pup. In addition, the loop structure we detected in our $L$ -band images points at a possible interaction of a hidden companion with the dusty wind from the central star. As discussed by \citetads{2009A&A...505.1221V}, the mere existence of a dusty disk around L$_2$\,Pup is also in itself an indication that a companion may be present, as disks in post-AGB stars appear inherently connected to binarity. L$_2$\,Pup presents interesting challenges for the modeling of the envelope of an evolved, moderately massive star. The geometric configuration that we propose, with a large disk seen almost edge-on, is particularly promising to test and develop our understanding of the formation of bipolar planetary nebulae in the post-AGB phase. Such a disk could also be a favorable environment to form large dust grains, and possibly planetesimals. The presence of circumstellar material around white dwarfs \citepads{2005ApJS..161..394F} could be the final result of this secondary planet formation episode in AGB dust disks such as L$_2$\,Pup's. | 14 | 4 | 1404.3189 |
1404 | 1404.7249_arXiv.txt | The microquasar \grs, exhibits a large variety of characteristic states, according to its luminosity, spectral state, and variability. The most interesting one is the so-called $\rho$-state, whose light curve shows recurrent bursts. This paper presents a model based on Fitzhugh-Nagumo equations containing two variables: $x$, linked to the source photon luminosity $L$ detected by the MECS, and $y$ related to the mean photon energy. We aim at providing a simple mathematical framework composed by non-linear differential equations useful to predict the observed light curve and the energy lags for the $\rho$-state and possibly other classes of the source. We studied the equilibrium state and the stability conditions of this system that includes one external parameter, $J$, that can be considered a function of the disk accretion rate. Our work is based on observations performed with the MECS on board \sax~ when the source was in $\rho$ and $\nu$ mode, respectively. The evolution of the mean count rate and photon energy were derived from a study of the trajectories in the count rate - photon energy plane. Assuming $J$ constant, we found a solution that reproduces the $x$ profile of the $\rho$ class bursts and, unexpectedly, we found that $y$ exhibited a time modulation similar to that of the mean energy. Moreover, assuming a slowly modulated $J$ the solutions for $x$ quite similar to those observed in the $\nu$ class light curves is reproduced. According these results, the outer mass accretion rate is probably responsible for the state transitions, but within the $\rho$-class it is constant. This finding makes stronger the heuristic meaning of the non-linear model and suggests a simple relation between the variable $x$ and $y$. However, how a system of dynamical equations can be derived from the complex mathematical apparatus of accretion disks remains to be furtherly explored. | It is known that phenomena occurring in accretion disks around black holes involve non-linear processes whose evolution can be described by a system of differential equations containing several quantities not directly observable. The only information we have concerns a fraction of the dissipated energy via electromagnetic radiation and usually observed in a rather limited frequency band. The stability of disk structures is also a very interesting subject of investigations since many years and theoretical analysis suggested that thermal and viscous instabilities can develop and establish a limit cycle behaviour. To now the most important X-ray source exhibiting a complex variability, that on some occasions were characterized by long series of bursts as those expected by a limit cycle is the bright microquasar \grs, discovered by \citet{Castrotirado1992}. Only recently, \citet{Altamirano2011} reported the discovery of IGR J17091+3624 that exhibits variability patterns very similar to those of \grs. The large variety of light curves of \grs, changing from quiescent states to fast series of short bursts and to much more complex patterns of alternating bursting and quiescent phases was classified in 12 types by \citet{Belloni2000} on the basis of a large collection of multi-epoch RXTE observations. New classes were added to these in the following years \citep{Naik2002,Hannikainen2003,Hannikainen2005} indicating that the source is potentially able to develop a rather large number of physical conditions from which more types of light curves can be originated. A description of such a complex phenomenology is given in the review paper by \citet{Fender2004}. From a general point of view the light curve variability classes of \citet{Belloni2000} can be grouped in three main types: $i$) light curves characterised only by small amplitude noisy fluctuations with respect to a stable average level (e.g. classes $\phi$, $\chi$, and $\delta$); $ii$) light curves presenting series of (positive or negative) pulses (e.g. classes $\gamma$, $\kappa$, and $\rho$), occasionally exhibiting a rather stable recurrence time; $iii$) light curves structured in sequences of fast spikes alternating with rather quiescent and low brightness states (e.g. classes $\theta$, $\lambda$, $\alpha$, $\beta$ and $\nu$). One of the most interesting variability classes is the $\rho$, lasting several days, whose light curves are quasi-regular series of bursts with a moderately variable recurrence time, usually in the range 40 -- 100 seconds. The time and spectral properties of $\rho$ class bursts have been investigated by several authors and the most recent papers on this subject are those by \citet{Neilsen2011, Neilsen2012} based on RXTE data and those by \citet{Massaro2010}, \citet{Mineo2012}, and \citet{Massa2013} who considered a long observation performed with \sax~ in October 2000. In particular, \citet{Massaro2010} reported that the mean recurrence time of the bursts increases with the source brightness, while \citet{Massa2013} investigated the properties of loops described by $\rho$ bursts in a dynamical space where the coordinates are the count rate and the mean energy of photons. Since the first analysis \citep{Taam1997} these recurrent bursts were associated with a limit cycle due to the onset of some disk instability. Several authors calculated possible theoretical light curves of the bolometric luminosity originating from disk instabilities. Complexity of hydrodynamic and thermodynamic equations does not allow a rather simple picture of the roles played by the involved physical quantities and the interpretation of data is not straightforward. Moreover, the limit cycle is often described in terms of disk quantities, such as the integrated density or the mass accretion rate, which are not directly observable In the present paper we adopt a different approach and study the solutions of non-linear systems of two and three ordinary differential equations, whose solutions have very close similarities with the observational data series. These systems are mainly applied in the simulation of neuronal behaviour, and are able to describe quiescent, spiking and bursting activity like the one exhibited by \grs. We will show that this approach makes possible to calculate light curves and phase space trajectories useful to investigate some dynamical aspects of the instability processes. \begin{figure}[tb] \includegraphics[width=1.0\columnwidth]{fig1.ps} \caption{ Two 300 second long segments of the count rate of the MECS [1.4 $-$ 10] keV for the data series A8b (top panel), F7 (bottom panel) of the long observation of October 2000 \citep[see][]{Massaro2010}. A running average smoothing over 3 bins is applied to reduce the statistical Poissonian noise. The bin size of both series is 0.5 s. In the central panel two curves reproducing the mean bursts' profile are shown: the green one on the left corresponds to the A8b data and the orange curve on the right to F7} \label{fig1} \end{figure} Non-linear oscillators were already considered in stellar physics for describing the convective energy transfer \citep{Moore1966} and the dynamics of pulsating variable stars \citep{Regev1981, Buchler1981, Buchler1993}. Non-linear processes are also present in the coupling of the hot plasma and the radiation field in an accreting disk around a compact object. It is, therefore, likely that such equations can represent a useful mathematical approximation of much more complex relations in a suitable neighborhood of an equilibrium point. In this paper, we will not deal with the physical description of an accretion disk but will limit our study to show how the behaviour of \grss can be described by a unique oscillator and that some observed changes can be related to variations of a single parameter. In Sect. 2 we describe the coarse structure of X-ray bursts and our method to compute the mean count rate and photon energy time curves. In Sect. 3 non-linear oscillator models are introduced and a solution with only two variables and constant parameters for the \grss data is presented; its equilibrium point and stability is studied in Sect. 4. In Sect. 5 we investigate the consequences of parameters' changes, and in Sect. 6 a possible extension to dynamical systems with three equations is presented. Finally, in Sect. 7 we discuss our results in the framework of current models for disk instabilities and limit cycles. | It is well known that the X-ray source \grs, the prototype of microquasars, exhibits a large number of variability classes changing from quasi-quiescent states to long and regular series of bursts, persisting for several days, and irregular variations on different time scales. Many theoretical computations, generally based only on radial disk model equations, i.e. integrated over the thickness, and assuming the $\alpha$ prescription \citep{Shakura1976} for the gas viscosity, have been performed in the past years since the early work by \citet{Taam1997}, with the goal of modelling these puzzling light curves. We followed a different approach and tried to reproduce some variability patterns of \grss by means of non-linear systems of differential equations, which have been extensively investigated in the literature in the contest of neuronal activity to explain quiescent, bursting and spiking states. Several systems of equations have been proposed, since the original work by \citet{Hodgkin1952}. We have shown that one of the simplest systems for neuronal model, developed by \citet{Fitzhugh1961} from the Banhoffer-van der Pol oscillator and electronically realized by \citet{Nagumo1962}, consisting only of two differential equations with a single non-linear term, is able to reproduce some features of the $\rho$ variability class of \grs. We wrote the system in a form containing only four parameters and studied its equilibrium state and the stability conditions for which is possible to obtain a limit cycle. In the following paragraphs we first summarize our results and then discuss a possible interpretation in comparison with some proposed instability mechanisms. \subsection{Summary of main results} FitzHugh-Nagumo equations contain four parameters, three of which, $\rho$, $\chi$ and $\gamma$, relate the $x$ and $y$ time derivatives to the variables and are named internal, while the only external parameter $J$ can play the same role of a forcing. We adjusted parameters' values to obtain a solution for $x$ reproducing the gross profile of the $\rho$ class bursts and, unexpectedly, we found that the other variable $y$ exhibited a time modulation remarkably similar to that of the mean energy (or the temperature) of photons as found by \citet{Massa2013} (FhN-A model). We underline that changes of $x$ and $y$ occur on two different time scales, fast and slow, respectively. This result is obtained with a constant $J$ value and therefore it implies that this bursting is intrinsic to the non-linear oscillations and do not require an external modulation, as in the well known self-oscillation phenomenon (see for instance the recent review paper by \citet{Jenkins2013}). Moreover, the the delay of the emission at high energy with respect to the low energy one, as resulting from the plots in Fig.~\ref{fig6}, is a direct consequence of the physical mechanism responsible for the bursting and other mechanisms as photon scattering from a hot corona are not necessary, in agreement with the results of spectral analysis \citep{Mineo2012}. All these results agree remarkably well with the delay measurements reported by \citet{Massa2013} and with the evolution of the disk and corona photon luminosity along the burst obtained with the spectral analysis presented by \citet{Mineo2012}. The FhN-A model, therefore, appears to have a relevant heuristic value and should not be simply considered an ad-hoc mathematical description of the observed data. It is also interesting to note that the non linearity of the FhN equations implies that the burst recurrence time is also depending upon the external parameter $J$. The lower right panel in Fig.~\ref{fig8} shows that changes of \trecs are mainly due to a modification of the {\it SLT} length. From the curves in Fig.~\ref{fig9}, we see that the change of \trecs from A8b to F7 data series can be accounted for an increase of $J$ by about 20\%, comparable to that of {\it BL} level in Fig.~\ref{fig1}. This finding suggests that this parameter can be likely related to an external mass-accretion rate ($\dot m$ at large radii) that is the main regulator of the disk photon luminosity. Slow variations of this quantity and the consequent changes of $J(\dot m)$ can thus move the oscillator across the boundary between the stability or instability region, and {\it vice versa} (see Appendix III) with a consequent appearance or disappearance of a bursting limit cycle. Effects of $\dot m$ changes may also be responsible of some of the variability classes as those classified by \citet{Belloni2000}. In Sect. 5.5 we found that a high and slowly modulated $J$ can produce solutions for $x$ with an alternance of spikes and quasi quiescent states quite similar to those observed in the $\nu$ class light curves. Under this respect, it appears more interesting the result obtained from the HR model, which includes one more variable and a corresponding equation. The bursting solution in Fig.~\ref{fig13} presents such a striking similarity with the data, such as the increasing recurrence time of bursts or the shape of the quiescent part (see lower panel in Fig.~\ref{fig10}), that appears very unlikely that it is only a chance result. Our solution is essentially of the same type of those discussed by \citet{Shilnikov2008} and the mathematical properties are extensively presented in that paper. We can conclude that the apparent complex behaviour of \grss seems to be mainly regulated by a single non-linear oscillator driven by a unique parameter, whose changes are responsible at least for some of variability classes. The non-linear oscillator model implies that there is an interplay between the two (or three) variables and therefore some caveats must be considered in the interpretation of spectral parameters' values derived by spectral fitting of the data, such as the widely used \textsf{diskbb} \citep{Mitsuda1984} or others in XSPEC. For instance, changes of the disk inner radius may alternatively be considered as a luminosity normalization rather that an evidence of a real change in the disk radial extension. It is unclear whether the models described in the present paper are the most appropriate ones for \grss or if other variables or terms must be introduced in the differential equations. It is an open problem how a system of dynamical equations can be derived from the complex mathematical apparatus of accretion disks and this requires new deep theoretical investigations. Useful indications in this direction, however, can be retrieved from some interesting previously published works. \subsection{Disk instabilities and the $\rho$ class limit cycle} Studies of the development of instabilities in accretion disks started several decades ago \citep[e.g.][]{Lightman1974, Pringle1973, Shakura1976} and up to now originated an extensive literature. \citet{Taam1984}, in particular, computed by means of numerical integration of the non-linear disk equations to investigate thermal-viscous instabilities and obtained a few theoretical light curves having recurrent bursts consisting by a slow rising portion followed by a very narrow and high peak, more similar to those in the right panel of Fig.~\ref{fig4} or in Fig.~\ref{fig12}, rather than to those in Fig.~\ref{fig5}. With the discovery of the $\rho$ class variability in \grs, \citet{Taam1997} investigated the time and spectral properties of the bursts and proposed an interpretation based on the instability discussed in the previous paper. However, these authors invoked for explaining the delayed hard emission a reflection in the frame of a disk-corona model. Later \citet{Nayakshin2000} to reproduce some classes of light curves of \grss proposed a disk model with a rapidly variable viscosity and an upper limit to the energy fraction transferred to the disk emission. \citet{Watarai2003} studied a model with a modified version of the $\alpha$-viscosity prescription law with respect to the standard one and introduced a power law dependence of viscosity stress tensor $\mathcal{T}_{r \varphi}$ on the ratio between the gas $p_{gas}$ and the total pressure $\beta = p_{gas} / (p_{gas} + p_{rad})$: \begin{equation} \mathcal{T}_{r \varphi} = - \alpha_0 \beta^{\mu} \Pi \end{equation} where $\Pi$ is the height integrated pressure. The resulting light curves exhibit the typical bursting behaviour and the variable recurrence time results from changes of the exponent $\mu$. In these models, however, there is no delay between temperature and photon luminosity as observed in the $\rho$ class bursts \citep{Massa2013}. A further investigation of the limit cycle light curves was performed by \citet{Merloni2006} who considered a magnetized disk in which magnetic turbulent stresses inside the disk scale with the pressure as ($0 < \mu < 2$): \begin{equation} \mathcal{T}_{r \varphi} = - \alpha_0 p_{tot}^{1 - \mu/2} p_{gas}^{\mu/2} \end{equation} Their calculated light curves for an accreting black hole of 10 $M_{\odot}$ and $\mu = 0.1$ have a recurrence time of bursts increasing with the mass accretion rate, in a qualitative agreement with our results. Unfortunately, the simultaneous temperature evolution is not given and a full comparison with the data and the results of the FhN-A model is not possible. However, the approach of an energy transfer instability in a magnetized disk appears one of the most promising for the understanding of physical processes regulating the instability. A model for the $\rho$ class has been recently proposed by \citet{Neilsen2012, Neilsen2011} who interpreted the bursting as a consequence of a similar modulation in the mass accretion rate. In these works, authors used RXTE/PCA and Chandra/HETGS data to characterize the spectral modifications according to the burst phase. A model of soft thermal disk component and hard Comptonized emission shows that changes in the parameters are smooth for most of the burst phases, but a significant spectral modification is observed during the pulse. At this phase it is observed a strong decrease of the inner disk radius (up to $\sim$ 2 R$_{g}$, that would require a spinning black-hole with an adimensional angular momentum per unit mass $a \simeq 0.9$ if this minimal radius is identified with that of the last stable orbit), and a strong increase in the coronal electron opacity (where most of the disk emission is Thomson scattered). Some authors \citep[e.g.][]{Artemova1996} have therefore argued that during the pulse a recurrent set of steps are operating: when at small disk radii, local Eddington limit is reached, a radiation pressure instability develops and, consequently, part of the inner disk is vaporized into an optically thick, completely ionized, cloud. This cloud emits also part of its energy as thermal bremsstrahlung emission (hard pulse). Modification of this primary radiation causes also changes at large outer disk radii, as it strongly modified the structure of any (thermally/radiation driven) disk wind. Because the fraction of the mass outflow that is dispersed into a wind (which if channelled by the disk magnetic field lines may become a jet) modifies the fraction of the accretion mass rate, this leads to generation of mass density waves that propagate toward the accretor, giving rise to the burst typical recurrent pattern. Such scenario appears to be consistent with a combination of spectroscopic detailed line diagnostic and broadband coverage of the spectral shape. However, our approach shows that the limit-cycle behaviour can also be understood independently from any fitted spectral decomposition. If the strong relation of the global mass accretion rate with $J$ holds, the link between the outflow rate with the inner mass accretion rate could not be strictly required. We have shown that the outer mass accretion rate is probably responsible for passages between one state to an another, but within the $\rho$-class state, $J$ is constant, and the oscillating mechanism is still at work. This does not mean that changes at small radii should not impact the wind physical properties, but only that the claimed strong feed-back of the two zones may not be necessary for the development of the limit-cycle instability. We note that a detailed modelling of the expected changes in the energy spectra would require a translation of the differential equations into the proper physical radiation components, which would lead beyond the aims of the present work. | 14 | 4 | 1404.7249 |
1404 | 1404.5285_arXiv.txt | The Askaryan Radio Array (ARA) is an ultra-high energy ($>10^{17}$~eV) cosmic neutrino detector in phased construction near the south pole. ARA searches for radio Cherenkov emission from particle cascades induced by neutrino interactions in the ice using radio frequency antennas ($\sim150-800$~MHz) deployed at a design depth of 200~m in the Antarctic ice. A prototype ARA Testbed station was deployed at $\sim30$~m depth in the 2010-2011 season and the first three full ARA stations were deployed in the 2011-2012 and 2012-2013 seasons. We present the first neutrino search with ARA using data taken in 2011 and 2012 with the ARA Testbed and the resulting constraints on the neutrino flux from $10^{17}-10^{21}$~eV. | The Askaryan Radio Array (ARA) aims to measure the flux of ultra-high energy (UHE) neutrinos above $10^{17}$~eV. While UHE neutrinos are so far undetected, they are expected both directly from astrophysical sources and as decay products from the GZK process \cite{Greisen:1966jv,Zatsepin:1966jv}, as first pointed out by Berezinsky and Zatsepin~\cite{Berezinsky:1969zz,Berezinsky:1970}. The GZK process describes the interactions between cosmic rays and cosmic microwave and infrared background photons above a $\sim10^{19.5}$~eV threshold. The interaction of a UHE neutrino in dense media induces an electromagnetic shower which in turn creates impulsive radiofrequency (RF) Cherenkov emission via the Askaryan effect~\cite{Askaryan:1962,Askaryan:1965,Zas:1991jv,Gorham:2000ed,Saltzberg:2000fk,Gorham:2004ny,Gorham:2006fy}. In radio transparent media, these RF signals can then be observed by antenna arrays read out with $\sim$~GHz sampling rates. Currently, the most stringent limits on the neutrino flux above $\sim10^{19}$~eV have been placed by the balloon-borne ANITA experiment sensitive to impulsive radio signals from the Antarctic ice sheet~\cite{Gorham:2010kv,Gorham:2010xy}. Below $10^{19}$~eV, the best constraints on the neutrino flux currently come from the IceCube experiment, a $1~\rm{km}^3$ array of photomultiplier tubes in the ice at the south pole using the optical Cherenkov technique~\cite{Aartsen:2013dsm}. IceCube has recently reported the first extraterrestrial high energy neutrino flux, which extends up to $\sim10^{15}$~eV. This is two orders of magnitude lower energy than ARA's energy threshold~\cite{Aartsen:2013jdh,Aartsen:2014gkd}. Due to the $\sim 1$~km radio attenuation lengths in ice ~\cite{Allison:2011wk, Barwick:2005zz}, radio arrays have the potential to view the $100$s of $\rm{km}^3$ of ice necessary to reach the sensitivity to detect $\sim10$ events per year from expected UHE neutrino fluxes. The first radio array in ice to search for UHE neutrinos, RICE, was deployed along the strings of the AMANDA detector, an IceCube predecessor, and placed competitive limits on the UHE neutrino flux between $10^{17}$ and $10^{20}$~eV~\cite{Kravchenko:2011im}. Next-generation detectors are under construction aiming to reach the $100$s of $\rm{km}^3$ target volume of ice. The Askaryan Radio Array (ARA)~\cite{Allison:2011wk} is one such detector being deployed in the ice at the south pole and the first physics results from a prototype station of this detector are presented in this paper. Another experiment with similar aims, ARIANNA, is currently being developed on the surface of the Ross Ice Shelf in Antarctica~\cite{Gerhardt:2010js}. ARA aims to deploy 37 stations of antennas at 200~m depth spanning $100~\rm{km}^2$ of ice as shown in Fig.~\ref{fig:ara37}. A design station consists of eight horizontally polarized (HPol) and eight vertically polarized (VPol) antennas at depth and four surface antennas for background rejection and cosmic ray detection via the geomagnetic emission in the atmosphere. The 200~m design depth was chosen because it is below the firn layer, where the index of refraction varies with depth due to the gradual compacting of snow into ice down to $\sim150$~m depth. The trigger and data acquisition are handled by electronics at the surface of the ice at each station. To date, one ARA prototype Testbed station and three full stations have been deployed in the ice. The Testbed station was deployed at a depth of $\sim30$~m in the 2010-2011 drilling season. The first full station, A1, was deployed at a depth of 100~m in the 2011-2012 drilling season. The next two stations, A2 and A3, were deployed at the 200~m design depth during the 2012-2013 season. At the time of publication, station A2 and A3 are operational while A1 is under repair. This paper presents three complementary analyses using data taken with the Testbed station. The first two analyses use a series of cuts to reject background signals in favor of neutrino events. The third analysis is template-based and searches for unique impulsive signals after correlating events. \begin{figure}[t] \centering \includegraphics[width=0.5\textwidth]{ARA_layout_v1_4.pdf} \caption{Diagram showing the layout of the proposed ARA37 array, with the location of the Testbed and the first three deployed deep stations highlighted in blue and black respectively, and proposed stations for the next stage of deployment, ARA10, highlighted in orange.} \label{fig:ara37} \end{figure} \begin{figure}[t] \centering \includegraphics[width=0.45\textwidth]{Testbed_schematic.pdf} \caption{Schematic of the ARA Testbed station.} \label{fig:testbedstation} \end{figure} | 14 | 4 | 1404.5285 |
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1404 | 1404.4871.txt | We present a support vector machine classifier to identify the K giant stars from the LAMOST survey directly using their spectral line features. The completeness of the identification is about 75\% for tests based on LAMOST stellar parameters. The contamination in the identified K giant sample is lower than 2.5\%. % Applying the classification method to about 2 million LAMOST spectra observed during the pilot survey and the first year survey, we select 298,036 K giant candidates. The metallicities of the sample are also estimated with uncertainty of $0.13\sim0.29$\,dex based on the equivalent widths of Mg$_{\rm b}$ and iron lines. %Comparing to the LAMOST parametrization pipeline, the advantage of the metallicity estimation developed in this work is that it can be applied to spectra with signal-to-noise ratio down to $\sim$3. A Bayesian method is then developed to estimate the posterior probability of the distance for the K giant stars, based on the estimated metallicity and 2MASS photometry. The synthetic isochrone-based distance estimates have been calibrated using 7 globular clusters with a wide range of metallicities. The uncertainty of the estimated distance modulus at $K=11$\,mag, which is the median brightness of the K giant sample, is about 0.6\,mag, corresponding to $\sim30$\% in distance. % As a scientific verification case, the trailing arm of the Sagittarius stream is clearly identified with the selected K giant sample. Moreover, at about 80\,kpc from the Sun, we use our K giant stars to confirm a detection of stream members near the apo-center of the trailing tail. These rediscoveries of the features of the Sagittarius stream illustrate the potential of the LAMOST survey for detecting substructures in the halo of the Milky Way. | The LAMOST {(the Large sky Area Multi-Object fiber Spectroscopic Telescope; also known as Guo Shou Jing Telescope)} project has carried out a pilot survey between October 2011 and June 2012 and obtained more than 700,000 spectra \citep{cui12,zhao12,lxw13}. The regular survey has operated since 2012 September and has already obtained about 2 million spectra as of June 2013. These spectra has been released as the DR1 catalog. A large fraction of them are K giant stars, which is of great interest in the studies of the Milky Way and in particular for the Galactic halo. K giant stars are luminous and thus allow us to probe the Galaxy far beyond the solar neighborhood. Typically, the absolute magnitude of K giant stars is between $M_r=2$ and -2\,mag. Given the limiting magnitude of $r=17.8$\,mag, the maximum distance at which LAMOST can detect K giant stars is $\sim$90\,kpc from the Sun. \citet{xue12} found distances to more than 4000 K giant stars in SDSS/SEGUE survey with accuracy of $\sim$12\%. Because the limiting magnitude of SEGUE spectra is $g=20.2$\,mag, the maximum distance is much larger than that of LAMOST. Although the K giant stars observed by LAMOST cannot compete with SDSS/SEGUE in terms of distance probed, the total number of this type of spectra in LAMOST will be two orders of magnitude larger than those in SDSS due to the huge {number of spectra} observed in the LAMOST survey and the fact that a larger fraction of bright stars are giants. With such a huge dataset, we should be able to address many interesting and important questions on our galaxy, e.g., the total mass of the Milky Way, the shape of the dark matter halo, the kinematic substructures in the stellar spheroid, the mass distribution of the Galactic disk, the chemo-dynamical features and the evolution history of the disk, etc. Specifically, it will significantly improve the observational evidence of the kinematic substructures in the stellar halo \citep{deng12}. In the 2MASS and SDSS surveys, many substructures have been discovered in the past decades, including the Sagittarius dwarf galaxy stream \citep{ibata01,newberg02,majewski03}, Monoceros ring \citep{newberg02,yanny03}, Orphan stream \citep{belokurov06}, Virgo overdensity \citep{newberg02,vivas06,newberg07}, Triangulum-Andromeda overdensity \citep{majewski04b,rochapinto04}, Hercules-Aquila cloud \citep{belokurov07}, Cetus polar stellar stream \citep{newberg09}, Pisces stellar stream \citep{bonaca12,martin13}, and many other cold and weak streams \citep[e.g., ][]{grillmair06}. Although some of these substructures are prominent in photometric catalogs, a tiny fraction of their member stars have spectroscopic observations. The identification of the K giant members in known tidal streams will be crucial to constrain the orbits of the tidal streams and to constrain the merging history of their progenitors \citep[e.g.,][]{law05,law10}. Moreover, it can also be used to measure the total mass of the Milky Way \citep[e.g.,][]{koposov10}. In addition, the K giant stars can be used to discover new substructures which are otherwise not possible by any previous approaches. According to the $\Lambda$CDM cosmology, the halo of a Milky Way-like galaxy should contain hundreds of subhaloes, in which dwarf galaxies may be embedded. Current observations only find a few tidal streams and dozens of satellite dwarf galaxies around the Galaxy. This is the so called \emph{missing satellite problem}, which challenges all current theories \citep{klypon99,koposov08}. Because some of the merging dwarf galaxies form tidal streams during accretion, the search for new tidal substructure is one important way to address this discrepancy. Ultimately, the study of tidal streams will allow a better understanding on the formation history and evolution of a galaxy. In order to make optimal use of the K giant sample, a clean and relatively complete K giant catalog with distance estimates is highly desirable. In principle, K giant stars can be identified from measurements of stellar parameters, e.g. effective temperature (\teff) and surface gravity (\logg). However, estimations of the stellar parameters can only be reliably achieved for the \emph{good} spectra, i.e., the high signal-to-noise ratio data or the well flux {calibrated data}. As a result, a majority of K giant spectra with moderate or low signal-to-noise ratio, which are usually located at further distances, are missing from the parameter table. In order to reach {a} larger detection volume and hence maximize the scientific value of the LAMOST survey data, we take an alternative approach of identifying K giant stars directly from spectra instead of stellar parameters. % In addition to the identification of the K giant stars, the metallicity is necessary for the distance estimation. Consequently, one of the aims of the current work is to develop a more robust and reliable metallicity estimation method, especially for those spectra with low or moderate S/N. Finally, the distance of the K giant samples is determined with a robust statistical method. A brief introduction to the data used in this work is given in section~\ref{sect:data}. In section~\ref{sect:class}, a machine learning algorithm is developed for the identification of K giant stars from the stellar spectra of the LAMOST survey. The success of the classification method is verified by using MILES and SDSS public data. The method is then applied to the LAMOST data and a complete K giant dataset is produced. % In section~\ref{sect:metal}, a thin-plate spline model (hereafter, LM2D) for \feh\ estimation based on the Mg$_b$ and iron lines is introduced and applied to the identified K giant stars. % Subsequently, the distance of the selected K giant stars with low extinction is estimated based on the isochrone comparison in section~\ref{sect:dist}. The well-known kinematic substructure, the Sagittarius stream, is then identified from the K giant stars in section~\ref{sect:sgr}. Finally, a short conclusion of the current work is given in the last section. | We have established a SVM classifier directly from the spectra features, and then apply it to LAMOST spectra for K giant star selection. The method does not depend on the stellar parameters, e.g., \teff\ and \logg, thus has a broader range of capability to work on spectra with S/N as low as 3. Tested with SDSS, MILES, and LAMOST data, the SVM classifier can select K giant stars from the survey dataset with 70-80\% completeness and a few percent contamination. % From the DR1 released $\sim$1.9 million stellar spectra, we identified about 290,000 K giant stars. Consequently, we expect that, when the survey will be concluded in five years, there will be a factor of 4 more K giant stars to be observed. In order to estimate the distance of the K giant stars, we have firstly estimated the metallicity using LM2D method. Comparisons with SDSS parameters indicates that the total error of the estimation is between 0.1\,dex and 0.3\,dex. The advantage of the estimation method is that we can provide metallicity for the identified K giant stars with signal-to-noise ratio down to 3. We have then developed a Bayesian method to estimate the distance of the K giant stars using 2MASS photometry and the estimated metallicity from LM2D. The synthetic isochrone-based method is calibrated with 7 globular clusters. Therefore, the systematic bias due to the discrepancy between the synthetic and observed data is corrected. The uncertainty of the distance estimation is investigated using the same globular clusters, which covers a wide range in metallicities. We conclude that the uncertainty in DM is around 0.5\,mag at $K\sim11$\,mag, corresponding to about 30\% in distance. Given the distance and radial velocities of the K giant stars selected from the survey, we successfully identified many candidate members of the Sgr stream. These identifications demonstrate that there may be thousands of K giant members of such tidal substructures to be observed and identified over a broad area of the sky by the end of the five-year survey. Consequently, it will be one of the most important homogeneous spectroscopic dataset to map the kinematics as well as the chemical abundance of them. This will provide a tight constraint on the dark matter mass in the Galactic halo as well as the forming history of the substructure themselves. %Moreover, by a preliminary analysis of the survey data using the new methods, we have found two new candidate substructure, {\bf L147-45} and {\bf L173-13}. The metallicity, distance, and line-of-sight velocity of the substructure member stars from more LAMOST spectra observed in the next few years may help us to unveil their origins. | 14 | 4 | 1404.4871 |
1404 | 1404.7413_arXiv.txt | {We investigated the molecular gas associated with 6.7 GHz methanol masers throughout the Galaxy using a $J=1-0$ transition of the CO isotopologues.} {The methanol maser at 6.7 GHz is an ideal tracer for young high-mass star-forming cores. Based on molecular line emissions in the maser sources throughout the Galaxy, we can estimate their physical parameters and, thereby, investigate the forming conditions of the high-mass stars. } {Using the 13.7-meter telescope at the Purple Mountain Observatory (PMO), we have obtained ${\rm ^{12}CO}$ and ${\rm ^{13}CO}$ $(1-0)$ lines for 160 methanol masers sources from the first to the third Galactic quadrants. We made efforts to resolve the distance ambiguity by careful comparison with the radio continuum and HI 21 cm observations. We examined the statistical properties in three aspects: first, the variation throughout the Galaxy; second, the correlation between the different parameters; third, the difference between the maser sources and the infrared dark clouds. In addition, we have also carried out ${\rm ^{13}CO}$ mapping for 33 sources in our sample.} {First, the maser sources show increased $^{13}$CO line widths toward the Galactic center, suggesting that the molecular gas are more turbulent toward the Galactic center. This trend can be noticeably traced by the ${\rm ^{13}CO}$ line width. In comparison, the Galactic variation for the H$_2$ column density and the $^{12}$CO excitation temperature are less significant. Second, the $^{12}$CO excitation temperature shows a noticeable correlation with the H$_2$ column density. A possible explanation consistent with the collapse model is that the higher surface-density gas is more efficient to the stellar heating and/or has a higher formation rate of high-mass stars. Third, comparing the infrared dark clouds, the maser sources on average have significantly lower H$_2$ column densities, moderately higher temperatures, and similar line widths. Fourth, In the mapped regions around 33 masers, 51 $^{13}$CO cores have been revealed. Among them, only 17 coincide with the radio continuum emission ($F_{\rm cm}>6$ mJy), while a larger fraction (30 cores) coincide with the infrared emissions. Only one maser source has no significant IR emission. The IR-bright and radio-bright sources exhibit significantly higher $^{12}$CO excitation temperatures than the IR-faint and radio-faint sources, respectively. } {The 6.7 GHz masers show a moderately low ionization rate but have a common-existing stellar heating that generates the IR emissions. The relevant properties can be characterized by the ${\rm ^{12}CO}$ and ${\rm ^{13}CO}~(1-0)$ emissions in several aspects as described above. } | The high-mass (O and early B-type) stars play a critical role in the mass distribution and chemical evolution of the galaxies. Yet, their forming processes are still not fully understood. The main difficulty in revealing their birth is that, most young high-mass stars are deeply obscured by a dust envelope and therefore, hard to observe at optical wavelengths. Moreover, they are usually at large distances of several kilo parsecs and have a clustered environment. Masers, such as CH$_3$OH masers~\citep{menten91,walsh98,beuther02}, were found to be an ideal tracer for the forming sites of young high-mass stars. In the targeted survey at early decades, the methanol masers were observed exclusively near the Ultra Compact (UC) H{\sc ii} regions \citep{menten92,sutton01} and totally absent in other types of objects, including the forming regions of low-mass stars, AGB star, and other galaxies. The subsequent observations \citep{phillips98,walsh98} have revealed a greater number of 6.7 GHz masers without a radio continuum counterpart and suggest that they could trace even earlier stages (prior to the UC H{\sc ii} stage). Based on the accumulated data and newly performed surveys, \citet{pestalozzi05} have presented a relatively completed catalogue of the 6.7 GHz methanol masers throughout the Galaxy. After that, more extensive molecular molecular line surveys \citep[][etc.]{minier05,purcell06,longmore06} were followed as a major procedure to investigate the physical and chemical properties in the methanol-maser sources. As a result, they are detected in many dense molecular tracers such as H$^{13}$CO$^+$, CH$_3$CN, and sulfur-bearing molecules. On the other hand, the different methanol maser transitions \citep[classified to be class-I and class-II][]{menten91} are found to trace different physical conditions. Besides the widely detected 6.7 GHz masers, which belong to class-II \citep{menten91}, various class-I masers were observed at the interface between the outflow and the ambient gas \citep[][etc.]{plambeck90,johnston97,voronkov05}. The latter observations with higher resolution showed that the Class-I masers arise from intense outflow and shock emissions \citep{cyganowski08,wu10}. These properties are consistent with the theoretical anticipation that the Class-I masers are stimulated by the collisional processes while the class-II transitions are mainly excited by the radiative processes \citep[][]{cragg92}. Using the 13.7-m millimeter telescope at the Qinghai station of the Purple Mountain Observatory, \citet{liu10a} observed 98 maser sources (including both type I and II) and studied the relation between their CO-line emissions and infrared luminosities. Since the 13.7-m telescope is appropriate for single-point and mapping observations over a large area, we carried out a more extensive observation towards the Galactic methanol-maser sources, aiming to get a more complete sample of the molecular lines and thereby analyze their physical parameters and statistical properties. The targeted 6.7 GHz maser sources (referred to as "maser sources" hereafter) for the current observation are taken from the \citet{pestalozzi05}'s catalogue and mainly in the northern sky (within the Dec. range available for the telescope) in $^{12}$CO and $^{13}$CO $(1-0)$. We estimated the physical parameters from these lines, examined their Galactic distribution and correlations. In addition, we made ${\rm ^{13}CO}$ maps for 33 sources in order to study the gas distribution around the maser sources. We report the observation and data reductions in Section 2. We show the measurement of the physical parameters in Section 3. In Section 4, we discuss the statistical properties of the physical parameters and made a comparison with the physical parameters in the infrared dark clouds (IRDCs) that are sampled by \citet{du08}. A summary of the major results is presented in Section 5. | \subsection{Variation with the Galactocentric distance} In Figure 4 we plot the variation of $\Delta V({\rm ^{13}CO})$, $N({\rm H_2})$, and $T{\rm _{ex}(^{12}CO)}$ as a function of the Galactocentric distance $R_{\rm gc}$ for our maser sources. We note that $R_{\rm gc}$ always has a single solution and is unaffected by the distance ambiguity. As a major result, the line width shows a noticeable decrease with $R_{\rm gc}$. At $R_{\rm gc}=4$ kpc, the average line width is $\Delta V=8$ km s$^{-1}$, and it drops to $\Delta V=2.5$ km s$^{-1}$ at $R_{\rm gc}=9$ kpc. The two statistical tests show that the different intervals vary with each other with $p<0.05$ in most cases. The $\Delta V-R_{\rm gc}$ relation may suggest that the gas becomes more turbulent in the maser sources closer to the Galactic center. The inner Galaxy on average has a higher star-and-gas density than the outer region. In a denser environment, the molecular cores can become more turbulent when affected by two aspects: a more frequent dynamical interaction with nearby molecular cores or clouds and the energy input from the stellar wind and radiation. Besides, the line broadening due to the optical depth should also be considered. Assuming that the optical depth is a Gaussian-shaped function of the radial velocity \citep{myers96}, $\tau(V)=\tau_0\exp[-(V-V_{\rm sys})^2/2\sigma^2]$, where $\tau_0$ is the optical depth at the systemic velocity $V_{\rm sys}$ and $\sigma$ is the velocity dispersion along the line of sight and can be measured from the intrinsic line width using $\sigma=\Delta V/\sqrt{8\ln2}$. The observed line profile would be $T_{\rm mb}(V)=J_\nu(T_{\rm ex})[1-\exp(-\tau(V)]$. From these equations, the ratio between the observed line width ($\Delta V_{\rm obs}$) and the intrinsic line width (broadening factor) is derived to be \begin{equation} \frac{\Delta V_{\rm obs}}{\Delta V}=[\frac{\ln{\tau_0/\ln[2/(1+e^{-\tau_0})] }}{\ln 2}]^{1/2}. \end{equation} For all our ${\rm {13}CO}$ components, the broadening factor in $^{13}$CO $(1-0)$ turns out to be less than 1.5. Thus its contribution to $\Delta V_{13}$ and the $\Delta V_{13}$-$R_{\rm gc}$ correlation would not be significant, and we suggest that the cores at smaller $R_{\rm gc}$ may indeed have larger velocity dispersions. A similar trend between $\Delta V$ and $R_{\rm gc}$ was also suggested for the CO gas in the IRDCs \citep{du08}. The other two parameters, $N({\rm H_2})$ and $T{\rm _{ex}(^{12}CO)}$ do not show significant Galactic variation. For the $N({\rm H_2})$ distribution, the 2-4 and 10-12 kpc intervals have very large probabilities to have similar distributions. The $T{\rm _{ex}}$ distribution shows a slight increase toward large $R_{\rm gc}$ with the difference reaching the significant level $(p>0.05)$ between 0-2 and 10-12 kpc intervals. However, its variation scale is still much weaker than the trend in $\Delta V$. \subsection{Correlation between the physical parameters} The relation between the different physical parameters are shown in Figure 5. Figure 5a shows that the $^{12}$CO excitation temperature significantly increases with the H$_2$ column density (with a slope of $3.3\pm0.3$ and a correlation factor of $R=0.4$). \citet{krumholz10} performed a hydrodynamic simulation about the molecular core collapse and star formation therein. The simulation shows that a higher surface density can significantly facilitate the formation of high-mass stars ($M>10~M_{\odot}$), thus lead to an increased temperature in the natal gas-and-dust core. In their densest case of $\Sigma=10$ g cm$^{-2}$ or $N({\rm H_2})=2\times10^{24}$ cm$^{-2}$, the final temperature in the surrounding gas exceeds $1000$ K as heated by the newly formed massive stars. In contrast, only a group of low-mass stars can be formed in the low-density case of $\Sigma=0.1$ g cm$^{-2}$, and the final temperature is $\sim100$ K. The simulation result shows a reasonable consistency with the observed $T_{\rm ex}-N({\rm H_2})$ correlation. Namely, the formation rate of the massive stars and/or heating efficiency would increase in higher-$N({\rm H_2})$ regions. The above explanation have some apparent uncertainties. The major question is whether the internal stellar heating can noticeably change $T{\rm _{ex}(^{12}CO)}$. Due to the large optical depth in $^{12}$CO, its surface temperature might be insensitive to the internal stellar heating and instead, more affected by the external emissions. Based on our observational data, there is one way to examine this problem. Our mapped regions have provided a number of $^{13}$CO cores that are not associated with radio continuum and/or IR emissions. These cores can naturally serve as a control group for us to evaluate the significance of the internal heating. We first compared the temperatures in the radio-bright and radio-faint cores ($F_{\rm cm}<6$ mJy). Their distributions are shown in Figure 6a. The Figure shows that the radio-bright group are apparently inclined to high temperatures. The M-W and t tests both indicate that radio-bright cores have significantly higher $T{\rm _{ex}}$ than the radio-faint ones. The average temperatures of the two groups are 26.4 K and 20.5 K, respectively. The second comparison is based on their IR emissions, as shown in Figure 6b. The IR-bright and IR-faint groups have average temperatures of 24 K and 16 K with the contrast being slightly larger. This is within our expectation, since the IR-faint cores are actually a sub-sample within the radio-faint group. The comparison suggests that the cores without IR and radio continuum emissions indeed tend to have the lower $T{\rm _{ex}(^{12}CO)}$. In the case that $T{\rm _{ex}(^{12}CO)}$ is sensitive to the internal stellar heating, the observed $T_{\rm ex}-N({\rm H_2})$ correlation would favor the explanation that the stellar emission is actually more intense and/or more efficient in the higher-$N({\rm H_2})$ cores. Nevertheless, our current data is still insufficient to confirm the physical connection between $N({\rm H_2})$ and star-forming activities. For example, due to the low resolution, we cannot determine whether the IR and radio sources are embedded in or separated from the densest gas in a given core. It calls for denser molecular tracers to more accurately determine the temperature and $N({\rm H_2})$ distributions and to better reveal their correlation with the star-forming processes. The relation between $\Delta V({\rm ^{13}CO})$ and $N({\rm H_2})$ is investigated and shown in Figure 9. The value of $\Delta V({\rm ^{13}CO})$ appears to have no significant correlation with the ${\rm H_2}$ column density. A linear fit provides a slope of 0.28 and the correlation factor of $R=0.09$ which are both much smaller than the corresponding values in the $T_{\rm ex}-N({\rm H_2})$ relation. This may be explained as a result from the Larson relation \citep{larson81}. \citet{larson81} showed that, $\Delta V$ is sensitive only to the spatial size, which reflects the nature of the hierarchical turbulence, and in the mean time, the number density is anti-correlated with the spatial size. These two factors would cause the column density to be almost independent on the spatial size, which is consistent with the observed weak correlation between $\Delta V({\rm ^{13}CO})$ and $N({\rm H_2})$. \subsection{Comparison between the maser sources and the infrared-dark cores} Besides the CH$_3$OH masers, the IRDCs also serve as a potential reservoir for high-mass cores at the earliest evolutionary stages \citep[e.g.][]{rathborne06}. \citet{du08} have performed a single-point and mapping survey of 61 IRDCs, selected from the prominent absorption feature at the MSX 8-micron band that uses the PMO 13.7 m telescope in the three isotopic CO $(1-0)$ lines. Our sample only has two sources (G35.19 and G173.71) in common with \citet{du08}. Even in these two regions, our $^{13}$CO cores have an offset larger than 5 arcmins from the observing center of \citet{du08}. A large fraction of the maser sources are also associated with IR absorption feature, as shown in \citet[][also see our Table 1]{peretto09}, but do not appear in their IRDC sample probably because the absorption is much less prominent than those shown on the MSX 8 $\micron$ band. In Figure 7, we plot the distributions of the physical parameters in the maser and IRDC samples. The two samples turn out to have largely different $N({\rm H_2})$ distributions. The IRDCs have a major fraction with $N({\rm H_2})>4\times10^{22}$ cm$^{-2}$ and have no distribution below $10^{22}$ cm$^{-2}$. The methanol masers, in contrast, are mainly concentrated at a small $N({\rm H_2})$ range, with the distribution largely decreasing at $N({\rm H_2})>10^{22}$ cm$^{-2}$. The IRDC sample is selected from the intense absorption features at MSX 8 $\micron$ band; thus, they are expected to have large $N({\rm H_2})$. Moreover, the difference between the two samples implies that the source selection based on the IR absorption feature could be biased toward high-$N({\rm H_2})$ regions, which misses out a considerable amount of high-mass star-forming cores inhabited in the clouds with moderate $N({\rm H_2})$. As shown in the middle and bottom panels in Figure 7, the two samples have similar $T_{\rm ex}({\rm ^{12}CO})$ and $\Delta V({\rm ^{13}CO})$ distributions much more similar, except that the maser sample has larger dispersion in $T_{\rm ex}({\rm ^{12}CO})$, which extends from 5 to 40 K. In comparison, the IRDCs show a concentration between 10 and 30 K. The possible explanation is that the methanol masers sources are generally at later evolutionary stages, thus having more various physical conditions. The stellar emission can either increase the temperature or dissipate the molecular gas and drive chemical reactions to consume CO. The latter aspect would cause a decrease in both the optical depth and beam filling factor, and lead to the smaller values in the observed $T_{\rm ex}$ (5 to 10 K), as compared to the IRDCs. | 14 | 4 | 1404.7413 |
1404 | 1404.0005_arXiv.txt | The formation of clouds affects brown dwarf and planetary atmospheres of nearly all effective temperatures. Iron and silicate condense in L dwarf atmospheres and dissipate at the L/T transition. Minor species such as sulfides and salts condense in mid-late T dwarfs. For brown dwarfs below \teff$\sim$450 K, water condenses in the upper atmosphere to form ice clouds. Currently over a dozen objects in this temperature range have been discovered, and few previous theoretical studies have addressed the effect of water clouds on brown dwarf or exoplanetary spectra. Here we present a new grid of models that include the effect of water cloud opacity. We find that they become optically thick in objects below \teff$\sim$350--375 K. Unlike refractory cloud materials, water ice particles are significantly non-gray absorbers; they predominantly scatter at optical wavelengths through \emph{J} band and absorb in the infrared with prominent features, the strongest of which is at 2.8 \micron. H$_2$O, NH$_3$, CH$_4$, and H$_2$ CIA are dominant opacity sources; less abundant species such as may also be detectable, including the alkalis, H$_2$S, and PH$_3$. PH$_3$, which has been detected in Jupiter, is expected to have a strong signature in the mid-infrared at 4.3 \micron\ in Y dwarfs around \teff=450 K; if disequilibrium chemistry increases the abundance of PH$_3$, it may be detectable over a wider effective temperature range than models predict. We show results incorporating disequilibrium nitrogen and carbon chemistry and predict signatures of low gravity in planetary-mass objects. Lastly, we make predictions for the observability of Y dwarfs and planets with existing and future instruments including the \emph{James Webb Space Telescope} and \emph{Gemini Planet Imager}. | Brown dwarfs link planetary and stellar astrophysics, with compositions like stars but the temperatures of planets. They form the tail of the initial mass function and, too low in mass to have core temperatures high enough to fuse hydrogen, they cool over time through the brown dwarf spectral sequence. As they cool, different molecules and condensates form and carve their spectra. With the discovery of very cool brown dwarfs we are able to investigate for the first time the physical and chemical processes that occur in atmospheres with effective temperature ranges that would be suitable for a warm beverage. While brown dwarfs are free-floating, they should share many of the same physical processes as the giant planets that will be uncovered by future surveys. \subsection {Discovery and Characterization of Y Dwarfs} The proposed spectral class Y encompasses brown dwarfs that have cooled below \teff$\sim$500 K. About 17 objects have been classified as Y dwarfs to date. Many of those have now been found using the Wide-field Infrared Survey Explorer (WISE) \cp{Cushing11, Kirkpatrick12, Liu12, Tinney13, Kirkpatrick13}. Additional objects have been discovered as wide-separation companions. \ct{Liu11} found a very cool ($\sim$Y0) companion to a late T dwarf; \ct{Luhman12} discovered a $\sim$300--350 K object orbiting a white dwarf. At these temperatures, NH$_3$ absorption features begin to appear in their near-infrared spectra, and sodium and potassium wane in importance in the optical as they condense into clouds. Recent follow-up studies have aimed to characterize the Y dwarf population. There has been a large effort to measure parallaxes of Y dwarfs: \ct{Marsh13} present results for 5 Y dwarfs and 3 late T dwarfs using a compilation of data from the ground and space. \ct{Dupuy13} present results using only the \emph{Spitzer} Space Telescope for 16 Y and T dwarfs. \ct{Beichman14} present results from a compilation of data from Keck II, the \emph{Spitzer} Space Telescope, and the \emph{Hubble} Space telescope for 15 Y and T dwarfs. Groups have also been collecting followup observations to better understand the spectral energy distributions of Y dwarfs. \ct{Leggett13} present followup near-infrared photometry for six Y dwarfs and a far-red spectrum for WISEPC J205628.90+145953.3. \ct{Lodieu13} observed 7 Y dwarfs in the \emph{z} band using the Gran Telescopio de Canarias. \subsection{Previous Models of Y dwarfs} A number of available models for brown dwarfs include models cold enough to represent Y dwarfs \cp{Allard12, Saumon12, Morley12}, but do not yet treat the effects of water clouds. The first models to incorporate the effects of water clouds into a brown dwarf atmosphere are those of \ct{Burrows03b}. These models generally find that water clouds do not strongly affect the spectrum of Y dwarfs, but there have been few followup studies. \ct{Hubeny07} also includes simple water clouds with a fixed mode particle size of 100 \micron. In Section \ref{burrows} we will discuss how our results compare to these early models. A number of studies have included water clouds in exoplanetary atmospheres; \ct{Marley99} and \ct{Sudarsky00} both modeled the effect of water clouds on the albedos of giant exoplanets; they find the formation of water clouds significantly increases the planetary albedos. \ct{Burrows04} also consider water clouds in exoplanets, using a similar approach as \ct{Burrows03b} but for irradiated planets; \ct{Sudarsky03} and \ct{Sudarsky05} calculate the thermal emission of exoplanets that include water clouds and find that they have a strong effect on the emergent spectrum. \subsection{Clouds in L and T dwarfs} Clouds have posed the greatest challenge for brown dwarf modeling since the first L dwarfs were discovered. As brown dwarfs cool along the L sequence from 2500 K to 1300 K, refractory materials like corundum, iron, and silicates condense to form thick dust layers \cp{Lunine86, Fegley96, Burrows99, Lodders02, Lodders03, Lodders06, Helling06, Visscher10} which thicken as the brown dwarf cools. These dust clouds shape the emergent spectra of L dwarfs \cp[see, e.g.][]{Tsuji96, Allard01,Marley02,Burrows06,Helling08,Cushing08,Witte11}. For field brown dwarfs these clouds clear over a very small range of effective temperature around 1200--1300 K and around the same temperature, methane features begin to appear in the near-infrared. The brown dwarf is then classified as a T dwarf and, for many years, mid to late T dwarfs were considered to be cloud-free. However, it has long been recognized that other somewhat less refractory materials such as sulfides and salts should condense in cooler T dwarfs \cp{Lodders99}. As late T dwarfs (500--900 K) were discovered and characterized, a population of objects redder in the near-infrared (e.g. $J-K$, $J-H$ colors) than the predictions of cloud-free models emerged. \ct{Morley12} included the clouds predicted to form by condensation of the sulfides and alkali salts and showed that by including thin layers of these clouds, the colors and spectra of these redder observed T dwarfs can be matched. As these T dwarfs are further characterized, variability has been observed in mid-late T dwarfs \cp{Buenzli12}; the sulfide clouds may play a role in this variability. \subsection{Directly-imaged Exoplanets} Spectra of directly-imaged planets are also strongly influenced by the opacity of clouds. The first multi-planet directly-imaged system, HR 8799, has four planets, all of which have infrared colors that indicate cloudy atmospheres, much like L dwarfs \cp{Marois08}. Other planetary-mass objects also appear to have spectral properties similar to L dwarfs including {$\beta$} Pictoris b \cp{Bonnefoy13} and 2M1207b \cp{Barman11b}. In fact, at similar effective temperatures planetary-mass objects appear to be even more cloudy than their brown dwarf counterparts \cp{Madhu11c, Barman11}, which has been used to suggest that the breakup of the iron and silicate clouds at the L/T transition may be gravity dependent \cp{Metchev06, Marley12}. Nonetheless the transition to a methane-dominated atmosphere and cloud-depleted near-infrared spectrum must happen at some effective temperature, with the resulting objects appearing as low-gravity `T' and `Y' dwarfs. The first such object discovered is GJ 504b \cp{Kuzuhara13} which is currently the coldest directly-imaged planet (\teff$\sim$500 K) and has colors very similar to T dwarfs; followup observations probing the methane feature at 1.6 \micron\ suggest that, as expected from thermochemical equilibrium calculations, methane is present in the atmosphere \cp{Janson13}. \subsection{Water clouds} In a cold solar composition atmosphere, water clouds will be a massive cloud and an important opacity source. Unlike the refractory clouds which have been extensively studied by a number of groups \cp{AM01, Helling06, Allard01, Tsuji96, Burrows06, Helling08}, the same attention has not been paid to volatile clouds in brown dwarfs. In this work, we aim to predict the effects that water clouds will have on brown dwarf atmospheres. We calculate pressure--temperature profiles, spectra, and colors for the coolest brown dwarfs. We study the signatures of the water clouds and their optical properties, estimate their likely particle sizes, and determine at which effective temperatures the cloud will become optically thick in the photosphere. We end by considering the observability of Y dwarfs with the four major instruments being built for the \emph{James Webb Space Telescope (JWST)} and the detectability of cool giant planets with new and upcoming ground-based instruments. | As brown dwarfs approach the effective temperatures of the solar system's planets, volatile clouds will form in their atmospheres. The first and most massive type of volatile cloud that forms is water ice clouds. Water ice clouds form in objects cooler than effective temperatures of $\sim$400 K. In order to converge atmospheric temperature structures self-consistently with both clouds and chemistry, we calculate models in which, like water clouds in the solar system planets, the clouds heterogeneously cover the surface (``patchy'' clouds). Our model grid covers the Y dwarf spectral class as well as giant planets with the same effective temperatures, from \teff=200--450 K and log g=3.0--5.0. Our main results include: 1. While water condenses high in the atmospheres of all objects below \teff$\sim$400 K, these clouds do not become optically thick until the object has cooled to 350--375 K. This result means that for the current set of Y dwarfs warmer than 400 K, water clouds will not strongly effect their spectra. 2. Water clouds, unlike other clouds in brown dwarf atmospheres, are very much non-gray absorbers. Using the \ct{AM01} cloud model, water ice particle sizes range from $\sim$1--20 \micron. For these particle sizes, the ice particles are strongly scattering in the optical through \emph{J} band and do not change the spectra significantly at those wavelengths. The ice particles absorb strongly in the infrared with prominent features, the strongest of which is at 2.8 \micron. 3. H$_2$O, NH$_3$, CH$_4$, and H$_2$ CIA are the dominant opacity sources in Y dwarf atmospheres. Less abundant species such as PH$_3$ may also be observable at 4--4.6 \micron, as well as H$_2$S in \emph{H} and \emph{Y} bands and the alkalis in the optical. 4. JWST's MIRI and NIRSpec instruments will be well-suited to characterizing cool brown dwarfs. \teff=400--500 K objects will be observable across their near- and mid-infrared spectra, and even \teff=200 K objects will be observable in the spectral window region between 3.8 and 5.0 \micron\ and at some wavelengths between 8 and 17 \micron. Existing and upcoming ground-based instruments such as GPI, SPHERE, and LBTAO will be capable of directly-imaging \teff=400--500 K planets around nearby G dwarfs. \vspace{0mm} | 14 | 4 | 1404.0005 |
1404 | 1404.5620_arXiv.txt | We present a spectral analysis of four coordinated \nustar+\xmm\ observations of the Seyfert galaxy \ngc. These exhibit an extreme level of spectral variability, which is primarily due to variable line-of-sight absorption, revealing relatively unobscured states in this source for the first time. Despite the diverse range of absorption states, each of the observations displays the same characteristic signatures of relativistic reflection from the inner accretion disk. Through time-resolved spectroscopy we find that the strength of the relativistic iron line and the Compton reflection hump relative to the intrinsic continuum are well correlated, as expected if they are two aspects of the same broadband reflection spectrum. We apply self-consistent disk reflection models to these time-resolved spectra in order to constrain the inner disk parameters, allowing for variable, partially covering absorption to account for the vastly different absorption states observed. Each of the four observations is treated independently to test the consistency of the results obtained for the black hole spin and the disk inclination, which should not vary on observable timescales. We find both the spin and the inclination determined from the reflection spectrum to be consistent, confirming \ngc\ hosts a rapidly rotating black hole; in all cases the dimensionless spin parameter is constrained to be $a^* > 0.97$ (at 90\% statistical confidence or better). | Black hole spin is a quantity of significant importance for addressing a variety of astrophysical topics, including the growth of the supermassive black holes powering active galactic nuclei (AGN; \eg \citealt{Dubois13}), the formation of black hole binaries in supernova explosions (\citealt{Miller11}), and potentially the launch of powerful relativistic jets (\citealt{BZ77}), although the exact role spin plays here is still controversial (\citealt{Steiner13, King13jet, Russell13}). For active galaxies, the best method available for measuring black hole spin is to measure the relativistic distortions of fluorescent line emission from the inner accretion disk, excited through irradiation by hard X-rays. These relativistic effects broaden and skew intrinsically narrow emission lines into a characteristic `diskline' profile (\citealt{Fabian89, kdblur}) which depends on black hole spin. The most prominent features produced by such irradiation are typically the iron \ka\ emission line at $\sim$6.4--7.0\,\kev\ (depending of ionization state) and a broad peak in the reflected continuum at $\sim$30\,\kev\ referred to as the Compton hump (\citealt{George91}). Roughly $\sim$40\% of X-ray bright AGN display evidence for broadened iron \ka\ emission (\citealt{Nandra07, dLCPerez10}), and the majority of AGN also show a `hard' excess above $\sim$10\,\kev\ (\eg \citealt{Nandra94, Perola02, Dadina07, Rivers13}), consistent with Compton reflection from the accretion disk (\eg \citealt{Walton10Hex, Nardini11}). Spin estimates for a growing sample ($\sim$20--30 sources) of local AGN have recently been obtained through study of these features, \eg \cite{kerrconv, Miniutti09sw2127, Zoghbi10, Brenneman11, Nardini12, Gallo13, Walton13spin}; see also \cite{Miller07rev, Reynolds13rev, Brenneman13book} for recent reviews. Current results indicate the majority of AGN may host rapidly rotating black holes, although the sample is still fairly small, and not yet well defined in a statistical sense. However, the identification of these spectral features with relativistic disk reflection is not without controversy. In particular, scenarios fully dominated by absorption and reprocessing from material relatively distant to the AGN have frequently been proposed as alternative interpretations to relativistic disk reflection (\eg \citealt{Miller08, LMiller09, Sim10}). If these absorbing and scattering structures are allowed sufficiently complex geometries, such models are also able to reproduce the observed X-ray spectra. Many AGN do indeed display evidence for partially ionised absorption in X-rays (\eg \citealt{Blustin05}), as well as evidence of reflection from distant, dense material in the form of a narrow iron \ka\ emission line (\eg \citealt{Bianchi09}), and a number also display evidence for variable absorption (\eg \citealt{Risaliti02}). The contributions of this absorption can be difficult to fully disentangle from relativistic disk reflection in some cases, particularly without access to sensitive hard X-ray ($>$10\,\kev) coverage. \begin{table} \caption{Basic Observational Details for the Coordinated \nustar+\xmm\ observations of \ngc.} \begin{center} \begin{tabular}{c c c c} \hline \hline \\[-0.2cm] Observation & Date & \multicolumn{2}{c}{Total Good Exposures (ks)} \\ & & \xmm\tmark[a] & \nustar\tmark[b] \\ \\[-0.3cm] \hline \hline \\[-0.15cm] 1 & July 2012 & 110/130 & 77 \\ \\[-0.25cm] 2 & Dec 2012 & 93/120 & 66 \\ \\[-0.25cm] 3 & Jan 2013 & 90/118 & 74 \\ \\[-0.25cm] 4 & Feb 2013 & 103/119 & 70 \\ \\[-0.25cm] \hline \hline \\[-0.25cm] \end{tabular} \end{center} $^{a}$ \xmm\ exposures are quoted for the \epicpn/each of the \epicmos\ detectors. \\ $^{b}$ \nustar\ exposures are quoted for each of the focal plane modules. \\ \label{tab_obs} \end{table} \begin{figure*} \epsscale{1.16} \hspace*{-0.6cm} \vspace*{0.5cm} \plotone{./figs/ngc1365_4obs_po_pcfabs_ratio_countspec.eps} \hspace*{-0.6cm} \plotone{./figs/ngc1365_4obs_po_pcfabs_ratio_countspec_nustar.eps} \vspace*{0.5cm} \caption{ \textit{Top-left panel:} time-averaged \xmm\ \epicpn\ spectra from each of the four coordinated \nustar+\xmm\ observations of \ngc, demonstrating the extreme spectral variability displayed. Observations 1, 2, 3 and 4 are shown in black, red, green and blue respectively. \textit{Top-right panel:} residuals to a simple $\Gamma = 1.75$ powerlaw continuum, modified by partially covering neutral absorption, and applied to the 2.5--4, 7--10 and 50--80\,\kev\ energy ranges. For clarity, we show the \xmm\ \epicpn\ data below 10\,\kev, and the \nustar\ FPMA/FPMB data above 10\,\kev. The same hallmarks of reflection from the inner accretion disk, \ie a relativistically broadened iron line at $\sim$6\,\kev\ and a strong Compton hump at $\sim$30\,\kev\ are seen in each of the four observations, despite the extreme variation in the line-of sight absorbing column. \textit{Bottom panels:} as for the top panels, but now displaying only the \nustar\ data, further highlighting the reduced variability at high energies compared to that seen at $\sim$2\,\kev, and the detection of the broad iron line in these data. The narrow component of the iron emission is less visually prominent in the \nustar\ data owing to the coarser spectral resolution in the iron \ka\ bandpass in comparison to \xmm. In the left panel, only the data from FPMA is shown for clarity. The data in all panels have been rebinned for visual purposes. } \label{fig_ratio} \end{figure*} Since the launch of the Nuclear Spectroscopic Telescope Array (\nustar; \citealt{NUSTAR}), \ngc\ has become central to the debate over the contribution of emission from the inner disk in AGN. \ngc\ ($z = 0.0055, D \sim 20$\,Mpc) is a well studied Seyfert 1.9 galaxy, hosting a $\sim$2 $\times 10^{6}$\,\msun\ black hole (\citealt{Schulz99, Kaspi05}) which displays evidence for a relativistically broadened iron line (\citealt{Risaliti09a, Walton10Hex, Brenneman13}) indicative of a rapidly rotating black hole. However, it is also known to display complex and variable absorption (\citealt{Risaliti05b, Risaliti05a, Risaliti09a, Maiolino10}). The unprecedented high energy data quality and the continuous $\sim$3--80\,\kev\ bandpass provided by \nustar\ is ideal for the study of X-ray reflection (\eg \citealt{Miller13grs, Tomsick14, Marinucci14}; Parker \etal\ 2014c, \textit{submitted}). Early in the mission, \nustar\ observed \ngc, coordinated with \xmm\ (\citealt{XMM}) for soft X-ray coverage, detecting both a relativistic iron line and a strong hard excess. The hard X-ray data from \nustar\ displayed excellent consistency with the prediction of the disk reflection interpretation from the \xmm\ data, and revealed that a Compton-thick absorber would be required to reproduce the high energy data without invoking disk reflection. The presence of such material was found to be inconsistent with the levels of reprocessing observed, either from neutral or partially ionised material (\citealt{Risaliti13nat}), providing a strong confirmation of the contribution from relativistic disk reflection. However, based on a set of simulated spectra, \cite{LMiller13} subsequently challenged this conclusion, suggesting that distant absorption/reprocessing could yet explain the spectra observed from \ngc, and claiming that AGN spins cannot be measured at all. Here we present results from the full series of four coordinated observations of \ngc\ performed by \nustar\ and \xmm, the first of which was initially presented in \cite{Risaliti13nat}. These observations probe an unprecedented range of absorption states with high signal-to-noise data, and also reveal a persistent contribution from the inner accretion disk. We use these observations to disentangle the relative contribution of these processes, and determine the inner disk parameters. This work is structured as follows: the data reduction procedure is outlined in section \ref{sec_red}, our analysis is presented in section \ref{sec_spec}, and the results obtained discussed in section \ref{sec_dis}. Finally, we summarize our conclusions in section~\ref{sec_conc}. | \label{sec_conc} We present the first results from the full joint observing campaign undertaken by \nustar\ and \xmm\ on the well known Seyfert galaxy \ngc. The four coordinated observations reveal an extreme level of spectral variability, which primarily appears to be due to variable line-of-sight absorption. However, while changes in absorption have been observed in \ngc\ before (\eg \citealt{Risaliti05a, Connolly14}), our observations display relatively unobscured states with high S/N for the first time. Despite the diverse range of absorption states displayed, each of the observations displays the same hallmarks of relativistic reflection from the inner accretion disk: a relativistically broadened iron line and a strong Compton reflection hump. These features therefore cannot be associated with line-of-sight absorption. Indeed, with a simple phenomenological analysis, we find that the strength of the relativistic iron line and the Compton hump relative to the intrinsic continuum are well correlated, despite treating each of these features independently, as expected if they are two manifestations of the same broadband reflection spectrum. Following this simple analysis, we perform time-resolved spectroscopy with physically self-consistent disk reflection models, allowing for variable, partially covering absorption, in order to constrain the inner disk parameters. We treat each of the four observations independently in order to test the consistency of the results obtained for the key physical parameters, \ie the black hole spin and disk inclination, which should not vary on observable timescales. Excellent consistency between these results obtained for these parameters from each of the four observations is found. Despite the recent controversial claim by \cite{LMiller13} that AGN spin cannot be measured, our results further demonstrate that it is possible to measure the spin of the black holes powering active galaxies, and we find that the central black hole in \ngc\ is indeed rapidly rotating. | 14 | 4 | 1404.5620 |
1404 | 1404.6529_arXiv.txt | A scaling relation has recently been suggested to combine the galaxy mass-metallicity (MZ) relation with metallicities of damped Lyman-$\alpha$ systems (DLAs) in quasar spectra. Based on this relation the stellar masses of the absorbing galaxies can be predicted. We test this prediction by measuring the stellar masses of 12 galaxies in confirmed DLA absorber - galaxy pairs in the redshift range 0.1~$<z<$~3.2. We find an excellent agreement between the predicted and measured stellar masses over three orders of magnitude, and we determine the average offset $\langle C_{\mathrm{[M/H]}} \rangle = 0.44 \pm 0.10$ between absorption and emission metallicities. We further test if $C_{\mathrm{[M/H]}}$ could depend on the impact parameter and find a correlation at the $5.5\sigma$ level. The impact parameter dependence of the metallicity corresponds to an average metallicity difference of $-0.022\pm0.004$ dex~kpc$^{-1}$. By including this metallicity vs. impact parameter correlation in the prescription instead of $C_{\mathrm{[M/H]}}$, the scatter reduces to $0.39$ dex in log $M_*$. We provide a prescription how to calculate the stellar mass ($M_*^{\mathrm{DLA}}$) of the galaxy when both the DLA metallicity and DLA galaxy impact parameter is known. We demonstrate that DLA galaxies follow the MZ relation for luminosity-selected galaxies at $z=0.7$ and $z=2.2$ when we include a correction for the correlation between impact parameter and metallicity. | During the last decade, large galaxy surveys have provided a wealth of information on the average properties of galaxies. Scaling relations of various physical properties are useful for our understanding of what is the driving parameter behind galaxy evolution. A well-established scaling relation between the galaxy stellar mass and the gas phase metallicity was cemented by investigations of 53,000 local galaxies in the Sloan Digital Sky Survey \citep[SDSS;][]{tremonti04} suggesting that a primary parameter that drives galaxy evolution is the stellar mass. The simple interpretation for the mass-dependence is a metal loss via galactic winds, where galaxies with shallow potential well have more efficient outflows. Deeper targeted surveys have extended the mass-metallicity (MZ) relation to redshifts of $\sim$1 \citep{savaglio05}, $\sim$2 \citep{erb06}, and $\sim$3 \citep{maiolino08}, and show that for a given stellar mass, galaxies have lower metallicities at increasing redshifts. Other scaling relations that also evolve with redshift involve galaxy stellar masses and star formation rates \citep{noeske07}. The three observables (star-formation rate, metallicity and stellar mass), have been shown to form a fundamental relation that does not evolve with redshift \citep{lara-lopez10}, although \citet{mannucci10} hint that the relation might change at $z>2.5$. Further analysis on the redshift evolution requires detailed spectroscopic data for individual high-redshift galaxies. While the luminosity selected galaxies are well studied, long integration times on near-IR spectrographs are necessary to measure metallicities based on rest-frame optical emission lines from high-redshift galaxies. Because of observational limitations, preferentially the most massive and luminous galaxies are targeted and thereby also relatively high-metallicity galaxies are investigated. Metallicities below 10\% solar are rarely inferred for galaxies at $z \gtrsim 2$ because of this selection effect. By observing intrinsically fainter, low-mass galaxies, such as gravitationally lensed galaxies, detailed analyses of galaxies at $z>2$ with metallicities about 5--10\% solar are feasible \citep{yuan09,wuyts12,christensen12,belli13}. From quasar absorption line studies on the other hand, we know that galaxies with much lower metallicities exist at $z \gtrsim 2$. In particular, damped Lyman-$\alpha$ systems (DLAs), that have neutral hydrogen column densities of log $N$(\ion{H}{i})~$>20.3$ cm$^{-2}$, reveal metallicities that are typically 1--10\% solar \citep[e.g.][]{pettini94,ledoux02,prochaska03}. At these redshifts, even cases of extremely low DLA metallicities between 0.1--1\% solar are known \citep{cooke11}. DLAs have a corresponding relation analogous to the MZ relation for luminosity selected galaxies. \citet{ledoux06} show that the velocity widths of DLA metal lines and their metallicities are correlated. As the velocity-metallicity relation has the same slope as the galaxy MZ relation, it is appealing to use the width of the absorption lines as a proxy for the stellar mass of the galaxies. This scaling relation demonstrates that low-metallicity DLAs trace low-mass galaxies that have lower luminosities than galaxies targeted in spectroscopic surveys. The velocity-metallicity relation of DLAs evolves with redshift \citep{ledoux06,moller13,neeleman13} again demonstrating a lower metallicity for a given velocity (or equivalently mass) at progressively higher redshifts. The hypothesis that low-metallicity DLAs trace galaxies at the low-mass end of the mass distribution is supported by models that include the galaxy luminosity, extension of a gas disc, metallicities and gradients \citep{fynbo08} and numerical simulations are able to reproduce the low DLA metallicities \citep{pontzen08}. Models suggest that metal-rich DLAs can be found at larger projected distances between the quasi-stellar object (QSO) and the absorbing galaxy, the so-called impact parameter, and this hypothesis is supported by observations \citep{krogager12}. In the remainder of this paper, we will call the galaxy which is responsible for the damped absorption in the QSO spectrum the `DLA galaxy'. The origin of DLA clouds relative to the DLA galaxies has been widely debated. Studies of the \ion{C}{ii}* fine structure line showed that some DLAs might arise in-situ in star-forming galaxies \citep{wolfe04} while others do not appear to be heated by very nearby star-forming regions \citep{wolfe03}. Observations have suggested that DLA clouds can be expelled through galactic winds \citep{noterdaeme12}, while another proposition is that the low-metallicity of DLAs is indicative of aggregates of pristine gas rather than gas processed by stars \citep{bouche13,fukugita14}. In this paper, we will not make any assumptions regarding the structure of the stellar- and gas distribution within DLA galaxies. The morphology of low-redshift DLA galaxies comprise a wide selection of types: irregular, bulge-dominated, low-surface brightness galaxies while others are genuine galaxy spiral discs \citep{chen03}. In this paper, we simply refer to DLA clouds as belonging to halos or extended outskirts of DLA galaxies irrespectively of their origin. Whereas the success rate of identifying DLA galaxies at low redshift ($z<1$) is close to 50\% \citep{chen03,rao03,chen05,rao11}, only few spectroscopically confirmed DLA galaxies at $z>2$ have been reported. As the galaxies are expected to have faint continuum emission, several searches have aimed at discovering the \lya\ emission line from the DLA galaxies. However, there are more failed attempts to discover the DLA galaxies as the Lyman-$\alpha$ emission line is resonantly scattered and easily absorbed by dust \citep[e.g.][]{kulkarni06,christensen07}. Instead, searches for the \halpha\ emission line would not be as hampered by dust absorption, but observations have only revealed a few detections at $z\sim1$ and $z\sim2$, while more upper detection limits are reported \citep{peroux12,bouche12}. Even though the majority of DLA galaxies are low-mass and hence low-luminosity galaxies, \citet{moller04} suggested that targeting the more metal-rich DLAs would imply a higher chance of discovering the DLA galaxy. Indeed, this is confirmed by recent observations \citep{fynbo10,fynbo11,noterdaeme12,krogager13,fynbo13}. Since we now have a growing sample of DLA galaxies, the next step is to understand the relations between DLAs and the galaxies detected in emission. Such a correlation is predicted by simulations of DLA galaxies \citep{pontzen08}. Combining the observed velocity-metallicity relation of DLAs with the MZ scaling relation from luminosity selected galaxies \citep{maiolino08}, \citet[][hereafter M13]{moller13} derive an equation to compute stellar masses, $M_*$, of DLA galaxies: \begin{equation} \log(M_*/M_{\odot}) = 1.76(\mathrm{[M/H]} + C_{\mathrm{[M/H]}} + 0.35z + 5.04), \label{eq:pmfit} \end{equation} where [M/H] is the measured DLA absorption metallicity and $z$ is the redshift. The remaining coefficient, $C_{\mathrm{[M/H]}}$ is a parameter required to make the absorption- and emission-line metallicities consistent with each other. M13 report an intrinsic scatter of 0.38 dex in [M/H] in this relation for DLAs at $0<z<5$. The aim of this paper is to carry out a critical test of this statistically derived mass-redshift-metallicity relation (MzZ relation hereafter) via comparison to individual direct measurements. To do this, we derive stellar masses from conventional spectral energy distribution (SED) fits to multi-band photometry of the DLA galaxies. The structure of the paper is as follows. In Section~\ref{sect:sample} we describe the sample of confirmed DLA galaxies included in this investigation and present the photometry for these objects. Based on the photometry we fit SED models in Section~\ref{sect:SEDfits}. In Section~\ref{sect:results} we compare the measured stellar masses with predictions. We discuss the results in Section~\ref{sect:discussion} and present our conclusions in Section~\ref{sect:conclusions}. | \label{sect:conclusions} The long standing quest for the nature of DLA galaxies is finally nearing its conclusion. It was recently shown (M13) that the stellar mass of DLA galaxies can be computed from a simple relation depending only on the metallicity of the absorbing gas, the redshift, and a parameter, $C_{\mathrm{[M/H]}}$, which is the offset between metallicity measured from the absorbing DLA gas and that measured from emission lines of the same galaxy. The $C_{\mathrm{[M/H]}}$ parameter is in most cases not known, and in this paper we have addressed how it may be determined or estimated in cases where it cannot be measured directly. $C_{\mathrm{[M/H]}}$ could be a function of several properties of the DLA galaxy, but in particular one of those is an obvious candidate. From studies at low redshifts it is known that galaxies have metallicity gradients such that they in general have a higher metallicity in the centre and in the mean correspondingly lower metallicity at increasing distance from the centre. In this paper we have addressed two questions. Since the prescription for computing DLA stellar masses provided in M13 was derived on a purely statistical basis we first tested, via comparison to stellar masses determined directly from SED fits to photometric data, if the prescription is correct. As a byproduct of this test we also determined individual values of $C_{\mathrm{[M/H]}}$ for each DLA galaxy in our sample. Secondly we then tested if our sample showed any evidence for the expected signature of metallicity gradients. Our conclusions on those two tests can be summarised as follows: \begin{enumerate} \item Our independent test confirms the statistical MzZ relation reported in M13. We find a mean value $C_{\mathrm{[M/H]}} = 0.44\pm0.10$ with a scatter of $0.31$. In case nothing else than metallicity and redshift is known about a DLA galaxy then we recommend to use this value in combination with the M13 prescription. \item We also find that the data show a correlation between $C_{\mathrm{[M/H]}}$ and impact parameter similar to known metallicity gradients at low redshift. We find a best fit for a gradient $-0.022\pm 0.004$ dex~kpc$^{-1}$ in the entire range of redshifts $z=0.1$ to $3.2$. The sample is still very small, and because of the distribution of impact parameters and redshifts in our sample, one could also interpret the correlation as a redshift evolution of $C_{\mathrm{[M/H]}}$ without metallicity gradients. The redshift evolution interpretation is in conflict with results from several large independent surveys, while the metallicity gradient interpretation is favoured because metallicity gradients are well documented in the local universe and out to at least $z=1$. \item The residual internal scatter of the relation is significantly reduced (for the same number of fitted parameters) in the metallicity gradient formulation of the prescription. This is additional independent support that we are indeed measuring metallicity gradients in the DLA galaxies. \item The sample includes three sub-DLA systems. If we exclude those from the analysis, the results remain unchanged. This suggests that high-column density sub-DLAs follow the same relation as laid out by classical DLAs. \end{enumerate} Based on those results we have expanded the $C_{\mathrm{[M/H]}}$ parameter and presented an improved prescription as given in Eq.~\ref{eq:newfit}. We recommend to use this updated form of the relation in cases where the impact parameter is known, or where at least limits can be placed on it. | 14 | 4 | 1404.6529 |
1404 | 1404.4376_arXiv.txt | {Multi-level non-local thermodynamic equilibrium (NLTE) radiation transfer calculations have become standard throughout the stellar atmospheres community and are applied to all types of stars as well as dynamical systems such as novae and supernovae. Nevertheless even today spherically symmetric 1D calculations with full physics are computationally intensive. We show that full physics NLTE calculations can be done with fully 3 dimensional (3D) radiative transfer. } { With modern computational techniques and current massive parallel computational resources, full detailed solution of the multi-level NLTE problem coupled to the solution of the radiative transfer scattering problem can be solved without sacrificing the micro physics description. } { We extend the use of a rate operator developed to solve the coupled NLTE problem in spherically symmetric 1D systems. In order to spread memory among processors we have implemented the NLTE/3D module with a hierarchical domain decomposition method that distributes the NLTE levels, radiative rates, and rate operator data over a group of processes so that each process only holds the data for a fraction of the voxels. Each process in a group holds all the relevant data to participate in the solution of the 3DRT problem so that the 3DRT solution is parallelized within a domain decomposition group. } { We solve a spherically symmetric system in 3D spherical coordinates in order to directly compare our well-tested 1D code to the 3D case. We compare three levels of tests: a) a simple H+He test calculation, b) H+He+CNO+Mg, c) H+He+Fe. The last test is computationally large and shows that realistic astrophysical problems are solvable now, but they do require significant computational resources. } {With presently available computational resources it is possible to solve the full 3D multi-level problem with the same detailed micro-physics as included in 1D modeling.} | In a series of papers \citet*[][hereafter: Papers I--X]{3drt_paper1, 3drt_paper2, 3drt_paper3, 3drt_paper4, 3drt_paper5,3drt_paper7,3drt_paper8,3drt_paper9,3drt_paper10}, we have described a framework for the solution of the radiative transfer equation in 3D systems (3DRT), including a detailed treatment of scattering in continua and lines with a non-local operator splitting method. In \citet{3drt_paper6} we described tests of the 3D mode of the \phx\ model atmosphere code package. Here, we describe the implementation and the results of detailed multi-level non-local thermodynamic equilibrium (NLTE) \phxT\ calculations and compare the results to equivalent 1D calculations with \phxO\ models. We will first describe the method we have implemented and discuss differences to the 1D version, then we will show and discuss the results of simple test calculations. As 3D hydrodynamical calculations become more common, detailed radiative transfer effects due to the 3D structure will be needed in order to directly compare the predictions of hydrodynamic results with observations. 3D effects due to convective structure are known to be important in the sun and other stars \citep{hayek11,AGS02,AspIII00,ANTS00,ANTS99}. It is also known that NLTE effects can play an important role \citep{bergemann12}. This is also the case for brown dwarfs, irradiated planets, and circumstellar disks \citep{huegelmeyer09,wawrzyn09,witte11}. 3D radiative transfer effects play a role in interpreting the spectra of active stars \citep{berkner13}. In addition, 3D radiative transfer effects are important in the binary environment of Type Ia supernovae \citep{kasen_hole04,thomas02,kasen01el03} and in the disks of AGN. Here, we present results for the 3D spherical coordinate system mode of \phxT. However, the method is coordinate system indenpendent. | In this paper we discussed a method to solve 3D multi-level radiative transfer problems with detailed model atoms. The method is a direct extension of the well-tested method we are using for 1D model atmosphere calculations. We have implemented this NLTE/3D module for \phxT\ and discussed a small to very large test calculations for code testing and validation. The results show that the method performs in 3D exactly as the 1D equivalent. The NLTE problem in 3D poses significant demands on the computing resources, therefore we designed the module for distributed memory parallel processing (MPI) and to use domain decomposition methods to reduce the memory requirements per process. With this, it is technically possible to even solve 3D NLTE problems for complex ions, e.g., the iron group, if large supercomputers are used. | 14 | 4 | 1404.4376 |
1404 | 1404.3283_arXiv.txt | {Analyzing measurements of the LOPES antenna array together with corresponding CoREAS simulations for more than 300 measured events with energy above $10^{17}\,$eV and zenith angles smaller than $45^\circ$, we find that the radio wavefront of cosmic-ray air showers is of approximately hyperbolic shape. The simulations predict a slightly steeper wavefront towards East than towards West, but this asymmetry is negligible against the measurement uncertainties of LOPES. At axis distances $\gtrsim 50\,$m, the wavefront can be approximated by a simple cone. According to the simulations, the cone angle is clearly correlated with the shower maximum. Thus, we confirm earlier predictions that arrival time measurements can be used to study the longitudinal shower development, but now using a realistic wavefront. Moreover, we show that the hyperbolic wavefront is compatible with our measurement, and we present several experimental indications that the cone angle is indeed sensitive to the shower development. Consequently, the wavefront can be used to statistically study the primary composition of ultra-high energy cosmic rays. At LOPES, the experimentally achieved precision for the shower maximum is limited by measurement uncertainties to approximately $140\,$g/cm\textsuperscript{2}. But the simulations indicate that under better conditions this method might yield an accuracy for the atmospheric depth of the shower maximum, $X_\mathrm{max}$, better than $30\,$g/cm\textsuperscript{2}. This would be competitive with the established air-fluorescence and air-Cherenkov techniques, where the radio technique offers the advantage of a significantly higher duty-cycle. Finally, the hyperbolic wavefront can be used to reconstruct the shower geometry more accurately, which potentially allows a better reconstruction of all other shower parameters, too.} | \label{sec_introduction} At the current state of technical development, air showers are the only access to ultra-high-energy cosmic-ray physics. Radio measurements of air showers become effective at primary particle energies $\gtrsim 10^{17}\,$eV. Distinguishing different scenarios for the still unknown origin of ultra-high energy cosmic rays requires knowledge of the cosmic-ray composition at these energies. Measuring the longitudinal air-shower development is the presently best method for the reconstruction of the mass of the primary particles, since the shower development depends on a statistical basis on the mass of the primary particle: heavy nuclei interact on average earlier in the atmosphere than light nuclei. Thus, the air-shower development of heavy nuclei starts at a higher altitude, which leads to a lower atmospheric depth of the shower maximum, $X_\mathrm{max}$, i.e.~a larger distance to ground, and consequently causes different signatures in all secondary products (particles and radiation) of the air shower. Established methods for $X_\mathrm{max}$ measurements and the derived cosmic ray composition are the detection of air-fluorescence and air-Cherenkov light of air showers. However, these methods are restricted to dark nights and good weather conditions. The radio emission of air showers is also sensitive to the longitudinal shower development \cite{2012ApelLOPES_MTD}, and can be detected with a considerably higher duty-cycle of almost $100\,\%$. However, it still has to be demonstrated that the $X_\mathrm{max}$ precision of radio measurements can be competitive, not only for very dense antenna arrays like LOFAR \cite{BuitinkLOFARIcrc2013}, but also for sparser, large-scale arrays which can be built at reasonable costs. The origin of the radio emission of air showers is well described in other papers. For instance, recent overviews are available in Refs.~\cite{RevenuExperimentsOverview_ARENA2012, HuegeTheoryOverview_ARENA2012, HuegeIcrc2013}. At typical measurement distances up-to a few $100\,$m of the shower axis, the radio emission is coherent for frequencies in the order of $\lesssim 100\,$MHz. The dominant mechanism for the emission is the geomagnetic deflection of the secondary electrons and positrons in the air shower inducing time-varying transverse currents \cite{KahnLerche1966, FalckeGorham2003}, but also other effects play a role. In particular, the Askaryan effect \cite{Askaryan1962, AugerAERApolarization2014} is non-negligible, i.e., radio emission due to a time variation of the net charge in the shower. Moreover, the refractive index of the air influences the coherence conditions, which leads to observable effects in the lateral distribution of the radio amplitude \cite{Werner2012}, and also affects the radio wavefront. All these effects are included in the CoREAS \cite{HuegeCoREAS_ARENA2012} Monte-Carlo-simulation code used for this paper. Other contributions to the radio emission might exist, but have not yet been predicted or demonstrated to be significant. The results presented in this paper, are based on interferometric LOPES measurements and CoREAS simulations made for the measured events. LOPES is a first-generation digital antenna array which was operating from 2003 to 2013 at the Karlsruhe Institute of Technology (KIT), Germany. LOPES is limited in precision, in particular because of the limited size and the large radio background. Nevertheless, LOPES has the advantage that it is triggered by the co-located particle-detector array of the KASCADE-Grande experiment, which provides well-calibrated measurements of the same air shower. Consequently, LOPES is a pathfinder experiment to study the principles of the radio emission and to develop analysis techniques for the radio measurements. But, it is not a precision experiment, which already could compete with the precision of established techniques for air showers, like air-fluorescence, air-Cherenkov, or secondary particle measurements. Consequently, the focus of the present analysis is the principal dependencies of the radio wavefront on other shower parameters and the development of a specific method for $X_\mathrm{max}$ reconstruction. More detailed analyses aiming at higher accuracy can better be done by recently started antenna arrays, like LOFAR \cite{SchellartLOFAR2013}, AERA \cite{Melissas_ARENA2012} and Tunka-Rex \cite{TunkaRexRICAP2013}. The longitudinal shower development and, thus, $X_\mathrm{max}$ can be accessed from radio measurements in at least three different ways: First, the lateral distribution of the radio amplitude \cite{HuegeUlrichEngel2008, deVries2010, 2012ApelLOPES_MTD}. For showers with more distant shower maxima, the lateral distribution is flatter. Vice versa, for closer shower maxima the amplitude decreases faster with increasing distance to the shower axis. This method has recently been exploited for a first reconstruction of $X_\mathrm{max}$ based on measured LOPES events \cite{2014ApelLOPES_MassComposition}. Second, the slope of the frequency spectrum of the radio signal and the pulse shape depend not only on the distance to the shower axis, but also contain information on $X_\mathrm{max}$ \cite{Grebe_ARENA2012}. However, the applicability and achievable precision of this method has not yet been studied in detail. At LOPES, this method cannot be applied due to the strong radio background. Third, the shape of the radio wavefront depends on the longitudinal shower development. This has been theoretically studied earlier \cite{Lafebre2010}, and the present work brings significant news in several aspects. Newer simulations are used including all known, significant effects of the radio emission, and a new analytical description, namely the hyperbolic wavefront, is proposed. Moreover, for the first time, the wavefront is applied to measured data for the reconstruction of the shower maximum. In addition, the hyperbolic wavefront brings the benefit that the reconstructed shower geometry can be improved compared to spherical or plane wave assumptions. \begin{figure}[t] \centering \includegraphics[width=0.7\columnwidth]{wavefronts.eps} \caption{Comparison of a spherical, a conical, and a hyperbolic wavefront for typical parameters. While the spherical wavefront is a good approximation for the hyperbola close to the shower axis, the conical wavefront becomes a sufficient approximation at axis distances $d \gtrsim 50\,$m. The parameters $\rho$, $b$, and $\kappa$ are defined later by the equations in section \ref{section_AnalyticDescirption}.} \label{fig_wavefront_examples} \end{figure} | We presented a first systematic study of the radio wavefront of air showers based on LOPES measurements as well as CoREAS simulations made for the situation of LOPES, in particular its altitude, geomagnetic field, and effective bandwidth. The simulated wavefront shows a slight asymmetry, which probably is due to the interference of the geomagnetic and the Askaryan radio emission. Still, compared to the measurement uncertainties, the wavefront is sufficiently well described by a symmetric hyperboloid, which can be simplified to a cone for axis distances $\gtrsim 50\,$m. The cone angle $\rho$ depends in first order on the distance of the shower maximum and can be used to reconstruct $X_\mathrm{max}$. Following the prototype character of LOPES, we put the emphasis on outlining the principle dependencies and the potential of this method in its simplest form. Improvements are likely possible, and desirable to achieve the best accuracy for $X_\mathrm{max}$. At LOPES, however the accuracy is limited by large measurement uncertainties. Nevertheless, the CoREAS simulations indicate that the $X_\mathrm{max}$ precision could be competitive with the currently best methods, namely air-fluorescence and air-Cherenkov measurements, provided that the measurement uncertainties of the wavefront are small enough. Consequently, the prospects of the wavefront method for $X_\mathrm{max}$ reconstruction lies in its application at other radio arrays in environments with lower radio background, like AERA, Tunka-Rex and LOFAR. The improved knowledge on the radio wavefront is beneficial also in other aspects: Applying the hyperbolic wavefront improves the reconstruction of the shower geometry, in particular the arrival direction, and potentially also the shower core. Now, in contrast to the situation a few years ago, the reconstruction is no longer limited by the missing knowledge of the correct wavefront \cite{NiglDirection2008}. Moreover, based on our measurements of the cone angle, it is possible to estimate what the impact of a simplified wavefront in the radio reconstruction would be. For example, in a plane wave reconstruction, the typical error on the arrival direction would be in the order of $\rho$, i.e., for LOPES in the order of $1^\circ$, and even larger for radio arrays at higher altitudes, since they are closer to the shower maximum. Consequently, we consider the improved description of the wavefront an important input for any future radio measurements of air showers when aiming at highest possible precision. | 14 | 4 | 1404.3283 |
1404 | 1404.3760_arXiv.txt | We present $JHK$ near-infrared (NIR) spectroscopy of 25 candidate Type II quasars selected from the Sloan Digital Sky Survey, using Triplespec on the Apache Point Observatory 3.5m telescope, FIRE at the Magellan/Baade 6.5m telescope, and GNIRS on Gemini. At redshifts of $ 2 < z < 3.4$, our NIR spectra probe the rest-frame optical region of these targets, which were initially selected to have strong lines of \ion{C}{4} and Ly~$\alpha$, with FWHM$<$2000~\kms\ from the SDSS pipeline. We use the \oiii$~\lambda 5007$ line shape as a model for the narrow line region emission, and find that \halpha\ consistently requires a broad component with FWHMs ranging from 1000 to 7500~\kms. Interestingly, the \ion{C}{4} lines also require broad bases, but with considerably narrower widths of $1000$ to $4500$~\kms. Estimating the extinction using the Balmer decrement and also the relationship in lower-$z$ quasars between rest equivalent width and luminosity in the \oiii\ line, we find typical $A_V$ values of $0-2$ mag, which naturally explains the attenuated \ion{C}{4} lines relative to \halpha. We propose that our targets are moderately obscured quasars. We also describe one unusual object with three distinct velocity peaks in its \oiii\ spectrum. | \label{sec:Introduction} A major stumbling block to understanding the accretion history of supermassive black holes (BHs) over cosmic time is determining the role of obscuration in the demographics of active galactic nuclei (AGN). Optical surveys are quite successful at finding luminous blue (unobscured Type I) quasars \citep[e.g.,][]{richardsetal2006,rossetal2013}, but are not sensitive to truly obscured (or Type II) quasars, where the quasar continuum and broad emission lines are completely hidden. Sensitive 0.5-10 keV X-ray surveys can find modestly obscured systems, but typically cover a limited solid angle, and thus are not sensitive to rare luminous objects \citep[e.g.,][]{brandthasinger2005,gillietal2007,xueetal2012, georgantopoulosetal2013}. Similar caveats apply to mid-infrared (MIR) selection using \spitzer\ \citep[e.g.,][]{lacyetal2004,sternetal2005,donleyetal2008, donleyetal2012,lacyetal2013}, while \emph{WISE} can unambiguously select only the most luminous AGN \citep[e.g.,][]{sternetal2012,assefetal2013, yanetal2013}. Many X-ray--based studies indicate a decreasing obscured fraction as a function of luminosity over a broad redshift range \citep[e.g.,][]{steffenetal2003,hasinger2008}, but at low redshift ($z < 0.8$), luminous optically selected samples suggest comparable numbers of obscured and unobscured systems \citep{reyesetal2008}. At high redshifts, at the peak of quasar activity ($z \simeq 2-3$), demographics are even more uncertain and a large-area survey of luminous obscured quasar activity is required to determine the obscured fraction. Although unified theories state that Type~I and Type~II quasars differ only in orientation \citep[e.g.,][]{antonuccimiller1985,antonucci1993,urrypadovani1995}, there are many hints that Type II quasars may represent a special phase in the growth of black holes. There have been numerous suggestions, both observational \citep[e.g.,][]{sandersetal1988,canalizostockton2001,pageetal2001,ho2005, stevensetal2005,veilleuxetal2009} and theoretical \citep[e.g.,][]{hopkinsetal2006}, that major galaxy mergers trigger an obscured phase of central BH growth. This obscured phase persists until the AGN grows powerful enough to expel all remaining gas out of the surrounding galaxy, leading to an optically luminous quasar phase. Samples of Type I quasars with moderate extinction hosted by merging galaxies provide some support for this scenario \citep[e.g.,][]{urrutiaetal2008}. Again, larger homogeneous samples of obscured quasars, at the peak epoch of BH growth, are needed to statistically address the growth phase of these objects. Finally, some obscuration may occur in a torus near the AGN, while some may be due to galaxy-scale dust \citep{rigbyetal2006}. The torus geometry or porosity may also depend on luminosity \citep[e.g.,][]{steffenetal2003,assefetal2013}. Larger samples of luminous obscured quasars could address the full distribution of obscuration as a function of bolometric luminosity. To date, Type II samples at high redshift number in the tens, including targets selected in the radio \citep[e.g.,][]{mccarthy1993,urrypadovani1995,sternetal1999}, X-ray \citep{normanetal2002,sternetal2002,bargeretal2003,iwasawaetal2012}, mid-infrared \citep{lacyetal2004,sternetal2005,donleyetal2012,eisenhardtetal2012,assefetal2013, lacyetal2013} and optical \citep{steideletal2002,bongiornoetal2010,hainlineetal2012, mignolietal2013}. \vbox{ \vskip +2mm \hskip -3mm \includegraphics[scale=.5,angle=0]{f1.pdf} \figcaption{ Redshift vs. $z-$band magnitude for the Alexandroff et al. Class A objects (open) and the sample spectroscopically targeted in the NIR (blue squares). Shaded bands indicate redshift regions where strong rest-frame optical emission lines fall in atmospherically transparent regions of the spectrum. Our spectroscopic subsample is representative of the full distribution. \label{fig:redshiftmag}} } \vskip 5mm \noindent The operational definition of obscured quasar depends on the selection technique. The typical X-ray definition of \ion{H}{1} column density $N_H > 10^{22}$ cm$^{-2}$ \citep[e.g.,][]{uedaetal2003} apparently corresponds to an $A_V \approx 0.47$ in AGN \citep{maiolinoetal2001,assefetal2013}. In contrast, optically selected Type II Seyfert galaxies typically have $A_V > 10$ \citep[e.g.,][]{veilleuxetal1997,zakamskaetal2005}. Finally, near-infrared selection criteria yield moderately reddened quasars with broad \halpha\ and typical $A_V \sim 0.3-6$ \citep[e.g.,][]{banerjietal2012, glikmanetal2012}. In this paper, we focus on Type II candidates selected in the rest-frame UV, to explore the $A_V$ distribution of objects selected on the basis of narrow UV emission lines. Low-redshift ($z < 0.8$) Type II quasars were successfully discovered in large numbers in the Sloan Digital Sky Survey \citep[SDSS; ][]{yorketal2000} based on their strong and narrow \oiii$~\lambda 5007$\AA\ emission \citep{zakamskaetal2003,reyesetal2008}, and subsequently shown to be bona fide obscured quasars \citep{zakamskaetal2005,zakamskaetal2006,zakamska08}. Not until the Baryon Oscillation Spectroscopic Survey \citep[BOSS;][]{eisensteinetal2011,dawsonetal2013}, which spectroscopically targeted quasars down to a magnitude limit of $g < 22$ or $r < 21.85$ \citep{rossetal2012}, did it become possible to select Type II quasar candidates with $z > 1$ with the SDSS. In \citet[][hereafter Paper I]{alexandroffetal2013} and this work, high redshift Type II quasar candidates are identified based on the presence of strong and narrow high-ionization lines in their rest-frame UV spectra (e.g., \ion{C}{4}). In Paper I, we presented a sample of 145 Type~II quasar candidates selected from the BOSS survey based on their narrow ($< 2000$~\kms) \ion{C}{4} and Ly $\alpha$ emission. The narrow linewidths and high rest equivalent widths (EWs) of the sample objects bear strong resemblance to those of other samples of Type II quasars. Furthermore, in the two objects we observed with a spectropolarimeter, we detected continuum polarization of $\sim 3\%$, inconsistent with typical unobscured quasars. On the other hand, our BOSS Type II quasar candidates are too luminous and blue in the UV continuum to be explained by galaxy light alone. They have typical rest-frame UV continuum luminosities of $-24$ AB mag at 1450~\AA, as compared to magnitudes of $\sim -22.5$ AB mag \citep{okegunn1983} for the most luminous UV-selected galaxies at similar redshifts \citep{shapley2011}. The AGN must contribute some UV light, whether it be directly transmitted or due to scattered light. Furthermore, the UV line ratios are more akin to Type I rather than Type II objects. Finally, in one object with broad spectral energy distribution (SED) coverage, the optical/UV is weaker than seen in typical Type I objects indicating some obscuration, but more prominent than in typical Type II objects. In the same sense, the optical/NIR colors of our Type II candidates are similar to unobscured quasars. Thus, based on the rest-frame UV spectra alone, it is difficult to determine the true nature of these sources. \begin{figure*} \vbox{ \vskip -8mm \hskip +25mm \includegraphics[scale=.8,angle=0]{tablesamplev3.pdf} } \vskip -0mm \label{tab:sample} \end{figure*} Here, we present NIR spectroscopy that probes the rest-frame optical spectra of 25 of the Type~II quasar candidates presented in Paper I. We use three NIR echellettes, Triplespec \citep{tspec2004} on the 3.5m at Apache Point Observatory (APO), the Folded-port InfraRed Echellette \citep[FIRE;][]{simcoeetal2013} at Magellan, and Gemini Near Infrared Spectrograph \citep[GNIRS;][]{eliasetal2006} on Gemini North, all three of which afford us $JHK$ spectroscopy in a single observation. We simultaneously measure \hbeta, \halpha, and the strong and ubiquitous \oiii$~\lambda 5007$ line in the majority of our targets. The \oiii\ line luminosity is known to correlate with the intrinsic luminosity of the quasar \citep{yee1980,heckmanetal2004,liuetal2009}, while the strength and width of the Balmer lines provide new insight into the level and scale of the extinction. Finally, the \oiii\ line shape unambiguously traces the low-density (narrow-line region) gas kinematics, and thus allows us to characterize any additional (broader) components in the permitted lines. In fact, we specifically targeted two galaxies with multiple velocity peaks in the \ion{C}{4} and/or \lya\ line (Paper I), to determine whether the peaks are caused by absorption or real kinematic structure in the gas. \begin{figure*} \vbox{ \vskip 0mm \hskip +10mm \includegraphics[scale=.75,angle=90]{f2.pdf} } \vskip -0mm \figcaption[]{The top three rows show fits to the [O {\tiny III}], \halpha, and C~{\tiny IV} regions of all five of the Magellan spectra with \halpha\ in the spectral region, while the C~{\tiny IV} is from the SDSS spectra. In the bottom row, we present the three higher redshift targets for which \halpha\ was not observed. The original spectra are binned by three pixels (thin black solid lines), and our best overall model fit (thick blue, red, or magenta solid lines for [O {\tiny III}], \halpha, and C~{\tiny IV} respectively), and when present the broad components are shown offset for clarity (thick dotted lines). In the fits to the \halpha\ and C~{\tiny IV} regions, the narrow component is constrained to match the [O {\tiny III}] model shape. The dashed vertical lines indicated the regions that were masked in fitting C~{\tiny IV}. See \S \ref{sec:Fitting} for details. \label{fig:nirfits}} \end{figure*} The paper proceeds as follows. In \S \ref{sec:Observations} we present properties of the sample and details of the observations. In \S \ref{sec:Reductions} we discuss the data reduction, while in \S \ref{sec:Fitting} we outline our line-fitting technique. We present our results in \S \ref{sec:Results}, and discuss the implications for obscured quasars in \S \ref{sec:Discussion}. We assume a concordance cosmology with H$_0 = 70$~\kms~Mpc$^{-1}$, $\Omega_{\rm M} = 0.3$, and $\Omega_{\rm M} = 0.7$ \citep{dunkleyetal2009}. \begin{figure*} \vbox{ \vskip 0mm \hskip +15mm \includegraphics[scale=.75,angle=90]{f3.pdf} } \vskip -0mm \figcaption[]{ Same as Figure \ref{fig:nirfits} above, but for twelve galaxies observed with APO/Triplespec. We show the original spectra in units of $10^{-17}$~erg~s$^{-1}$~cm$^{-2}$~\AA$^{-1}$ (thin black solid lines), our best overall model fit (thick blue solid lines), and when present the broad components are shown offset for clarity (thick dotted lines). In the case of the \halpha\ and C~{\tiny IV} regions, the narrow component is constrained to match the [O {\tiny III}] model shape. The dashed vertical lines indicated the regions that were masked in fitting C~{\tiny IV}. See \S \ref{sec:Fitting} for details. \label{fig:nirfitsAPO}} \end{figure*} | \label{sec:Discussion} We started with a sample of Type II quasar candidates selected from BOSS, with relatively narrow and high-EW \ion{C}{4} emission lines. In this paper we present NIR spectroscopy in the $JHK$ bands, covering \hbeta\ and \oiii\ emission in all cases, and \halpha\ in most. Our primary motivation is to investigate the nature of these targets, specifically whether they are in fact obscured quasars. Overall, our analysis points to a population of moderately obscured ($A_B \sim 0-3$ mag) quasars powered by $\sim 10^9$~\msun\ BHs radiating at a healthy $\sim 10\%$ of their Eddington limits. From Paper I, we know that our quasar targets have UV luminosities that are too high to be described by star formation alone. On the other hand, we did detect polarization at the level of $\sim 3\%$ in the two observed targets (Paper I), larger than the $0.5\%$ typical of unobscured quasars \citep{berrimanetal1990}. Furthermore, we see evidence that the UV luminosities are somewhat suppressed, in the broad-band SED of SDSS J0958+0135 presented in Paper I and also in the low ratio of UV to \emph{WISE} luminosity (Figure \ref{fig:wiselum}). Thus, the continuum measurements support a moderate-obscuration scenario. We use multiple techniques to estimate the level of extinction. The narrow-line equivalent widths point to modest extinction; in general \oiii\ has higher EW than a typical unobscured quasar, but not as high as the locus of Type II quasars at $z \approx 0.5$ \citep{zakamskaetal2003}. Turning the observed EW discrepancy into an estimate of the extinction produces $0 < A_B < 3$ mag or $A_V \approx 0-2.2$ mag. Based on this $A_B$, the intrinsic UV luminosities would be boosted by $0.5 -1 $ dex. We also estimate the extinction using the non-detection of broad \hbeta, and find rough agreement with the reddening estimates based on \oiii\ EW. The broad permitted line widths are also consistent with a moderate-obscuration scenario. Specifically, we detect significant broad emission lines in \halpha\ with line widths ranging from $1000$ to $7500$~\kms. In the UV, on the other hand, the \ion{C}{4} line fluxes are fainter than expected based on \halpha\ (assuming an SMC extinction law), and show considerably narrower widths, ranging only from $1000$ to $4500$~\kms. Of course, by originally selecting narrow \ion{C}{4} lines, we naturally identified targets at one extreme end of the line-width ratio distribution. At least part of the broad emission lines in the UV are likely unobservable due to extinction. Whether the broadest components are preferentially obscured, leading to the narrow line widths, or whether we simply lack the S/N to find the extended (faint) broad wings is difficult to determine from these data. However, at least part of the broad-line region is directly transmitted in the UV. This broad component in \ion{C}{4} also explains the low ratios of \ion{He}{2} to \ion{C}{4} reported in Paper I, which are consistent with broad-line rather than narrow-line objects \citep[e.g.,][]{nagaoetal2006}. The targets presented here display broad \halpha, and thus do not obey classic definitions of Type~II active nuclei \citep[e.g.,][]{khachikyanweedman1971}. Furthermore, in general, the extinction associated with classical, optically selected Type~II sources is larger than measured here. For lower luminosity Seyfert galaxies, $A_{\rm V}$ has been estimated using the ratios of Pa$\alpha$ to \halpha, with values of more than 10 being common \citep[e.g., ][]{rixetal1990,goodrichetal1994,veilleuxetal1997}. In Type II quasars at $z \approx 0.5$, the weak continuum and lack of strong NIR emission suggests $A_{\rm B}> 13$ \citep{zakamskaetal2005}. At more comparable redshifts to our targets, composite spectral energy distribution modeling of Type II AGN with a galaxy+AGN template yields similarly high values of $A_B > 13$ in most cases \citep[e.g.,][]{hickoxetal2007,mainierietal2011,hainlineetal2012, assefetal2013,lussoetal2013}. The obscuration levels reported here, in contrast, are comparable to those seen in so-called ``Seyfert 1.8'' galaxies \citep[e.g.,][]{osterbrock1981,rixetal1990}, and the large ratios of narrow-to-broad line FWHM seen in \halpha\ are also characteristic of this moderately obscured class. A more luminous population with interestingly similar characteristics are ``red quasars,'' selected as Type~I reddened quasars in the rest-frame optical/NIR \citep[e.g.,][]{glikmanetal2007,urrutiaetal2009,urrutiaetal2012,banerjietal2012, glikmanetal2013,banerjietal2013}. When selected in the rest-frame optical/NIR, such objects make up $\sim 20\%$ of the quasar population \citep[][]{glikmanetal2012,elitzur2012}. Like our targets, these so-called red quasars have moderate extinction, $A_V \approx 0.3-4.5$ mag, such that broad \halpha\ is observed. Our targets are typically more luminous in \emph{WISE} by at least an order of magnitude than those in \citet{glikmanetal2012}, but are also typically found at higher redshifts. The Banerji objects are selected from deeper NIR photometry and thus comprise somewhat more extincted ($A_V \approx 2-6$ mag) and more intrinsically luminous objects (by factors of a few) at comparable redshifts to ours. Eventually we will be able to compare these samples in the rest-frame UV as well (Glikman, private communication). Sources selected in the mid-IR \citep[e.g.,][]{deyetal2008,sternetal2012,assefetal2013} tend to be factors of a few more luminous in the MIR and redder than our rest-frame UV selected sample \citep[e.g.,][]{wujetal2012}. A few quasars with similarly moderate extinction inferred from the rest-frame optical/UV have also been uncovered in X-ray surveys, sometimes with significant obscuring columns in the X-ray \citep[e.g.,][]{almainietal1995,georgantopoulosetal1999,georgantopoulosetal2003, piconcellietal2005}. X-ray spectroscopy of some of our quasars would allow the relative levels of X-ray and optical/UV obscuration to be assessed. Substantial apparent differences between such obscuration levels are often found, likely owing to the presence of some X-ray absorption within the dust-sublimation radius \citep[e.g.,][]{maiolinoetal2001}. Obviously, each selection method imposes a preferred distribution of reddening and luminosity on the final sample. \citet{assefetal2013} have recently measured a distribution of $E(B-V)$ for luminous \emph{WISE}-selected quasars at $z < 1$. Interestingly, they find two natural breaks in the distribution. The first is at $E(B-V) \approx 0.15, A_V \approx 0.5$ mag, corresponding roughly to the sources observed here. They find a second transition at $E(B-V) \approx 2, A_V \approx 6$ mag. They postulate that the moderate extinction may arise on galaxy-wide scales while the second transition is due to the orientation of a dusty torus in the nucleus. Perhaps our \hst\ imaging will allow us to distinguish these two scenarios for our candidates (Strauss et al. in prep.). Taken altogether, our observations paint a nuanced picture of a mildly-obscured population of high-redshift quasars selected with the BOSS survey. How they fit into the broader picture of quasar demographics at this epoch remains to be seen. As a class of objects with obscuration intermediate between Type~I and Type~II sources, they may be at intermediate orientation in a unification picture, or just result from a patchy torus \citep[e.g.,][]{elitzur2012}. Alternatively, the host galaxy may provide some large fraction of the obscuration, in an evolutionary picture \citep[e.g.,][]{sandersetal1988,lacyetal2007,hopkinsetal2006}. We may hope to get some clues to their star formation properties from higher S/N NIR spectra. We also have many more BOSS targets to study; the sample properties of the targets presented in Paper I are heterogeneous, and the faintest targets may yet harbor some bona-fide Type II quasars. We are also planning to obtain uniform NIR imaging, to preferentially select the faintest targets in the rest frame optical, which are most likely to be heavily obscured. Combining broad-band SED fitting, \hst\ imaging, spectropolarimetry, and more NIR spectroscopy, may provide a more complete picture of the nature of these enigmatic targets. | 14 | 4 | 1404.3760 |
1404 | 1404.5004.txt | We studied the temporal evolution of the magnetic topology of the active region (AR) 11158 based on the reconstructed three-dimensional magnetic fields in the corona. The \nlfff\ extrapolation method was applied to the 12 minutes cadence data obtained with the \hmi\ (HMI) onboard the \sdo\ (SDO) during five days. By calculating the squashing degree factor Q in the volume, the derived quasi-separatrix layers (QSLs) show that this AR has an overall topology, resulting from a magnetic quadrupole, including an hyperbolic flux tube (HFT) configuration which is relatively stable at the time scale of the flare ($\sim 1-2$ hours). A strong QSL, which corresponds to some highly sheared arcades that might be related to the formation of a flux rope, is prominent just before the M6.6 and X2.2 flares, respectively. These facts indicate the close relationship between the strong QSL and the high flare productivity of AR 11158. In addition, with a close inspection of the topology, we found a small-scale HFT which has an inverse tear-drop structure above the aforementioned QSL before the X2.2 flare. It indicates the existence of magnetic flux rope at this place. Even though a global configuration (HFT) is recognized in this AR, it turns out that the large-scale HFT only plays a secondary role during the eruption. In final, we dismiss a trigger based on the breakout model and highlight the central role of the flux rope in the related eruption. | It has been widely accepted that the different behaviors of the solar atmosphere in response to the plasma motions and instabilities are intensely related to the different topologies of the coronal magnetic field \citep{Berger1991}.Null points, separatrices and separators, where the connectivity of the magnetic field line is discontinuous, are classic topological structures that are preferential for the formation of electric current and the occurrence of energetic event. Flares and coronal mass ejections (CMEs) are the most energetic events taking place in the solar atmosphere and the energy needed to power them originates from the magnetic field in the corona. Some flares happen with null points in their associated magnetic configurations \citep[e.g.,][]{Aulanier2000,Demoulin2000,Manoharan2005,Jiang2013b} while others without any coronal null points \citep[e.g.,][]{Li2006b,Mandrini2006,Schmieder2007b,Chandra2011}. The concept of null point as well as separatrix has been extended to quasi-separatrix layer (QSL) in the last two decades \citep[see review by][and references therein]{Demoulin2006}. QSLs are defined as 3D magnetic volumes with very sharp gradients of magnetic field connectivity \citep[e.g.,][]{Demoulin1996a,Titov2002} QSLs are preferential sites for the build-up of electric currents and the development of magnetic reconnection \citep[e.g.,][]{Galsgaard2003,Aulanier2005,Pariat2006,Masson2009,Guo2013}. Narrow current sheets form dynamically in non-potential magnetic field and are responsible for flaring activity \citep{Aulanier2005}. Magnetic quadripolar configuration can enclose an hyperbolic flux tube (HFT) \citep{Titov2002}, which is a particular subdomain of the QSL and located at the intersection of several QSL branches. The HFT generalize the concept of magnetic separator. QSLs, especially the HFTs, are central in the flaring processes of AR \citep{Titov2002}. Multiple types of boundary motions can induce the spontaneous formation of strong currents layers at QSLs \citep{Demoulin1996a} which can induce reconnection when the current sheet width reach the dissipative scales \citep{Aulanier2005}. Magnetic pinching due to large-scale shearing motion at the photospheric footpoints of an HFT also causes the effective growth of current density in the HFT \citep{Titov2003}. Unlike reconnection happening at a 2D null point, where field lines reconnect in pair and change their connectivities suddenly, 3D reconnection at a QSL induce a continuous exchange of connectivity \citep{Aulanier2006}. Neighbouring field lines continuously exchange their connectivities within the QSL current sheet which induce an apparent slipping motion of the field lines relatively to each other \citep[see also][]{Aulanier2007,Torok2009,Masson2009,Masson2012}. As reconnection occurs in the QSLs, particles accelerated by reconnection are flowing within the QSLs and therefore flare ribbons are expected to be cospatial with the photospheric footprints of the QSLs \citep[e.g.,][]{Demoulin1997}. Many observational studies have analyzed the intersection of the QSLs and the photosphere, and compared them to flare ribbons, providing indirect evidence of magnetic reconnections as the triggering mechanism of solar eruptive events \citep[][]{Schmieder1997,Mandrini1997,Mandrini2006,Masson2009,Chandra2011} CMEs may severely affect the space environment and have been extensively studied both in theories and observations \citep[see review by][]{Forbes2006}. Reviews about the CME trigger processes can be found in \citet{Aulanier2013}. Three kinds of CME models have been generally accepted so far: the \lq\lq magnetic breakout\rq\rq model \citep{Antiochos1999,Chenpf2000}, the \lq\lq tether-cutting\rq\rq model \citep{Moore1980,Moore2001,Lynch2004} and the \lq\lq flux rope\rq\rq models \citep[]{Forbes1991,Amari2000,Amari2004}. All these models have received various observational confirmations \citep[e.g.,][]{Aulanier2000,Guo2010,Guoyang2012,Chengxin2013a}. Each of these models requires a current carrying structure, an ensemble of field lines storing non-potential energy, e.g., a twisted magnetic flux rope, or a sheared magnetic arcades system. While the current carrying structure is the only requirement for the \lq\lq flux rope\rq\rq models, the other models require other type of topological configurations and are therefore not completely equivalent. The \lq\lq tether-cutting\rq\rq model involves magnetic reconnection bellow the current carrying structure. Therefore a topological structure that would allow current build-up, such as separatrices or QSLs, shall be placed bellow the current carrying structure. On the other hand, the \lq\lq magnetic breakout\rq\rq model requires the development of reconnection above or on the side of the current structure in order to partially open the magnetic configuration for the flux rope to erupt. Hence it requires the existence of overall global topological structure located above the non-potential structure. While in the original study a 2D null point was invoked, such topological structure could also be a separator or an HFT. Observationally, active region generally presents multiple topological structures that can be consistent with different models. Several studies have addressed the specific topologies associated to diverse eruption models \citep[e.g.,][]{Ugarte2007,Aulanier2000,Guo2010,Guoyang2012,Chengxin2013a}. All these works usually only focus on one particular time of the pre-flare topology. However, null points, separators, QSLs and HFTs do not magically appear in active regions. They are the consequence of the construction of the active region induced by flux emergence and by reconfiguration with the surrounding coronal field. Several numerical simulations have focus on the formation of these structures \citep[][]{Torok2009, Archontis2005, Galsgaard2007, Moreno-Insertis2013}. However, they are all based on an idealized magnetic configuration, which is a simplification of the real condition and can hardly represent the realistic magnetic field. To reveal the real procedure in solar atmosphere, data-driven simulation based on the photospheric magnetograms from observations has been suggested in \citet{Fanyl2011} (also see in \citet{Cheung2012,Jiangchaowei2012,Jiang2013b}). In the present study, we use a static approach by reconstructing magnetic field in the corona from the observations in the photosphere at different times before the flare. This work is a first attempt to follow the evolution of the topology of an active region in time, by computing time series of QSLs map from successive magnetic field extrapolation. Our target is the NOAA 11158 active region, which has been remarkable for being the source of multiple violent active events. It has been extensively studied in various aspects, such as the sunspot motions \citep{Jiangyunchun2012}, the magnetic non-potentiality increase \citep{Vem2012}, its formation, and flare-associated magnetic field changes (like during the M6.6 and X2.2 class flares, see in Figure 1) \citep[][]{Liuchang2012,Wangshuo2012,Petrie2012,Gosain2012}. However, the topology evolution has not been really followed even though \citet[]{Dalmasse2013} showed the existence of different quasi-separatrices. We focus on the topological analysis of AR 11158 during 3 days before the X2.2 flare and one day after it in this work. It is the first attempt to use a set of static topology analysis to study the evolution of the magnetic topology of an active region, which benefits from the 12 minutes cadence of the HMI vector magnetograms. Observations and data reduction, including non-linear force-free field (NLFFF) extrapolation method, are presented in Section 2. In Section 3, we introduce the method used to calculate $Q$ values and our results. We give our summary and discuss the physical issues of QSLs in Section 4. | In this paper, we conducted topological analysis of AR 11158 based on the computed $Q$ values. The findings are summarized and discussed as follows: Based on the vertical cuts of $Q$ maps perpendicular to the X- and Y-axis, we describe the main topology of AR 11158 at 23:58 UT on 14 February as an HFT configuration, which is the typical topological structure of a quadrupole. This configuration is similar to the ideal result obtained by \citet{Titov2002}, i.e.,\ two quasi-separatrix domes crossing each other in the corona. Some other structures also appeared beside the main HFT configuration, as a result of the complex connectivity of observed magnetic field, which are not identified in the magnetic configuration of the modeled point-like sources. From the temporal series of $Q$ maps in 3D, we noticed that the quadrupole is relatively stable and lasted for at least 36 hours, starting from 11:58 UT on 13 February, which was there even during the large flares. From the photospheric traces of the HFT configuration (Figure \ref{fig04}), we see that two main QSLs (D1 and D2) are stable since 11:58 UT on 13 February. An elongated QSL Q0 (marked by yellow arrows in Figure \ref{fig04} (d)), which is always located in the vicinity of the PIL, is considered to be related to the high activity of AR 11158. From the coronal traces of the HFT configuration (Figure \ref{fig05}), large-scale HFT always exists (before 11:58 UT on 15 February) and is stable for 36 hours since 11:58 UT on 13 February. \citet{Titov2003} also studied this kind of large-scale HFT structure and suggested that the magnetic pinching inside caused by the large-scale shearing motion on the photosphere could produce a large flare. However, in our case, there is no large flare directly related to this HFT. The possible reconnection at this place may induce the UV enhancement at the intersection of HFT and the photosphere (i.e.,\ D1 and D2), which were not identified in the beginning of the flare in our observation. Hence, QSLs D1 and D2 are not activated during the X2.2 class flare. Some brightening appears at the end of the flare along QSL D2, indicating reconnection eventually happened at the large-scale HFT. It is possibly induced by the interaction between the erupting flux rope and the HFT. The evolution of the emerging flux region and the initiation of eruption has been investigated through MHD simulations with modeled magnetic configuration which is a simplification of real observation. With photospheric magnetograms, the data-driven MHD simulations may give a more realistic result. To the best of our knowledge, our work is probably the first investigation of the topological evolution of emerging flux region from observation. We also investigated the QSLs related to the X2.2 class flare, which is the first X-class flare in solar cycle 24. From the $Q$ map in the photosphere at 23:58 UT on 14 February, a strong QSL (Q0) exists between P1 and N2, which corresponds to some highly sheared structures that include the twisted flux rope (i.e.,\ field lines in green and yellow in Figure \ref{fig07}) as well as the short sheared arcades (i.e.,\ field lines in blue in Figure \ref{fig07}). From the evolution of the photospheric traces of the magnetic topology (see in Figure \ref{fig08}), the shape of the QSLs which are located around the footpoints of the twisted flux rope changes drastically around the flare time, indicating that the eruption involves these field lines. A small-scale HFT, which has an inverse tear-drop shape and is about 0.4 Mm above the photosphere, appears 2 hours or even longer before the flare. The inverse tear-drop structure disappears just after the flare peak, which confirms the eruption of the twisted flux rope. The remained QSLs after the flare probably correspond to sheared arcades with very low height. \citet{Savcheva2012a} also found an HFT structure with a height of around 3 Mm under a long-lasting sigmoid, which exists for several hours before the eruption. Investigation of coronal flux rope formation mechanism and eruption through MHD simulations suggested the formation of an HFT before eruption \citep{Aulanier2010}. The flare ribbons in the 304 \AA\ image at 01:50 UT on 15 February (six minutes after the flare onset) are located on both sides of QSL Q0 and between the two QSLs (D1 and D2). This manifests that the ribbons are initially involve QSL Q0 while D1 and D2 are not activated during the flare. According to previous studies \citep{Demoulin1997,Mandrini1997,Bagala2000,Masson2009}, the UV flare ribbons are usually located next to, or along the chromospheric traces of QSLs. The different locations referring to the closest QSLs may be caused by the separating motion of ribbons, as they expand after the flare onset \citep[e.g.,][]{Aulanier2012}. However, the ribbons will be confined inside the closest large-scale QSLs \citep{Chenpf2012,Guoyang2012}. In our observation, the flare ribbons stopped at the photospheric traces of the large-scale HFT (i.e.,\ D1 and D2). In this study, we have obtained two HFT structures in our extrapolation, the large-scale one is in the corona while the small-scale one is in the chromosphere. There is no evidence for the strong current formation in the large-scale HFT before the X2.2 flare since no corresponding brightenings are found at the photospheric traces of this HFT before the flare. Besides, the large-scale HFT remains relatively stable while the small-scale flux rope associated HFT changes drastically around the flare. Hence, this large-scale HFT may only play a secondary role in the eruption. While our investigation would dismiss a trigger based on the breakout model, the precise identification of the trigger mechanism as well as the flux rope formation goes beyond the present study. Our topological analysis however clearly identifies a twisted flux rope priori to the flare which disappears after and which is related to the initial flare ribbons. The trigger is therefore likely to involve this particular twisted flux rope. | 14 | 4 | 1404.5004 |
1404 | 1404.2599_arXiv.txt | Damped Ly$\alpha$ absorbers (DLAs) are a well-studied class of absorption line systems, and yet the properties of their host galaxies remain largely unknown. To investigate the origin of these systems, we have conducted an imaging survey of 32 quasar fields with intervening DLAs between $z\sim 1.9-3.8$, leveraging a technique that allows us to image galaxies at any small angular separation from the background quasars. In this paper, we present the properties of the targeted DLA sample, new imaging observations of the quasar fields, and the analysis of new and archival spectra of the background quasars. | 14 | 4 | 1404.2599 |
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1404 | 1404.0887_arXiv.txt | The most promising near-term observable of the cosmic dark age prior to widespread reionization ($z\sim15-200$) is the sky-averaged $\lambda21$\,cm background arising from hydrogen in the intergalactic medium. Though an individual antenna could in principle detect the line signature, data analysis must separate foregrounds that are orders of magnitude brighter than the $\lambda21$\,cm background (but that are anticipated to vary monotonically and gradually with frequency, e.g., they are considered ``spectrally smooth"). Using more physically motivated models for foregrounds than in previous studies, we show that the intrinsic spectral smoothness of the foregrounds is likely not a concern, and that data analysis for an ideal antenna should be able to detect the $\lambda21$\,cm signal after subtracting a $\sim 5^{\rm th}$ order polynomial in $\log \nu$. However, we find that the foreground signal is corrupted by the angular and frequency-dependent response of a real antenna. The frequency dependence complicates modeling of foregrounds commonly based on the assumption of spectral smoothness. Our calculations focus on the Large-aperture Experiment to detect the Dark Age (LEDA), which combines both radiometric and interferometric measurements. We show that statistical uncertainty remaining after fitting antenna gain patterns to interferometric measurements is not anticipated to compromise extraction of the $\lambda 21$\,cm signal for a range of cosmological models after fitting a $7^{\rm th}$ order polynomial to radiometric data. Our results generalize to most efforts to measure the sky-averaged spectrum. | The predicted transition from the cosmological dark age ($z\simgreat 30$) to the epoch of reionization (EoR; $z \simless 15$) was marked by the appearance of the first generation of stars, supernovae, and black holes. These objects initiated a reheating and reionization of the intergalactic medium (IGM; e.g., \citealt{madau97}). The $\lambda$21\,cm transition of hydrogen is potentially sensitive to these processes even at $z\simgreat 15$, redshifts that likely cannot be probed with other known observables. Most theoretical studies have focused on the origin of (and detection prospects for) angular fluctuations in $\lambda$21\,cm brightness (\citealt{madau97,zaldarriaga04,mcquinn06,furlanetto06,morales10}). However, the sky-averaged spectrum of $\lambda$21\,cm brightness encodes independent information \citep{shaver99,gnedin04,sethi05,furlanetto06a,pritchard10,mirocha13}. In fact, the instrumentation required to detect the sky-averaged signal differs markedly from that needed to detect spatial fluctuations in the $\lambda$21\,cm signal. The latter requires an interferometer with thousands of square meters of collecting area to have adequate sensitivity, whereas a single dipole could have sufficient sensitivity to detect the sky-averaged spectrum. In either case, the principle challenge arises from foreground emission that is at least four orders of magnitude brighter than both the anticipated angular fluctuations \citep[i.e.,][]{bernardi09,bernardi10,ghosh12,pober13,paciga13} and the sky-averaged signal \citep[i.e., ][]{deoliveiracosta08,rogers08}. Previous works have relied on the anticipated spectral smoothness of the foregrounds in frequency to separate them from the less-smooth 21cm signal: The 21cm signal should vary over kHz scales in pencil--beam observations, and the sky--averaged 21cm signal is predicted to show variations over scales of $\sim$10~MHz. However, it is thought that the foregrounds follow an approximate power-law, with deviations on scales much larger than 10~MHz (a contention investigated here). Recently, measurements of the sky-averaged signal from the EoR and earlier epochs have received renewed attention owing to limits placed on reionization models by the Experiment to Detect the Global EoR Signature \citep[EDGES,][]{bowman10}. This has inspired several theoretical investigations of the constraining potential and optimal survey/analysis strategies for measurements \citep{pritchard10,harker12,morandi12,liu12,switzer14}, as well as new detection efforts. The Shaped Antenna measurement of the background RAdio Spectrum \citep[SARAS;][]{patra12} project targets the EoR whereas the Large-aperture Experiment to detect the Dark Age \citep[LEDA;][]{greenhill12, taylor12} the LOFAR Cosmic Dawn Search \citep[LOCOS;][]{vedantham13} and SCI--HI \citep{voytek14} target the transition era between the dark age and EoR ($z\sim 20$). Finally, the Dark Age Radio Explorer \citep[DARE;][]{burns11} space mission concept is intended to enable study of the sky-averaged $\lambda21$\,cm signal from the EoR up to $z \sim 30$. This paper focuses on the detection of the sky-averaged $\lambda$21\,cm signal from the neutral IGM at the close of the dark age and beginning of the EoR. This epoch is forecast to appear as an absorption trough much greater in magnitude than the emission feature associated with the EoR in current theoretical models \citep[]{furlanetto06a,pritchard10}. The trough morphology is determined by (1) the onset, the strength, and the evolution of coupling to the Ly$\alpha$ background from the first generations of stars and (2) the heating by X-rays from byproducts of stellar evolution such as supernovae and black holes \citep[i.e.,][]{furlanetto06a,fialkov14,mirocha14}. Other processes such as dark matter annihilation \citep[]{valdes07,valdes08,valdes10,valdes13} or more exotic mechanisms (e.g., \citealt{mack08}) may also affect the amount of $\lambda21$cm absorption. We study the effect of antenna response on the apparent frequency spectrum of foreground emission. \cite{vedantham13} were the first to include the effect of a broadband antenna gain pattern and showed that, in the case of LOFAR dipoles, angular and spectral response has a considerable effect. We expand on the results of this initial investigation in several ways: (1) we develop a more physical understanding of how the spectrum and angular distribution of the foregrounds impact sky-averaged measurements in a realistic instrument [where the foreground structure couples to the angular and spectral response of the antenna]. (2) After finding that the instrumental response is the limiting factor for sky-averaged spectra, we explore the benefits of calibrating the antenna gain pattern through interferometric measurements. (3) Previous studies did not quantify how well the foregrounds must be modeled to be able to detect the HI signal. We forecast the model complexity needed to yield an unbiased detection. In outline, Section~\ref{sec:instrument} first describes our simulations of the instrument and foreground sky and then investigates how well different foregrounds models can be subtracted as a smooth polynomial both for ideal instruments and for when a realistic antenna gain pattern is assumed. Section~\ref{leda_approach} shows how calibration of the dipole gain pattern used to detect the global signal through an interferometric array helps the foreground modeling and subtraction. First-order forecasts of effectiveness for LEDA at constraining the cosmological signal are presented in Section~\ref{sec::fisher}, with conclusions thereafter.\\ | \label{sec::conclusions} This paper investigated the impact on global $\lambda$21\,cm signal measurements of spectral structure that is either intrinsic to the foregrounds or induced by the antenna response. We focused on the measurement of the HI signal from the dark age, focusing on the LEDA instrument, but our results generalize to other sky-averaged $\lambda$21\,cm experiments. We carried out realistic simulated observations, including a variety of physically-motivated $\lambda$21\,cm signals, foreground models, and antenna gain patterns. First, we considered more physical models for the spectral structure of the foregrounds than done previously. Prior studies had primarily parametrized the foregrounds with a low order polynomial in $\log T_b - \log \nu$. We found that the intrinsic spectral shape of optically-thin synchrotron emission -- the dominant foreground -- likely can be removed with a $\sim 4^{\rm th}$ order polynomial to $<10$~mK, as is required to isolate the signal. Even in the most pathological case imaginable of a mono-energetic population of synchrotron electrons, we found that the foregrounds could be subtracted with a $\sim 6^{\rm th}$ order polynomial. We argued that including the additional emission from point sources, free-free emission, and self-absorption requires a modest increase in polynomial order over that required in the optically-thin synchrotron case. The primary result of this paper concerns the coupling between the antenna response to the foregrounds. We found that the coupling between the foregrounds and the (inevitable) spatially and spectrally-dependent antenna gain pattern generates spectral structure that requires additional orders to subtract the foregrounds. For LEDA, this induced structure can still be adequately fit with a $7^{\rm th}$ order polynomial in $\log{\nu}$ and a large variety of HI models can still be measured. We found, however, that the subtraction of a $7^{\rm th}$ order polynomial can still leave a non negligible bias in the estimate of the HI parameters. The inclusion of an $8^{\rm th}$ order polynomial in the foreground modeling may preclude the detection of the faintest HI models but leads to an unbiased estimate of the parameters. {As LEDA observes in the 40-90~MHz band, our conclusions are limited to $\lambda$21cm absorption lines narrower than this band. We would expect worse constraints for wider $\lambda$21cm models. In general, our results suggest that the commonplace approach of assuming \emph{all} frequency structure can be removed with a low order (i.e., $3^{\rm rd}$) function is too optimistic. The combination of interferometric array and single dipole observations can in principle enable the measurement of the antenna parameters and mitigate antenna gain pattern uncertainties as a source of spectral structure. We simulated the impact of statistical errors on the antenna gain pattern and found that interferometric measurements should constrain sufficiently the antenna gain pattern so as not to compromise the measurement of the cosmological signal. This study ignored two effects: (1) the additional frequency structure generated at the stage of signal acquisition that is independent of the antenna gain pattern (i.e., signal reflection due to cable mismatch) and (2) ionospheric refraction and atmospheric absorption. Accounting for the structure in frequency of the sky-averaged signal resulting from the former effect requires a more complete model of the instrument \citep[i.e.,][]{bowman08,rogers12} that will be the focus of future work. Regarding the latter, the ionosphere can have a twofold effect. First, it can affect the measurement of the antenna primary beam \citep[i.e.,][]{tasse13}. As the ionosphere is expected to vary on time, frequency and spatial scales that are very different than the antenna beam, the problem can effectively be decoupled and ionospheric effects corrected by providing a list of point sources that can be used to measure ionospheric offsets \citep[]{mitchell08}. Second, chromatic effects (owing to refraction in the upper atmosphere) might induce curvature in the spectrum of the global sky signal \citep{vedantham13}, and compromise the logarithmic--space foreground removal method (although not necessarily for the $7-8^{\rm th}$ order polynomials in $\log{\nu}$ considered here). However, \citet{vedantham13} also showed that ionospheric effects can be understood with simple physical principles, which suggests that they can be modeled prior to fitting out the foregrounds and, therefore, do not seem to represent a major obstacle for the measurement of the global sky signal. This seems also to be confirmed by \cite{voytek14} who achieve an average $\sim$500~mK residual spectra in the 60-90~MHz band after foreground subtraction without including any ionospheric modeling.\\ We thank the referee for useful comments that improved the manuscript. GB is grateful to Ravi Subrahmanyan for useful discussions that initiated this work and to Oleg Smirnov for useful discussions on calibration. MM acknowledges support by the National Aeronautics and Space Administration through the Hubble Postdoctoral Fellowship and also from NSF grant AST~1312724. LEDA is supported by NSF grants AST-1106045, AST-1105949, AST-1106059, and AST-1106054. | 14 | 4 | 1404.0887 |
1404 | 1404.7143_arXiv.txt | We report on two regularly rotating galaxies at redshift $z \approx 2$, using high resolution spectra of the bright [CII] $158\mu$m emission line from the {\it HIFI} instrument on the {\it Herschel} Space Observatory. Both \s0901full\ (``\sdss0901'') and \clonefull\ (``\clone'') are strongly lensed and show the double-horned line profile that is typical of rotating gas disks. Using a parametric disk model to fit the emission line profiles, we find that \sdss0901\ has a rotation speed $v \sin(i) \approx 120 \pm 7 \,\kms$ and gas velocity dispersion $\sigma_g < 23\, \kms$ ($1\sigma$). The best fitting model for \clone\ is a rotationally supported disk having $v\sin(i) \approx 79 \pm 11 \, \kms$ and $\sigma_g \la 4\,\kms$ ($1\sigma$). However \clone\ is also consistent with a family of dispersion-dominated models having $\sigma_g = 92 \pm 20 \,\kms$. Our results showcase the potential of the [CII] line as a kinematic probe of high redshift galaxy dynamics: [CII] is bright; accessible to heterodyne receivers with exquisite velocity resolution; and traces dense star-forming interstellar gas. Future [CII] line observations with {\it ALMA}\/ would offer the further advantage of spatial resolution, allowing a clearer separation between rotation and velocity dispersion. | Typical star-forming galaxies in the nearby universe are supported by systematic rotation, with random velocities playing a relatively minor role. This indicates a degree of maturity--- the galaxies are old and established, and their reservoirs of star-forming gas are dominated by material that was accreted at least one orbital time ago. However, at the epoch when cosmic star formation reached its peak, it is likely that galaxies were still accreting gas rapidly. The relative roles of rotation and velocity dispersion in providing support to such galaxies could thus be significantly different. Certainly, the morphologies of star-forming galaxies at $z\sim 2$ suggest {\it some} differences in their typical properties: regular spirals constituted a much smaller fraction of galaxies at $z\sim 2$ than they do today. Dynamical observations of star-forming galaxies at $z\sim 2$ are challenging. One successful approach has been to study strong rest-frame optical emission lines, which are redshifted to near-IR wavelengths \citep[e.g.][]{ForsterSchreiber09,Lehnert13,Rhoads13b}. Spatial resolution is generally limited by seeing to $\ga 0.5''$, which yields a few resolution elements across the disk of the galaxy. For a minority of cases it has been possible to achieve significantly higher spatial resolution, either by using adaptive optics \citep[e.g.][]{Law09}, or by observing strongly lensed galaxies \citep{Jones10,Frye12,Wuyts12,Jones13}. Spectral resolution is also usually modest ($R\la 6000$, corresponding to $\Delta v \ga 50 \kms$), since the faint flux levels of $z\sim 2$ emission lines usually preclude the lower sensitivity of high resolution spectrographs. We here adopt a complementary approach to studying the dynamical support of $z\sim 2$ star-forming galaxies. We use [CII] 158 \micron\ line observations from the {\it Herschel} Extreme Lensing Line Observations (HELLO) program \citep{Malhotra14}, obtained using the {HIFI} instrument \citep{deGraauw10} on the {\it Herschel} Space Observatory \citep{Pilbratt10}. The resulting line profiles are at exquisite spectral resolution, though entirely unresolved spatially. In the present paper we analyze the galaxies \s0901full\ \citep[][hereafter \sdss0901]{Diehl09} and \clonefull, also called ``\clone'' \citep{Lin09}. Both galaxies show the double-horned rotation profile that is characteristic of rotationally supported disks. The shape of this profile contains considerable information on the disks' dynamical properties. C$^+$ is the main coolant of neutral gas in galaxies. Typically, 0.3\% of far-infrared luminosity emerges in the [CII] 158 $\mu$m line. Thus, it can be an excellent tracer of ISM kinematics. The question then is where the [CII] emission comes from. [CII] can trace neutral gas, since carbon has a lower ionization potential than hydrogen. The brightest [CII] emission in a galaxy comes from photon-dominated regions (PDRs). These are surface layers of dense molecular clouds, where UV light from nearby star formation is dissociating molecular gas. [CII] probes primarily a density range from a few $\cm^{-3}$, which is required to excite the transition, up to the critical density of $\sim 10^{3.5} \cm^{-3}$. The integrated [CII] emission from whole galaxies includes potentially important contributions from diffuse ionized gas \citep{Bennett94} and also from diffuse HI, although the fractions are debated \citep[e.g.][]{Madden93,Heiles94,Contursi02}. The radial distribution of [CII] in nearby galaxies generally follows CO \citep[e.g.][for M33 and the Milky Way, respectively]{Kramer13,Pineda13}, although [CII] emission has also been observed in outflows \citep{Contursi13} and in turbulently heated gas in nearby radio-galaxies \citep{Guillard13}. The galaxies studied in this paper have typical [CII]/FIR ratios \citep{Malhotra14}, and do not show the [CII] deficiency seen in some luminous nearby systems \citep[e.g.][]{Malhotra97,Malhotra01,Carilli13}. We describe our sample and observations in section~\ref{sec:samp_dat}. We discuss our Markov Chain Monte Carlo spectral line fitting methods and results in section~\ref{sec:fitting}, and compare them to H$\alpha$ observations of the same objects in section~\ref{sec:halpha}. We close with a discussion of implications and future directions in section~\ref{sec:discuss}. Throughout the paper, we adopt a $\Lambda$-CDM ``concordance cosmology'' with $\Omega_M = 0.27$, $\Omega_\Lambda = 0.73$, and $H_0 = 71 \kmsMpc$. | \label{sec:discuss} Our [CII] spectra of \sdss0901\ and \clone\ showcase the potential of heterodyne spectroscopy for kinematic studies of high-redshift galaxies. \citet{ForsterSchreiber09} find that about 1/3 of $z\sim 2$ galaxies are reasonably described as rotation-dominated disks, based on H$\alpha$ integral field unit spectra. However, they are not able to resolve spectral features narrower than $\sim 60\kms$. Thus, our measured upper limits on the velocity dispersion of \sdss0901, $\sigma_g < 23\kms$ ($46 \kms$) at $1 \sigma$ ($2\sigma$), are one of the tightest limits to date on the velocity dispersion of a high redshift galaxy. While our results are less definitive for \clone, the maximum likelihood fits have $\sigma < 4 \kms$ ($14 \kms$) at $1 \sigma$ ($2\sigma$), and 65\% of our simulations yield $\Delta v / (2 \sigma_g) \approx \vrot / \sigma_g > 0.4$--- a (semi-empirical) criterion advocated by \citet{ForsterSchreiber09} for a disk to be considered rotationally supported. Spatially resolved observations at similar spectral resolution and signal-to-noise ratio will be possible for some $z\ga 2$ galaxies using (sub)mm interferometric line observations. This will enable cleaner measurements of the line-of-sight velocity dispersion. {\it ALMA}\/ (the Atacama Large Millimeter Array) will be the most powerful such instrument for the foreseeable future, offering spectral resolution comparable to HIFI, coupled with higher sensitivity and spatial resolution as fine as $\sim 0.2''$. For our two particular objects, {\it ALMA}\/ will not supersede our {\it Herschel} [CII] observations: The [CII] line in \sdss0901\ lies in a gap between {\it ALMA}'s frequency bands, and \clone\ is too far north ($\delta = +51^\circ$) for {\it ALMA}\/ observation. Fortunately, other strong lens systems will unlock the full potential of {\it ALMA}\/ for this science. In conclusion, the {\it Herschel} observations of the [CII] 158 $\mu$m line that we present here underscore the promise of the bright [CII] line as a kinematic tracer for high redshift galaxies. They provide a unique look at the internal dynamics of two $z\approx 2$ galaxies, and show that very small internal velocity dispersions can be found in the high redshift universe. \begin{figure} \plottwo{example_rotcurves.eps}{example_profiles.eps} \caption{This figure illustrates the correspondence between rotation curve and line profile for three ``toy models,'' each of which is dominated by a single kinematic component. In both panels, blue corresponds to a halo-dominated rotation curve (with gas velocity dispersion $\sigma_g =7.5\kms$), black to a disk-dominated rotation curve ($\sigma_g=7.5\kms$), and red to a dispersion-dominated galaxy ($\sigma_g=75 \kms$). {\it Left:}\/ The rotation curves (with shading for the region $v_c(r)\pm \sigma_g$). The two green curves show $dL_{\rm [CII]}/dr$ and its integral, $L_{\rm [CII]}(r)$, (i.e., the enclosed [CII] luminosity), both normalized to their respective peaks. They show how the different portions of the rotation curve are weighted in the line profile. {\it Right:}\/ The resulting line profiles. } \label{fig:examples} \end{figure} \begin{table} \begin{tabular}{lllllllll} Object & $\vdhalf$ & $\vhhalf$ & $\sigma_g$ & $x_{d}$ & $x_{h}$ & Flux & $\Delta \log(L)$\tablenotemark{a} & Line\\ & ($\kms$)& ($\kms$)& ($\kms$) & & & ($\Kkms$) & & style \\ \tableline SDSS~0901 &{\bf 121} & 2 &{\bf 29} & {\bf 0.11} & 9.3 & 1.359 & 0 & solid red \\ \tableline \clone & {\bf 78} & 2 & {\bf 1} & 1.52 & 0.7 & 0.2657 & 0 & dashed red\\ \clone & {\bf 20} & {\bf 100} & {\bf 8} & {\bf 0.07} & {\bf 6.2} & 0.365 & -1.4 & solid red \\ \clone & 0 & 2 & {\bf 98} & 0.5 & 0.26 & 0.371 & -3.3 & dotted red\\ \clone & {\bf 70} & 2 & {\bf 94} & {\bf 1.1} & 0.05 & 0.386 & -3.44 & solid blue\\ \tableline (none) & {\bf 75} & 1 & 7.5 & {\bf 0.22} & 0.1 & - & - & black\\ (none) & 1 & {\bf 75} & 7.5 & 1 & {\bf 0.1} & - & - & blue \\ (none) & 10 & 10 & {\bf 75} & 1 & 1 & - & - & red \end{tabular} \caption{Parameters of selected model fits plotted in the figures. \label{tab:bestfitparams}} \tablecomments{ We include the best fitting model for \sdss0901\ (top line, plotted in figure~\ref{fig:s0901_spec}); four representative model fits for \clone\ (lines 2--5, plotted in figure~\ref{fig:clone_spec}); and three sample ``toy models'' chosen to illustrate features of the rotation curve model (lines 6--8, plotted in figure~\ref{fig:examples}). In each case, parameters associated with the dominant component(s) determining the line profile shape are given in bold face, and small changes to the remaining parameters would have small or negligible effects on the model line profile. } \tablenotetext{a}{{}$\Delta\log(L)$ is the log of likelihood, relative to the maximum likelihood model identified for the same observed line.} \end{table} | 14 | 4 | 1404.7143 |
1404 | 1404.2285_arXiv.txt | We present a study of the structure of the Galactic interstellar medium through the $\Delta$-variance technique, related to the power spectrum and the fractal properties of infrared/sub-mm maps. Through this method, it is possible to provide quantitative parameters which are useful to characterize different morphological and physical conditions, and to better constrain the theoretical models. In this respect, the \emph{Herschel}\footnote{\emph{Herschel} is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.} Infrared Galactic Plane Survey carried out at five photometric bands from 70 to 500~$\mu$m constitutes an unique database for applying statistical tools to a variety of regions across the Milky Way. In this paper, we derive a robust estimate of the power-law portion of the power spectrum of four contiguous $2^{\circ} \times 2^{\circ}$ Hi-GAL tiles located in the third Galactic quadrant ($217^{\circ} \lesssim \ell \lesssim 225^{\circ}$, $-2^{\circ}\lesssim b \lesssim 0^{\circ}$). The low level of confusion along the line of sight testified by CO observations makes this region an ideal case. We find very different values of the power spectrum slope from tile to tile but also from wavelength to wavelength ($2 \lesssim \beta \lesssim 3$), with similarities between fields attributable to components located at the same distance. Thanks to the comparison with models of turbulence, an explanation of the determined slopes in terms of the fractal geometry is also provided, and possible relations with the underlying physics are investigated. In particular, an anti-correlation between ISM fractal dimension and star formation efficiency is found for the two main distance components observed in these fields. A possible link between the fractal properties of the diffuse emission and the resulting clump mass function is discussed. | One of the most intriguing tasks in the observational study of the interstellar medium (ISM) is to extract information about the 3-dimensional structure of the clouds, starting from the 2-dimensional maps of these objects, generally taken at different wavelengths and with different techniques and resolutions. Although a certain degree of self-similarity of the ISM maps over a given range of spatial scales can be in many cases perceived by eye, there are numerous more solid arguments suggesting this can be the case, starting from the work of \citet{sca90}. In this respect the phenomenon mainly responsible of self-similar morphologies is turbulence. This is a largely recognized fact in molecular clouds, being a typical scale-free phenomenon inducing fractality \citep[see, e.g.,][]{sre89}. It is indeed characterized by the lack of a specific length scale, then it can produce a fractal distribution of matter in a molecular cloud over a wide range of scales. Therefore, to determine the starting and the ending point of these ranges is generally considered a tentative way to get an estimate of the turbulence injection and dissipation scales. An extensive and detailed review of the observational evidences of the presence of turbulence in molecular clouds and its role in shaping their structure in fractal sense can be found in \citet{vaz99} and \citet{sch11}. It is noteworthy that the ISM clouds belong to the category of the \emph{stochastic fractals}, whose structure does not appear perfectly self similar, but rather \emph{self-affine}: although a given set and a part of it have not exactly the same appearance, they have the same statistical properties and it is still possible to use a fractal description for them. There are many observational grounds supporting the fractal scenario. The observations of the low-$J$ $^{12}$CO and $^{13}$CO emission lines in several star-forming molecular cloud complexes \citep[e.g.,][]{fal96,sch98,wil99b} show that the measured line intensities, shapes and ratios cannot be produced in clouds of uniform gas temperature and density, suggesting the idea that these interstellar objects are far from being homogeneous, being instead organized in small clumps with a filling factor lower than unity \citep{elm97a}. Interestingly, such a structure is also able to justify further observed characteristics of the investigated region, as for example the clump mass function \citep{sha11} and the stellar initial mass function \citep{elm02}. These remain meaningful observables although in the last years the picture of the ISM has changed with the recognition of filaments as intermediate structures \citep[e.g.,][]{ros96,wil99b}, which have definitely been found ubiquitous in the recent Herschel observations \citep[e.g.,][]{mol10b,sch13}. In any case, the cloud description based on a hierarchical decomposition in recognizable substructures \citep{hou92} is not incompatible with the fractal approach. Indeed \citet{stu98} have shown that these two points of view are consistent: an ensemble of clumps with a given mass and size spectrum can give rise to a fractal structure of the cloud. Statistical descriptors which, in general, can be related to the fractal properties of a cloud are powerful methods to characterize its structure. The techniques initially used to estimate the fractal dimension of the interstellar clouds were based on the isocontours of the images, as for example the \emph{perimeter-ruler} and the \emph{area-perimeter} relation \citep[see e.g.][and references therein]{san05}. Subsequently, statistical tools have been applied, namely descriptors based on the value and the spatial distribution of the single pixels, providing quantitative information on one or more aspects of the investigated morphology \citep[a relevant part of them is summarized in][]{elm04}. The direct estimate of the power spectrum \citep[e.g.][]{ing04,miv07,mar10,gaz10} can be used to infer the fractal structure of the ISM, although to deal with real observational sets other algorithms have been demonstrated to be more adequate \citep{stu98}. Other statistical estimators are the structure function \citep{padc02,pad03,kri04,cam05,gus06,kow07,row11}, the $\Delta$-variance (see below), the autocorrelation function \citep{cam05}, and the adapted correlation length \citep{car06}, whereas a further development of these monofractal descriptors is represented by the multifractal spectrum \citep{cha01,vav01}. In particular, the $\Delta$-variance method was introduced by \citet{stu98} and subsequently improved by \citet{ben01} and \citet{oss08a} to analyze the drift behavior of observed scalar functions such as the intensity distribution in molecular clouds, real or synthesized. It has been applied not only to maps of line emission \citep[see also][]{ben01,oss01,oss08a,sch11,row11} and dust extinction \citep{cam04,sch11} or emission \citep{rus13}, but also to the recovered velocity field \citep{oss06,fed10}, or to 3-dimensional density fields of turbulence simulations \citep{fed09}. The aim of this paper is to contribute both to the enlargement of the sample of the regions whose structural properties have been studied by means of fractal techniques, and to the improvement in characterizing the response of statistical tools to different observing conditions. The Hi-GAL survey \citep[\emph{Herschel} Infrared GALactic plane survey,][]{mol10a} represents an extraordinary resource for carrying out statistical studies of the ISM. Indeed a large coverage is obtained in five different bands, so that a large variety of morphologies and physical conditions can be investigated at unprecedented spatial resolution. Moreover, these large \emph{Herschel} maps offer the chance to probe a wide range of spatial scales, since the number of available pixels is very important for the reliability of the statistical descriptors. Galactic plane observations suffer from confusion due to the superposition of different components along the line of sight, especially in the first and fourth Galactic quadrants. To minimize the problem of confusion, the first available observations of the third Galactic quadrant (in the range $217.0^{\circ} \lesssim \ell \lesssim 224.3^{\circ}$) are studied as a first test case, in which we are more confident that the observed ISM emission corresponds to a morphology which is quite coherent from the spatial point of view. These observations have been presented by \citet{eli13} \citepalias[hereafter][]{eli13}, and are briefly summarized in Section~\ref{obs}. As a paradigm of synthetic cloud images used for testing the statistical tools used in this work we consider the class of so-called \emph{fractional Brownian motion} images (hereinafter fBm). They have been already used, for example, by \citet{stu98,ben01,kha06,miv07,sha11} for testing their algorithms. We briefly discuss the properties of this class of images in Section~\ref{fbm_par}. In this paper we adopt the $\Delta$-variance algorithm to derive a robust estimate of the power spectrum slope of the maps. In Section~\ref{dvar_par} this method is briefly described, and its application to synthetic maps is discussed to characterize the response of the algorithm in case of departure of the analyzed image from the ideal fBm-like behavior. In Section~\ref{dvarhigal_par} we preent the results of our $\Delta$-variance analysis, and discuss the obtained power spectrum slopes and self-similarity ranges, searching for cross-correlations among different maps and observational wavebands. Moreover, links with turbulence and observables related to star formation (as star formation efficiency and mass functions) are investigated. Finally, the results are summarized in Section~\ref{summary}. | 14 | 4 | 1404.2285 |
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1404 | 1404.0908_arXiv.txt | Active galactic nucleus (AGN) feedback provides the link between the central black hole and its host galaxy. We assume AGN feedback driven by radiation pressure on dust, which sweeps up the ambient dusty gas into an outflowing shell, and consider feedback-triggered star formation in the outflow. An upper limit to the characteristic size of galaxies may be defined by the critical radius beyond which radiation pressure on dust is no longer able to drive the shell. The corresponding enclosed mass may be compared with the host galaxy bulge mass. We show that the resulting relation between characteristic radius and mass, of the form $R \propto \sqrt M$, corresponds to the observed mass-radius relation of early-type galaxies. We suggest that such simple physical scalings may account for a number of observed galaxy scaling relations. In this picture, both the size and structural evolution of galaxies can be interpreted as a consequence of AGN feedback-driven star formation, mainly associated with the spheroidal component. The accreting black hole is responsible for triggering star formation in the host galaxy, while ultimately clearing the dusty gas out of the host, thus also contributing to the chemical evolution of galaxies. We discuss the importance of radiation pressure on dust in determining the galaxies large-scale properties, and consider the possibility of the central black hole directly shaping its host galaxy through AGN feedback. | Observations over the past decades have revealed important connections between the central supermassive black hole and its host galaxy \citep[see the recent review by][and references therein]{Kormendy_Ho_2013}. The observed correlations suggest a close coupling, supporting the so-called black hole-galaxy `co-evolution' scenario. However, the difference in physical scales between the central black hole and the host galaxy is huge; and at first sight, one would not expect any causal connection between the black hole and the galaxy-scale star formation. On the other hand, the energy released by the accreting black hole can easily exceed the binding energy of the galaxy bulge. The key question is how the tiny black hole at the centre can influence, and possibly even determine, the fate of an entire galaxy. It is now widely agreed that the required link is provided by some form of `feedback' from the central active galactic nucleus (AGN), and different AGN feedback models have been proposed in the literature \citep[][and references therein]{Silk_Rees_1998, Fabian_1999, King_2003, Murray_et_2005, King_2010, Fabian_2012}. Feedback can operate in both radiative and kinetic modes, via jets, winds, and radiation pressure. In the context of galaxy evolution, AGN feedback is most generally invoked to suppress star formation in the host galaxy, either by removing or heating the ambient gas. This is the well established negative feedback scenario in which most of the past studies have been discussed. However, feedback from the central black hole may also play other roles in galaxy evolution. Different forms of positive feedback have been considered in the past. For instance, triggering of star formation due to radio jet activity has been proposed to explain the alignment of radio and optical structures observed in high redshift radio galaxies \citep[][]{Rees_1989, Begelman_Cioffi_1989}. Based on these early models, \citet{Chokshi_1997} suggested that jet-triggered star formation may be responsible for the formation of elliptical galaxies, with the most powerful jets associated with giant ellipticals and lower power jets linked to smaller spheroids and central bulges. AGN jet-induced star formation, leading to enhanced star formation rates, has also been considered as a source powering luminous starbursts \citep{Silk_2005}. More recently, numerical simulations of radio jet-triggered star formation in gas-rich disc galaxies have been performed \citep{Gaibler_et_2012}. We also note that `mixed' scenarios, involving both positive and negative feedback, have been recently debated in the literature \citep{Silk_2013, Zubovas_et_2013, Zinn_et_2013}. We have previously studied the possibility of AGN feedback triggering star formation in the host galaxy \citep{Paper_1}, and suggested that this particular form of galaxy growth may be linked to the observed size evolution of massive galaxies over cosmic time \citep{Paper_2}. Indeed, numerous observational studies show that massive, quiescent galaxies at high redshift ($z \sim 2$) are much smaller than galaxies of comparable mass in the local Universe, implying a significant size evolution over the past $\sim$10 Gyr \citep[e.g.][]{Bezanson_et_2009, vanDokkum_et_2010, Patel_et_2013}. The observed increase in size seems to follow a characteristic `inside-out' growth pattern, whereby most of the growth takes place at large radii, leading to the gradual build-up of an outer envelope. Observations also indicate that, coupled with the increase in radius, significant structural and morphological changes occur over the same time span, as seen by variations in the Sersic index \citep{vanDokkum_et_2010, Patel_et_2013, Buitrago_et_2013}. This suggests a parallel evolution in the size and structure of the growing galaxies, which need to be simultaneously accounted for. Here we explore whether the galaxies overall evolution can be interpreted within a single physical framework in which the central black hole plays a major role. In particular, we examine how the accreting black hole may determine the characteristic properties of its host galaxy through AGN feedback driven by radiation pressure on dust. | Recent observations have reported detections of galactic-scale molecular outflows in a number of active sources \citep[e.g.][]{Sturm_et_2011, Cicone_et_2014}. The measured outflow parameters (velocities, kinetic powers, momentum rates) seem to be consistent with model predictions based on energy-driven flows \citep{Zubovas_King_2012a}, thus favouring energy-driving over momentum-driving. However, the observed large momentum boosts ($\dot{M} v \sim 10 L/c$) do not necessarily rule out radiation pressure driving, since matter can be optically thick to reprocessed infrared radiation, leading to momentum fluxes reaching several times the single scattering limit \citep{Debuhr_et_2011, Roth_et_2012}. On the other hand, it has been argued that the coupling between matter and radiation can be inefficient in a range of contexts, due for instance to instabilities developing in the ambient medium \citep{Faucher-Giguere_Quataert_2012, Krumholz_Thompson_2013}. A clearer picture depends on the details of multi-dimensional effects, and demands a better understanding of radiative physics. In any case, we consider radiation pressure on dust as a viable mechanism for driving large-scale outflows, although the most extreme examples may require other acceleration processes. One should also keep in mind that the observational samples are often biased towards powerful sources with previously known outflow detections \citep{Cicone_et_2014}. Various physical mechanisms aimed at explaining the observed size and structural evolution of galaxies have been discussed in the literature. In general, both the size and structural changes are interpreted in terms of external processes, such as a sequence of merger events. At present, some form of `two-phase' galaxy assembly, with an initial in-situ star formation epoch followed by a later phase of satellite accretion, seems to emerge as the favoured scenario \citep[e.g.][]{Hilz_et_2013, Dubois_et_2013}. Such transitions may or may not involve feedback from the central AGN. For instance, based on hydrodynamical cosmological simulations, \citet{Dubois_et_2013} show that the inclusion of jet feedback leads to the quenching of in-situ star formation and switch to the stellar accretion phase. As the accreted stars tend to settle in the outer regions, the galaxy's effective radius increases; at the same time, the randomisation of stellar orbits due to satellite accretion also leads to an increased importance of velocity dispersion over regular rotation. This induces a transition from compact, rotationally-supported discs into extended, dispersion-dominated ellipsoidal systems. Both the size growth and the morphological transformation are then attributed to AGN feedback. However, the overall evolution is actually driven by the switch in the galaxy growth modes, i.e. from in-situ star formation to satellite accretion, and may be only indirectly caused by AGN feedback. In our case, it is the AGN feedback itself that triggers the formation of new stars at outer radii, leading to the development of extended stellar envelopes, which are responsible for the galaxy's size growth. The newly born stars initially move on nearly-radial orbits with high radial velocities, in marked contrast to the well-ordered, rotational motion characteristic of disc galaxies. Thus structural changes are intrinsically coupled to the size growth, as a result of star formation occurring in the feedback-driven outflow, and the overall evolution may be naturally interpreted in terms of a radially growing stellar distribution. Although one usually tends to consider a combination of distinct processes, such as static star formation and external mergers in the `two-phase' scenario, it could be more interesting to consider one single physical scheme in which different aspects of galaxy evolution can be interpreted. It has long been conjectured that the central black hole regulates the stellar content of its host galaxy, but the exact physical mechanism is still under debate. In our model, the growth of the accreting black hole and the build-up of the host galaxy are inherently coupled through feedback-driven star formation, which provides a direct physical link between the two scales. We have seen that the global properties of galaxies, such as characteristic radius and mass, may be directly determined by the effects of radiation pressure on dust. In particular, the resulting scaling between radius and mass, of the form $R \propto \sqrt M$, may account for the observed mass-radius relation of early-type galaxies. It is interesting to note that the predicted scaling agrees with the size-mass relation of early-type objects, while late-type galaxies are observed to follow a scaling with a different slope. This might be a further indication that the important connection is with the spheroidal component. In our picture, the chemical evolution is also directly affected by the action of radiation pressure on dust, and the dust content may be an important factor in determining the global shape of galaxies \citep{Santini_et_2014}. Radiation pressure on dust thus seems to control the large-scale properties of the host galaxy, further setting the black hole-to-bulge mass ratio. If this is indeed the case, then the central black hole is actually shaping the basic structure of its host galaxy through AGN feedback. Summarising, the connection between AGN feedback and star formation on galactic scales is likely to be more complex than previously thought. In particular, the central black hole may not just quench star formation, as generally assumed in the standard negative feedback paradigm. In fact, disparate aspects of galaxy evolution may be interpreted within a single framework in which the central black hole plays a major role in shaping its host galaxy through AGN feedback. | 14 | 4 | 1404.0908 |
1404 | 1404.2620_arXiv.txt | We have observed a snapshot of our N-body/Smoothed Particle Hydrodynamics simulation of a Milky Way-sized barred spiral galaxy in a similar way to how we can observe the Milky Way. The simulated galaxy shows a co-rotating spiral arm, i.e. the spiral arm rotates with the same speed as the circular speed. We observed the rotation and radial velocities of the gas and stars as a function of the distance from our assumed location of the observer at the three lines of sight on the disc plane, $(l,b)=(90,0), (120,0)$ and (150,0) deg. We find that the stars tend to rotate slower (faster) behind (at the front of) the spiral arm and move outward (inward), because of the radial migration. However, because of their epicycle motion, we see a variation of rotation and radial velocities around the spiral arm. On the other hand, the cold gas component shows a clearer trend of rotating slower (faster) and moving outward (inward) behind (at the front of) the spiral arm, because of the radial migration. We have compared the results with the velocity of the maser sources from \citet{rmbzd14}, and find that the observational data show a similar trend in the rotation velocity around the expected position of the spiral arm at $l=120$ deg. We also compared the distribution of the radial velocity from the local standard of the rest, $V_{\rm LSR}$, with the APOGEE data at $l=90$ deg as an example. | \label{intro-sec} Spiral arm structures are the beautiful structures that have fascinated astronomers for a long time. One of the long-time mysteries of the spiral arm was the so-called ``winding-dilemma''. From the observations of the rotation curve of disc galaxies, it is known that the stars in the inner region of the disc rotate faster, i.e. the angular speed is higher, than the stars in the outer region. Therefore, if the spiral arm is a material arm, i.e. the spiral arm is moving at the same speed as the stars, the spiral arm should wind up quickly \citep[e.g.][]{ejw896}. Spiral density wave theory described in \citet{ls64} solved the issue by considering the spiral pattern as a density wave. Then, the density wave can be a rigidly rotating feature with a constant pattern speed, irrespective of the stellar rotation speed, and consequently long-lived. Recently, thanks to the powerful computational facilities, the resolution of three-dimensional N-body simulations has improved significantly, and the artificial heating from which the previous low-resolution simulations suffered is minimized \citep[e.g.][]{fbsmk11,jas13}. Such high-resolution simulations allow us to study further the spiral arm theory. However, even with such high-resolution simulations, so far no single N-body simulation reproduces a long-standing spiral arm feature such as that is suggested in \citet{ls64} \citep{jas11}. Recent studies show that the spiral arms in the numerical simulations are transient and recurrent \citep[e.g.][]{cldb06,wbs11,gkc12a,gkc12b,rdqw12,bsw13,dvh13,rvfrv13}. For example, \citet{gkc12a,gkc12b} demonstrated that the spiral arm was rotating with the same speed as the stars, i.e. co-rotating \citep[see also][]{wbs11}, and therefore winding. Still in each snapshot, the spiral arms are always apparent, and the spiral arms are constantly forming and disrupting, i.e. recurrent, with a lifetime of about 100 Myr. Although the co-rotating spiral arm leads to the winding-dilemma, \citet{gkc13} demonstrated that the spiral arms were disrupted before they wound up completely, and the pitch angle of the spiral arms correlated with the shear rate of the disc, as observed \citep[e.g.][]{sbbh06}. Interestingly, the winding nature of the spiral arm seen in N-body simulations can naturally explain the observed scatter in the correlation between the pitch angle and the shear rate \citep[see][for more thorough discussion]{gkc13}. \citet{gkc12a} demonstrated that the spiral arms in N-body simulations were forming with a similar mechanism to the so-called swing amplification theory suggested by \citet{jt66} and \citet{at81} \citep[see also][]{bsw13,dvh13}. However, while the swing amplification is considered to happen at a single co-rotation radius, where the spiral arm pattern speed is consistent with the rotation speed of the stars, in the numerical simulations the co-rotation resonance occurs at all radii, and the swing amplification is happening (or propagating) at every radius. This is one of the current explanations for the transient and winding spiral arm features. In others, for example, the transient features of the spiral arm can be interpreted as overlapping multiple-wave modes \citep[e.g.][]{qdbmc11,rdqw12,sc14}, where each mode appears around the co-rotation radius and is relatively long lived. Still, there is no clear explanation of the origin and nature of the spiral arms, which remains as a challenge for the galactic astronomer. Interestingly, there is also observational evidence against long-lived spiral arms. For example, \citet{mrm06} analysed the pattern speed of the spiral arm as a function of radius for NGC 1068 using their generalized version of the method from \citet{tw84}, so-called Tremane-Weinberg method. They showed that the pattern speed of the spiral arm decreases with radius, and therefore the lifetime of the spiral arm must be short. Similar pattern speeds were also observed with the same technique in other galaxies \citep[e.g.][]{mrmds08,mrmsv08,mrm09,sw11,sw12}. However, the accuracy and validity of the Tremaine-Weinberg method are still needed to be tested against the future observations \citep[e.g.][]{mrmds08,rvfrv13}. Another observational test is the so-called ``offset'' method. If there is a long-lived rigidly rotating spiral arm, one can define the co-rotation radius. Since the angular velocity of gas and stars is observed to be faster in the inner region, the gas and stars in the region inside (outside) the co-rotation radius will move faster (slower) than the spiral arm. The gas component piles up in the spiral arms, experiencing a shock that induces star formation \citep{mf68,wr69}. In this scenario, the youngest stars born from the molecular clouds in the spiral arms would be found slightly ahead of the arm traced by the molecular gas, if located within the co-rotation radius, and behind the arm outside of the co-rotation radius. Therefore, if we observe the tracers of the different stages of star formation, such as HI, CO and H$\alpha$, an offset among them as a function of radius would be expected. By combining H$\alpha$ imaging and $Swift/UVOT$ Near-Ultraviolet (NUV) data, \citet{fckph12} distinguished the regions with ongoing star formation and the regions with star formation a few hundred million years ago in the grand-design spiral galaxy, M100. Contrary to the expectation from the density-wave theory, no offset was found between these two regions. The same conclusion was reached in \citet{frdlw11}, although some studies claimed to find a significant offset for some galaxies \citep[e.g.][]{eksnk09,trwbd08,mggl13,hkbeh14}. The Milky Way is a (barred) spiral galaxy \citep[e.g][]{ds01,bcbim05,jpv13} which we can observe in great detail. For example, the detailed map of HI and CO observations provide the global position and kinematics of the spiral arm in the gaseous phase \citep[e.g.][]{dht01,ns03,ns06,kk09}. Star clusters provide us with reasonable photometric distances, and young star clusters can be used to trace the spiral arm and also measure the pattern speed of the spiral arm using a similar technique to the offset method mentioned above \citep[e.g.][]{dl05,ns07}. The influence of the spiral arms on the stellar motion has also been measured and compared with the models \citep[e.g.][]{fft01,avpmff09,jas10,sfbbf12,fsf14}. The maser sources associated with high-mass star forming regions are recognized as a unique source to trace the spiral arm structures, because Very Long Baseline Interferometry (VLBI) observations allow their parallaxes and proper motions to be measured with great accuracy, $\sim10$ $\mu$as. For example, recently the Bar and Spiral Structure Legacy (BeSSeL) Survey and Japanese VLBI Exploration of Radio Astrometry (VERA) provided the parallaxes and proper motion measurements for over 100 maser sources \citep{rmbzd14}. In the future, the European Space Agency's {\it Gaia} satellite (launched in December 2013) will produce accurate measurements of the parallax and proper motion for about a half billion disc stars \citep[e.g.][]{rlrig12}. To study the nature of the spiral arms from these observations, we need to compare the observational data with the theoretical prediction from different scenarios of the origins of spiral arms. Although there are many successful studies for reconstructing the Galactic bar structure and the pattern speed by comparing the observational data with the theoretical model prediction, it is more complicated for the spiral arms \citep[e.g. see][for a review]{og11}. \citet{mq08} assumed the rigid rotation of the spiral arm, and made predictions of the radial velocity distribution of stars in the cases of different number of arms, pitch angles and pattern speed. \citet{afrpvm11} studied how the rigidly-rotating spiral structures affect the stellar kinematics and the distribution of radial and rotational velocities of the stars \citep[see also][]{qdbmc11}. \citet{rafvrp14} studied the vertex deviation map from both rigidly-rotating spiral arms and transient spiral arms. \citet{bammsw09} discussed the origin of the large peculiar velocities observed for the maser sources at that time \citep{rmzbm09}. They argued that such large peculiar velocities are difficult to be explained with the density wave theory, but using N-body/Smoothed Particle Hydrodynamics (SPH) simulations, they showed that the observed large peculiar velocities of the maser sources can be reproduced by the transient and recurrent spiral arms. Therefore, more predictions for the observable signatures from the transient and recurrent spiral arms in the numerical simulations should be valuable for future and on-going observational surveys. In this paper, we study the kinematic structure of both the star and gas components around a spiral arm in a simulated barred galaxy similar in size to the Milky Way. The simulated galaxy has a transient, recurrent and co-rotating spiral arm similar to that seen in \citet{gkc12b}. We target a spiral arm similar to the Perseus arm. We then make a prediction of the observational signatures of the kinematics of the stars and gas around the Perseus arm, if it is also a transient, recurrent and co-rotating spiral arm. Section~\ref{meth-sec} describes briefly the numerical simulation code and numerical models. Section~\ref{res-sec} presents the results. A summary of this study is presented in Section~\ref{sum-sec}. | \label{sum-sec} We observed our N-body/SPH simulation of a Milky Way-sized disc galaxy in a similar way to how we can observe the Milky Way, with particular interest in the stellar and gas motion around the spiral arm. As our first study, we have focused on the three lines of sight on the disc plane, $(l,b)=(90,0), (120,0)$ and (150,0) deg, and analysed the rotation and radial velocity of stars and gas as a function of the distance from our assumed location of the observer. Similarly to the recent literature based on N-body simulations, our simulated galaxy shows a co-rotating spiral arm, i.e. the spiral arm is rotating with the same speed as the circular velocity, at the lines of sight selected. We show that the stars around the spiral arm show a large variation in both radial and rotational velocities owing to the co-rotating spiral arm. If the spiral arm is indeed a co-rotating spiral arm, we should observe a similar variation of the rotation and radial velocities around the spiral arm at every Galactocentric radius. An accurate measurement of the distance, proper motion and radial velocity of the stars is required, and the {\it Gaia} data will be a critical test for the co-rotating spiral arm. We show that the stars behind the spiral arm always gain angular momentum, while the stars at the front of the spiral arm lose angular momentum. The stars tend to rotate slower (faster) behind (at the front of) the spiral arm and move outward (inward). Because of the epicycle motion of the stars, we also see the stars with high (low) rotation velocity behind (at the front of) the spiral arms. We find that these stars came from the outer (inner) region and decelerated (accelerated) at the front of (behind) the arm. Then, they are passed by (passed) the spiral arm and are observed at their peri-centre (apo-centre) phase. These are consistent with \citet{gkc14}, and indicate a variety of orbits owing to the co-rotating spiral arm. These variety of orbits are likely to be closely related to the formation and disruption of the spiral arm. However, we need further investigation to reach a firm conclusion. Still, this study indicates that numerical simulations provides useful tests in the study of the nature of spiral arms. We have also analysed the rotation and radial velocity of the cold gas component. This is much simpler than the stars. We found a clear trend in the gas component which rotates slower (faster) and moves outward (inward) behind (at the front of) the spiral arm. We have compared the results with the observed data of the maser sources from \citet{rmbzd14}. Interestingly, the data show similar trend in $V_{\rm rot}$ around the expected position of the spiral arm around $l=120$ deg. More data from the accurate astrometric measurement of the maser sources will provide additional constraints on the nature of the spiral arm. Although we have observed three lines of sight for one snapshot of the numerical simulation, the observed gas and stellar motions are naturally expected features from our previous studies \citep{gkc12a,gkc12b,gkc14}, and therefore the observed trend should be common features in the co-rotating spiral arms in N-body/SPH simulations. We have analyzed several snapshots at different timesteps of the simulation, and confirmed that similar kinematic trends are always observed. Encouraged by the success of this study, we are currently working to make a quantitative prediction for the upcoming {\it Gaia} data for the co-rotating spiral arm, by taking into account the stellar population, dust extinction and expected {\it Gaia} errors by improving the methods in \citet{pck12} and \citet{hk14}. The entire topic will be further illuminated by another set of theoretical models, e.g. the analytical model of the stellar kinematics from the spiral arm, and also the numerical simulations with a fixed spiral arm potential and a constant pattern speed including both gas and stars \citep[e.g.][]{wbs11,dpn14}. | 14 | 4 | 1404.2620 |
1404 | 1404.7579_arXiv.txt | We present cosmological hydrodynamic simulations performed to study evolution of galaxy population. The simulations follow timed release of mass, energy, and metals by stellar evolution and employ phenomenological treatments of supernova feedback, pre-supernova feedback modeled as feedback by radiation pressure from massive stars, and quenching of gas cooling in large halos. We construct the fiducial model so that it reproduces the observationally estimated galaxy stellar mass functions and the relationships between the galaxy stellar mass and the host halo mass from $z = 4$ to 0. We find that the fiducial model constructed this way naturally explains the cosmic star formation history, the galaxy downsizing, and the star formation rate and metallicity of the star-forming galaxies. The simulations without the quenching of the gas cooling in large halos overproduce massive galaxies at $z < 2$ and fail to reproduce galaxy downsizing. The simulations that do not employ the radiation pressure feedback from young stars predict too strong redshift evolution of the mass-metallicity relation. Furthermore, the slope of the relation becomes too steep at low redshift without the radiation pressure feedback. The metallicity dependence in the radiation pressure feedback is a key to explain the observed mass-metallicity relation. These facts indicate that these two processes in addition to supernova feedback are essential for galaxy evolution. Our simple phenomenological model is suitable to construct a mock galaxy sample to study physical properties of observed galaxy populations. | Understanding galaxy formation is a challenging problem whose solution will require a concerted approach combining observational and theoretical work. There have been substantial advances on both fronts in the past decades. Numerical simulations are a powerful theoretical tool to study cosmic structure formation. $N$-body simulations are now able to predict non-linear growth of the dark matter-dominated density perturbations in great detail \citep{millennium, aquarius, ViaLacteaII, boylan-kolchin09}. Consequently, gravitational assembly of structure in a $\Lambda$-dominated Cold Dark Matter ($\Lambda$CDM) Universe is well understood and mostly consistent with observations. In order to make a direct comparison with observations, simulations must involve luminous matters (baryons) besides dark matter and dark energy. While semi-analytic models (e.g. \cite{WF91}; \cite{kwg93}; \cite{sp99}; \cite{clbf00}; \cite{on04}; \cite{nuGC}) can paint galaxies onto dark matter distribution, hydrodynamic simulations can directly explore evolution of the galaxy population and the intergalactic medium (IGM) simultaneously and self-consistently (e.g. \cite{khw92}; \cite{whk97}; \cite{keres05}; \cite{od06}; \cite{ocvirk08}; \cite{gimic}; \cite{owls}; \cite{vogelsberger13}). The baryonic processes that are essential for galaxy formation, such as gas cooling, star formation, and stellar and active galactic nuclei (AGN) feedback, constitute a complicated and highly non-linear network. Modeling them appropriately in hydrodynamic simulations is hence the major challenge for the theoretical studies of galaxy formation (see \cite{oka05}; \cite{Aquila}). Some recent simulations successfully produce realistic galaxies (\cite{ofjt10, gov10, eris, okamoto13, magicc, marinacci13}). The key ingredient is undoubtedly stellar feedback such as supernova (SN) feedback that ejects gas from galaxies to prevent too efficient star formation. While it is possible to drive winds by resolving the detailed structure of the interstellar medium (ISM) in very high resolution simulations \citep{hopkins12a}, most of cosmological simulations invoke phenomenological treatments of feedback because of limited numerical resolution. Some studies employ explicit winds, either hydrodynamically decoupled \citep{sh03} or coupled \citep{ds08}. The wind properties may depend on the galaxy properties \citep{od06, ofjt10}. Other popular way of implementing effective feedback is injecting thermal energy into the ISM and then shutting off cooling of heated gas for a while \citep{tc01, sti06, magicc}. Adding the feedback energy as non-thermal energy (e.g. turbulence) which decays in time-scale much longer than the cooling time has a similar effect \citep{teyssier13}. We have applied the feedback model developed by \citet{onb08} to large scale simulations to study high redshift galaxy populations, such as Lyman-$\alpha$ emitters \citep{shimizu11}, sub-mm galaxies \citep{shimizu12}, and Lyman break galaxies at $z > 7$ \citep{shimizu14, inoue14}. While these simulations reproduce many observed properties of high redshift galaxies, our studies utilizing the large scale simulations have been limited to high redshift because too massive galaxies form at low redshift (see \cite{shimizu12}). We also note that too many stars form in low mass halos at high redshift if we normalize the model to reproduce the luminosity (or stellar mass) function of the local faint galaxies \citep{moster13, okamoto13}. The first problem is well-known; stellar feedback alone cannot prevent monster galaxies from forming and hence we need a physical process that operates preferentially in large halos to quench gas cooling there (e.g. \cite{ben03}). The top candidate of such a process is so-called AGN {\it radio mode} feedback \citep{croton06, bower06}. \citet{sijacki07} and \citet{onb08} suggest that this radio mode feedback is naturally realized by considering the change of the accretion modes onto a supermassive blackhole. In fact, simulations including this feedback roughly reproduce galaxy stellar mass functions and stellar mass to halo mass relations for massive galaxies \citep{vogelsberger13, torrey14}. A remedy for the second problem has been recently identified by \citet{magicc}; feedback prior to an SN, such as stellar winds and radiation from massive stars, is needed to match stellar mass-halo mass relations over a wide redshift range \citep{magicc, kannan13, aumer13}. The aim of this paper is to update our galaxy formation model originally developed by \citet{onb08} and \citet{ofjt10} by adding several new feedback processes so that we can apply it for studies of galaxy population over wider mass and redshift ranges. We test our models against various observations and reveal roles of each feedback process to present a fiducial model. The paper is organized as follows. In section 2, we describe our simulations and provide descriptions of our modeling of baryonic processes. We present our results at $0 \le z \le 4$ and compare them with the available observational estimates in section 3. We investigate resolution effects in section 4. Finally, we summarize our results and discuss future applications of the new model in section 5. | We have updated the galaxy formation model described by \citet{ofjt10} to study evolution of galaxy population. The new model employs suppression of gas cooling in large halos and momentum injection by radiation pressure from massive stars in addition to SN feedback. We normalize the model parameters so that the fiducial simulation matches the observationally estimated stellar mass functions and galaxy formation efficiencies from $z = 4$ to 0. Interestingly, the fiducial model also well reproduces other observational properties of galaxy population: the cosmic star formation rate density, the main sequence of star-forming galaxies, the stellar age-stellar mass relation, and the mass-metallicity relation over a wide range of redshift. In order to investigate the roles of individual feedback processes, we have performed the simulations by switching on and off each of them alternately. The suppression of the gas cooling in large halo, which we view as a phenomenological treatment of the radio mode AGN feedback, is necessarily to explain the high mass-end of the galaxy stellar mass functions and the decline of the cosmic star formation rate density at low redshift. Our simple quenching model well describes the star formation properties in massive galaxies. This process makes the stellar age of massive galaxies older and nicely reproduces the galaxy downsizing for massive galaxies with $M_* \gtrsim 10^{10}~M_\odot$. On the other hand, our high resolution simulations show that the stellar age of the less massive galaxies is nearly constant for $M_* \lesssim 10^{10}~M_\odot$, while the observations suggest that the less massive galaxies have younger stellar age. This discrepancy for the low mass galaxies might suggest that our galaxy formation model is still too simple and we need processes that make effective star formation time-scale longer in smaller galaxies. When we do not consider the radiation pressure feedback, the redshift evolution of the mass-metallicity relation is slightly too strong and the slope of the relation is too steep at low redshift. The metallicity dependence of the radiation pressure feedback helps to make the simulation result broadly consistent with the observational estimates. This fact provides a strong case for the radiation pressure feedback. We find that the introduction of the AGN-like feedback and the radiation pressure feedback little affects the results at high redshift ($z > 2$). We thus expect that our conclusions derived from the simulations of high redshift galaxy population \citep{shimizu11, shimizu12, shimizu14, inoue14}, which only take the SN feedback into account, still hold. However the lack of the galaxies with SFR $\gg 100~M_\odot$~yr$^{-1}$ at $z > 2$, which exist in `SN' model, might become a problem to account for the sub-mm source number counts. We leave this issue for future work. The resolution study shows that the simulation results are converging numerically although the perfect numerical convergence has not been achieved at the current resolution. We show that, from a high resolution simulation, consistent results with the intermediate resolution simulation can be obtained by applying slightly stronger stellar feedback while the AGN-like feedback is remain unchanged. We expect that we would need little change in the parameter values if we employed even higher resolution because the simulation results in \citet{ofjt10} and \citet{okamoto13} nicely converged with $m_{\rm SPH}^{\rm orig} \lesssim 10^7~M_\odot$ for Milky Way-sized galaxies and with $m_{\rm SPH}^{\rm orig} \lesssim 10^6~M_\odot$ even for the Local Group satellite galaxies. The new model can apply for wider ranges of redshift and mass than the previous model that forms too massive galaxies in large halos, in particular, at low redshift. This simple model is well suited for simulations that relate high redshift galaxy population to the local one and for studies of coevolution of cluster galaxies and an ICM. \bigskip We would like to thank Ryu Makiya and Masahiro Nagashima for helpful discussion. Numerical simulations were carried out with Cray XC30 in CfCA at NAOJ and T2K-Tsukuba in Center for Computational Sciences at University of Tsukuba. TO acknowledges the financial support of Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Young Scientists (B: 24740112). IS acknowledges the financial support of JSPS Grant-in-Aid for Young Scientists (A: 23684010). YN acknowledges the financial support of JSPS Grant-in-Aid for Scientific Research (25287050) and the FIRST program Subaru Measurements of Images and Redshifts (SuMIRe) by the Council for Science and Technology Policy. | 14 | 4 | 1404.7579 |
1404 | 1404.5867_arXiv.txt | We investigate the relation between the optical (g-band) and X-ray (0.5–10 keV) luminosities of accreting nonmagnetic white dwarfs. According to the present-day counts of the populations of star systems in our Galaxy, these systems have the highest space density among the close binary systems with white dwarfs. We show that the dependence of the optical luminosity of accreting white dwarfs on their X-ray luminosity forms a fairly narrow one-parameter curve. The typical half-width of this curve does not exceed 0.2--0.3 dex in optical and X-ray luminosities, which is essentially consistent with the amplitude of the aperiodic flux variability for these objects. At X-ray luminosities $L_{\rm x}\sim 10^{32}$ \lum\ or lower, the optical g-band luminosity of the accretion flow is shown to be related to its X-ray luminosity by a factor $\sim$2--3. At even lower X-ray luminosities ($L_{\rm x}\sim 10^{30}$ \lum\ ), the contribution from the photosphere of the white dwarf begins to dominate in the optical spectrum of the binary system and its optical brightness does not drop below $M_{\rm g}\sim 13-14$. Using the latter fact, we show that in current and planned X-ray sky surveys, the family of accreting nonmagnetic white dwarfs can be completely identified to the distance determined by the sensitivity of an optical sky survey in this region. For the Sloan Digital Sky Survey (SDSS) with a limiting sensitivity $m_{\rm g}\sim 22.5$, this distance is $\sim$400--600 pc. | 14 | 4 | 1404.5867 |
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1404 | 1404.4861_arXiv.txt | { We study the evolution of two planets around a star, in mean-motion resonance and undergoing tidal effect. We derive an integrable analytical model of mean-motion resonances of any order which reproduce the main features of the resonant dynamics. \modif{ Using this simplified model, we obtain a criterion showing that depending on the balance of the tidal dissipation in both planets, their final period ratio may stay at the resonant value, increase above, or decrease below the resonant value.} \modif{Applying this criterion to} the two inner planets orbiting \object{GJ~163}, we deduce that the current period ratio (2.97) could be the outcome of dissipation in the 3:1 MMR provided that the innermost planet is gaseous (slow dissipation) while the second one is rocky (faster dissipation). We perform N-body simulations with tidal dissipation to confirm the results of our analytical model. \modif{We also apply our criterion on \object{GJ~581}b, c (5:2 MMR) and reproduce the current period ratio (2.4) if the inner planet is gaseous and the outer is rocky (as for \object{GJ~163}).} Finally, we apply our model to the \textit{Kepler} mission's statistics. We show that the excess of planets pairs close to first order MMR but in external circulation, i.e., with period ratios $P_{out}/P_{in} > (p+1)/p$ for the resonance $(p+1)$:$p$, can be reproduced by tidal dissipation in the inner planet. \modif{There is no need for any other dissipative mechanism, provided that these systems left the resonance with non-negligible eccentricities.} } | \label{sec:introduction} It has been shown that planets in first order mean-motion resonances (MMR) that undergo tidal dissipation naturally leave the resonant configuration by moving away from each other \citep{papaloizou_dynamics_2010,papaloizou_tidal_2011,lithwick_resonant_2012,delisle_dissipation_2012,batygin_dissipative_2013}. The tidal dissipation first induces a decrease of both eccentricities (as expected) and the system initially stays in resonance. However, when eccentricities reach low values, the ratio between the orbital periods of the outer planet and the inner one begins to increase (diverging orbits) as the eccentricities continue to decrease. If the timescale of the dissipation is sufficiently short (compared to the age of the system), the period ratio can significantly depart from the resonant value. It is important to note that during this process, the system never crosses the resonance separatrix. Indeed, the separatrix simply disappears at low eccentricities, and the system end-up with a period ratio $P_{out}/P_{in}$ greater than the resonant value \citep[e.g.][]{delisle_dissipation_2012}. However, if the amplitude of libration in the resonance becomes sufficiently high, the system may cross the separatrix before it disappears and may end-up either in the internal or the external circulation areas \citep[e.g.][]{novak_interesting_2003,goldreich_overstable_2014}. External circulation refers to the configuration where planets are close to a MMR $(p+q)$:$p$, but with a period ratio greater than the resonant value ($P_{out}/P_{in}>(p+q)/p$). On the contrary, internal circulation refers to the configuration $P_{out}/P_{in}<(p+q)/p$. In this study, we obtain a simple criterion on the dissipation undergone by planetary systems in MMR of any order to end-up in the resonant area, the internal or the external circulations areas. In section~\ref{sec:an-integr-simpl} we present a method to obtain a simple integrable model for resonances of any order. In section~\ref{sec:diss-reson-syst} we consider the evolution of the dynamics under dissipation. We focus on the evolution of the amplitude of libration in the resonance depending on the balance of dissipation in both planets. In section~\ref{sec:applications} we apply our reasoning to \object{GJ~163} (3:1 MMR) and \object{GJ~581} (5:2 MMR) planetary systems. Finally, in section~\ref{sec:kepler} we discuss the impact of resonance breaking induced by tides on \textit{Kepler} mission's multi-planetary systems statistics. | \label{sec:conclusion} We presented an integrable model of mean-motion resonances of any order. This model is highly simplified and cannot reproduce all the features of the resonant dynamics. However it allows to deduce a very simple criterion on the tidal dissipation undergone by both planets to end-up inside the resonance, or on a side or the other of the resonance. The main factors that enter into account are the balance of tidal dissipation between both planets ($T_1/T_2$ or $\Delta t_2/\Delta t_1$) and the position of the libration center (especially the ratio $e_1/e_2$). \modif{Using this criterion on the two inner planets orbiting \object{GJ~163} we deduce that the current period ratio (2.97) could be the outcome of dissipation in the 3:1 MMR provided that $\Delta t_2/\Delta t_1 \sim 1000$.} Using N-body simulations with dissipation we reach the same conclusion with slightly refined bounds for $\Delta t_2/\Delta t_1$. Both methods clearly imply that the inner planet should be gaseous and the outer planet should be rocky. The minimum masses of both planets (respectively 10.7 $M_\earth$ and 7.3 $M_\earth$) are compatible with this hypothesis, but since the inclinations and the radii are currently unknown, some uncertainty remains. \modif{We also applied this model to \object{GJ~581}b, c and could reproduce the current configuration with tidal dissipation in the 5:2 MMR if $\Delta t_2/\Delta t_1 \sim 300$. As for \object{GJ~163}, we conclude that the inner planet should be gaseous and the outer planet should be rocky, which is compatible with the minimum masses of both planets (respectively 15.86 $M_\earth$ and 5.34 $M_\earth$ for the inner and the outer planets). } As we noted in the case of \object{GJ~163}, some secondary resonances can affect the outcome of the considered system. \modif{Our integrable model of resonances is not able to predict such a complex behavior, as well as chaotic motion. This might be a limitation for high order resonances, which may show large chaotic areas.} Moreover, we make all our estimates using a constant eccentricity ratio ($e_1/e_2$) which is computed at the center of libration of the resonance. As eccentricities are being damped, the position of the libration center evolves and the eccentricity ratio is not constant. Depending on the resonance and on the considered range of eccentricities, the changes on the eccentricity ratio at the libration center can be non-negligible \citep[e.g.][]{michtchenko_stationary_2006}. Besides, when the amplitude of libration is small, eccentricities of both planets should be close to the values at the libration center, but when the system reaches the separatrix and leaves the resonance, the eccentricities can be significantly different. Therefore, this estimate of the eccentricity ratio is the main limit in our model and in the computation of criteria on the lag time ratio. However, as we observed in the cases of \object{GJ~163} and \object{GJ~581}, with this approximation we still obtain a good estimate of the order of magnitude of the lag time ratio and a better understanding of the mechanisms that are at stake in determining the outcome of the dissipative process. The most interesting cases to study are those in internal circulation because we can obtain strong constraints on the nature of the planets for our scenario to be possible (as for \object{GJ~163} and \object{GJ~581}). However, our mechanism also applies to many systems that are observed in external circulation. Indeed, in most cases, the tidal dissipation in the outer planet is negligible compared to the dissipation in the inner planet, and the most probable outcome for the system is external circulation. For first order MMR, external circulation can also be obtained when eccentricities are very low without crossing the separatrix of the resonance \citep[the separatrix simply disappear\modif{s} at low eccentricities, e.g.][]{delisle_dissipation_2012}. However, the subsequent evolution of the period ratio is very slow due to the smallness of the eccentricities. \citet{lee_kepler_2013} showed that for many systems the evolution of the period ratio is too slow to reach the current value on a reasonable timescale. We \modif{show} that a gain of 3-5 orders of magnitude on the timescale is obtained by considering a scenario of resonance breaking due to tides at non-negligible eccentricities ($e_1 \gtrsim 0.15$). \modif{This allows to explain the presence of an excess of planets in external circulation in \textit{Kepler} data without introducing any other mechanism than tidal dissipation.} | 14 | 4 | 1404.4861 |
1404 | 1404.1219_arXiv.txt | Radiatively inefficient, hot accretion flows are widely considered as a relevant accretion mode in low-luminosity AGNs. We study spectral formation in such flows using a refined model with a fully general relativistic description of both the radiative (leptonic and hadronic) and hydrodynamic processes, as well as with an exact treatment of global Comptonization. We find that the X-ray spectral index--Eddington ratio anticorrelation as well as the cut-off energy measured in the best-studied objects favor accretion flows with rather strong magnetic field and with a weak direct heating of electrons. Furthermore, they require a much stronger source of seed photons than considered in previous studies. The nonthermal synchrotron radiation of relativistic electrons seems to be the most likely process capable of providing a sufficient flux of seed photons. Hadronic processes, which should occur due to basic properties of hot flows, provide an attractive explanation for the origin of such electrons. | 14 | 4 | 1404.1219 |
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1404 | 1404.5506_arXiv.txt | \noindent We report the results of VLBI observations of H$_{2}$O masers in the IRAS 20143+3634 star forming region using VERA (VLBI Exploration of Radio Astronomy). By tracking masers for a period of over two years we measured a trigonometric parallax of $\pi = 0.367 \pm 0.037$ mas, corresponding to a source distance of $D = 2.72 ^{+0.31}_{-0.25}$ kpc and placing it in the Local spiral arm. Our trigonometric distance is just 60\% of the previous estimation based on radial velocity, significantly impacting the astrophysics of the source. We measured proper motions of $−2.99 \pm 0.16$ mas yr$^{-1}$ and $−4.37 \pm 0.43$ mas yr$^{-1}$ in R.A. and Decl. respectively, which were used to estimate the peculiar motion of the source as $(U_{s},V_{s},W_{s}) = (-0.9 \pm 2.9, -8.5 \pm 1.6, +8.0 \pm 4.3)$ km s$^{-1}$ for $R_0=8$ kpc and $\Theta_0=221$ km s$^{-1}$, and $(U_{s},V_{s},W_{s}) = (-1.0 \pm 2.9, -9.3 \pm 1.5, +8.0 \pm 4.3)$ km s$^{-1}$ for $R_0=8.5$ kpc and $\Theta_0=235$ km s$^{-1}$. IRAS 20143+3634 was found to be located near the tangent point in the Cygnus direction. Using our observations we derived the angular velocity of Galactic rotation of the local standard of rest (LSR), $\Omega_{0} = 27.3 \pm 1.6$ km s$^{-1}$ kpc$^{-1}$, which is consistent with previous values derived using VLBI astrometry of SFRs at the tangent points and Solar circle. It is higher than the value recommended by the IAU of $\Omega_{0} = 25.9$ km s$^{-1}$ kpc$^{-1}$ which was calculated using the Galactocentric distance of the Sun and circular velocity of the LSR. | The Galactic circular rotation velocity evaluated at the position of the Sun, $\Theta_{0}$, and the Galactocentric distance to the Sun, $R_{0}$, are two of the fundamental parameters used in discussing the structure and kinematics of the Milky Way. These parameters are central to estimating the kinetic distance of Galactic sources, thus influencing estimations of their physical properties. Furthermore, these parameters affect the shape of the Galactic rotation curve which has long been an essential tool for evaluating the dynamical mass distribution in the Milky Way. The International Astronomical Union (IAU) recommends values of $R_{0} = 8.5$ kpc and $\Theta_{0}=220$ km s$^{-1}$ for the Galactocentric distance of the Sun, and Galactic circular velocity of the LSR \citep{Kerr86}. However a growing number of astrometric observations utilising very long baseline interferometer (VLBI) suggest the need to revise these values (\citet{Reid09,Honma12} \emph{and references therein}), further stressing the importance of VLBI astrometry in our understanding of the Milky Way. It is possible to estimate $\Theta_{0}$ and $R_{0}$, hereby referred to as the Galactic constants, by measuring the distance and motion of many sources in the disk of the Milky Way, with respect to the local standard of rest (LSR). Historically, they have been derived from global sinusoidal patterns shown in the proper motions and radial velocities of nearby stars \citep{Oort27}. However, this method is based on the assumption that the systematic motion of the Solar neighbourhood does not deviate from Galactic circular motion. To circumvent this problem we must extend the sampling region to beyond the optical observable range, which is limited by interstellar extinction. VLBI astrometry is a viable approach since radio observations do not suffer from interstellar extinction. There are two approaches to estimating the Galactic constants. One method uses a sample of sources widely distributed on the Galactic disk. With a kinematic model of the Galaxy, multi-parameter fitting determines the Galactic constants. Although this approach has the advantage of statistically reducing the random motion inherent in the source sample by increasing the number of sources, the reliability of this method is undermined by the high number of variable parameters that are simultaneously solved for. The other approach focuses on sources at special locations where the Galactic constants can be derived with a lower dependancy on the model of Galactic kinematics. Two such locations are positions on the Solar circle and at the tangent point, defined as the position closest to the Galactic center on the assigned line of sight. Astrometric observations of a source near these locations can give the ratio of the constants, $\Omega_0=\Theta_0/R_0$, with appropriate accuracy even if we do not know the exact location of the source \citep{Nagayama11a,Ando11}. IRAS 20143+3634 is an intermediate to high mass star forming region (SFR), as shown in this paper. Furthermore, IRAS 20143+3634 resides near the tangent point in the Cygnus direction. A source at the tangent point, with negligibly small deviation from the Galactic circular motion, moves only along the line of sight to the Sun. Thus we can infer that any lateral proper motion observed on the sky reflects only the Galactic rotation of the LSR, which leads to a simplified estimation of $\Theta_{0}$, independent of the shape of the rotation curve. In this work, our aim was to use the astrometry of H$_{2}$O masers in IRAS 20143+3634 to measure its trigonometric distance and motion in the Galactic plane. Using these results, and those of other sources at the tangent points and Solar circle, we investigated the Galactic constants with fewer assumptions on Galactic structure and kinematics. This simplified approach may be considered more robust than the multi-parameter fitting method. IRAS 20143+3634 is an infrared source listed in the IRAS point source catalogue \citep{IRAS88}, undergoing intermediate to high mass star formation. This source exhibits a highly compact core, seen in CS$(J=2-1)$ observations \citep{Ao04}, and wide velocity wings in $^{12}$CO($J=1-0$) indicative of the presence of outflows \citep{Yang02}. Disentangling the proper and parallactic motions of masers requires precise astrometric observations. Such precision is available through VLBI maser monitoring using VLBI Exploration of Radio Astronomy (VERA) \citep{Koba03}. All astrometric observations used in this paper were obtained by positionally referencing 22 GHz H$_{2}$O masers with respect to a well defined quasar position, which gives the source position in six dimensional phase-space. The first detection of H$_{2}$O maser emission in IRAS 20143+3634 was made by \citet{Sunada07}. In this paper we present the first VLBI observations of the annual parallax and proper motions of H$_{2}$O masers in IRAS 20143+3634. Using these measurements we measured the distance of IRAS 20143+3634 from the Sun and evaluated the Galactic constants. This paper continues as follows: Observations and data reduction are discussed in \S2. Results are reported in \S3, including the methods used to evaluate the parallactic, internal and systemic motions of masers, and motion of the driving source. In \S4 we re-evaluate the physical parameters of IRAS20143+3634 from archive data, using our new distance estimate. We then discuss in detail the evaluation of $\Omega_{0}$, the ratio of the Galactic constants, for a variety of methods and sources. Finally, we make comparisons between the observationally determined values of $\Omega_{0}$, and that which is derived from the ratio of the IAU recommended Galactic constants. Conclusions made in this paper are summarised in \S5. | By observing H$_{2}$O masers for a period of over two years with VERA, we measured the parallactic distance of IRAS 20143+3634. Our distance of $D = 2.72 ^{+0.31}_{-0.25}$ kpc is 60\% of the previous distance estimate based on the LSR velocity. The new distance places IRAS 20143+3634 in the Local spiral arm, near to the tangent point in the Cygnus direction. With our distance estimate, we re-estimated the virial and core masses of IRAS 20143+3634 to be $M_{\rm vir} =213 M_{\odot}$ and $M_{\rm LTE} = 22 M_{\odot}$ using data from \cite{Ao04}, which were 360 $M_\odot$ and 64 $M_\odot$ in the original paper, respectively. The source appears to be more violent than those authors previously thought and has yet to have dissipated turbulent motions inherent in the core. Nevertheless, their conclusions on the general trend of YSOs are still valid. Combining this view with an SED compiled from mid- and far-infrared fluxes from AKARI and WISE, IRAS 20143+3634 appears as a young, 7.62 $M_{\odot}$ intermediate to high mass YSO. Our distance gives the location of IRAS 20143+3634 to be near the tangent point. As \citet{Nagayama11a} show, astrometric observations of a source near the tangent point provide the ratio of the Galactic constants $\Omega_{0}$ with little dependence of the Galactocentric distance of the Sun, $R_{0}$. From the astrometry of IRAS 20143+3634 we obtained $\Omega_0=27.3\pm1.6$ km s$^{-1}$ kpc$^{-1}$. The value changes only $\pm0.02$ km s$^{-1}$ kpc$^{-1}$, if we vary the value of the Galactocentric distance to the Sun between $7 \le R_{0} \le 9$ kpc. The values of $\Omega_0$ derived from previous VLBI astrometric observations of sources near the tangent points and the Solar circle are consistent with each other. This consistency supports the simple circular rotation model of the Milky Way. The average value of these estimates is $\Omega_{0} =27.6\pm0.7$ km s$^{-1}$ kpc$^{-1}$. This value is also consistent with values based on other procedures and it is worth noting that all but few are higher than that calculated from the ratio of the Galactic constants recommended by the IAU since 1985 \citep{Kerr86}. The peculiar motion of IRAS 20143+3634 deviates from the simple circular rotation by about 10 km s$^{-1}$, which is consistent with the random velocity of sources in the Galactic disk. \null R.B. would like to acknowledge the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan for financial support under the Monbukagakusho scholarship. \null T.H. acknowledges support from Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation (number R2308) by Japan Society for the Promotion of Science (JSPS). \null We would also like to thank the anonymous referee for thoroughly checking our work, and providing the necessary comments and advice that contributed to improving the manuscript. | 14 | 4 | 1404.5506 |
1404 | 1404.0609_arXiv.txt | On the surface of a rapidly rotating neutron star, the effective centrifugal force decreases the effective acceleration due to gravity (as measured in the rotating frame) at the equator while increasing the acceleration at the poles due to the centrifugal flattening of the star into an oblate spheroid. We compute the effective gravitational acceleration for relativistic rapidly rotating neutron stars and show that for a star with mass $M$, equatorial radius $R_e$, and angular velocity $\Omega$, the deviations of the effective acceleration due to gravity from the nonrotating case take on a universal form that depends only on the compactness ratio $M/R_e$, the dimensionless square of the angular velocity $\Omega^2R_e^3/GM$, and the latitude on the star's surface. This dependence is universal, in that it has very little dependence on the neutron star's equation of state. The effective gravity is expanded in the slow rotation limit to show the dependence on the effective centrifugal force, oblate shape of the star and the quadrupole moment of the gravitational field. In addition, an empirical fit and simple formula for the effective gravity is found. We find that the increase in the acceleration due to gravity at the poles is of the same order of magnitude as the decrease in the effective acceleration due to gravity at the equator for all realistic value of mass, radius and spin. For neutron stars that spin with frequencies near 600 Hz the difference between the effective gravity at the poles and the equator is about 20\%. | \label{s:intro} Slowly rotating neutron stars have properties that show a surprising universality that appear to be independent of the equation of state (EOS): given a neutron star's moment of inertia, a simple formula then determines the star's quadrupole moment and tidal Love number \citep{Yagia,Yagib}. This type of universal relation has been extended to the star's ellipticity \citep{Baubock2013} and to rapidly rotating neutron stars \citep{Doneva2014,Yagi2014}. These ``I-Love-Q" relations have only an implicit dependence on the EOS: the EOS limits the possible values of mass and radius that a star with given spin may have. Once the mass, radius and spin are determined, the other properties are determined through the universal relations. In other words, the EOS limits the values the star's moment of inertia may take, but once this is known, the I-Love-Q relations determine the Love number and quadrupole moment. In this paper, we derive equations for the effective acceleration due to gravity on the surface of a rapidly rotating neutron star that only have an implicit dependence on EOS. The effective acceleration due to the gravity, also known as the effective gravity, is an important property in astrophysics, and is required in many applications, such as atmosphere modeling \citep{Heinke06,Sul}, X-ray bursts \citep{Spitk,Cooper}, and Eddington limited X-ray bursts \citep{Ozel2013}. The results in this paper can be applied to any neutron star spinning with a frequency less than the break-up limit, however the results are most relevant for the stars that spin with frequencies above approximately 500 Hz. There are at least 15 accretion and rotation powered neutron stars with spins in this range \citep{Watts,Papitto2014}. The I-Love-Q relations could be derived by first noting that the expressions for moment of inertia $I$, Love number and quadrupole moment $q$ depend only (after spin is factored out) on the dimensionless compactness ratio, defined by \be x = \frac{M}{R_e} \ee where $R_e$ is the radius of the star's equator as measured using the Schwarzschild radial coordinate. We use geometric units where $G=c=1$. If we have a function for the moment of inertia of the form $I(x)$, this can (assuming good mathematical behaviour) be inverted to form an equation for the compactness of the form $x(I)$. If we have an equation for $q$ that is also of form $q(x)$, then this is equivalent to the universal form $q(I)$. In this way, a formula for any quantity that depends only on the compactness can be thought of as universal. The introduction of rapid rotation requires the introduction of another dimensionless ratio, the dimensionless angular velocity $\bOmega$, \be \bOmega = \Omega \left(\frac{R_e^3}{M}\right)^{1/2}. \ee Properties of a rotating star that depend only the two dimensionless ratios are universal in the following sense: given an EOS, the possible values of the two ratios are determined. Once values for $x$ and $\bOmega$ are known, then the property of the star is known with only an implicit dependence on the EOS. This type of universality has previously been noted for the star's oblate shape \citep{Morsink2007}, and the universality has been an important feature allowing the extraction of mass-radius constraints for accretion-powered pulsars \citep{Morsink2011,Leahy2011}. In this paper, we derive the dependence of the effective gravity on the two dimensionless parameters and show that it too has a universal nature that is almost independent of the equation of state. This universality allows us to find a simple empirical formula for the effective gravity. In Section \ref{s:rotate} we introduce the metric for rotating stars, as well as the slow rotation expansion of the metric. The parametrized expansion that we use to construct universal relations is introduced in Section \ref{s:para} and applied to the moment of inertia, quadrupole moment and stellar oblateness, since these quantities will be required in the computation of the effective gravity. The derivation of the formula for the effective gravity is made in Section \ref{s:accel} and universal nature of its dependence on the dimensionless parameters demonstrated. In Section \ref{s:slow}, the slow rotation expansion is applied to the formula for the effective gravity in order to aid the intuition in how it depends on the moment of inertia, quadrupole moment and oblate shape. In Section \ref{s:rapid} we derive a simple empirical formula for the effective gravity on the surfaces of rapidly rotating stars. Finally, we conclude in Section \ref{s:final} with a discussion of astrophysical applications. | \label{s:final} In this paper we computed the effective acceleration due to gravity as measured in the rotating frame on the surface of a rapidly rotating relativistic neutron star. We find that the effective gravity can be written as the simple function $g(\theta) = c(M/R_e, \Omega^2 R_e^3/(GM),\theta) g_0$, where $g_0 = GM/(R_e^2\sqrt{1-2GM/R_ec^2})$ is the acceleration due to gravity on the surface of a non-rotating relativistic star. The dimensionless function $c$ has a universal form in that it is almost independent of the neutron star's equation of state, and only depends on the dimensionless parameters $x=M/R_e$ and $\bOmega^2 = \Omega^2 R_e^3/(GM)$ as well as latitude on the star's surface. The dimensionless function $c$ is expanded in the slow rotation limit to bring about an intuitive understanding of the contributions to the effective gravity arising from the centrifugal force, the oblate shape and the quadrupole moment of the gravitational field. In addition, we provide an empirical fit to the function $c$ for rapid rotation. As expected, the effective centrifugal force decreases the effective gravity, while the centrifugal flattening of the star into an oblate shape increases the effective gravity at the poles. In addition, the quadrupole moment of the gravitational field increases the effective gravity at the equator and decreases it at the poles, however the quadrupole correction is a small correction to the main effects due to the effective centrifugal force. For all rotation rates and compactness ratios, the increase in the effective gravity at the poles is of the same order of magnitude as the decrease in the effective gravity at the equator. The slow rotation limit ($\bOmega^2 \le 0.1$) is a good approximation for neutron stars and pulsars with spin frequencies up to about $600$ Hz. This statement is EOS dependent, but it would take a very low mass and large radius (say $1.0 M_\odot$ and 15 km) to bring $\bOmega^2$ up to 0.3 which is the maximum value of the spin parameter that the slow rotation limit can be applied to. For the observed ms-period pulsars and accreting neutron stars, the slow rotation approximation for the effective acceleration, Equation (\ref{eq:slowaccel}), is valid. Using this approximation, the difference between the effective acceleration at the pole and equator is \be {g_p - g_e} = g_0 \bOmega^2 (|c_p| + |c_e|) = g_0 \bOmega^2 ( 1.93 - 2.2 M/R_e ). \ee Similarly, the fractional change (compared to the equator) is \be \frac{g_p - g_e}{g_e} = \bOmega^2( |c_p| + 2 |c_e|) = \bOmega^2 (2.72 - 3.0 M/R_e), \ee which is close to 3 times larger than the estimate $(g_p-g_e)/g_e \sim \bOmega^2$ used by many authors (for example, see \citet{Watts}). For one of the representative stellar models with $\bOmega^2=0.1$ and $M/R_e = 0.195$ given in Table \ref{tab:HLPS2}, the fractional change in the effective acceleration with respect to the equator is 0.2, or a 20\% change. Most atmosphere models include a dependence on the effective acceleration due to gravity as one of the parameters.Typically, the dependence is on the logarithm of the surface gravity. It is useful then to compute the difference in the logarithm of the surface gravity at the pole and at the equator, \be \log(g_p) - \log(g_e) = \bOmega^2 (|c_p| + |c_e|) . \ee For the same representative models, this is a difference of 0.15 in dex. Although this seems like a small change, this is the same change in acceleration one would find by changing the mass of the star by 15\%. Changes of this order of magnitude make small but visible changes to the flux predicted by Hydrogen atmosphere models \citep{Heinke06}, which are used to model X-ray transients and X-ray ms-pulsars. The X-ray pulsars studied by \citet{Bog} are rotating slowly enough ($\nu_\star\sim 200$ Hz) that the latitudinal dependence of the effective acceleration is not important. However, the X-ray transients (such as EXO 0748-676 with a spin frequency of 552 Hz) are spinning rapidly enough that the change in gravity over latitude may affect the interpretation of observations such as those by \citet{Degen}. Similarly, atmosphere models \citep{Sul} for neutron stars undergoing Type I X-ray bursts also depend the effective gravity. The Type I X-ray bursts observed in some X-ray binaries are caused by unstable nuclear burning on the surfaces of neutron stars (see \citet{Galloway} for a review). There are at least 10 bursting neutron stars with spin frequencies of 500 Hz or more \citep{Watts}, which is fast enough that the change in gravitational acceleration over the surface is a significant factor. In early studies of Type I X-ray bursts \citep{Spitk}, it was argued that the ignition would take place at the equator since that is where the effective acceleration due to gravity is smallest. However, \citet{Cooper} showed that the critical mass-accretion rate, which is the largest rate that allows unstable nuclear burning, varies with the effective gravity as $\dot{M} \sim g(\theta)^{3/2}$. This leads to range of mass accretion rates that are too high to allow ignition at the equator, but allow ignition at higher latitudes due to the higher surface gravity. Since the fractional change in the effective acceleration is about 2.5 times larger than that estimated by \citet{Cooper}, the range of mass accretion rates that could lead to high latitude ignition is larger, roughly 20-30\% of the critical mass accretion rate at the equator. \citet{Maurer} have shown that there is good evidence that off-equatorial burst ignition is taking place in the burster 4U 1636-536 and may be relevant in other Type I X-ray bursters. The Eddington luminosity at the surface of a neutron star can be written \be L_{Edd} = L_0 \frac{ R^2(\theta) (1-2M/R(\theta)) g(\theta)}{M}, \label{eq:edd} \ee where $L_0$ is the regular expression for the Eddington luminosity (see \citet{Ozel2013} for a review) in flat space \be L_0 = \frac{ 8\pi G M m_p c}{(1+X)\sigma_T}, \ee which is independent of the star's radius. In Equation (\ref{eq:edd}), the factor $(1-2M/R)$ corresponds to the gravitational redshift of the light, and we are not considering (at this time) the extra Doppler shift due to rotation. The dependence of the Eddington luminosity on the effective gravity leads directly to a reduction of the Eddington limit at the star's equator and an increase at the poles. The Eddington limit at the equator is \be L_{Edd,e} = L_0 ( 1 - 2M/R_e )^{1/2} (1 - |c_e| \bOmega^2), \ee while at the pole it is \be L_{Edd,p} = L_0 ( 1 - 2M/R_p )^{1/2}, \ee where we are approximating the effective gravity at the pole by just the oblate term given by Equation (\ref{eq:goblate}). The ratio of the gravitational redshift terms at the pole and equator is of order $\bigo(\bOmega^2 \times M/R)$ so the term proportional to $c_e$ is the most important correction due to rotation. For stars with a rotation parameter near $\bOmega^2=0.1$, we then expect a difference in the Eddington limit of up to 10\% between the poles and equator. It should be noted that \citet{LM95} carefully considered the effect of rotation on the Eddington limit and found no changes. However, their analysis was for stars rotating more slowly than the ones that we consider, so there is no conflict in our results. During a photospheric radius expansion (PRE) burst, the flux generated by the Type I X-ray burst is large enough to exceed the Eddington limit, causing the photosphere to expand to many times the radius of the star \citep{Lewin}. The change in the Eddington limit given above is only valid when the atmosphere is in hydrostatic equilibrium and co-rotating with the rest of the star. As the photosphere expands, if the material continues to co-rotate, it will quickly reach the mass shed limit which will have the effect of taking the material in the photosphere out of co-rotation. At the end of the burst, the flux is reduced to below the Eddington limit and the photosphere "touches down" onto the surface of the star, regaining hydrostatic balance and co-rotation. Since the Eddington limit is largest at the poles and smallest at the equator, we expect that touch-down first occurs at the poles and then quickly moves down to the equator as the atmosphere cools. The relevant Eddington flux that should be equated with the asymptotic "touch-down" flux is the Eddington flux at the equator. This will introduce correction terms for the masses and radii derived (for example see \citet{Ozel12}) from measurements of PRE-bursts for the most rapidly rotating stars, such as KS 1731-260 which has a spin of 524 Hz. A full treatment of the corrections arising from rapid rotation on the masses and radii derived from PRE burst is beyond the scope of this paper and requires an examination of the apparent area of the bursting star \citep{Baubock2012} as well as raytracing to find the mapping between the locally produced flux and the flux measured at infinity. | 14 | 4 | 1404.0609 |
1404 | 1404.7735_arXiv.txt | We extend the Kolmogorov--Smirnov (K-S) test to multiple dimensions by suggesting a $\mathbb{R}^n \rightarrow [0,1]$ mapping based on the probability content of the highest probability density region of the reference distribution under consideration; this mapping reduces the problem back to the one-dimensional case to which the standard K-S test may be applied. The universal character of this mapping also allows us to introduce a simple, yet general, method for the validation of Bayesian posterior distributions of any dimensionality. This new approach goes beyond validating software implementations; it provides a sensitive test for all assumptions, explicit or implicit, that underlie the inference. In particular, the method assesses whether the inferred posterior distribution is a truthful representation of the actual constraints on the model parameters. We illustrate our multidimensional K-S test by applying it to a simple two-dimensional Gaussian toy problem, and demonstrate our method for posterior validation in the real-world astrophysical application of estimating the physical parameters of galaxy clusters parameters from their Sunyaev--Zel'dovich effect in microwave background data. In the latter example, we show that the method can validate the entire Bayesian inference process across a varied population of objects for which the derived posteriors are different in each case. | \label{sect:Introduction} The Kolmogorov--Smirnov (K-S) test and its close variants are the most widely-accepted methods for testing whether a set of continuous sample data is drawn from a given probability distribution function $f(x)$ \citep[see, e.g.,][ch. 14.3.3]{NumericalRecipes2007}. The test is based on the computation of the maximum absolute distance $D$ between the cumulative distribution functions (CDFs) of the data and of $f(x)$. In particular, it has the advantage that, in the `null hypothesis' that the data are indeed drawn from $f(x)$, the distribution of $D$ is both independent of the form of $f(x)$ (i.e. the test is `distribution-free') and can be calculated, at least to a good approximation. Moreover, the test is invariant under reparameterizations of $x$. In its standard form, however, the K-S test is restricted to one-dimensional data, since a CDF can only be defined uniquely in the univariate case. Considerable effort has been made to extend the K-S test to $n$-dimensional data sets, much of it building on the pioneering work of \cite{Peacock_KS}, but this has proved very challenging precisely because a CDF is not well-defined in more than one dimension. Working initially in two dimensions, Peacock's original insight was to replace the notion of a CDF with the integrated probability in each of the four natural quadrants around any given data point $(x_i,y_i)$, and define the distance measure $D$ as the maximum absolute difference (ranging both over data points and quadrants) of the corresponding integrated probabilities for the data and the theoretical distribution $f(x,y)$. This basic idea can, in principle, be extended straightforwardly to higher dimensions, but in practice suffers from an exponential growth in complexity, since the number of independent integrated probabilities about any given data point is $2^n-1$ in $n$-dimensions, although \cite{Franceschini1987} suggest an algorithm with better scaling. Perhaps a more notable deficit is that, in the null hypothesis, the distribution of $D$ is {\em not} independent of the form of $f(x,y)$, although \cite{NumericalRecipes2007} reassure us that extensive Monte Carlo simulations show the distribution of the two-dimensional $D$ to be very nearly identical for even quite different distributions, provided they have the same correlation coefficient \citep{Franceschini1987} . \cite{Lopes2008} contains a review that ranks the performance of a range of different multidimensional K-S tests that are variants of Peacock's original proposal. A completely different approach to extending the K-S test to multiple dimensions was advanced by \cite{Justel1997} and employs the Rosenblatt transformation, which maps any distribution into the unit hyper-cube \citep{rosenblatt1952}. Despite this approach being formally sound, the authors report insurmountable difficulties when extending the test to more than two dimensions. In this paper, we present a new proposal for extending the K-S test to multiple dimensions, which is free from the weaknesses discussed above and scales straightforwardly with the dimensionality of the data-set. Our approach is to introduce the $\mathbb{R}^n \rightarrow [0,1]$ mapping from any given (data) point $\bmath{x}_i$ in the $n$-dimensional parameter space to the probability mass $\zeta$ of the putative theoretical distribution $f(\bmath{x})$ contained within the highest probability density (HPD) region having $\bmath{x}_i$ on its boundary. This mapping has the convenient property that under the null hypothesis that the data are drawn from $f(\bmath{x})$, the probability mass $\zeta$ is uniformly distributed in the range $[0,1]$, independently of the form of $f(\bmath{x})$. The set of values $\{\zeta_i\}$ corresponding to the data points $\{\bmath{x}_i\}$ can then be compared with the uniform distribution in a standard one-dimensional K-S test (or one of its variants). The ability to test the hypothesis that a set of data samples are drawn from some general $n$-dimensional probability distribution $f(\bmath{x})$ has an interesting application in the validation of Bayesian inference analyses (indeed this application provided our original motivation for seeking to extend the K-S test to multiple dimensions). Bayesian methods are now pervasive across all branches of science and engineering, from cognitive neuroscience \citep{Doya:2007} and machine learning \citep{Bishop:2006:PRM:1162264}, to spam filtering \citep{Sahami98abayesian} and geographic profiling (\citealt{geographic_profiling}, \citealt{LandminesBayesianDetection}). In precision cosmology, Bayesian inference is the main tool for setting constraints on cosmological parameters \citep{PlanckParameters,WMAP9Parameters}, but very few attempts have been made to assess whether the derived posterior probability distributions are a truthful representation of the actual parameter constraints one can infer from the data in the context of a given physical model. This lack of validation has been highlighted by several authors, with the strong dependence of the inference results on the priors being of particular concern \citep{GeorgeBayes,LindMiq}. There have been attempts to address this issue, ranging from the approach of \citet{Cook06validationof}, which was designed with software validation solely in mind, to a method based on the inverse probability integral transform (Smirnov transform) applied to posterior distributions, that extends to spaces of higher dimensionality via marginalisation \citep{FnlVal}. Also, validation of the Bayesian source-finding algorithm of \cite{PwSII} was performed in \citet{PlanckResultsSZ}, but only point estimates deduced from the posterior distributions were actually verified. Our method for addressing this problem is based on our applying our multidimensional extension of the K-S test to sets of Monte-Carlo simulations of the data and the posterior distributions derived therefrom. In particular, it can take advantage of the fact that one may typically generate simulations that are of greater sophistication and realism than may be modelled in the inference process, and thus allows for a more thorough validation of the inference than has been possible with the methods developed previously. In particular, our validation procedure enables us to test all the assumptions made (explicitly or implicitly) in the inference process, such as the statistical description of the data, model assumptions and approximations, as well as the software implementation of the analysis. Moreover, we consider the full posterior distribution, regardless of its dimensionality and form, without the need to resort to marginalization, and thereby keeping intact its $n$-dimensional character. This paper is organised as follows. Section~\ref{sect:MathFrame} provides the mathematical background for our extension of the K-S test to multiple dimensions and Section~\ref{sec:Validation} describes its application to the validation of Bayesian inference analyses. In Section~\ref{sect:ToyModel} we apply our multidimensional K-S test to a simple toy problem, and in Section~\ref{sect:PlanckSZcase} we illustrate our Bayesian inference validation procedure by applying it to the real astronomical example of detecting and characterising galaxy clusters in observations of the microwave sky through their Sunyaev--Zel'dovich effect. We conclude in Section~\ref{sect:Conclusions}. | \label{sect:Conclusions} In this paper we firstly present a practical extension of the K-S test to $n$-dimensions. The extension is based on a new variable $\zeta$, that provides a universal $\mathbb{R}^n \rightarrow [0,1]$ mapping based on the probability content of the highest probability density region of the reference distribution under consideration. This mapping is universal in the sense that it is not distribution dependent. By exploiting this property one may perform many simultaneous tests, with different underlying distributions, and provide an ensemble goodness-of-fit assessment. We then present a new statistical procedure for validating Bayesian posterior distributions of any shape or dimensionality. The power of the method lies in the capacity to test all of the assumptions in the inferential machinery. The approach goes beyond the testing of software implementation and allows robust testing of the assumptions inherent in the construction of the likelihood, the modelling of data and in the choice of priors. This approach enables the observables to inform our understanding of the importance the various components of the model given the data. It is, therefore, possible to tune the complexity of a model to reflect the information actually available in the posterior, improving the parsimony of the inference in keeping with Occam's Razor. Conversely, important hidden parameters or overly-restrictive prior assumptions can be identified and treated properly. In the application to SZ cluster parameter inference from \planck data, we demonstrate how the method can be applied to a large population where the posterior distributions vary. The information from a full cluster population can be combined to test the inference in the presence of varying stochastic and systematic uncertainties, as well as a varying signal component. For this application, we have found that the simplified \planck cluster likelihood is robust to real world complications such as Galactic foreground contamination and realistic beams. The sensitivity of the inference to prior assumptions on the outer slope of the pressure profile has been identified, as has the insensitivity to assumptions on the pressure profile in the core regions of the cluster for the inference of the integrated Compton-Y parameter. This approach could be of use in improving the pool of available SZ data from high-resolution microwave experiments, which to date have provided either non-Bayesian point estimates for cluster parameters or parameter proxies (\citealt{act}, \citealt{spt}), or unvalidated Bayesian posterior distributions \citep{ami}. These experiments have different dependencies on cluster parameters given their different resolutions, parameterisations and observation frequencies. A fuller understanding of the nature of these dependencies and the sensitivity of the derived posteriors to assumptions of the cluster model will ensure the robustness of the results and maximise the wider scientific returns due to the complementarity of the data-sets. Beyond astronomy, the methodology we have introduced may be applied to Bayesian inference more generally, in any situation where higher levels of complexity and fidelity can be introduced into simulations than can be allowed for in a tractable analysis, or where there exists a pool of pre-existing real data with known outcomes. | 14 | 4 | 1404.7735 |
1404 | 1404.2056_arXiv.txt | We analyse the stellar populations in the host galaxies of 53 X-ray selected optically dull active galactic nuclei (AGN) at 0.34$<$z$<$1.07 with ultra-deep (m$_{AB}$$=$26.5, 3$\sigma$) optical medium-band (R$\sim$50) photometry from the Survey for High-z Absorption Red and Dead Sources (SHARDS). The spectral resolution of SHARDS allows us to consistently measure the strength of the 4000 \AA{} break, \Dnu, a reliable age indicator for stellar populations. We confirm that most X-ray selected moderate-luminosity AGN (L$_X$$<$10$^{44}$ erg s$^{-1}$) are hosted by massive galaxies (typically M$_*$ $>$10$^{10.5}$ M$_\odot$) and that the observed fraction of galaxies hosting an AGN increases with the stellar mass. A careful selection of random control samples of inactive galaxies allows us to remove the stellar mass and redshift dependences of the AGN fraction to explore trends with several stellar age indicators. We find no significant differences in the distribution of the rest-frame U-V colour for AGN hosts and inactive galaxies, in agreement with previous results. However, we find significantly shallower 4000\AA{} breaks in AGN hosts, indicative of younger stellar populations. With the help of a model-independent determination of the extinction, we obtain extinction-corrected U-V colours and light-weighted average stellar ages. We find that AGN hosts have younger stellar populations and higher extinction compared to inactive galaxies with the same stellar mass and at the same redshift. We find a highly significant excess of AGN hosts with \Dnu$\sim$1.4 and light weighted average stellar ages of 300--500 Myr, as well as a deficit of AGN in intrinsic red galaxies. We interpret failure in recognizing these trends in previous studies as a consequence of the balancing effect in observed colours of the age-extinction degeneracy. | In the current paradigm of galaxy evolution, the growth of supermassive black holes (SMBH) and the galaxies that host them are intertwined \citep[see][, for a review]{Alexander12}. Observational evidence includes the tight correlation between the mass of the SMBH and the velocity dispersion in the bulge of the galaxies \citep[the so-called M-$\sigma$ relation;][]{Magorrian98, Ferrarese00,Gebhardt00,Marconi04} as well as a remarkable similarity between the redshift evolution of the cosmic star formation rate density and the integrated black hole accretion rate ($\dot M_{\rm BH}$), with both having their peak at $z$$\sim$1--3 and a steep decline from $z$$\sim$1 to the present \citep[e.g.,][]{Boyle98,Franceschini99,Merloni04,Chapman05,Merloni08,Silverman08,Bouwens09,Aird10}. In addition, active galactic nuclei (AGN), like star-forming galaxies, display a form of `downsizing' by which the bulk of SMBH growth and star formation shifts to lower luminosity or less massive systems at later epochs \citep{Cowie03,Fiore03,Hasinger05,Bongiorno07}. Star formation takes place in one of two regimes. The majority of star formation \citep[up to 90\% at $z$$\sim$1--3;][]{Rodighiero11} occurs in secularly evolving systems, where internal processes (e.g. disc instabilities, turbulence) are responsible for gas dynamics that drive star formation \citep[e.g.][]{Elbaz07,Elbaz11,Tacconi08, Daddi10, Genzel10}. In these systems, the star formation rate (SFR) at a given redshift is roughly proportional to the galaxy mass, defining the so-called `main-sequence' \citep{Noeske07}. However, a small fraction of galaxies sustain more efficient star formation in compact starbursts, which are commonly associated with mergers. Since both major mergers and internal processes are considered to be able to transport dust and gas to the inner regions of a galaxy \citep[e.g.][]{Kormendy04,Hopkins06}, finding the trigger for nuclear activity is not straightforward. Early works suggested nuclear activity to be closely linked with major mergers, largely due to the high fraction of quasars that appear to be associated with merging systems \citep[e.g.][]{Sanders88,Sanders96,Surace98,Canalizo01,Ivison10}. However, later studies on the morphology of lower luminosity (L$_X$$<$10$^{44}$ erg s$^{-1}$) AGN hosts suggested that moderate levels of nuclear activity are typically associated with secular evolution rather than major mergers \citep[e.g.][]{Grogin05, Cisternas11, Schawinski11}. The interplay between nuclear activity and star formation is not well understood. The luminosity and accretion rate of the most powerful AGN is found to correlate with the SFR in the host galaxy \citep[e.g.][]{Shi07,Chen13}, suggesting an important contribution of major mergers to the build up of the M-$\sigma$ relation. On the other hand, the majority of low and intermediate-luminosity AGN are not associated with major mergers, as many of them are hosted by ``normal'' discs \citep{Gabor09, Cisternas11, Ellison11, Schawinski11, Silverman11, Kocevski12}. Albeit high resolution observations of local Seyferts have shown hints of a correlation between AGN activity and circumnuclear SFR in scales $\lesssim$1 kpc \citep[e.g.][]{Diamond-Stanic12,Esquej14}, several studies of moderate luminosity AGN at low and intermediate redshift find only a weak correlation with the SFR of the galaxy as a whole \citep{Silverman09,Shao10,Rosario12}. This is in qualitative agreement with results from simulations performed by \citet{Hopkins10}, which show an increasingly strong correlation of the SFR-$\dot M_{\rm BH}$ relation with decreasing physical scales from several kpc to $<$10 pc. Further insight into the connection between AGN and star formation can be gained through the study of the stellar populations of the host galaxy. This usually requires to carefully remove the unresolved AGN component in ground-based images of local galaxies \citep[e.g.][]{Trump13} or, at higher redshifts, using HST data \citep{Jahnke04, Ammons11}. Another option is to select only low luminosity or obscured AGN that contribute a negligible fraction of the combined (AGN+galaxy) optical emission \citep[e.g.][]{Kauffmann03b,Alonso-Herrero08,Silverman09}. Early studies showed that the rest-frame colours of AGN hosts are often in or close to the green valley, which led to speculation about the influence of the AGN in the transition from the blue cloud to the red sequence \citep[e.g.][]{Nandra07,Salim07,Bundy08,Silverman08,Georgakakis08,Schawinski09,Cimatti13}. Later works, however, recognized the importance of stellar mass selection effects when comparing the colours of active and inactive galaxies. Some of these works found that AGN host colours are similar to those of inactive star-forming galaxies for the same mass and redshift \citep{Xue10,Rosario13}, while others suggested they are slightly redder \citep[e.g.:][]{Bongiorno12}. Conflicting results have been associated at least in part to biases in the AGN or non-AGN control samples \citep{Xue10,Aird12,Rovilos12,Rosario13}. The strong evolution in the frequency of AGN detection with the stellar mass and redshift of the host, and AGN luminosity, implies that all three parameters need to be carefully controlled for meaningful comparisons between samples. One basic difficulty in comparing the stellar populations of AGN hosts and inactive galaxies through rest-frame colours is that they depend not only on stellar age, but also on metallicity and extinction. This degeneracy implies that age differences can be either exaggerated or masked by differences in extinction. Extinction-corrected colours based on SED-fitting with libraries of synthetic templates can in principle solve this issue \citep[see e.g.][]{Cardamone10}, albeit at the cost of the results becoming model-dependent \citep[][, hereafter HC13]{Hernan-Caballero13}. The strength of the 4000\AA{} break, \Dnu, and the H$_\delta$ line are two well known spectral indicators of stellar age \citep{Balogh99,Kauffmann03b}. Using a large sample of Sloan Digital Sky Survey (SDSS) spectra from local galaxies ($z$$<$0.3), \citet{Kauffmann03a} calibrated the star formation history (SFH) of low-z emission-line selected AGN. They found that the typical stellar ages of AGN hosts are younger than those of inactive galaxies while their mean SFR are higher. Post-starburst spectroscopic signatures are also found to be strong in local AGN hosts \citep{Wild07}, and there is mounting evidence for the AGN activity peaking a few hundred Myr after the star formation does \citep{Davies07,Wild10,Alonso-Herrero13}. At higher redshifts, \citet{Silverman09} demonstrated that \Dnu, the restframe U-V colour, and the SFR (based on the [OII] 3727\AA{} line) of a bright sample ($i_{acs}$$<$22.5) of X-ray selected AGN hosts are all consistent with each other, and match those of younger star-forming galaxies at the same redshift. However, spectroscopic surveys are limited to brighter magnitudes that do not include the bulk of the X-ray selected samples, which peak at fainter magnitudes. Recently, several intermediate band optical and near infrared surveys have provided deep photometry with enough spectral resolution to infer the strength of the 4000 \AA{} spectral break at $z$$\lesssim$1 (HC13) and at higher redshifts \citep{Kriek11,Straatman14}. In HC13 we analysed the stellar populations of a mass-selected sample of galaxies in the GOODS-N field with intermediate band photometry taken with the 10.4 m GTC telescope from the Survey for High-z Absorption Red and Dead Sources \citep[SHARDS;][]{Perez-Gonzalez13}. The SHARDS filterset consists of 24 contiguous medium-band (R$\sim$50) optical filters spanning the range 500--950 nm. SHARDS provides an uniform depth of $m$=26.5, (3$\sigma$) with sub-arcsec seeing in all its filters. We showed that measurements of the \Dn index on the SHARDS photospectra agree within $\sim$10\% with those obtained from full resolution spectra (see Figure A4 in HC13), while they prove fainter magnitudes than the deepest spectroscopy available. We also showed that, when combined with the rest-frame U-V colour, \Dn provides a powerful diagnostic of the extinction affecting the stellar population that is relatively insensitive to degeneracies with age, metallicity or star formation history. Using this novel approach, we estimated de-reddened colours and light-weighted stellar ages for individual sources. We explored the relationships linking stellar mass, rest-frame (U-V) colour, and \Dn for the non-active sources in the sample, and compared them to those found in local galaxies. In this work we study the stellar populations in the host galaxies of X-ray selected AGN in the redshift range 0.34$<$$z$$<$1.07 and within the fraction of the GOODS-N field covered by the SHARDS survey. We compare rest-frame colours, \Dn indices, and average stellar ages of the AGN hosts with those of carefully matched comparison samples of inactive galaxies with the same underlying redshift and mass distributions. The outline of the paper is as follows: \S\ref{sample-selection-sec} describes the selection of the AGN sample and the comparison sample of inactive galaxies. \S\ref{sect-analysis} deals with the obtention of stellar masses, rest-frame colours, \Dn indices, and average stellar ages. \S\ref{sect-results} presents our results regarding the stellar populations of AGN hosts. \S\ref{sect-discussion} discusses the systematics that could influence our results. \S\ref{sect-conclusions} summarizes our conclusions. Throughout this paper we use a cosmology with $H_0$ = 70 km s$^{-1}$ Mpc$^{-1}$, $\Omega_M$ = 0.3, and $\Omega_\Lambda$ = 0.7. All magnitudes refer to the AB system. | We analyse the stellar populations in the host galaxies of 53 X-ray selected moderate luminosity (L$_X$$<$10$^{44}$ erg s$^{-1}$) optically faint AGN at 0.34$<$$z$$<$1.07 in the area of the GOODS-N field covered by the SHARDS survey. The ultra-deep ($m_{AB}$$<$26.5) optical medium-band (R$\sim$50) photometry from SHARDS allows us to consistently measure the strength of the 4000 \AA{} break. This, in conjunction with the rest-frame (U-V) colour, provides a robust measurement of the extinction that is independent of assumptions on the metallicity and SFH of the galaxies. This allows us to obtain extinction-corrected (U-V) colours and light-weighted average stellar ages ($t_{ssp}$). We confirm a steep increase in the frequency of AGN with the stellar mass of an order of magnitude between 10$^{10}$ and 10$^{11}$ M$_\odot$. 50\% of our X-ray selected AGN are in hosts more massive than 10$^{11}$ M$_\odot$ and $\sim$95\% have M$_*$$>$10$^{10}$ M$_\odot$. A careful selection of random control samples of inactive galaxies allows us to remove the stellar mass and redshift dependences of the AGN fraction to explore trends with stellar age. We confirm that X-ray selected AGN hosts have rest-frame U-V colours comparable to those of inactive galaxies at the same mass and redshift. In particular, 2/3 of the AGN hosts in our sample and a comparable fraction of inactive galaxies are in the red sequence. However, we find that the fraction of AGN hosts with UVJ colours in the quiescent locus is only half the fraction found in inactive galaxies. The other half are instead dusty star-forming galaxies with bluer extinction-corrected colours. \Dn measurements and extinction-corrected U-V colours both support significantly younger stellar populations in the AGN hosts, with a strong deficit of AGN among galaxies with older ($t_{ssp}$$>$1 Gyr) stellar populations. We find that X-ray detected moderate luminosity AGN ($\log$(L$_X$/erg s$^{-1}$)$\sim$41.5--44.0) are more prevalent in galaxies with intermediate stellar ages (0.3$<$$t_{ssp}$$<$0.5 Gyr) compared to younger or older galaxies, consistent with a delayed onset of AGN activity after a star formation episode. | 14 | 4 | 1404.2056 |
1404 | 1404.5676_arXiv.txt | \\ We have constructed a sample of radio-loud and radio-quiet quasars from the Faint Images Radio Sky at Twenty-one centimetres (FIRST) and the Sloan Digital Sky Survey Data Release 7 (SDSS DR7), over the H-ATLAS Phase 1 Area ($9^{h}$, $12^{h}$ and $14.5^{h}$). Using a stacking analysis we find a significant correlation between the far-infrared luminosity and 1.4-GHz luminosity for radio-loud quasars. Partial correlation analysis confirms the intrinsic correlation after removing the redshift contribution while for radio-quiet quasars no partial correlation is found. Using a single-temperature grey-body model we find a general trend of lower dust temperatures in the case of radio-loud quasars comparing to radio-quiet quasars. Also, radio-loud quasars are found to have almost constant mean values of dust mass along redshift and optical luminosity bins. In addition, we find that radio-loud quasars at lower optical luminosities tend to have on average higher FIR and 250-$\mu$m luminosity with respect to radio-quiet quasars with the same optical luminosites. Even if we use a two-temperature grey-body model to describe the FIR data, the FIR luminosity excess remains at lower optical luminosities. These results suggest that powerful radio jets are associated with star formation especially at lower accretion rates. | \subsection{AGN and star-formation connection} Star formation and Active Galactic Nucleus (AGN) activity play important roles in the formation and evolution of galaxies. Over the past two decades a significant number amount of evidence has demonstrated the close connection between AGNs and their hosts. A tight correlation exists between black hole and galaxy bulge masses \citep[e.g.][]{Boyle1998,Ferrarese2000,McLure2001,Merloni2004}. In addition, the evolutionary behaviour of AGN shows a strong correlation with luminosity: the space density of luminous AGN peaks at $z\sim2$, while for lower luminosity AGN it peaks at $z\sim1$ \citep[e.g.][]{Hasinger2005,Babic2007,Bongiorno2007,Rigby2011}. This so-called anti-hierarchical evolution is similar to the downsizing behaviour of galaxy star-formation activity \citep[e.g.][]{Cowie1996,Fontanot2009} which, in some cases, is associated with the decline in frequency of major mergers \citep[e.g.][]{Treister2012}. Although AGN activity and star formation in galaxies do appear to have a common triggering mechanism, recent studies do not find strong evidence that the presence of AGN affects the star-formation process in the host galaxy \citep[e.g.][]{Bongiorno2012,Feltre2013}. Theoretical models suggest that these possible correlations arise through feedback processes between the galaxy and its accreting black hole. Such regulation has been shown to be important in large cosmological simulations \citep[e.g.][]{DiMatteo2005,Springel2005, Croton2006}. In general these can take two forms, AGN-winds (often referrred to as quasar-mode) which comprise wide-angle, sub-relativistic outflows and tend to be driven by the radiative output of the AGN, and jets (often referred to as radio-mode), which are relativistic outflows with narrow opening angles that are launched directly from the accretion flow itself. In the case of quasar-mode the objects are accreting rapidly, at near their Eddington rate and their radiation can couple to the gas and dust in the interstellar medium, driving winds that may shut down further accretion onto the black hole or even drive material out of the galaxy, thereby quenching star formation \citep[e.g.][]{DiMatteo2005}. Although there is no compelling evidence for AGN feedback quenching star formation, there is mounting evidence for quasar-driven outflows \citep[e.g.][]{Maiolino2012}.However recent surveys find little evidence that X-ray luminous AGN quench star formation (\citealp{Harrison2012} cf. \citealp{Page2012}). Similarly, the radio-mode and the role of radio-loud AGN and their jets in the evolution of galaxies has been studied intensively suggesting that jets can have positive as well as negative feedback on star-formation rates with the observational consensus being mixed. Certainly, some studies advocate that radio-jets effectively suppress or even quench star formation \citep[e.g.][]{Best2005,Croton2006,Best2012,Karouzos2013,Chen2013} by warming-up and ionizing the interstellar medium (ISM) which leads to less efficient star formation, or through direct expulsion of the molecular gas from the galaxy, effectively removing the ingredient for stars to form \citep[e.g.][]{Nesvadba2006,Nesvadba2011}. On the other hand, positive feedback can enhance star formation which could be explained by shocks driven by the radio-jets in the ISM that compress it and eventually lead to enhanced star-formation efficiency \citep[e.g.][]{SilkNusser10,Kalfountzou2012,Gaibler2012,Best2012}. It is therefore apparent, that although some form of feedback is needed to explain the observational results supporting co-evolution of central spheroids and their galaxies, much still remains unclear. Radio-loud and radio-quiet quasars provide ideal candidates for the study of star formation in powerful AGN under the presence of jets or otherwise. Indeed, optically selected radio-loud quasars are found to have enhanced star formation at lower luminosities using optical spectral feature as a diagnostic \citep{Kalfountzou2012}. The latter result raises the question of why such an effect is not seen at high radio power and/or AGN activity which could be explained under the assumption of a dominant mechanical feedback at low Eddington luminosities, in which case this would plausibly be the major source of positive feedback. However, spectral diagnostics are not immune to AGN contamination and optical diagnostics, in particular, are susceptible to the effects of reddening. Indeed, the measurement of the star-formation activity in the host galaxy is difficult, mainly due to contamination by the AGN. Many studies have attempted to determine the star-formation activity in quasar host galaxies using optical colours \citep[e.g.][]{Sanchez2004} or spectroscopy \citep[e.g.][]{Trichas2010,Kalfountzou2011,Trichas2012}. or X-ray selection \citep[e.g.][]{Comastri2003,Treister2011}. In addition, AGN emission can outshine both the ultra-violet (UV) and optical emission from young stars. By contrast, the far-infrared (FIR) emission is shown to be dominated by emission from dust in the host galaxy, except in the most extreme cases \citep[e.g.][]{Netzer2007,Mullaney2011}, and to be a proxy of its star formation activity that is largely uncontaminated by the AGN \citep[e.g.][]{Haas2003,Hatziminaoglou2010}. \subsection{Radio-loud and radio-quiet quasars} A property of quasars is the existence of radio-loud and radio-quiet populations. One of the more controversial topics in studies of these objects is whether these radio-loud and radio-quiet quasars form two physically distinct populations of objects. Radio-loud quasars are often defined to be the subset of quasars with a radio-loudness satisfying $R_{i}>10$, where $R_{i}=L({\rm 5GHz})/L({\rm 4000\AA})$ \citep{Kellermann1989} is the ratio of monochromatic luminosities measured at (rest frame) 5~GHz and 4000~\AA. Radio-quiet quasars must minimally satisfy $R_{i}\leq10$. However, even radio-quiet quasars quasars can be detected as radio sources \citep{Kellermann1989}. This has led to two opposing views of the radio-loudness distribution which have long been debated. The first is that the radio-loudness distribution is bimodal \citep[e.g.][]{Kellermann1989,Miller1990,Ivezic2002}. The other is that the distribution is continuous with no clear dividing line \citep[e.g.][]{Cirasuolo2003,LaFranca2010,Singal2011,Singal2013,Bonchi2013}. Typically, optically selected radio-loud quasars are only a small fraction, $\sim$10-20 per cent, of all quasars (e.g. \citealp{Ivezic2002} but see also \citealp{Richards2006} with a small radio-loud fraction of 3 per cent), with this fraction possibly varying with both optical luminosity and redshift \citep{Jiang2007}. In contrast, X-ray selected samples show lower fractions of radio-loud AGN $<5$ per cent \citep[e.g.][]{Donley2007,LaFranca2010}. However, many low-power radio sources in these samples might be star formation-driven \citep[e.g.][]{Massardi2010}. X-ray selections overall probe much higher (or complete) portions of the AGN populations than optical ones. This may affect the comparison of same subsamples (i.e., radio-loud) selected with different methods. Radio-loud quasars usually reside in very massive galaxies and have typically a lower optical or X-ray output at given stellar mass (i.e. lower $L/L_{\rm Edd}$ at given $L_{\rm Edd}$, \citealp{Sikora2007}) compared to radio-quiet quasars. This means that an $L_{X}$-limited sample will have a lower radio-loud quasars fraction, compared to a mass-limited sample. However, in the case of a strictly limited selection of X-ray-Type I AGN, then possibly the subsamples of radio-loud AGN might end up being more comparable to optical ones. While a definitive physical explanation of this dichotomy remains elusive, a large number of models have been put forward to explain it. Both types of quasars are likely powered by similar physical mechanisms \citep[e.g.][]{Urry1995,Shankar2010}, but their radio loudness has been shown to be anti-correlated with accretion rate onto their central supermassive black holes \citep[e.g.][]{Fernandes2011}. Additionally, it has been demonstrated that, relative to radio-quiet quasars, radio-loud quasars are likely to reside in more massive host galaxies (\citealp{Kukula2001,Sikora2007}). However, \cite{Dunlop2003} found that spheroidal hosts become more prevalent with increasing nuclear luminosity such that, for nuclear luminosities ${\rm M_{V} < -23.5}$, the hosts of both radio-loud and radio-quiet AGN are virtually all massive ellipticals. Along with the idea of different host galaxies it has been found that radio-loud quasars require more massive central black holes than radio-quiet quasars (e.g. \citealt{Dunlop2003, McLure2004}; see also \citealp{Shankar2010}, who finds this to be redshift dependent) and it has also been suggested that radio-loud quasars host more rapidly spinning black holes than radio-quiet quasars (e.g. \citealt{BlandfordZnajek1977, Punsly1990, Wilson1995, Sikora2007, Fernandes2011}; but see also \citealp{Garofalo2010}). The low radio-loud fraction also suggests a change in jet occurrence rates among active super-massive black holes at low luminosities. This could be linked to changes in the Eddington fraction, evolutionary state of the black hole, or the host galaxy mass, evolutionary state, or environment.% Recently, \cite{Falder2010} showed that radio-loud AGN appear to be found in denser environments than their radio-quiet counterparts at $z\sim 1$, in contrast with previous studies at lower redshifts (e.g. \citealp{McLure2001}). However the differences are not large and may be partly explained by an enhancement in the radio emission due to the confinement of the radio jet in a dense environment (e.g. \citealp{Barthel1996}). If the radio-loudness is due to the physics of the central engine and how it is fueled, and the environment plays a relatively minor role, the quasar properties may be connected with the star formation in their host galaxies \citep[e.g.][]{Herbert2010,Hardcastle2013}. On the one hand, AGN feedback could be stronger in the case of the radio-loud quasars due to their higher black hole masses and therefore potentially stronger radiation field, reducing the star-formation rate compared to radio-quiet quasars; on the other hand radio jets could increase the star-formation activity by compressing the intergalactic medium \citep[e.g.][]{Croft2006, SilkNusser10}. \subsection{This work} With the \textit{Herschel} Space Observatory \citep{Pilbratt2010} we are able to measure the FIR emission of AGN host galaxies and hence the cool-dust emission. \textit{Herschel} offers an ideal way of measuring the instantaneous star-formation rate (SFR) of AGN \citep[e.g.][]{Bonfield2011}. Until \textit{Herschel}, hot dust emission has typically been determined from Spitzer data at near/mid-infrared wavelengths, but emission from the torus can also contribute at these bands, especially in the case of quasars. With \textit{Herschel} we are able to determine the level of cool dust emission in AGN, providing a detailed picture of how the full SEDs of AGN change as a function of luminosity, radio-loudness and redshift. Under these circumstances, \textit{Herschel} provides a good tool to study the star formation and AGN activity in a special type of AGN: quasars. We are also able to study the star formation in different types of quasars (e.g. radio-loud and radio-quiet quasars) and thus to say how it might be affected by the presence of powerful radio jets. The paper is structured as follows. In section \ref{data} we discuss the selection of the sample and the observations we have used. In section \ref{sec:FIR} we describe the statistical methods and the models we have used in order to estimate the FIR parameters (e.g. FIR luminosity, dust temperature, dust mass) of our sample. Here we also present the results of the comparison of the FIR parameters between the radio-loud and radio-quiet quasars. Finally, in sections \ref{sec:discussion} and \ref{sec:conclusions}, we explore the general conclusions that can be drawn from our results. Throughout the paper we use a cosmology with $H_{0}=70{~\rm km~s^{-1}~Mpc^{-1}}$, $\Omega_{m}=0.3$ and $\Omega_{\Lambda}=0.7$. | \label{sec:conclusions} In this paper we have studied the far-infrared properties and the star-formation of matched samples of radio-loud and radio-quiet quasars. The main result of our study is that radio-loud quasars have higher star-formation rates than radio-quiet quasars at low optical luminosities. This result is in agreement with our previous work \citep{Kalfountzou2012} where the [\mbox{O\,{\sc ii}}] emission was used as a tracer of the star-formation. Additionally, we have found a strong correlation between jet activity and the star-formation, controlling the effect of redshift, in the case of radio-loud quasars and especially at low optical luminosities and redshifts. This correlation supports the idea of the jet-induced star-formation. The possible differences we found between the two populations regarding the dust mass and dust temperature could explain the differences in star-formation rate, but they also point the way forwards further investigation of the evolution of their host galaxies and their environment and their correlation with AGN activity. | 14 | 4 | 1404.5676 |
1404 | 1404.0786_arXiv.txt | Magnetic field measurements in the upper chromosphere and above, where the gas-to-magnetic pressure ratio $\beta$ is lower than unity, are essential for understanding the thermal structure and dynamical activity of the solar atmosphere. Recent developments in the theory and numerical modeling of polarization in spectral lines have suggested that information on the magnetic field of the chromosphere-corona transition region could be obtained by measuring the linear polarization of the solar disk radiation at the core of the hydrogen Lyman-$\alpha$ line at 121.6~nm, which is produced by scattering processes and the Hanle effect. The Chromospheric Lyman-$\alpha$ Spectropolarimeter (CLASP) sounding rocket experiment aims to measure the intensity (Stokes $I$) and the linear polarization profiles ($Q/I$ and $U/I$) of the hydrogen Lyman-$\alpha$ line. In this paper we clarify the information that the Hanle effect can provide by applying a Stokes inversion technique based on a database search. The database contains all theoretical $Q/I$ and $U/I$ profiles calculated in a one-dimensional semi-empirical model of the solar atmosphere for all possible values of the strength, inclination, and azimuth of the magnetic field vector, though this atmospheric region is highly inhomogeneous and dynamic. We focus on understanding the sensitivity of the inversion results to the noise and spectral resolution of the synthetic observations as well as the ambiguities and limitation inherent to the Hanle effect when only the hydrogen Lyman-$\alpha$ is used. We conclude that spectropolarimetric observations with CLASP can indeed be a suitable diagnostic tool for probing the magnetism of the transition region, especially when complemented with information on the magnetic field azimuth that can be obtained from other instruments. | The chromosphere and the transition region of the Sun lie between the cooler photosphere, where the ratio of gas to magnetic pressure $\beta>1$, and the $10^6$ K corona, where $\beta<1$. It is believed that in this interface region the magnetic forces start to dominate over the hydrodynamic forces, and that local energy dissipation and energy transport to the upper layers via various fundamental plasma processes are taking place. Recent observations \citep[e.g.,][]{Shibata2007,Katsukawa2007,DePontieu2007,Okamoto2007,Okamoto2011,Vecchio2009} have revealed ubiquitous dynamical chromospheric activities such as jets, Alfv\'enic waves, and shocks, which are thought to play a key role in the heating of the chromosphere and corona and in the acceleration of the solar wind. However, we do not have any significant empirical knowledge on the strength and direction of the magnetic field in the upper solar chromosphere and transition region. The information on the magnetic field of the solar atmosphere is encoded in the polarization that some physical mechanisms introduce in the spectral lines. The familiar Zeeman effect can introduce polarization in the spectral lines that originate in the upper solar chromosphere and the transition region. However, because such lines are broad and the magnetic field there is expected to be rather weak, the induced polarization amplitudes will be very small (except perhaps in sunspots), and the Zeeman effect has limited applicability. Fortunately, the Hanle effect \citep[the magnetic-field-induced modification of the linear polarization caused by scattering processes in a spectral line,][]{Casini2008} in some of the allowed UV lines that originate in the upper chromosphere and transition region is expected to be a more suitable diagnostic tool \citep{Trujillo2011,Trujillo2012,Belluzzi2012}. The hydrogen Lyman-$\alpha$ line ($\lambda=121.567$~nm) is particularly suitable because (1) the line-core polarization originates at the base of the solar transition region, where ${\beta}{\ll}1$ \citep{Trujillo2011,Belluzzi2012b,Stepan2012}, (2) collisional depolarization plays a rather insignificant role \citep[e.g.,][]{Stepan2011}, and (3) via the Hanle effect the scattering polarization is sensitive to the magnetic fields expected for the upper chromosphere and transition region \citep{Trujillo2011}. The Chromospheric Lyman-Alpha Spectropolarimeter (CLASP) is a sounding rocket experiment developed by researchers from Japan, USA, and Europe \citep[][]{Ishikawa2011,Narukage2011,Kano2012,Kobayashi2012}, which is expected to fly in 2015. The first, very important goal of this sounding rocket experiment is the measurement of the linear polarization signals produced by scattering processes in the Lyman-$\alpha$ line. The second goal is the detection of the Hanle effect action on the core of $Q/I$ and $U/I$ in order to constrain the magnetic field of the transition region from the observed Stokes profiles. CLASP will measure the linear polarization profiles of the Lyman-$\alpha$ line within a spectral window of at least $\pm0.05$~nm around the line center, where in addition to the line core polarization itself (where the Hanle effect operates), we expect the largest linear polarization signals produced by the joint action of partial frequency redistribution and $J-$state interference effects \citep{Belluzzi2012b}. Polarization sensitivities of 0.1\% and 0.5\% are required in the line core (i.e., $\pm0.02$~nm around the line center) and in the line wings (at $>\pm0.05$~nm), respectively. In order to achieve these polarization sensitivities, the $400\arcsec$ spectrograph slit will be fixed at the selected observing target during the CLASP observation time of $<5$~min. Furthermore, after the data recovery, we will add consecutive measurements and perform spatial averaging. In this paper, we clarify the information we expect to determine with the CLASP experiment, providing a strategy suitable for highlighting the ambiguities of the Hanle effect and the complexity of the ensuing inference problem. To this end, we have used a plane-parallel (one-dimensional) semi-empirical model of the solar atmosphere, and we have created a database of theoretical Stokes $Q/I$ and $U/I$ profiles for all possible strength, inclination, and azimuth values of the magnetic field vector. Then, we investigate the possibility of recovering the magnetic field information using the characteristics of CLASP (noise level, spectral resolution, etc.) and the ambiguities and limitation inherent to the Hanle effect. We also discuss the most suitable observing targets and data analysis strategy for constraining the magnetic field information. The ambiguities inherent to magnetic field diagnostics can be reduced by exploiting the joint action of the Hanle and Zeeman effect, where both linear and circular polarization signals are used to constrain the magnetic field vector \citep[][see also \citealt{Asensio2008,Centeno2010, Anusha2011}]{Landi1993,Landi1982,Trujillo2002,Lopez2003}. Unfortunately, while the Lyman-$\alpha$ line is most advantageous to explore the magnetism of the various regions in the transition region (where $\beta\ll1$), it is challenging to measure the contribution of the Zeeman effect to the circular polarization in UV lines. Here we propose alternative ways to alleviate this issue in the subsequent sections. We assume that the quiet solar atmosphere can be represented by a plane-parallel semi-empirical model atmosphere, even though the upper solar chromosphere is a highly inhomogeneous and dynamic physical system, much more complex than the idealization of the one-dimensional static semi-empirical model used here. Such inhomogeneity and dynamics causes larger amplitudes and spatial variations in the scattering polarization signals \citep{Stepan2012,Stepan2014}. However, it is of interest to note that \citet{Trujillo2011} showed that the amplitude and shape of the $Q/I$ profiles calculated in the quiet-Sun plane-parallel semi-empirical model of \citet{Fontenla1993} are qualitatively similar to the temporally-averaged profiles obtained from the Stokes $I$ and $Q$ signals computed at each time step of the chromospheric hydro-dynamical model of \citet{Carlsson1997}. Moreover, spatial and temporal averaging of the scattering polarization calculated in three-dimensional (3D) atmospheric models tend to produce $Q/I$ Lyman-$\alpha$ signals more or less similar to those calculated in plane-parallel semi-empirical model atmospheres \citep{Stepan2014}. In the case of the CLASP experiment, which will require both spatial ($\sim10\arcsec$) and temporal averaging ($\sim$5~min) to attain the necessary signal-to-noise ratio, the model atmosphere for a first approximate interpretation of the CLASP data could be a plane-parallel semi-empirical model. We believe that the post-launch data analysis will pave the way for further improvements, for example via forward modeling calculations of the Lyman-$\alpha$ scattering polarization signals using increasingly realistic 3D models of the solar chromosphere. | \subsection{Required additional information} We have performed Stokes inversion simulations to clarify the information which can be inferred via the Hanle effect in the hydrogen Lyman-$\alpha$ line, assuming that the chromosphere and transition region of the quiet Sun can be represented by the FAL-C semi-empirical model. We conclude that UV spectro-polarimetry with the CLASP experiment is a suitable diagnostic tool of the magnetic field in the upper atmosphere, if combined with complementary information from other relevant observations. Though we have the ambiguity and uncertainty that is inherent to the Hanle effect when only the scattering polarization in one spectral line is available, this should not be taken as a drawback. As we have shown, we need additional observations to uniquely determine the field strength, azimuth, and inclination. Clearly, we cannot measure the very small contribution of the Zeeman effect to the Stokes $V$ of the Lyman-$\alpha$ line, but there are several options for resolving this issue. Ideally, we would like to perform simultaneous spectro-polarimeteric observations also in other spectral lines of the upper chromosphere, which have different critical field strengths for the onset of the Hanle effect \citep{Trujillo2012,Belluzzi2012}. However, in this paper, we propose a simpler, but useful, third method for determining the azimuthal magnetic field direction using the fibrils seen in the high-resolution intensity images from IRIS, AIA, and ground-based observations. \subsection{Observing target} The Lyman-$\alpha$ line starts to approach the Hanle saturation regime above $\sim$50~G, where the linear polarization changes only with the inclination and azimuth of the magnetic field, not with its strength. Furthermore, nearly vertical fields do not produce any significant Hanle effect (i.e., the magnetic modification of the linear polarization), and at the solar disk center the linear polarization created by the Hanle effect of slightly inclined fields is too small to be detected. Thus, inclined, relatively weak ($B<50$~G) magnetic fields should be observed. Based on the properties of the Hanle effect studied in this paper, we can now discuss the possible observing region and observing target for the CLASP experiment. Our primary goal with the CLASP experiment is to detect for the first time the linear polarization caused by the atomic level polarization produced by the absorption and scattering of anisotropic radiation in the upper solar atmosphere. To this end, it is desirable to choose a quiet region close to the limb (e.g., around $\mu{\approx}0.3$) because such locations are the most suitable ones for detecting the line-core polarization in the hydrogen Lyman-$\alpha$ line \citep{Trujillo2011,Belluzzi2012b,Stepan2014}. Our second goal is to detect the Hanle effect, in order to constrain the magnetic field vector of the chromosphere-corona transition region. One of the popular spectral lines for magnetic field measurements in the upper atmosphere is the He~{\sc i} 1083~nm triplet \citep[e.g.,][]{Asensio2008}. By exploiting the spectro-polarimetric data obtained with this multiplet, the magnetic properties of prominences, filaments, spicules and active regions have been investigated by several authors \citep[e.g.,][]{Trujillo2002,Lagg2004,Marenda2006,Centeno2010,Xu2010}. However, it is not easy to measure the intensity and polarization of the He~{\sc i} 1083 nm triplet in quiet regions of the solar disk \citep[e.g.,][]{Asensio2008}, and there are few studies on the quiet-Sun magnetic fields of the upper solar atmosphere. Thus, our primary targets are the network and internetwork regions of the quiet Sun. The network fields are expected to form magnetic canopy structures in the upper chromosphere and transition region, and they are expected to be largely inclined and relatively weak. \citet{Wiegelmann2010} investigated the fine structure of the magnetic fields in the quiet Sun using photospheric magnetic field measurements from the SUNRISE imaging magnetograph experiment (IMaX). \citet{Wiegelmann2010} found that most magnetic loops rooted in the quiet Sun photosphere would reach into the chromosphere or higher. In addition to the canopy field, such magnetic loops in regions of the quiet Sun would also be interesting observing targets. \subsection{Atmospheric model} Finally, we discuss another issue that we should address further in future investigations: the influence of the atmospheric model on the inference of the magnetic field via the interpretation of the scattering polarization and the Hanle effect in Lyman-$\alpha$. \citet{Belluzzi2012b} calculated the scattering polarization profiles of the hydrogen Lyman-$\alpha$ line taking into account partial frequency redistribution (PRD) and $J-$state interference effects, and using the plane-parallel atmospheric models C, F, and P of \citet{Fontenla1993}, which can be considered as illustrative of quiet, network, and plage regions. They showed that the shape and amplitude of the Lyman-$\alpha$ linear polarization profiles are sensitive to the thermal structure of the model atmosphere in the line wings, and to a lesser extent also in the line core (where the Hanle effect operates). Thus, in order to determine the importance of the choice of the atmospheric model, we must clarify how much uncertainty arises in the inference of the magnetic field vector when the chosen atmospheric model is different. It is important to emphasize that the upper solar chromosphere and transition region are highly inhomogeneous and dynamic plasmas. Such inhomogeneity and dynamics causes larger $Q/I$ amplitudes and non-zero $U/I$ signals, along which their spatial and temporal variations \citep{Stepan2012,Stepan2014}. Thus, we must consider also other strategies for interpreting the CLASP observations, such as detailed forward modeling of the observed scattering polarization signals using increasingly realistic 3D models of the solar chromosphere, taking into account the limited spatial and temporal resolution of the CLASP observations. In order to monitor the local non-uniformity of the Lyman-$\alpha$ radiation field, the intensity images from the CLASP slit-jaw and IRIS observations will be useful. Furthermore, the intensity and the linear polarization profiles in the line wings, which are insensitive to the magnetic field but very sensitive to the temperature structure, may also help us to constrain the temperature structure of the solar atmosphere. All these steps will facilitate the interpretation of the line-core polarization signals of Lyman-$\alpha$ that CLASP aims at observing. In this way, we expect that the CLASP experiment will lead to the first significant advancement in the investigation of the magnetism of the upper solar chromosphere and the transition region via the Hanle effect in the UV spectral region. \begin{figure} \epsscale{0.8} \plotone{horizontal_3d_light.eps} \caption{Plots (a), (b), and (c), and plots (g), (h), and (i) represent the $\chi^2$ maps in the field strength, azimuth, and inclination parameter space for a horizontal magnetic field ($\theta_B=90^{\circ}$) input with the close-to-limb ($\mu=0.3$) and the disk center ($\mu=1.0$) geometries, respectively. Plots (d), (e), and (f) and plots (j), (k), and (l) represent the $\chi^{2}$ maps projected onto the inclination and field strength parameter space. The left, middle, and right columns show $\chi^2$ maps with a noise level of $\sigma=0.033\%$ for the inputs of weak field ($B=10$~G), marginal field ($B=50$~G), and strong field ($B=250$~G), respectively, The black regions represent the magnetic parameters with $\Delta\chi^2\le 3.53$. The input magnetic parameters are shown with gray circles.} \label{fig:3dchi_horizontal} \end{figure} \begin{figure} \epsscale{0.8} \plotone{vertical_3d_light.eps} \caption{The plots shown here are the same as those in Figure~\ref{fig:3dchi_horizontal} with an almost vertical magnetic field ($\theta_B=20^{\circ}$) input value.} \label{fig:3dchi_vertical} \end{figure} | 14 | 4 | 1404.0786 |
1404 | 1404.4446_arXiv.txt | Little observational data are available on the weak stellar winds of hot subdwarf stars of B spectral type (sdB). Close binary systems composed of an sdB star and a compact object (white dwarf, neutron star or black hole) could be detected as accretion-powered X-ray sources. The study of their X-ray emission can probe the properties of line-driven winds of sdB stars that can not be derived directly from spectroscopy because of the low luminosity of these stars. Here we report on the first sensitive X-ray observations of two sdB binaries with compact companions. \cd\ is the sdB binary with the shortest known orbital period (1.2~h) and its companion is certainly a white dwarf. \pg\ is an sdB binary considered the best candidate to host a black hole companion. We observed these stars with \xmm\ in August 2013 for 50~ks and in July 2009 for 36~ks, respectively. None of them was detected and we derived luminosity upper limits of $\sim1.5\times10^{29}$~erg~s$^{-1}$ for \cd\ and $\sim5\times10^{29}$~erg~s$^{-1}$ for \pg . The corresponding mass loss rate for \pg\ is poorly constrained, owing to the unknown efficiency for black hole accretion. On the other hand, in the case of \cd\ we could derive, under reasonable assumptions, an upper limit of $\sim3\times10^{-13}$ $\msun~yr^{-1}$ on the wind mass loss rate from the sdB star. This is one of the few observational constraints on the weak winds expected in this class of low mass hot stars. We also report the results on the X-ray emission from a cluster of galaxies serendipitously discovered in the field of \cd . | Luminous hot stars are characterized by strong winds with mass loss rates $\mdot_{\mathrm{W}}\sim10^{-7}$--$10^{-5}$~$\msun$~yr$^{-1}$ and terminal velocities reaching a few thousands km s$^{-1}$ (see, e.g., \citealt{kud00}). These winds are driven by the resonant absorption and re-emission of the star optical/UV photons by the wind atoms, which results in a net gain of radial momentum. The theory of line-driven winds predicts that the mass-loss rate scale with the luminosity approximately as $L^{1.5}$ and depend on the wind composition, since most of the relevant spectral lines are provided by metals. The observations of O- and B-type stars of different luminosity, from main sequence to supergiants, agree reasonably well with these general predictions \citep{pul08}. Much less is known, from the observational point of view, about the winds of less luminous hot stars, which, according to the models, should have weaker winds. Evidence of mass loss has been seen in the central stars of planetary nebulae, as well as in a few extreme helium stars and O-type subdwarfs, with $\mdot_{\mathrm{W}}$ as low as $\sim$$10^{-10} \msun$~yr$^{-1}$ \citep{ham10}. It is not clear if the theory and scaling relations derived for luminous stars can be simply extended to such weak winds. Hot subdwarfs are evolved low--mass stars that have lost most of their hydrogen envelopes and are now in the stage of helium core burning (see \citealt{heb09} for a review). They are spectroscopically classified in the mostly hydrogen-rich sdB (with effective temperature $T\sim25,000$--40,000 K) and the predominantly helium-rich sdO stars (with $T$ \gtsim 40,000 K). The abundance patterns of sdBs are strongly affected by atomic diffusion processes, that is by gravitational settling and radiative levitation leading to the depletion of some elements, e.g. helium, and strong enhancement of heavy metals by factors of up to 10$^4$ \citep{oto06,bla08,nas11}. The possible presence of winds in hot subdwarfs has been invoked to explain some of the abundance anomalies observed in these stars. Early diffusion modelling \citep{mic89} predicted that the helium abundances should be a hundred times lower than the average observed ones. Since the time scale for helium diffusion ($\approx$10$^4$ yr) is much shorter than the extreme horizontal branch (EHB) life time ($\approx$10$^8$ yr), equilibrium abundances should be established rapidly. To slow down helium diffusion, a stellar wind has been suggested \citep{fon97}. Indeed \citet{ung01} showed that the observed helium abundances can be explained if a stellar wind with $10^{-14} \msun$~yr$^{-1}<\mdot_{\mathrm{W}}<10^{-12} \msun$~yr$^{-1}$ is present. \citet{vin02} calculated mass loss rates for EHB stars based on the line-driven wind theory and give upper limits for the mass loss rates of $\mdot_{\mathrm{W}}<10^{-11} \msun$~yr$^{-1}$ . For weak mass loss rates ($\mdot_{\mathrm{W}}<10^{-12} \msun$~yr$^{-1}$ ), calculations by \citet{ung08,ung08b} show that the wind might fractionate, that is metals decouple from hydrogen and helium, and for rates below $\mdot_{\mathrm{W}}<10^{-16} \msun$~yr$^{-1}$ become purely metallic. Since the wind is driven by metal lines, the results depend on the adopted metallicity or more precisely on the abundance of those ions that contribute most to the radiation pressure. Selective winds could explain some anomalous metal abundances, but fail to explain the observed helium abundances. An alternative explanation was offered by \citet{mic11}, who considered turbulent mixing of the outer 10$^{-7} \msun$ to reproduce the observed abundance anomalies. No observational evidence for a stellar wind in a sdB star has yet been found. In optical spectra, the H$\alpha$ line profile is the most sensitive indicator for the presence of a stellar wind. \citet{heb03} analysed the H$\alpha$ line profiles of a sample of sdB and sdOB stars using the hydrostatic, fully metal line blanketed LTE model atmospheres. For all sdB stars the H$\alpha$ profiles were matched indicating no evidence for a stellar wind. Only in the case of two sdOB stars the lines were not matched and slight asymmetries in the profile may hint at the presence of a stellar wind. Those objects, however, have already evolved off the EHB and are considerably more luminous than the sdB stars under study in this paper. In view of the conflicting results of diffusion modelling it is of utmost importance to detect signatures of stellar winds observationally. Such an opportunity arises if the sdB is orbited by a compact companion. About two thirds of the sdB stars are in close binary systems \citep{max01}, supporting the idea that non-conservative mass transfer during a common envelope phase caused the loss of the massive hydrogen envelopes necessary to form hot subdwarfs. Both evolutionary computations and radial velocity surveys indicate that sdB binaries contain compact objects, i.e. white dwarfs (WD) or, possibly but less frequently neutron stars (NS) or black holes \citep{han02,gei11}. These systems can be detected as accretion-powered X-ray sources, if some of the mass lost from the subdwarf is transferred at a sufficiently high rate onto the compact object. Their study can thus provide a way to investigate the properties of the sdB winds, as is routinely done for more luminous O and B stars. Up to now, the only hot subdwarfs detected in the X-ray range are two sdO stars: \hd\ and \bd . \hd\ is an extensively studied single-lined spectroscopic binary in a 1.5 days orbit with a 13.2 s X-ray pulsar, most likely a massive WD \citep{mer09}. \bd\ has similar optical properties, but it was believed to be a single star until the recent discovery of X-ray emission with a periodic modulation at 19.2 s \citep{lap12}, suggesting also in this case the presence of a compact companion. Compared to the majority of hot subdwarfs, \hd\ and \bd\ have relatively strong winds with $\mdot_{\mathrm{W}}\sim3\times10^{-9} \msun$~yr$^{-1}$ \citep{ham10}. Their X-ray luminosity is consistent with the accretion rate expected from their wind properties. A search for X-ray emission from a sample of candidate sdB+WD/NS binaries was carried out with the \sw\ satellite, but none of the targets was detected. The derived upper limits on their X-ray luminosity, of the order of $L_{\mathrm{X}}\sim10^{30}$--$10^{31}$ erg s$^{-1}$ \citep{mer11b}, indicate sdB mass loss rates $\mdot_{\mathrm{W}}<10^{-13}$--$10^{-12} \msun$~yr$^{-1}$, in the hypothesis of NS companions. On the other hand, if the compact objects in these sdB binaries are WD, the implied limits on $\mdot_{\mathrm{W}}$ are about three orders of magnitude higher and not particularly constraining. Here we report on sensitive X-ray observations of two particularly interesting sdB binaries carried out with the \xmm\ satellite. Our targets are \cd , which is the tightest known sdB+WD binary, and \pg , which is the best candidate sdB binary with a black hole companion. We also report the results on the X-ray emission from a cluster of galaxies serendipitously discovered in the field of \cd . \begin{table*} \caption{Parameters of the target sdB binaries.} \label{parameters} \begin{tabular}{lccclcl} \hline Parameter & Units & \multicolumn{2}{c}{\cd\ } & References & \pg\ & References \\ & & Solution 1 & Solution 2 & & & \\ \hline Orbital period & [d] & \multicolumn{2}{c}{0.048979072$\pm$0.000000002} & 1 & 0.3630$\pm$0.0003 & 2 \\ Effective temperature & [K] & \multicolumn{2}{c}{ 29200$\pm$400} & 1 & 26900$\pm$500 & 3 \\ Surface gravity (log g) & [cm s$^{-2}$] & \multicolumn{2}{c}{ 5.66$\pm$0.05} & 1 & 5.71$\pm$0.05 & 3\\ Helium abundance (log y) & & \multicolumn{2}{c}{ --1.50$\pm$0.07} & 1 & --1.47 & 4 \\ sdB mass & [$\msun$] & 0.47$\pm$0.03 & 0.54$\pm$0.02 & 1 & 0.45$^a$ & \\ sdB radius & [$\rsun$] & 0.169$\pm$0.005 & 0.179$\pm$0.003 & 1 & 0.16$\pm$0.01 & 3\\ Companion mass & [$\msun$] & 0.74$\pm$0.02 & 0.79$\pm$0.01 & 1 & $>$6 & 3\\ Companion radius & [$\rsun$] & 0.0100$\pm$0.0004 & 0.0106$\pm$0.0002 & 1 & -- & \\ Orbital inclination & [deg] & 83.8$\pm$0.6 & 82.9$\pm$0.4 & 1 & $<$14 & 3 \\ Orbital separation & [$\rsun$] & 0.599$\pm$0.009 & 0.619$\pm$0.005 & 1 & $>$ 4 & 3\\ Roche-lobe radius & [$\rsun$] & 0.204 & 0.214 & & 0.75 & \\ Distance & [pc] & \multicolumn{2}{c}{364$\pm$31} & 1 & 570& 5 \\ X-ray luminosity & [erg s$^{-1}$] & \multicolumn{2}{c}{$<1.5\times10^{29}$ } & 6 & $<5\times10^{29}$ & 6 \\ \hline \end{tabular} References: 1) \citet{gei13}, 2) \citet{ede05}, 3) \citet{gei10}, 4) \citet{saf94}, 5) \citet{alt04}, 6) this work $^{a)}$ Assumed value. \end{table*} | Exploiting the high sensitivity of the \xmm\ EPIC instrument we have carried out the first deep X-ray observations of two sdB binaries containing compact companions and obtained upper limits on their luminosity much lower than those previously available. In fact, \cd\ was never pointed before with X-ray satellites and it was not detected in the ROSAT All Sky Survey (0.1--2.4 keV). The ROSAT survey data, with an exposure of only 200 s at its position, give an upper limit of several $10^{31}$ erg s$^{-1}$. A short \sw\ observation of \pg\ \citep{mer11b} resulted in an upper limit of $\sim$$3\times10^{30}$ erg s$^{-1}$ (0.3--10 keV), for a power law with photon index $\Gamma=2$ (about ten times higher than that obtained here for the same spectrum). The new upper limits on the X-ray luminosity of \cd\ and \pg , of the order of a few $10^{29}$ erg s$^{-1}$ for most spectral assumptions for the count rate to flux conversion, are the most constraining ever derived for hot subdwarf binaries. Note that in the case of \cd\ the presence of a WD companion is certain, while the presence of a compact companion in \pg , as well as in most of the other sdB binaries from which X-ray emission has been searched with \sw\ \citep{mer11b}, relies on the assumption that the sdB star rotates synchronously with the orbital period (this is required to derive the system inclination which, coupled to the mass functions, leads to lower limits on the companion mass). The lack of detectable X-ray emission in the two observed binaries can be used to derive unprecedented constraints on the wind mass loss from the hot subdwarfs in these systems. If the companion to \pg\ is a black hole we have to face a large uncertainty on the conclusions that can be drawn, owing to the unknown value of the efficiency factor $\eta$. The low X-ray luminosity could indicate a small mass loss rate from \pg , but it could also be due to a very low efficiency in the conversion of accretion power to X-ray luminosity. This is not unexpected in the case of low rate, spherically symmetric accretion onto a black hole. It is also possible that most of the accretion luminosity is released in a different range, e.g. at much lower energies. In the case of \cd, however, the presence of a WD of known mass and radius allows us to make more robust considerations. The limits on $\mdot_{\mathrm{W}}$ we derived for this sdB are one of the few observational constraints on the weak winds expected in this class of low mass hot stars. It is interesting to make some comparison with the predictions of theoretical models. \citet{vin02} computed the mass loss rates for horizontal branch and sdB stars expected from the theory of radiation driven winds. They derived a scaling relation linking $\mdot_{\mathrm{W}}$ with the star's effective temperature, luminosity, mass and metallicity. For the parameters of \cd\ this relation yields a mass loss rate $\mdot_{\mathrm{W}}$ = $1.2\times10^{-12} Z^{0.97}$ $\msun$~yr$^{-1}$, where $ Z$ is the metallicity. \citet{ham10} derived a mass loss vs. luminosity relation for evolved hot, low mass stars, which are more than ten times as luminous as the sdB stars. Extrapolation of that relation (Fig. 10 of \citet{ham10}) yields a mass loss rate for \cd\ consistent with the prediction of \citet{vin02}. Our derived upper limit on $\mdot_{\mathrm{W}}$, of the order of $3\times10^{-13}$ $\msun$~yr$^{-1}$ for most spectral assumptions, seems difficult to reconcile with the prediction by \citet{vin02} if \cd\ has a solar, or higher, metallicity. The metal abundance pattern of \cd\ (and \pg ) has not yet been determined. In order to make a more meaningful comparison, it would be most important to determine the abundances of heavy elements such as iron, nickel and trans-iron elements, the lines of which dominate the radiation pressure for sdB stars. This determination requires high-resolution UV spectroscopy (see, e.g., \citealt{oto06}). We finally note that our upper limit on $\mdot_{\mathrm{W}}$ is in the range of mass loss rates which, according to \citet{ung01}, can explain the He abundances of sdB stars. \appendix | 14 | 4 | 1404.4446 |
1404 | 1404.1055_arXiv.txt | This paper explores if the mean properties of Early-Type Galaxies (ETG) can be reconstructed from ``genetic'' information stored in their GCs (i.e., in their chemical abundances, spatial distributions and ages). This approach implies that the formation of each globular occurs in very massive stellar environments, as suggested by some models that aim at explaining the presence of multi-populations in these systems. The assumption that the relative number of globular clusters to diffuse stellar mass depends exponentially on chemical abundance, [Z/H], and the presence of two dominant GC sub-populations ({\it blue} and {\it red}), allows the mapping of low metallicity halos and of higher metallicity (and more heterogeneous) bulges. In particular, the masses of the low-metallicity halos seem to scale up with dark matter mass through a constant. We also find a dependence of the globular cluster formation efficiency with the mean projected stellar mass density of the galaxies within their effective radii. The analysis is based on a selected sub-sample of galaxies observed within the ACS Virgo Cluster Survey of the {\it Hubble Space Telescope}. These systems were grouped, according to their absolute magnitudes, in order to define composite {\it fiducial} galaxies and look for a quantitative connection with their (also composite) globular clusters systems. The results strengthen the idea that globular clusters are good quantitative tracers of both baryonic and dark matter in ETGs. | \label{INTRO} The characteristics of living creatures, as well known, can be linked to their DNA properties. In a similar fashion we may ask if, given the features of a Globular Cluster System (GCS) (defined in terms of spatial distribution, chemical composition and ages), they can yield ``genetic'' information about the field stellar populations of the Early-Type Galaxies (ETGs) they belong to. This question can be extended to late-type galaxies regarding the formation of their stellar halos and bulges. A number of papers in the literature have pointed out differences between field stars and globular clusters (GCs) rather than similarities \citep[e.g.][]{KISS09}. Although such differences should take into account that GCS properties come in {\it number weighted} form, contrasting with those of galaxy properties, that we read in a {\it luminosity weighted} way, the generalized conclusion seems to indicate that GCs and field stars have followed different formation histories. In the meantime, the discovery of multi-stellar populations in GCs suggests processes where the GC formation was {\it ``a for more titanic event than ever imagined before''} \citep[see][]{REN13}. These scenarios involve large amounts of field stars per GC that would share some characteristics of the clusters \citep{DER08,CARR10}. Despite some difficulties (e.g. the required high star formation efficiencies; see \citealt{BAS13}), these models seem consistent with the idea that GCs could be tracers of much more massive diffuse stellar populations. This kind of approach was explored in \citet[][hereafter, FFG05]{FFG05}, \citet[][FFG07]{FFG07}, \citet[][FVF09]{FVF09} and \citet[][FVF12]{FVF12}. In a recent paper, \citet[][HHA13 in what follows]{HAR13}, present an extensive compilation of several structural parameters that characterize GCS and their parent galaxies. These authors also discuss the implications of a number of correlations that arise considering GCs as a whole, i.e. not including the effects of GCs sub-populations. One of their conclusions indicates that the total number of GCs is not a good estimator of the total stellar mass of a galaxy. In fact, a linear {\it log-log} fit between these quantities shows deviations both at the low and high galaxy mass regimes. They also show that, in a GC population so defined, there is a clear trend between the mass fraction locked in GCs, $S_m$, and the total stellar galaxy mass that adopts a {\it U-shaped} form, already noted by \citet{PEN08}, in terms of the {\it GC specific frequency} $S_n$ (number of GCs per V-luminosity in $M_V=-15$ units). HHA13 interpret that this shape is the consequence of a decrease of the star formation efficiency, both at the low and high mass regimes produced by mass loss and by the energetic events connected with the nuclei of galaxies, respectively. In this paper we attempt to elaborate further on those results by introducing the effect of GC bi-modality, i.e., the presence of {\it blue} and {\it red} GCs. In particular, we aim at exploring the usefulness of these distinct GC populations to trace large scale features of galaxies as, total stellar mass, the relative contribution of halos and bulges to that mass, chemical abundances, stellar mass to luminosity ratios and, indirectly, dark matter content. A preliminary attempt to link galaxies with their GCS in terms of the blue and red populations, was presented in FVF09 for galaxies observed within the ACS Virgo Cluster Survey of the {\it Hubble Space Telescope} \citep{COT04}. In this work, we revise that approach taking advantage of later developments, namely, the accessibility to the original photometry of GCs in the ACS Virgo galaxies \citep{JOR09}, the multicolour photometry of these galaxies \citep{CHE10}, and the C-griz' colour-metallicity grid from \citet[][hereafter, F13]{FOR13}. As in previous works, we stand on the idea that GC formation is not a singular event but, rather, is associated with large volumes of star formation that eventually lead to the origin of distinct populations: a low metallicity and spatially extended stellar halo, associated with the blue globulars, and a more concentrated and chemically more heterogeneous stellar population, connected with the red GCs. The presence of extended low-metallicity halos has been noticed by different means, for example, in NGC\,3379 \citep{HAR07} and NGC\,4472 \citep{MIHHA13}. This work assumes that the GCs colour bi-modality is the consequence of the genuine bimodal nature of their chemical composition distributions \citep[see][]{BRO12}, i.e., not an artifact of some eventually non-linear integrated colour-metallicity relations. On the other side, and as noted in F13, this last kind of relations does not reject necessarily the possibility of a genuine chemical bi-modality. The paper is organized as follows. The definition of {\it fiducial} galaxies is given in Section\,\ref{FIDUCIALS}. The analysis of the GCs colour distributions, as well as their modelling in terms of chemical abundance, are described in Section\,\ref{Color}. The link between GCs and the diffuse stellar populations of the galaxies is presented in Section\,\ref{FIELD}, while the photometric scales for globular clusters and galaxies are discussed in Section\,\ref{ZEROPOINTS}. The model results based on galaxy colours and integrated brightness are discussed in Section\,\ref{COLOURS}. The analysis of the shape of the relation between total number of GCs and galaxy masses is presented in Section\,\ref{BREAK}. The connection between the S\'ersic parameter and the projected stellar surface mass density for the fiducial galaxies is presented in Section\,\ref{Sersic}. The results of modelling the low-metallicity stellar halo, bulge-like component, and total stellar masses, as well as the GC {\it formation efficiency} are presented in Section\,\ref{HALOBULGE}. The relation between the dark matter content of each galaxy and their low-metallicity stellar haloes is discussed in Section\,\ref{LOWMETDARK}. The case of the Fornax spheroidal galaxy is described in Section\,\ref{Fornax}, and the final conclusions are given in Section\,\ref{CONCLU}. | \label{CONCLU} This paper revisits the connection between GCs and the stellar populations of 67 galaxies included in the ACS Virgo Cluster Survey \citep{COT04}. The main results are: \renewcommand{\labelenumi}{\arabic{enumi})} \begin{enumerate} \item The definition of composite {\it fiducial} galaxies was useful in clarifying the quantitative connection bteween GCs and the stellar populations of the galaxies they belong to. These fiducial galaxies are just a representation of average properties that arise as a result of different ``nature-nurture'' events that take place along the life of a galaxy. The possibility of reproducing the integrated colours of galaxies through the analysis of their GCs, and with a constant parameter $\delta$ (Equation\,\ref{eqn5}), strongly suggests the existence of a common mechanism that regulates the link between clusters and field stars. The value of that parameter indicates higher GC formation efficiency as metallicity decreases. This dependence may be indicating a background process connected with enviromental conditions (through a metallicity-stellar density link) as noted in Section\,\ref{HALOBULGE}. We stress that the proposed GCs-field stars link also gives a proper representation of the chemical distribution of field stars for low-mass galaxies (e.g. the Fornax dwarf spheroidal) although it requires higher $\delta$ values, something we cannot justify yet on observational basis. \\ \item The separation of GCs in two families, according to their respective chemical scale lengths $Z_s$, shows that blue and red clusters increase their number with total stellar galaxy mass but with distinct behaviours. Once combined as a ``single population'', the $log(N_{GCs})$ versus $log (M_{*})$ relation found for the Virgo ACS galaxies, is consistent with the non-linear trend (in a {\it log-log} plane) pointed out by HHA13. \\ \item The mean total stellar mass of the fiducial galaxies follows a linear relation with the {\it dynamical mass}, given in terms of the stellar dispersion and effective radius presented by \citet{WOL10} and correlated with $L_V$ in HHA13. \\ \item The empirical approach proposed to connect GCs and field stars allows an estimate of the low-metallicity halo and bulge-like stellar masses. In particular, these last structures arise in galaxies with stellar masses larger than $\approx10^9~M_{\odot}$ and grow up rapidly for more massive galaxies. In this sense, they appear to be more ``pseudo-bulges'' (originated in the ability of the galaxies to retain their chemical outputs) than bulges that grow as a consequence of environmental effects. We also emphasize that bi-modality is a very solid feature since ``dry merging'' of any of the bimodal fiducial galaxies ends up as a new, but also bimodal, GCs colour distribution, although with different $Z_{sb}$ and $Z_{sr}$ parameters. \\ \item The behaviour of the number of the blue or red GCs per stellar mass units of the populations they are respectively associated (halo or bulge-like) as a function of total stellar mass, exhibits a similarity and a difference. On one side, they are both {\it U-shaped} and reach minimum values in the mass range defined by the fiducial galaxies 4 and 5. On the other, the red GCs show a marked (inverse) dependence with surface stellar mass density. This dependence is not detectable for the blue GCs as the total stellar mass is dominated by bulge like stars. \\ \item The ratio of the low-metallicity stellar halo mass to total stellar mass exhibits a strong similarity (once properly normalized) with the ratio of total dark matter mass to stellar mass as presented in \citet{SHA06}. In some way, the low-metallicity halo seems a kind of ``subtle echo'' of the dark matter content if the dark to stellar mass ratios given by \citet{SHA06} are adopted. \end{enumerate} It is intriguing that the increase of the $\Gamma$ and $t_{dark}$ trends with galaxy mass, occurs approximately at the so called {\it critical mass} as defined by \citet{DEK03}; the mass value that suggests a ``dichotomy'' in the galaxy formation process as argued by \citet{KOR09}; the ``pivot'' mass defined by \citet{LEA12}; and, as pointed out in this paper, the stellar mass where the projected stellar surface density $\Sigma$ reaches a maximum value. The reason for that increase is not clear although the dramatic change of the effective radii of these galaxies with brightness (and stellar mass), leading to low stellar densities, suggests that this kind of environments may favour the GCs formation efficiency (speculatively, through better survavility conditions for the cooling flows where GCs would form). In fact, the hierarchical models by \citet{OSE10} indicate that the most massive galaxies, exhibit less in-situ star formation, have less concentrated halos, and also lower central densities. These authors also show that the size of these galaxies, and a large fraction of their masses, are the result of the accretion of objects formed ``far'' from the central regions of the galaxies. In our approach, the $Z_s$ scale lengths are a measurement of the spread of the metallicity of the blue GC/low-metallicity halo and of the red GC/bulge stars. The distinction between these ``two'' components is in fact a ``working definition'' in the sense that they provide a good match to the integrated galaxy colours. Even though the low-metallicity component is rather homogeneous and would be properly identified as a ``single population'', this is not the case of the bulge-like component which, according to their larger $Z_s$ scales, suggests a rather inhomogeneous mix of stars with very different chemical abundances. \citet{FORB97} already suggested that GCs bimodality may be the result of a ``two phases'' process. The meaning of ``phase'', however, seems still an open issue in the context of some recent results. For example, several works point out that re-ionization has played a role (e.g. \citealt{KAT12}, \citealt{SPI12}; \citealt{ELM12}; \citealt{GRI13}) in the formation of the metal poor blue GCs that would appear at high redshifts and before the red (and more heterogeneous chemically) GCs. \citet{TON13} (and also see \citealt{MUR10}) gives arguments to support the existence of a discrete temporal sequence in the frame of hierarchical models, indicating that blue GCs form at a redshift of $\approx4$ and are later accreted by galaxies that already have their own metal rich GCs (formed in-situ) at redshifts of $\approx2$. This is similar to the scenario presented by \citet{FOR82} for the particular case of NGC\,4486 and later generalized by \citet{COT98}. \citet{TON13} also concludes that red GCs only form in galaxies with stellar masses larger than $10^9~M_{\odot}$, in approximate agreement with the results presented in this paper regarding to these clusters and their associated bulge-like structures. In contrast with that landscape, and as noted by \citet{LEA13} (and also see \citealt{VAN13}) the results for the Milky Way GCs, rather than discrete events, shows a continuous and bifurcated age sequence. These results indicate that both metal poor and metal rich GCs seem coeval and display the same range of ages ($\approx2$ Gy), although shifted in metallicity by $\approx0.6$ dex. In their view, blue GCs may need not to have formed in a truncated epoch and as separated episodes. A 2 Gy difference between the low (NGC\,6397) and the high metallicity (47\,Tuc) Milky Way GCs, is also found by \citet{HAN13} on the basis of the study of the white dwarf sequences in these clusters. In our analysis, we find that the chemical scale lengths of the blue GCs, $Z_b$, slowly increase with total galaxy mass, i.e., at least a fraction of them have a link with these galaxies. In a tentative explanation, and coincident with \cite{CARR13}, we suggest that blue GCs may be a mix of clusters formed in-situ (and showing a dependence with galaxy mass) and other accreted, more stochastically, from less massive fragments/galaxies. If a bifurcated age sequence as in the Milky Way exists, the chemical abundances of both the blue and red GCs are genuine ``in phase'' clocks. This would indicate that the term ``phase'' (in the context of \citealt{FORB97}) is more a feature connected with environment than with time. To the question posed by HHA13 regarding {\it ``what determines the size of a GC population?''}, this paper suggests that it is a competing mechanism where the number of GCs depends on the availability of potential formation sites, that increases with galaxy mass and, at the same time, has an inverse dependence with stellar density. As a final conclusion, we find support for the idea that GCs in fact codify information about the large scale features of ETGs. However, the complete code is not yet conclusively understood. | 14 | 4 | 1404.1055 |
1404 | 1404.6505_arXiv.txt | We present an analysis of high proper motion objects that we have found in a recent study and in this work with multi-epoch astrometry from the {\it Wide-field Infrared Survey Explorer (WISE)}. Using photometry and proper motions from 2MASS and {\it WISE}, we have identified the members of this sample that are likely to be late type, nearby, or metal poor. We have performed optical and near-infrared spectroscopy on 41 objects, from which we measure spectral types that range from M4--T2.5. This sample includes 11 blue L dwarfs and five subdwarfs; the latter were also classified as such in the recent study by Kirkpatrick and coworkers. Based on their spectral types and photometry, several of our spectroscopic targets may have distances of $<20$~pc with the closest at $\sim12$~pc. The tangential velocities implied by the spectrophotometric distances and proper motions indicate that four of the five subdwarfs are probably members of the Galactic halo while several other objects, including the early-T dwarf WISE J210529.08$-$623558.7, may belong to the thick disk. | Proper motions have long been used to identify members of the solar neighborhood. Measurements at optical wavelengths have been sensitive to stellar masses \citep{bar16,wol19,ros26,van44,gic71,luy79,sal03,ham04,lep02,lep03,lep05a,lep08a,sub05,boy11,fin12} while data in near-infrared (IR) bands have reached substellar objects \citep{art06,art10,dea05,dea09,dea11,dea07,sch09e,sch10d,she09,kir10,smi14}. The near-IR proper motion surveys have been enabled primarily by the Two Micron All-Sky Survey \citep[2MASS,][]{skr06}, the Deep Near-Infrared Survey of the Southern Sky \citep[DENIS,][]{ep99}, the Sloan Digital Sky Survey \cite[SDSS,][]{yor00}, the United Kingdom Infrared Telescope Infrared Deep Sky Survey \citep[UKIDSS,][]{law07}, and Pan-STARRS1 \citep{kai02}. In 2010, the imaging available for proper motion surveys was extended to mid-IR wavelengths by the {\it Wide-field Infrared Survey Explorer} \citep[{\it WISE},][]{wri10}. Proper motions have been measured by combining the {\it WISE} astrometry with optical and near-IR catalogs \citep{liu11,sch11,sch12,giz11a,giz11b,giz12,cas12,cas13,bih13} and by employing only the multiple epochs of data obtained by {\it WISE} \citep{luh13,luh14a,tho13,wri14,kir14}. In one of the latter surveys, \citet{luh14a} searched for a distant companion to the Sun via the large parallactic motion that it would exhibit. During the course of that study, several hundred new high proper motion objects were found. In this paper, we investigate the nature of those objects by using photometry and proper motions from 2MASS and {\it WISE} to identify the ones that are likely to be late type, nearby, or metal poor (Section~\ref{sec:phot}). We then use spectroscopy (Section~\ref{sec:spec}) and kinematics (Section~\ref{sec:kin}) to characterize in more detail a subset of that sample, focusing on the most promising candidates for L/T dwarfs and subdwarfs. | We have analyzed a sample of 781 high proper motion objects found with multi-epoch astrometry from {\it WISE} \citep[Table~\ref{tab:hipm};][]{luh14a}. Using 2MASS and {\it WISE} photometry and proper motions, we have identified the members of this sample that are most likely to be nearby, cool, or metal poor. We have obtained spectra of 41 of these objects, arriving at spectral types of M4--T2.5. Our spectroscopic sample includes 11 blue L dwarfs and five subdwarfs. All of the latter were independently found as high proper motion objects and classified as subdwarfs by \citet{kir14}. Two of our candidate subdwarfs that we did not observe spectroscopically, WISE J070720.48+170533.0 and WISE J020201.24$-$313644.7, have been confirmed as such through spectra collected by \citet{wri14} and \citet{kir14}. The most promising remaining candidate subdwarf from our sample that lacks spectroscopy is WISE J141143.25$-$452418.3. We have estimated spectrophotometric distances and tangential velocities for the members of our spectroscopic sample. The closest system appears to have a distance of $\sim12$~pc, and several others may have distances within 20~pc. A few objects that lack spectra also may fall within 20~pc, as shown in Figure~\ref{fig:cmd}. Assuming that previous samples of high proper motion stars have been thoroughly searched for nearby stars, our proper motion survey and that of \citet{kir14} imply that the current census of neighbors within 10~pc has a high level of completeness for spectral types of T and earlier. The tangential velocities in our sample are higher for bluer near-IR colors, which is the same trend found in previous studies. Four of the five subdwarfs exhibit velocities of 300--400~km~s$^{-1}$, which are indicative of membership in the Galactic halo. Several additional objects have velocities that are suggestive of the thick disk ($V_{tan}\sim150$--200~km~s$^{-1}$), including the early-T dwarf WISE J210529.08$-$623558.7. More definitive characterizations of the kinematics of these candidate members of the halo and thick disk will require measurements of parallaxes and radial velocities. | 14 | 4 | 1404.6505 |
1404 | 1404.3102_arXiv.txt | Recent detection of $B$-mode polarization induced from tensor perturbations by the BICEP2 experiment implies so-called large field inflation, where an inflaton field takes super-Planckian expectation value during inflation, at a high energy scale. We show however, if another inflation follows hybrid inflation, the hybrid inflation can generate a large tensor perturbation with not super-Plankian but Planckian field value. This scenario would relax the tension between BICEP2 and Planck concerning the tensor-to-scalar ratio, because a negative large running can also be obtained for a certain number of e-fold of the hybrid inflation. A natural interpretation of a large gravitational wave mode with or without the scalar spectral running might be multiple inflation in the early Universe. | The detection of $B$-mode polarization from gravitational wave mode perturbation has been reported by BICEP2~\cite{Ade:2014xna}. From the amplitude of the tensor perturbation, the tensor-to-scalar ratio is read as \begin{equation} r _T = 0.20^{+0.07}_{-0.05} , \end{equation} for a lensed-$\Lambda$CDM plus tensor mode cosmological model, \begin{equation} r _T = 0.16^{+0.06}_{-0.05} , \end{equation} after the foreground subtraction based on dust models. Those values appear to be under the tension with the upper bound $r _T < 0.11$ reported by the Planck~\cite{Ade:2013zuv-1,Ade:2013zuv-2}. As a possible way to resolve this tension, in Ref.~\cite{Ade:2014xna} the introduction of a large negative running of the scalar spectral index has been proposed. However, we note that after the BICEP2 paper~\cite{Ade:2014xna}, doubts about inappropriate treatments on dust emissions in their analysis have been raised~\cite{Liu:2014mpa,Flauger:2014qra,Mortonson:2014bja}. The Planck collaboration have released the polarized dust emission data away from Galactic plane~\cite{Adam:2014bub}, the joint analysis of BICEP2 and the Planck dust polarization data found no evidence~\cite{Cheng:2014pxa}. The large tensor mode has a remarkable implication to inflation. Such a large tensor mode can be generated in the so-called large field inflation models, where the field value of inflaton during inflation takes super-Plankian, while small field inflation models can not generate large $r_T$, but $r_T \leq {\cal O}(10^{-2})$~\cite{LythBound}. Thus, since the BICEP2 results were announced, polynomial chaotic inflation models have been studied intensively in light of the BICEP2 data~\cite{ChaoticAfterBicep1,ChaoticAfterBicep2, ChaoticAfterBicep3,ChaoticAfterBicep4,ChaoticAfterBicep5,ChaoticAfterBicep6,ChaoticAfterBicep7, ChaoticAfterBicep8,ChaoticAfterBicep9,ChaoticAfterBicep10}. However, the construction of so-called large field model looks nontrivial from supergravity viewpoint as well as field theoretical viewpoint. For various attempts, see, e.g., Ref.~\cite{Yamaguchi:2011kg-1,Yamaguchi:2011kg-2}. In this respect, hybrid inflation is appealing since the inflaton $\varphi$ takes a field value less than or of the order of Planck scale~\cite{Hybrid-1,Hybrid-2}. However generally speaking, hybrid inflation models have been disfavored. Firstly, while simple (non-)supersymmetric hybrid inflation predicts the density perturbation with the scalar spectral index $n_s > (1) \,\, 0.98 $~\cite{Hybrid-1,Hybrid-2,Dvali:1994ms,Linde:1997sj}~\footnote{ In fact, in order to reduce $n_s$, non-minimal Kahler potentials have been examined~\cite{NonMinK-1,NonMinK-2}.}, the WMAP~\cite{Hinshaw:2012aka} and Planck~\cite{Ade:2013zuv-1,Ade:2013zuv-2} data indicate $n_s \simeq 0.96$. Secondly, topological defects, usually cosmic strings, are formed at the end of a hybrid inflation, when the water fall field develops the vacuum expectation value (vev). The expected mass per unit length of the formed cosmic string is not compatible with data of the temperature anisotropy $\delta T/T$ in the cosmic microwave background radiation (CMB)~\cite{StringProblem}. Thirdly, hybrid inflation cannot generate gravitational wave mode with a large amplitude~\cite{Civiletti:2014bca-1,Civiletti:2014bca-2,Civiletti:2014bca-3} because the potential energy scale is too low, in other word the potential is too flat when we normalize the amplitude of the density (scalar) perturbation with $\delta T/T$. We point out a possible way to overcome those problems of hybrid inflation. The second problem due to cosmic strings is avoided by considering somewhat complicated potential such as shifted hybrid inflation~\cite{Jeannerot:2000sv} or smooth hybrid inflation~\cite{Lazarides:1995vr}. The other two can be simultaneously solved if we give up a large enough number of e-folds $N$ by a hybrid inflation to solve problems in the standard Big Bang cosmology. A smaller $N$ corresponds to a larger slow roll parameters, which leads to a smaller $n_s$ and a larger $r_T$. Of course, we need to solve the horizon and flatness problems and generate the density perturbation at super-horizon scales. This may be achieved by an inflation following after the hybrid inflation, so-called double inflation scenario, where the Universe has undergone an inflationary expansion in the early Universe more than once. Such double inflation scenarios~\cite{DoubleInflation} have been considered with various motivations, e.g., low multipole anomaly in the CMB sky~\cite{Lowpole-1,Lowpole-2,Lowpole-3}, the generation of primordial black holes~\cite{PBH1,PBH2-1,PBH2-2,PBH2-3}, and the dilution of unwanted relics~\cite{Lyth:1995ka-1,Lyth:1995ka-2,Lyth:1995ka-3}. In this paper, we show if the secondary inflation takes place with a sufficient number of e-folds, say $N \simeq 40 - 50$, a kind of supersymmetric hybrid inflation is available and could generate not only an appropriate density perturbation and its spectrum as in Ref.~\cite{Lazarides:2007dg} but also large $r_T = {\cal O}(0.1)$, in contrast with the previous work~\cite{Civiletti:2011qg} where the possibility of $r_T\simeq 0.02$ has been pointed out. | In this paper, we have examined the possibility of viable hybrid inflation generating a large tensor-to-scalar ratio as BICEP2 indicated. The result is that it is possible if an additional inflation follows the hybrid inflation whose number of e-fold is not large enough to solve the horizon and flatness problems, which is crucial and essential assumption. Provided the additional inflation successfully works, the observed cosmological scale would correspond to a few $ \lesssim N \lesssim 10$ of the hybrid inflation. In this case, $n_s \simeq 0.96$ and $r_T = {\cal O}(0.1)$ can be realized at the cosmological scale. One observation here is that if we work on double inflation scenario, we do not need super-Planckian field value of the inflaton. As shown in Figs.~\ref{Fig:10} and \ref{Fig:6}, the order of Planck field value is sufficient. Another feature is that a large negative $\alpha_s$ can be obtained for $N\sim 6$. This would offer a possibility to resolve the tension between BICEP2 and Planck. In double inflation scenario, the present large scale exits the Hubble horizon during the high scale hybrid inflation and the small scale does during the following low scale inflation. Hence, a cosmological implication of double inflation is strong scale dependence of amplitude of gravitational wave mode. | 14 | 4 | 1404.3102 |
1404 | 1404.4514_arXiv.txt | {We explore a sample of 148 solar-like stars to search for a possible correlation between the slopes of the abundance trends versus condensation temperature (known as the T$_{c}$ slope) with stellar parameters and Galactic orbital parameters in order to understand the nature of the peculiar chemical signatures of these stars and the possible connection with planet formation. We find that the T$_{c}$ slope significantly correlates (at more than 4$\sigma$) with the stellar age and the stellar surface gravity. We also find tentative evidence that the T$_{c}$ slope correlates with the mean galactocentric distance of the stars (R$_{mean}$), suggesting that those stars that originated in the inner Galaxy have fewer refractory elements relative to the volatiles. While the average T$_{c}$ slope for planet-hosting solar analogs is steeper than that of their counterparts without planets, this difference probably reflects the difference in their age and R$_{mean}$. We conclude that the age and probably the Galactic birth place are determinant to establish the star's chemical properties. Old stars (and stars with inner disk origin) have a lower refractory-to-volatile ratio.} | Despite the huge progress in developing instrumentation and observational techniques during the past decade, the study of extrasolar planets' properties via direct observations is still a very difficult task, and the precise study and characterization of known extroplanets cannot be dissociated from the study of planet host stars. The connection between stellar and planetary properties has been widely explored. In particular, the very first correlation observed in this field of research, that of giant-planet - metallicity \citep[e.g.,][]{Gonzalez-97, Santos-01, Santos-04, Fischer-05, Sousa-11}, was one of the most important constraints on planet formation theories \citep[e.g.,][]{Mordasini-09}. Afterwards it was shown that not only does the presence of planets correlate with metallicity (usually abundance of iron), but planet-host stars also show a systematic enhancement of other elements \citep[e.g., $\alpha$-elements - ][]{Haywood-08b, Adibekyan-12a, Adibekyan-12b}. More recently, several studies have revealed that stellar metallicity also plays an important role in the architecture of planetary orbits \citep[e.g.,][]{Dawson-13, Beauge-13, Adibekyan-13a}. Naturally, this connection is bidirectional: not only do stellar properties play an important role in planet formation and evolution, but the planet formation can also have an impact on stellar properties. As an example, \cite{Israelian-09} and \cite{DelgadoMena-13} find strong evidence that solar analogs with planets show enhanced Li depletion compared to their non-host counterparts. The studies mentioned above are not the only ones. Recently, \cite{Melendez-09} have claimed that the Sun shows a deficiency in refractory elements with respect to other solar twins probably because they were trapped in the terrestrial planets in our solar system. The same conclusion has also been reached by \cite{Ramirez-09} who analyzed 64 solar twins and analogs. However, recent results by \cite[][- GH10,13]{Jonay-10, Jonay-13} strongly challenge the relation between the presence of planets and the abundance peculiarities of the stars. Other works also have examined this possible connection between the chemical peculiarities and formation of planets \citep[e.g.,][]{Smith-01, Ecuvillon-06, Gonzalez-10, Gonzalez-11, Jonay-11, Schuler-11, Ramirez-14}. In this letter, we explore the origin of the possible trend observed between [X/H] (or [X/Fe]) and condensation temperature ($T_{c}$) using a sample of 148 solar-like stars. | We used a sample of 148 solar-type stars from GH10,13 to explore the main factors responsible for the abundance trends with condensation temperature. For these stars the stellar atmospheric parameters and the T$_{c}$ slopes were taken from the above-mentioned studies, while the stellar ages, Galactic orbital parameters, and velocity components are from \cite{Casagrande-11}. Our study reveals a strong correlation between stellar ages and T$_{c}$ slope: old stars show steeper slope i.e., less refractory elements relative to volatiles. The same result reflects the statistically significant correlation between T$_{c}$ slopes and surface gravity: more evolved (old) stars have a lower refractory-to-volatile ratio. Moving one step further, we found tentative evidence that the T$_{c}$ slopes also correlate with the mean galactocentric distance of the stars; this suggest that stars which probably have origin in the inner Galaxy (small R$_{mean}$) have steeper slopes. The result fits well in the recent evolution picture of the Milky Way, showing that some fraction of old stars in the solar neighborhood might have its origin in the inner disk \citep[e.g.,][]{Minchev-13}. Briefly exploring the possible reasons why one can see a difference in T$_{c}$ slopes for planet-hosting solar analogs and solar analogs without detected planets, we found that in the current sample these two subsamples have different distributions of age and R$_{mean}$ that correlate with the T$_{c}$ slope. These differences might explain the differences in T$_{c}$ slope distribution, suggesting that there are no signatures of planet formation in the observed abundance trends with the condensation temperature. We may conclude that the T$_{c}$ slope depends on the age of a star at a fixed galactocentric radius. At the same time, stars with smaller galactocentric radii show stepper T$_{c}$ slopes at a fixed time (age). In other words, the age and galactic birth place may determine the chemical pattern of the stars. | 14 | 4 | 1404.4514 |
1404 | 1404.1794_arXiv.txt | {The recent discovery of B-modes in the polarization pattern of the Cosmic Microwave Background by the BICEP2 experiment has important implications for neutrino physics. We revisit cosmological bounds on light sterile neutrinos and show that they are compatible with all current cosmological data provided that the mass is relatively low. Using CMB data, including BICEP-2, we find an upper bound of $m_s < 0.85$ eV ($2\sigma$ Confidence Level). This bound is strengthened to 0.48 eV when HST measurements of $H_0$ are included. However, the inclusion of SZ cluster data from the Planck mission and weak gravitational measurements from the CFHTLenS project favours a non-zero sterile neutrino mass of $0.44^{+0.11}_{-0.16}$ eV. Short baseline neutrino oscillations, on the other hand, indicate a new mass state around 1.2 eV. This mass is highly incompatible with cosmological data if the sterile neutrino is fully thermalised ($\Delta \chi^2>10$). However, if the sterile neutrino only partly thermalises it can be compatible with all current data, both cosmological and terrestrial.} | Over the past few years cosmology has established itself as one of the primary laboratories for neutrino physics. In particular, observations of the Cosmic Microwave Background and Large Scale Structure have severely constrained parameters such as the absolute neutrino mass and the cosmic energy density in neutrinos (see e.g.\ \cite{Ade:2013zuv}). These two parameters are also of significant interest in the context of eV-mass sterile neutrinos currently hinted at by short baseline neutrino oscillation experiments. At the same time neutrino oscillation experiments seem to point to the existence of at least one additional mass state around 1 eV with significant mixing with the active sector. Even though this mass state is mainly sterile the mixing leads to almost complete thermalisation in the early universe (see e.g.\ \cite{Hannestad:2012ky, Melchiorri:2008gq}) and the additional mass state effectively affects structure formation in the same way as a 1 eV active neutrino. Such a high mass has seemed at odds with cosmological data \cite{Hamann:2011ge}, and has led to a number of attempts to reconcile the existence of eV sterile neutrinos with cosmology. Examples include modifications to the background potential due to new interactions in the sterile sector \cite{Hannestad:2013ana,Dasgupta:2013zpn,Bringmann:2013vra,Ko:2014bka,Mirizzi:2012we,Saviano:2013ktj} or modifications to the cosmic expansion rate at the time where sterile neutrinos are produced \cite{Rehagen:2014vna}. However, the very recent publication of new data from the BICEP2 experiment \cite{Ade:2014xna} has indicated a high tensor to scalar ratio, and this in turn significantly modifies constraints on neutrino related parameters. Here we investigate how constraints on eV mass sterile neutrinos are influenced by the new BICEP2 discovery, and demonstrate that eV mass sterile neutrinos are not significantly constrained by current cosmological data. Section 2 contains a discussion of the cosmological parameter estimation and Section 3 a short summary of our SBL likelihood analysis. In Section 4 we present the results of the joint analysis and finally Section 5 contains a thorough discussion of our results. | We have performed an analysis of light sterile neutrinos in the context of both cosmology and short baseline neutrino oscillation experiments. Previous analyses have shown that while SBL data points to the existence of a mainly sterile mass state around 1 eV, this is not compatible with cosmological data unless the additional state is somehow prevented from being fully thermalised in the early Universe \cite{Archidiacono:2012ri}. The inclusion of new data from the BICEP-2 experiment favours a higher dark radiation content, but this actually tightens the cosmological bound on the mass of the sterile neutrino because $m_s$ and $\ns$ are highly anti-correlated. Cosmological data from the CFHTLenS survey and the Planck SZ cluster counts actually favour a non-zero mass of the sterile neutrino because it alleviates the tension between the value of $\sigma_8$ inferred from the CMB measurements and the minimal $\Lambda$CDM model and the lower value indicated by data CFHTLenS and PSZ data. The inclusion of these two data sets points to a sterile mass around 0.5 eV, but with relatively low $\ns$. Provided that $\ns$ is low the allowed mass stretches to higher values. The SBL data strongly constrains $m_s$, but not $\ns$, and indicates a mass not much lower than 1 eV. At the same time the mixing angle is large enough that the additional state is almost fully thermalised. However, this scenario is highly disfavoured by cosmological data (with a $\Delta \chi^2>10$) which for a mass of 1 eV requires $\ns$ to be quite low. Indeed a model with a mass of 1 eV and a low $\ns$ is compatible with cosmology within roughly $2\sigma$ confidence level. The conclusion is that light sterile neutrinos as indicated by SBL data are close to being ruled out by cosmological data unless they are somehow prevented from thermalising in the early Universe. Recently, a number of papers on how to resolve this apparent conflict have appeared. A possible way out of this problem is that sterile neutrinos have new interactions which induce a non-standard matter potential and block thermalisation \cite{Hannestad:2013ana,Dasgupta:2013zpn,Bringmann:2013vra,Ko:2014bka,Mirizzi:2012we,Saviano:2013ktj}. This model can easily have 1 eV sterile neutrinos and an $\Neff$ not much beyond 3 and thus be compatible with all existing data. While this scenario certainly works well and can possibly also explain some of the astrophysical anomalies related to cold dark matter, there are without a doubt other possible ways of making eV sterile neutrino compatible with both SBL and cosmological data. For example some models with low temperature reheating or non-standard expansion rate of the universe at the MeV scale where the new state is thermalised can also prevent thermalisation \cite{Rehagen:2014vna}. Thus, eV mass sterile neutrinos remain an intriguing possibility which potentially has wide ranging implications for cosmology. | 14 | 4 | 1404.1794 |
1404 | 1404.7384_arXiv.txt | {} {The main goal of this research is to determine the angular size and the atmospheric structures of cool giant stars ($\epsilon$~Oct, $\beta$~Peg, NU~Pav, $\psi$~Peg, and $\gamma$~Hya) and to compare them with hydrostatic stellar model atmospheres, to estimate the fundamental parameters, and to obtain a better understanding of the circumstellar environment.} {We conducted spectro-interferometric observations of $\epsilon$~Oct, $\beta$~Peg, NU~Pav, and $\psi$~Peg in the near-infrared K band (2.13-2.47 $\mu$m), and $\gamma$~Hya (1.9-2.47 $\mu$m) with the VLTI/AMBER instrument at medium spectral resolution ($\sim$1500). To obtain the fundamental parameters, we compared our data with hydrostatic atmosphere models (PHOENIX).} {We estimated the Rosseland angular diameters of $\epsilon$~Oct, $\beta$~Peg, NU~Pav, $\psi$~Peg, and $\gamma$~Hya to be 11.66$\pm$1.50\,mas, 16.87$\pm$1.00\,mas, 13.03$\pm$1.75\,mas, 6.31$\pm$0.35\,mas, and 3.78$\pm$0.65\,mas, respectively. Together with distances and bolometric fluxes (obtained from the literature), we estimated radii, effective temperatures, and luminosities of our targets. In the $\beta$~Peg visibility, we observed a molecular layer of CO with a size similar to that modeled with PHOENIX. However, there is an additional slope in absorption starting around 2.3\,$\mu$m. This slope is possibly due to a shell of H$_{2}$O that is not modeled with PHOENIX (the size of the layer increases to about 5\% with respect to the near-continuum level). The visibility of $\psi$~Peg shows a low increase in the CO bands, compatible with the modeling of the PHOENIX model. The visibility data of $\epsilon$~Oct, NU~Pav, and $\gamma$~Hya show no increase in molecular bands.} {The spectra and visibilities predicted by the PHOENIX atmospheres agree with the spectra and the visibilities observed in our stars (except for $\beta$~Peg). This indicates that the opacity of the molecular bands is adequately included in the model, and the atmospheres of our targets have an extension similar to the modeled atmospheres. The atmosphere of $\beta$~Peg is more extended than that predicted by the model. The role of pulsations, if relevant in other cases and unmodeled by PHOENIX, therefore seems negligible for the atmospheric structures of our sample. The targets are located close to the red limits of the evolutionary tracks of the STAREVOL model, corresponding to masses between 1~$M_{\odot}$ and 3~$M_{\odot}$. The STAREVOL model fits the position of our stars in the Hertzsprung-Russell (HR) diagram better than the Ekstr\"om model does. STAREVOL includes thermohaline mixing, unlike the Ekstr\"om model, and complements the latter for intermediate-mass stars.} | \begin{table*} \caption{VLTI/AMBER observations} \centering \begin{tabular}{lcccccccc} \hline \hline Target (Sp. type) & Date & Baseline & Projected Baseline & PA & Calibrator \\ & & & m & deg & \\ \hline $\epsilon$ Oct (M5 III) & 2012 Jun 25 & D0-A1-C1 & 28.9/15.4/15.1 & -119/79/-138 & HIP 104755\\ & 2012 Aug 02 & B2-A1-C1 & 10.26/15.62/7.83 & -96.1/57.8/22.7 & HIP 104755\\ $\beta$ Peg (M2.5 II-III) & 2012 Jun 25 & D0-A1-C1 & 30.4/15.6/16.4 & -122/76.6/140 & HIP 114144 - HIP 1168 \\ & 2012 Aug 09 & B2-A1-C1 & 11.1/14.5/7.0 & -69.2/82.80/35.20 & HIP 114144 - HIP 1168\\ NU Pav (M6 III) & 2012 Aug 02 & B2-A1-C1 & 10.9/15.8/9.8 & -70.6/71.6/28.8 & HIP 82363 \\ $\psi$ Peg (M3 III) & 2012 Jun 16 & D0-I1-G1 & 82.1/32.8/66.1 & 102/-128/124.5 & HIP 114144 - HIP 1168\\ $\gamma$~Hya (G8 III) & 2013 Mar 16 & A1-G1-J3 & 74.9/132.2/135.7 & 118/15.3/47.7 & K Hya\\ \hline \end{tabular} \tablefoot{Details of our observations. The AMBER instrument mode is K-2.3\,$\mu$m (2.12-2.47\,$\mu$m). The projected baseline is the projected baseline length for the AT VLTI baseline used, and PA is the position angle of the baseline (North through East). $\gamma$~Hya has been observed in K-2.1 and K-2.3 bands, which together cover the range 1.9-2.47\,$\mu$m.} \label{Log_obs} \end{table*} The motivation for our study is to improve our understanding of the circumstellar environment of asymptotic giant branch stars (AGBs) close to the photosphere, to obtain estimates about their fundamental parameters, and to locate them in the Hertzsprung-Russell (HR) diagram. The location of the stars in the HR diagram is very important for calibrating stellar evolutionary models for intermediate-mass stars. Interferometric techniques at visible and IR wavelengths are important for resolving the stellar disk to better understand the circumstellar environment (Quirrenbach et al. \cite{Quirrenbach1993}, Perrin et al. \cite{Perrin2004}). Recent studies with VLTI/AMBER and VLTI/MIDI have provided information about the pulsation and the mass-loss of AGB stars (Ohnaka et al. \cite{Ohnaka2006}, \cite{Ohnaka2007}; Wittkowski et al. \cite{Wittkowski2007}; Chiavassa et al. \cite{Chiavassa2010}; Karovicova et al. \cite{Karovicova2011}, \cite{Karovicova2013}) and about the structure of the molecular distribution in AGB stars (Wittkowski et al. \cite{Wittkowski2008}, \cite{Wittkowski2011}; Mart{\'{\i}}-Vidal et al. \cite{Marti2011}). Quirrenbach et al. (\cite{Quirrenbach1993}, \cite{Quirrenbach2001}) studied the TiO band (around 712\,nm) in the atmosphere of cold giant stars (spectral type M). Their interferometric observations were made with two filters, one centered on the TiO band, and the other on the continuum close to that band. They observed an increase of the size of the star corresponding to the TiO band with respect to the size in the continuum. After fitting the PHOENIX models (Hauschildt \& Baron \cite{Hausch1999}) to their data, they concluded that the diameter ratio between the TiO band and the continuum agreed with models computed for a mass of 0.5\,$M_{\odot}$; but the evolutionary models predict for these stars masses of about 5\,$M_{\odot}$. This disagreement might be explained by the existence of a transition zone at the base of the stellar wind (Tsuji \cite{Tsuji2008}), which could provide sufficient opacity in the TiO band to make the AGB larger than the size predicted by the PHOENIX model. Mart{\'{\i}}-Vidal et al. (\cite{Marti2011}) observed RS~Cap (AGB star of spectral type M6/M7III) with the VLTI/AMBER instrument in the K band. They found that the apparent size of the star increased around 12\% in the CO band (2.29\,$\mu$m-2.47\,$\mu$m). The fit to the data with MARCS models (Gustafsson et al. \cite{Gustafsson2008}) was reasonable, although the lower visibilities in the CO band were not reproduced. These authors added an ad hoc spherical water envelope around the star (Perrin et al. \cite{Perrin2004}) that made the synthetic visibilities and the observations in the CO bands appear consistent. Cruzal{\`e}bes et al. (\cite{Cruzalebes2013}) observed sixteen red giants and supergiants with VLTI/AMBER over a two-year period. They used MARCS models to fit their data. Their estimates of the angular diameters were moderately dependent on the variation of the model input parameters T$_{eff}$, log(g), and $\xi_{turb}$. Eight of these sources were studied for the first time but the others had been studied earlier with Long-Baseline Interferometry (LBI), and the angular diameter estimates obtained with both methods were similar. Cusano et al. (\cite{Cusano2012}) studied five giant stars while investigating planet formation around stars more massive than the Sun. They estimated the uniform disk (UD) and limb-darkened (LD) angular diameters and the effective temperatures of these sources. The measurements of both angular diameters (UD and LD) were consistent within 1.5$\sigma$, the differences being smaller than 0.8\%. Their estimates were also consistent with the values derived by da Silva et al. \cite{Silva2006}. In this paper we study a sample of cool giant stars with VLTI/AMBER. We locate our targets in the HR diagram and compare our results with those of the red supergiant stars studied in Arroyo-Torres et al. (\cite{Arroyo2013}). The remainder of this paper is structured as follows: in Sect. 2, we describe our AMBER observations and the data reduction, in Sect. 3, we present the PHOENIX model used, in Sect. 4, we report and discuss our results. Finally, we present our conclusions in Sect. 5. | Our spectro-interferometric near-infrared observations of $\epsilon$~Oct, NU~Pav, $\psi$~Peg, and $\gamma$~Hya show that synthetic visibilities from hydrostatic atmospheric models are consistent with the observations, concluding that their atmospheres can be modeled with a limb-darkened disk. In $\epsilon$~Oct, NU~Pav, and $\gamma$~Hya, the uniform disk diameter is constant across the band, and the CO bandheads present a similar size to that of the continuum. On the other hand, the data of $\psi$~Peg show a low increase in the CO band, similar to the one obtained in the model. According to these results, the atmospheres of $\epsilon$~Oct, NU~Pav, $\psi$~Peg, and $\gamma$~Hya are compatible with hydrostatic atmospheres and the role of pulsation does not seem to be important. However, the data from $\beta$~Peg (at least in the 2012 June epoch) show a layer (possibly of H$_{2}$O) that is not modeled by PHOENIX, but CO bands similar to those modeled with PHOENIX. The uniform disk diameter of the star at the CO band increases about 5.3\% with respect to the continuum (less than the 14\% increase of diameter observed in RS~Cap). We used the continuum near 2.2\,$\mu$m, which is free from molecular band contamination, to estimate the angular diameter of the targets (see Table \ref{angular_diam}). We also estimated fundamental parameters such as the luminosity, Rosseland radius, and temperature (shown in Table \ref{fund_parameters}). Finally, we located each of our targets in the HR diagram using the effective temperature and the luminosity calculated from the Rosseland angular diameter, the bolometric flux, and the distance. In the HR diagram, we also showed the evolutionary tracks from Lagarde et al. (\cite{Lagarde2012}). The positions of the stars in this HR diagram are close to the Hayashi limit. Their positions are close to evolutionary tracks corresponding to stars of initial masses between 1.0\,$M_{\odot}$ and 3\,$M_{\odot}$ ($\epsilon$~Oct, $\psi$~Peg, $\gamma$~Hya, and RS~Cap), between 1.25\,$M_{\odot}$ and 4\,$M_{\odot}$ ($\beta$~Peg), and between 2.5\,$M_{\odot}$ and 6\,$M_{\odot}$ ($\gamma$~Hya). We also compared the position of our stars with the evolutionary tracks from Ekstr\"om et al. (\cite{Ekstrom2012}). The STAREVOL model fits the positions of our stars in the HR diagram better than the Ekstr\"om model. This is probably because the STAREVOL model is designed for low-mass stars on the red giant branch and for intermediate-mass stars on the early-AGB. It is complementary to the Ekstr\"om model for low- and intermediate- mass stars. | 14 | 4 | 1404.7384 |
1404 | 1404.7667_arXiv.txt | {We present the first results of an ALMA spectral survey of strong absorption lines for common interstellar species in the $z$=0.89 molecular absorber toward the lensed blazar \PKS1830. The dataset brings essential information on the structure and composition of the absorbing gas in the foreground galaxy. In particular, we find absorption over large velocity intervals ($\gtrsim$100\,\kms) toward both lensed images of the blazar. This suggests either that the galaxy inclination is intermediate and that we sample velocity gradients or streaming motions in the disk plane, that the molecular gas has a large vertical distribution or extraplanar components, or that the absorber is not a simple spiral galaxy but might be a merger system. The number of detected species is now reaching a total of 42 different species plus 14 different rare isotopologues toward the SW image, and 14 species toward the NE line-of-sight. The abundances of CH, H$_2$O, HCO$^+$, HCN, and NH$_3$ relative to H$_2$ are found to be comparable to those in the Galactic diffuse medium. Of all the lines detected so far toward \PKS1830, the ground-state line of ortho-water has the deepest absorption. We argue that ground-state lines of water have the best potential for detecting diffuse molecular gas in absorption at high redshift. } | The spectroscopic study of absorption lines toward bright background continuum sources is a powerful technique for investigating the composition of the interstellar medium, as illustrated by the detection of the first interstellar molecules along the line-of-sight toward bright nearby stars (\citealt{swi37,mckel40,dou41}). Since the absorption signal is not diluted by distance, the sensitivity is only limited by the brightness of the background continuum source, allowing even rare molecular species to be detected. The discovery of molecular-rich absorption systems in four objects located at intermediate redshifts (0.24$<$$z$$<$0.89, e.g., see a review by \citealt{com08}) has opened up the possibility to explore the chemical contents of galaxies up to look-back times of half the age of the Universe. At intermediate to high redshifts, molecules can serve as interesting cosmological probes. For example, the evolution of the temperature of the cosmic microwave background (CMB) has been investigated up to $z$$\sim$3 using UV-band CO absorption-line systems observed in quasar spectra (\citealt{not11}). More recently, \cite{mul13} have obtained a precise and accurate measurement of the CMB temperature, \Tcmb=5.08$\pm$0.10\,K at $z$=0.89, based on a multi-transition excitation analysis of a set of different molecular species seen in absorption toward the blazar \PKS1830. This value is fully consistent with the value \Tcmb=2.725\,K$\times$(1+$z$)=5.14\,K at $z$=0.89, yielded by adiabatic expansion of the Universe. Molecular absorbers are also widely used to probe the cosmological variations of fundamental constants of nature, such as the fine structure constant, $\alpha$, or the proton-to-electron mass ratio, $\mu$, (see e.g., \citealt{uza11}). Since different molecular transitions have different frequency dependence on the constants, the comparison of their velocity shift provides constraints on the constancy of the constants. The most used species are H$_2$, OH, CH$_3$OH, and NH$_3$. The tightest constraints to date yield null results down to $\Delta\mu$/$\mu$ of a few 10$^{-7}$ over 6--7\,Gyr (\citealt{kan11,bag13b}). Moreover, molecular isotopologues provide a way to probe the nucleosynthesis enrichment of the Universe by comparing the isotopic ratios at different redshifts. Significant differences are found between $z$=0 and $z$=0.89, e.g., for $^{18}$O/$^{17}$O, $^{28}$Si/$^{29}$Si, and $^{32}$S/$^{34}$S (\citealt{mul06,mul11}). At a look-back time of $\sim$7\,Gyr \footnote{corresponding to $z$=0.89}, it is expected that low-mass stars contribute less than nowadays to the ISM pollution by their nucleosynthesis products, and the observed isotopic ratios at $z$=0.89 should mostly reflect the yields of massive stars. Finally, from a ground-based observation point of view, the redshift can help shift lines (e.g., lines falling in bad atmospheric windows) to more favorable bands. This is the case, for example, of the fundamental 557\,GHz transition of ortho-water, which is completely impossible to observe from the ground at $z$=0, but could be detected in absorption at $z$=0.68 and $z$=0.89 by ground-based millimeter radio telescopes (\citealt{com97} and \citealt{men08}, respectively). The most notable of the known redshifted molecular-rich absorbers is the $z$=0.89 galaxy toward the blazar \PKS1830\ (\citealt{wik96,wik98}). It has the highest redshift, the brightest background continuum, and the largest amount of absorbing material of all known molecular absorbers. The galaxy appears as a face-on spiral (\citealt{win02,koo05}) and acts as a gravitational lens, splitting the background blazar ($z$=2.5, \citealt{lid99}) into two main compact cores (NE and SW) separated by $\sim$1$''$ and embedded in a fainter pseudo-Einstein ring seen at cm-wavelengths (\citealt{jau91}). Molecular absorption features are seen along the lines-of-sight toward both compact lensed images (at $v$$\sim$0\,\kms\ and $v$$\sim$$-$147\,\kms, heliocentric frame and with $z$=0.88582, toward the SW and NE images, respectively), intercepting the disk of the $z$=0.89 galaxy on either side of its bulge. At millimeter wavelengths, the angular size of the continuum images corresponds to a scale on the order of one parsec at $z$=0.89, yielding a remarkably sharp pencil beam view through the disk of the absorbing galaxy. The first unbiased radio spectral survey toward \PKS1830\ (at 30--50~GHz, \citealt{mul11}) has extended the molecular inventory up to a total of 34 different species toward the SW line-of-sight, making it the extragalactic object with the largest number of detected molecular species. The molecular abundances are found to be typical of Galactic diffuse-translucent clouds, and the physical conditions of the absorbing gas are well constrained (\citealt{hen08,hen09,mul13}). In contrast, only a handful of molecular species are detected toward the NE image, and the physical conditions of the absorbing gas in this line-of-sight remain poorly known. Interestingly, \cite{mul11} discovered several additional velocity components, at $-$300, $-$224, $-$60, and +170~km\,s$^{-1}$ seen in the lines of HCO$^+$ and HCN. However, the continuum emission of the lensed blazar could not be resolved and the locations of these velocity components could not be determined. The absorption line profiles are known to vary with a timescale of months (\citealt{mul08}), which is most likely due to morphological changes in the continuum emission from the blazar core/jet structures (\citealt{gar97,jin03,nai05}). So far, the variability has only been monitored in the lines of HCO$^+$ (and to a lesser extend of HCN, \citealt{mul08}) and CS (\citealt{sch14}). The time variations have the potential to reveal sub-parsec scale structures in the absorbing gas and the chemical correlation between different molecular species. While the absorber in front of \PKS1830\ offers interesting opportunities as a cosmological probe, it is important to improve our knowledge of this source to understand and address systematics (e.g., \citealt{mul13} about the determination of the cosmic microwave background temperature at $z$=0.89 and \citealt{bag13b} about a constraint of the varation of $\mu$). The high angular resolution and sensitivity now available with the Atacama Large Millimeter/submilliter Array (ALMA) offer new possibilities in investigating the structure of the absorption and the molecular inventory along the two independent lines-of-sight toward \PKS1830. We have targeted the strongest absorption lines of some common interstellar molecules, such as CO, H$_2$O, CH, HCO$^+$, HCN, and NH$_3$, in addition to some other species which have transitions expected to be detectable within the same tuning bands. The main goals of this survey are: \begin{enumerate} \item resolve the structure of the absorption, locate the different velocity components, and obtain high signal-to-noise ratio line profiles; \item investigate the chemistry and the nature of the absorbing gas. Is it similar to the Galactic diffuse component? Is there evidence of different (e.g., diffuse, dense) components? Or of different chemistry among the different velocity components? \item study the time variations of the absorption profiles; \item possibly detect new species in frequency ranges yet unexplored toward this source; \item constrain the cosmological variations of fundamental constants and better understand the underlying systematics; \item measure isotopic ratios from various isotopologues at a look-back time of more than half the present age of the Universe. \end{enumerate} Some of these goals (1 to 4) are addressed in this first paper, while others (5 and 6) will be discussed in forthcoming publications. The structure of the paper is as follows: in section \S\,\ref{sec:data}, we present the ALMA Cycle~0 observations and data reduction. In section \S\,\ref{sec:census}, we update the inventory of chemical species detected toward \PKS1830. The absorption profiles along the two lines-of-sight are analyzed in section \S\,\ref{sec:absprofiles}. Possible interpretations of the wide velocity spread seen along both lines-of-sight are reviewed in \S\,\ref{sec:thickmoldisk}. We investigate water as a tracer of molecular gas in absorption at high redshift in section \S\,\ref{sec:water}. A summary is given in section \S\,\ref{sec:conclusions}. The complete ALMA spectral scans are shown in Appendix\,\ref{appendix:spec}. | \label{sec:conclusions} We present the first results from an ALMA Early Science Cycle~0 spectral survey of the $z$=0.89 molecular absorber located in front of the blazar \PKS1830. Four spectral tunings at frequencies near 100, 250, 290, and 300\,GHz, were selected to cover strong absorption lines from common interstellar species, namely CO, H$_2$O, HCO$^+$, HCN, C\,I, and NH$_3$. The first results of this survey can be summarized as follows: \begin{enumerate} \item We enlarge the chemical inventory in this molecular-rich absorber with the detection of new species toward both lines-of-sight. In particular, the redshift of the absorber allows us to detect submillimeter lines observed recently with Herschel and inacessible or difficult to observe from the ground in the local $z$=0 ISM, such as those from CH, H$_2$O and H$_2$Cl$^+$. The inventory of species now reaches a total of 42 different species in the main absorption toward the SW image (plus 14 different rare isotopologues), and 14 species toward the NE image. \item The observation of strong lines provide us with high signal-to-noise ratio spectra, with the two continuum images of \PKS1830\ spatially resolved. This allows us to reveal the absorption profiles along the two lines-of-sight with unprecedented detail. Toward the NE image, the absorption profile is resolved into a collection of narrow velocity components (5--10\,\kms\ wide) covering a wide velocity range of more than 100\,\kms. Toward the SW image, the main broad absorption also covers a velocity interval of more than 100\,\kms. In addition, the weak velocity component at +170\,\kms, previously detected but with unknown location, is now identified toward the SW image, i.e., presenting a remarkable large velocity offset of +170\,\kms\ with respect to the main ($v$=0\,\kms) absorption feature. \item The large velocity interval seen along both lines-of-sight suggests either that the galaxy has an intermediate inclination and that we sample velocity gradients or streaming motions in the disk plane, that the gas in the foreground galaxy has a large vertical distribution (e.g., a thick molecular disk) or extraplanar components (e.g., high velocity clouds), or that the absorber has a more complex geometry than a simple rotating disk (e.g., it is a merger system). \item We measure the continuum source covering factor toward the SW image from saturated lines, and find that it varies little with frequency, from $\sim$90\% at 100\,GHz for the HCO$^+$/HCN 2-1 line to 95\% at 300\,GHz for the H$_2$O 1$_{10}$-1$_{01}$ line. Either the covering factor is different for the different species (i.e., they are not co-spatial), or the size of the continuum emission is roughly the same between 100 and 300\,GHz. \item The ALMA observations were taken (serendipitously) at the time of a strong $\gamma$-ray flare of the background blazar. A study of the temporal and chromatic variations of the flux ratio between the lensed images of the blazar during the flare is reported by \cite{mar13}. Over the time span of the observations ($\sim$two months), we find only minor variations in the spectral line profiles, mostly in the wings of saturated lines. \item Of all the lines detected so far toward \PKS1830, the H$_2$O 1$_{10}$-1$_{01}$ line (557\,GHz rest frame) has the deepest absorption. We argue that ground-state water lines are excellent probes of molecular absorption at high-redshift. \end{enumerate} An accompanying paper (\citealt{mul14}) focusses on the first extragalactic detection of the chloronium ion, H$_2$Cl$^+$, toward \PKS1830, and includes a measurement of the $^{35}$Cl/$^{37}$Cl isotopic ratio at $z$=0.89. Forthcoming publications will deal with constraints of the variations of fundamental constants, chemistry, and isotopic ratios in the $z$=0.89 absorber toward \PKS1830, based on these ALMA Cycle~0 data. \begin{acknowledgement} This paper makes use of the following ALMA data: ADS/JAO.ALMA\#2011.0.00405.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada) and NSC and ASIAA (Taiwan), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. The financial support to Dinh-V-Trung from Vietnam’s National Foundation for Science and Technology (NAFOSTED) under contract 103.08-2010.26 is gratefully acknowledged. \end{acknowledgement} | 14 | 4 | 1404.7667 |
1404 | 1404.5986_arXiv.txt | The precipitation of energetic neutral atoms, produced through charge exchange collisions between solar wind ions and thermal atmospheric gases, is investigated for the Martian atmosphere. Connections between parameters of precipitating fast ions and resulting escape fluxes, altitude-dependent energy distributions of fast atoms and their coefficients of reflection from the Mars atmosphere, are established using accurate cross sections in Monte Carlo simulations. Distributions of secondary hot atoms and molecules, induced by precipitating particles, have been obtained and applied for computations of the non-thermal escape fluxes. A new collisional database on accurate energy-angular dependent cross sections, required for description of the energy-momentum transfer in collisions of precipitating particles and production of non-thermal atmospheric atoms and molecules, is reported with analytic fitting equations. 3D Monte Carlo simulations with accurate energy-angular dependent cross sections have been carried out to track large ensembles of energetic atoms in a time-dependent manner as they propagate into the Martian atmosphere and transfer their energy to the ambient atoms and molecules. Results of the Monte Carlo simulations on the energy-deposition altitude profiles, reflection coefficients, and time-dependent atmospheric heating, obtained for the isotropic hard sphere and anisotropic quantum cross sections, are compared. Atmospheric heating rates, thermalization depths, altitude profiles of production rates, energy distributions of secondary hot atoms and molecules, and induced escape fluxes have been determined. | The evolution of planetary atmospheres is governed, in the simplest of terms, by energy input, transfer, and output. In planetary bodies without intrinsic magnetic fields, large amounts of energy may be supplied by {\color{black} solar wind} ions into the atmosphere. Precipitating ions can capture electrons in collisions with atmospheric gas and very quickly become {\color{black}energetic neutral atoms (}ENAs{\color{black})} which penetrate deeply into the atmosphere before transferring their energy to the thermal gases present. It was estimated that ENA precipitation delivers 10$^9$ eV cm$^{-2}$ s$^{-1}$ to the atmosphere of Mars and is comparable to the energy input from EUV photons at solar minimum \citep[]{Kallio:1997}. Loss of neutral planetary atmospheres occurs through both thermal (Jeans) escape and non-thermal energy transfer processes, leading to atomic and molecular escape. Significant numbers of atmospheric non-thermal processes are induced by precipitating {\color{black} solar wind} ions. While thermal escape on Mars is efficient only for atomic and molecular hydrogen, the non-thermal energy transfer and escape may be the dominant source for evolution of heavier atmospheric constituents \citep[]{Hunten:1982,Johnson:2008}. The atmosphere of Mars has been the focus of investigations of planetary atmospheres for a long time, in particular analysis of its current and past compositions which sheds light on the loss of liquid water which is thought to have once existed on the surface of the planet \citep[]{Owen:1977,Krasnopolsky:2002,Shematovich:2007,Lammer:2013}. Previously calculated thermal and non-thermal escape rates of hydrogen, as well as sputtering and ion pickup, have led to estimates of an entire ocean of water with global mean depth of 30 m being lost on Mars in the past 3.8 billion years \citep[]{Krasnopolsky:2002}. Kinetics and energy relaxation involved in collisions between fast and thermal atoms are fundamentally important for the escape process and thus also on atmospheric evolution \citep[]{Kharchenko:1997,Bovino:2011,Fox:2014}. Previous works have looked at effects of {\color{black}solar wind} protons precipitating into the atmosphere of Mars using both isotropic {\color{black} hard sphere} and angular dependent forward peaked cross sections \citep[]{Kallio:2001}, as well as with accurate quantum mechanical cross sections \citep[]{Shematovich:2004,Krestyanikova:2005,Johnson:2008,Fox:2014}, but accurate energy-angular dependent cross sections have never been fully used to study non-thermal, atom-atom and atom-molecule, energy transfer and induced escape fluxes in a planetary atmosphere. Precipitating ENAs are created through {\color{black}charge exchange} collisions between {\color{black}solar wind} ions and atmospheric gases in the Martian atmosphere and in this work we consider these ENAs as a source for non-thermal atomic and molecular escape and compare the ENA induced escape to previously reported escape fluxes. The precipitation of ENAs into planetary atmospheres can be an efficient source of atmospheric heating as well as a production mechanism for {\color{black}secondary hot} atoms and molecules. {\color{black}Secondary hot} atoms and molecules created by ENAs essentially have non-thermal distributions and contribute significantly to total planetary escape fluxes. Nascent ENAs created through {\color{black}charge exchange} collisions between {\color{black}solar wind} ions and atmospheric gases maintain the vast majority of the {\color{black}solar wind} ions velocity and thus have significantly large energies, ranging from hundreds of eV/amu to several keV/amu \citep[]{Reeves:2013}. As the nascent ENAs precipitate through the planetary atmosphere, their energy is transferred, via elastic and inelastic collisions, to the atmospheric gases with major constituents being H, He, O, Ar, H$_{2}$, N$_{2}$, CO, and CO$_{2}$ \citep[]{Krasnopolsky:2002}. Extremely forward peaked differential cross sections \citep[]{Lewkow:2012} for keV collisions result in relatively small energy transfer per collision. This leads to several thousand collisions and deep penetration into the planetary atmosphere before thermalizing. Modeling of energy deposition altitude profiles requires realistic descriptions of energy transfer and thus accurate differential and total cross sections for binary collisions. Anisotropic {\color{black}quantum mechanical} differential cross sections, unlike isotropic {\color{black}hard sphere} approximations, are extremely forward peaked for center of mass collision energies above 1 eV. We have calculated with high accuracy a majority of atom-atom collision cross sections. At the same time, ab initio calculations of atom-molecule cross sections at keV energies, such as atomic collisions with CO$_{2}$ molecules, are not realistic and semi-empirical methods should be applied. Unknown cross sections of atom-molecule collisions between ENAs and some species of the Mars atmosphere were treated using an angular-energy dependent scaling method to provide reasonable forward peaked differential cross sections as well as integrated total cross sections. These scaling cross sections are useful in the atmosphere of Mars where CO, CO$_{2}$, H$_{2}$, and N$_{2}$ are large constituents and accurate {\color{black}quantum mechanical}, ab initio computations at keV/amu collision energies look as very formidable problems. All collisions between ENAs and these atmospheric molecules utilize the scaling cross sections, while all known atom-atom collisions (H+H, He+H, He+He, He+O) use computed ab initio quantum mechanical cross sections in this work. Computed cross sections as well as results of quantum scaling have been verified with available experimental data \citep[]{Gao:1989,Newman:1986,Nitz:1987,Smith:1996,Schafer:1987}. Through use of {\color{black}quantum mechanical} and scaling cross sections, accurate time-dependent calculation of ENA transport, momentum transfer energy loss, {\color{black}secondary hot} atomic and molecular production and escape was carried out using three-dimensional {\color{black}Monte Carlo} simulations with large ensembles of test particles. Direct connections between the mechanisms of energy deposition and the intensities of induced escape fluxes for neutral atoms and molecules has been established using realistic cross sections, simulating {\color{black}quantum mechanical} binary collisions, combined with classical {\color{black}Monte Carlo} transport. Energy distributions for both thermalizing and escaping ENAs were found for ensembles of mono-energetic precipitating ENAs as well as realistic ENA energy distributions which reflect the actual energy distributions in {\color{black}solar wind} ions \citep[]{Reeves:2013}. Energy-deposition and escape flux comparisons between realistic anisotropic cross sections and isotropic {\color{black}hard sphere} models were made to further analyze differences in thermalization parameters between the two cross section models. Details on determination of both differential and total cross sections used in this study are given in section 2. Section 3 discusses production rates of ENAs in the upper atmosphere of Mars for the different atmosphere compositions appropriated to low, high, and mean solar activity while section 4 examines all details of the {\color{black}Monte Carlo} simulation developed for this work. Results obtained by the simulations and the implications for atmospheric evolution are covered in sections 5. Concluding remarks follow. | Precipitation of ENAs, produced in the interaction between SW ions and atmospheric gas, has been investigated for the Mars atmosphere at different solar conditions. For an accurate description of the energy relaxation process, the parameters for accurate descriptions of energy-momentum transfer in atomic and molecular collisions have been developed using both {\color{black}QM} methods and empirical models. Properties of {\color{black}ENAs}, originating in the interaction between the SW ions and atmospheric gas, were calculated for the upper atmosphere of Mars using neutral atmosphere models for minimum, mean, and maximum solar activity. {\color{black}MC} simulations were constructed to transport nascent {\color{black}ENAs} through the Martian atmosphere to determine properties of energy transfer, thermalization, production of {\color{black}SH} atoms and molecules, and reflection characteristics. Time-dependent energy distributions were obtained in addition to thermalization altitudes and atmospheric heating profiles. Production rates and energy distributions for {\color{black}SH} atoms and molecules were extracted and utilized to determine induced atomic and molecular escape fluxes form Mars. The information obtained from our {\color{black}MC} simulations demonstrates the need for accurate, energy-angular dependent cross sections in modeling the energy relaxation, sputtering and escape processes in planetary atmospheres as results obtained varied significantly between ensembles utilizing accurate cross sections and those which utilized isotropic, {\color{black}HS} cross sections. | 14 | 4 | 1404.5986 |
1404 | 1404.5724_arXiv.txt | Because of {their} brightness, gamma-ray burst (GRB) afterglows are viable targets {for investigating} the dust content in their host galaxies. Simple intrinsic spectral shapes of GRB afterglows allow us to derive the dust extinction. Recently, the extinction data of GRB afterglows are compiled up to redshift $z=6.3$, in combination with hydrogen column densities and metallicities. This data set enables us to investigate the relation between dust-to-gas ratio and metallicity {out} to high redshift {for} a wide metallicity range. By applying our evolution models of dust content in galaxies, we find that the dust-to-gas ratio derived from GRB afterglow extinction data are excessively high such that they can be explained with a fraction of gas-phase metals condensed into dust ($f_\mathrm{in}$) $\sim 1$, while theoretical calculations on dust formation in the wind of asymptotic giant branch stars and in the ejecta of Type II supernovae suggest a much more moderate condensation efficiency ($f_\mathrm{in}\sim 0.1$). Efficient dust growth in dense clouds has difficulty in explaining the excessive dust-to-gas ratio at metallicities $Z/\mathrm{Z}_{\sun}<\epsilon$, where $\epsilon$ is the star formation efficiency of the dense clouds. However, if $\epsilon$ is as small as 0.01, the dust-to-gas ratio at $Z\sim 10^{-2}$ Z$_{\sun}$ can be explained with $n_\mathrm{H}\ga 10^6$ cm$^{-3}$. Therefore, a dense environment hosting dust growth is required to explain the large fraction of metals condensed into dust, but such clouds should have low star formation efficiencies to avoid rapid metal enrichment by stars. | \label{intro} One of the important problems in astrophysics is the origin and evolution of dust in the Universe, since various aspects of galaxy evolution are significantly influenced by the optical and material properties and the total abundance of dust. For example, dust governs the absorption, scattering, and reemission of the stellar light, affecting the radiative transfer in the interstellar medium (ISM) \citep[e.g.][]{yajima12}. Furthermore, the surface of dust grains is the main site for the formation of some molecular species, especially H$_2$, which could affect the star formation properties of galaxies \citep{hirashita02,yamasawa11}. Therefore, clarifying the origin and evolution of dust content is essential for revealing how galaxies have evolved in the Universe. It is widely believed that the scenario of the evolution of dust content in galaxies comprises dust formation in stellar ejecta, dust destruction in supernovae (SN) remnants, and grain growth by the accretion of metals onto preexisting grains in molecular clouds \citep[e.g.][]{dwek98,hirashita99,inoue03,zhukovska08,valiante11,mattsson12}. These processes depend on the age and metallicity of galaxies. In particular, the dominant mechanism of dust enrichment is suggested to switch from the supply by the stellar ejecta to the accretion of metals at a certain metallicity level \citep{inoue11,asano13}. For the purpose of acquiring the general trend of the evolution of dust content in galaxies at different ages and metallicities, the approaches using extinctions of bright sources of which the intrinsic spectra are well known, for example quasars (QSOs) and GRB afterglows, are regarded as viable methods, since they are bright enough to be detected even at high redshift. Quasars are usually used to probe the foreground galaxies in absorption, while GRB afterglows are often utilized to probe the ISM of their own host galaxies. Recently, \citet{zafar13} compiled and analyzed GRB afterglow data in a wide redshift range of $z=0.1-6.3$. By using the $A_V/N_\mathrm{H}$ [$A_V$ is the extinction at the $V$ band {(0.55 $\micron$)}, and $N_\mathrm{H}$ is the H \textsc{i} column density] ratio as an indicator of dust-to-gas ratio, they show that the relation between dust-to-gas ratio and metallicity is on a natural extension of the local galaxy sample, even at low metallicities down to $Z\sim 10^{-2}$ Z$_{\sun}$ ($Z$ is the metallicity and Z$_{\sun}$ is the solar metallicity). This indicates that the fraction of metals condensed into dust is as high as the local galaxy sample even at such a low metallicity. They did not find any systematic difference between the GRB sample and a QSO absorption sample used as a comparison sample, rejecting the systematics of the GRB sample relative to other samples. Therefore, they argue that there is a close correspondence between dust formation and metal formation; in other words, any delay between the formation of metals and dust must be shorter than typically a few Myr [i.e.\ the time-scale of metal enrichment by supernovae (SNe)]. They finally propose two possibilities of dominant dust formation mechanisms consistent with the close association between metals and dust: (i) rapid dust enrichment by condensation in the ejecta of SNe; and (ii) rapid grain growth by the accretion of gas-phase metals onto dust grains in the ISM. In this study, we utilize the GRB afterglow extinction data to investigate the evolution of dust content in their host galaxies. In particular, we judge if the above two possibilities (i) and (ii) are theoretically supported or not, by applying a dust enrichment model developed in our previous studies. Through this work, we will be able to obtain or constrain some essential parameters for dust enrichment, especially, the efficiencies of dust condensation and growth. This paper is organized as follows. In Section \ref{sec:data}, we present the observational data adopted. In Section \ref{sec:model}, we overview our theoretical models used to interpret the data. In Sections \ref{sec:result} and \ref{sec:discussion}, we provide results and discussions, respectively. The conclusions are given in Section \ref{sec:conclusion}. In this paper, we adopt $\mathrm{Z}_{\sun}=0.02$ for the solar metallicity. | \label{sec:conclusion} The dust-to-gas ratios derived from GRB afterglow extinction data are excessively high such that they can be explained with an extremely efficient condensation of metals into dust in stellar ejecta, while theoretical calculations on dust formation in the wind of AGB stars and in the ejecta of SNe suggest much more moderate condensation efficiencies. We alternatively adopt a moderate condensation efficiency and a more efficient grain growth in dense clouds. Even with efficient grain growth, the excessive dust-to-gas ratio can only be explained if we assume a low star formation efficiency, which is equivalent with slow metal enrichment. Therefore, some GRB host galaxies in which most of the dust-composing metals are condensed into dust can be explained with enhanced grain growth in dense clouds, whose time-scale should be shorter than the metal enrichment time-scale (or equivalently the star formation efficiency in dense clouds is as small as $\la 0.01$). | 14 | 4 | 1404.5724 |
1404 | 1404.4933_arXiv.txt | Galaxy mergers play a key role in the evolution of galaxies and the growth of their central supermassive black holes (SMBHs). A search for (active) SMBH binaries (SMBHBs) at the centers of the merger remnants is currently ongoing. Perhaps the greatest challenge is to identify the {\bf \it inactive} SMBHBs, which might be the most abundant, but are also the most difficult to identify. Liu et al. predicted characteristic drops in the light curves of tidal disruption events (TDEs), caused by the presence of a secondary SMBH. Here, we apply that model to the light curve of the optically inactive galaxy SDSS J120136.02+300305.5, which was identified as a candidate TDE with {\it XMM-Newton}. We show that the deep dips in its evolving X-ray light curve can be well explained by the presence of a SMBHB at its core. A SMBHB model with a mass of the primary of $M_{\rm BH} = 10^7 M_\sun$, a mass ratio $q \simeq 0.08$, and a semimajor axis $a_{\rm b} \simeq 0.6\, {\rm mpc}$ is in good agreement with the observations. Given that primary mass, introducing an orbital eccentricity is needed, with $e_{\rm b} \simeq 0.3$. Alternatively, a lower mass primary of $M_{\rm BH} = 10^6 M_\sun$ in a circular orbit fits the light curve well. Tight binaries like this one, which have already overcome the ``final parsec problem,'' are prime sources of gravitational wave radiation once the two SMBHs coalesce. Future transient surveys, which will detect TDEs in large numbers, will place tight constraints on the SMBHB fraction in otherwise non-active galaxies. | \label{introduction} During the hierarchical formation of galaxies, merging galaxies quickly bring two supermassive black holes (SMBHs) into their center, forming a hard SMBH binary (SMBHB) at parsec scale \citep{beg80,qui96,vol03,may07,tan09,kul12,kul13}. Further evolution of hard SMBHBs depends very much on the detailed nuclear structures. A hard SMBHB may stall at the parsec scale for a timescale longer than the Hubble time in the spherical and isotropic galactic nuclei \citep{beg80}, but can be driven to the strong gravitational wave (GW) regime at milliparsec scale by efficient stellar dynamical processes in non-spherical, anisotropic, and/or rotating nuclear clusters \citep{mer04,ber06,pre07,pre11}, or by hydrodynamic processes in massive gas disks \citep[][and references therein]{gou00,koc12,col11}. If the orbits of SMBHBs could be highly eccentric \citep{arm05,ber06,pre11,iwa11,ses11,che11}, the strong GW regime may extend far out and the SMBHBs can quickly evolve to the GW regime. The SMBHBs in the strong GW regime coalesce within a Hubble time. They are the primary targets for the proposed {\it Laser Interferometer Space Antenna} ({\it eLISA}) and ongoing Pulsar Timing Arrays (PTAs). A few observations of SMBHBs in gaseous systems have been reported, ranging from spatially resolved binary active galactic nuclei \citep[AGNs; e.g.,][]{kom03,rod06,gre10,liu10,fab11}, to candidate un-resolved binary systems. The observational evidence for the latter is based on double-peaked broad emission lines in quasars and their variability \citep[e.g.,][]{tsa11,ju13,she13}; characteristic spatial structures in radio jets \citep[e.g.,][]{beg80,con95,liu07,rol08,bri12}; quasi-periodic outbursts in some blazars \citep[e.g.,][and references therein]{sil88,liu95,liu97,liu06,liu02,qia07,val11}; and swift jet reorientation in X-shaped radio galaxies \citep{liu04}. Further, some candidate systems of coalesced SMBHBs have been identified, based on double-double radio galaxies that show an interruption and recurrence of jet formation \citep{liu03}, or based on evidence for recoiled SMBHs \citep[e.g.,][]{kom08,liu12a,civ12}. All the observational evidence for SMBHBs in AGNs is consistent with the scenario of rapid migration of SMBHBs within massive gas disks. However, most SMBHBs may form quiescently either in gas-poor or minor galaxy mergers without driving AGN activities. The high frequency of minor and gas-poor galaxy mergers is important in the formation and evolution of both late type and massive elliptical galaxies \citep[e.g.,][]{dok10,naa09,mcw12}, therefore it is essential to understand the evolution of SMBHBs in quiescent galaxies, not only for the GW detections with {\it LISA} and PTA, but also to test the galaxy formation and evolution models. It is a challenge to detect dormant SMBHBs and observationally constrain their evolution in galactic nuclei. A dormant SMBH can be investigated observationally when it tidally disrupts stars passing by and becomes a transient AGN \citep{hil75,lum85,ree88,phi89,lod09}. More than 20 candidates for stellar tidal disruptions (TDEs) by SMBHs have been reported in wavebands from $\gamma$-ray and X-ray through UV and optical to radio frequencies (\citep[e.g.,][]{kom99,kom02,kom08b,gez08,gez12,zau11,blo11,bur11,sax12}; \citep[see][for a review]{kom12}). Recently, it was suggested that dormant SMBHBs in non-active galaxies could also be investigated when one of the SMBHs tidally disrupted a star, because SMBHBs can give some key imprints on the event rates, locations, and the environment in the galactic nuclei, light curves, and spectra of tidal flares \citep{iva05,kom08c,che08,che09,che11,liu09,weg11,sto11,sto12a,li12,che13,liu12}. SMBHBs can dramatically change the tidal disruption rates of stars in galactic nuclei. Our investigations showed that stellar tidal disruption rates by ultra-compact SMBHBs, particularly in the GW dominated regime, are at least one order of magnitude lower \citep{che08}, while those by bound (but not-hard) SMBHBs \citep{che09,che11} or dual SMBHs in merging galaxies \citep{liu12} can be up to three orders of magnitudes higher than the estimated tidal disruption rates by single SMBHs in isolated galaxies \citep{wan04}. However, despite the significant difference in the tidal disruption rates, the separate contributions of stellar tidal disruptions by single, bound and hard binaries, and dual SMBHs to the total stellar disruption events during cosmic time are comparable to one another \citep{liu12}, implying that some of the observed tidal disruption flares are probably from SMBHB systems. Numerical and analytic computations indicated that the stellar tidal disruption flares in SMBHB systems would show temporary interruptions and recurrences. The interruptions are due to the perturbation of the companion SMBH on the plasma streams of the tidally disrupted star \citep[][LLC09 hereafter]{liu09}. This is one of the key signatures for SMBHBs in galactic nuclei. In this paper, we report the first candidate for a SMBHB in a quiescent galaxy. The galaxy SDSS J120136.02+300305.5 (SDSS J1201+30 hereafter) at redshift $z=0.146$ was observed to be at outburst in X-rays with {\it XMM-Newton}, during the slew-survey observation on 2010 June 10, most probably due to the tidal disruption of a star by a SMBH at its center \citep[][S2012 hereafter]{sax12}. Follow-up observations in X-rays with the {\it Swift} and {\it XMM-Newton} space telescopes made by S2012 showed that the X-ray flux of the flare is, on average, consistent with a $t^{-5/3}$ power law, as predicted by the canonical fallback model for tidal disruption \citep{ree88,eva89}. Superposed on this overall decline are rapid, strong dips in the X-ray flux. No absorption and no radio jet was detected in the observations. In particular, the light curve showed that SDSS J1201+30 decayed in the X-ray flux by more than about 50 times within seven days and became completely invisible to {\it Swift} between 27 and 48 days after discovery. Then, it recurred to follow the original power-law decay from 2010 October 24 to December 23. Here, we will show that all the striking features in the light curve of the event are challenging to understand by the TDE model in the presence of a single SMBH, but are fully consistent with the key predictions of the model for stellar tidal disruption in a SMBHB system, given by LLC09. Applying the binary black hole model for tidal disruption to SDSS J1201+30 and using the observations, we constrain well the parameters of the SMBHB system despite the gaps in the light curve coverage. This paper is organized as follows. In Section~\ref{obs}, we introduce the fallback model for tidal disruptions of stars by SMBHs and give some general constraints on the model parameters for SDSS J1201+30, based on the observations given by S2012. In Section~\ref{bin}, we briefly describe the model for stellar tidal disruption in a SMBHB system (Section~\ref{intr:an}) and present the numerical results of employing the binary black hole model to SDSS J1201+30 in Section~\ref{mod}. We show that the observed light curve in X-rays can be well reproduced by a simple SMBHB model. In particular, the question of whether SMBHB orbits show eccentricity is important, both for the evolution of SMBHBs in galactic nuclei and the detection of GW radiation. We explore the effect of the orbital eccentricity of SMBHBs on the light curves, and show that the orbit of the SMBHB in SDSS J1201+30 must be elliptical, if the central black hole has a mass $\sim 10^7 M_\sun$ in Section~\ref{ecc}. After critically investigating the alternatives in Section~\ref{sec:alt}, we provide our discussion of the orbital parameters of the SMBHB system in SDSS J1201+30 in Section~\ref{sec:para}, the GW emission of the SMBHB system in Section~\ref{sec:gw}, and the frequency of SMBHBs among known TDEs in Section~\ref{sec:freq}. Throughout the paper, we assume a $\Lambda$CDM cosmology with parameters $H_0 = 70 \, {\rm km\; s^{-1}\; Mpc^{-1}}$, $\Omega_\Lambda = 0.73$, and $\Omega_M = 0.27$. | \label{dis} \subsection{SMBHB model and alternatives} \label{sec:alt} Several candidate small-separation SMBHBs have emerged in recent years. They are not spatially resolved, but the SMBHBs' presence has been indirectly inferred from semi-periodicities in light curves or structures in radio jets (see Section~\ref{introduction} for the observational evidence for SMBHBs; see also \citet{kom06} for a complete review). We have shown that the presence of a SMBHB can naturally explain the characteristics of the light curve of the TDE in SDSS J1201+30, based on models of LLC09. In fact, other possible explanations that might at first glance come to mind, do not well reproduce the features of the light curve, or the overall multi-wavelength properties of SDSSJ1201+30. We comment on each of them in turn. \subsubsection{Jetted TDEs, and a comparison with SwiftJ1644+57} Rapid, short-timescale variability has been detected in the light curve of the TDE candidates Swift J1644+57 \citep[e.g.,][]{bur11,blo11} and Swift J2058+0516 \citep{cen12}. However, unlike SDSS J1201+30, which has no detectable radio emission, both Swift J1644+57 and Swift J2058+0516 are accompanied by strong radio emission, and their isotropic X-ray luminosity, up to a few times $10^{47-48} {\rm erg\; s^{-1}}$, is well above the Eddington limit. Therefore, beaming has been suggested to explain these events \citep[e.g.,][]{bur11,blo11,lev11,zau11}. In particular, it has been suggested that the rapid dips of the X-ray light curve of Swift J1644+57 are linked to the presence of a jet, and are due to jet precession/nutation \citep[e.g.,][]{sax12b}, or wobbling \citep{tch13}. Since no radio jet was detected in SDSS J1201+30, it is highly unlikely that similar scenarios are at work in this source. \subsubsection{Temporary absorption due to blobs in the accretion disk, or stellar streams, or an expanding disk wind} If an optically thick blob in the accretion disk extends vertically above a slim disk and crosses the line-of-sight (l.o.s; the disk is always optically thick in the radial direction for the slim or standard thin disk in which we are interested), the absorption by the blob may lead to a sharp drop in the flux. Because the largest Keplerian period at $r_{\rm d}$ is about 7.8 hr and independent of the black hole mass, the blob should be extended to be an annulus in the phi-direction, if the entire duration of the interruption period of at least a few days is due to the eclipse. Such an annulus should be also extended in the radial direction to the entire disk, in order for the eclipse time to last about 21 days, at least 10--100 times the disk viscous timescale (cf. Equation~(\ref{eq:tvisc})). Therefore, in this scenario, the disk must be a spherical accretion flow instead of a slim accretion disk. This is very unlikely because of the conservation of angular momentum. A blob with radius $r_{\rm b} \geq r_{\rm d}$ in the stellar streams may completely shield the accretion disk if it crosses the l.o.s. by chance with a probability $P\sim 6 \times 10^{-4} \beta^{-3/2} M_6^{-1/2} m_*^{1/2}$. If the blob is a fraction $\lambda$ of the star and not bound by self-gravity, it expands following the ejection of unbound plasma from the system with volume $V(t) \approx 4\pi r_b^3 /3 \approx \lambda^3 R_*^3 \zeta^3$, where $\zeta = (t-t_{\rm D})/ t_{\rm e}$ is the expansion parameter and $t_{\rm e} \approx 1120 \, {\rm s}\, \beta^{-4/3} m_*^{-1/2} r_*^{3/2}$ \citep{kas10}. At the last detection of 2010 June 30, $\Delta t = t- t_{\rm D} \simeq 27.7 \, {\rm days}$ in the object rest frame suggests an expansion parameter $\zeta \approx 2137$, or a blob with expanded size $r_{\rm b} \approx 6.6 \beta \lambda M_6^{-1/3} m_*^{1/3} r_{\rm d}$. For a blob with $\lambda \sim 1$, the blob is large enough to fully shield the tidal accretion disk and also still optically thick because of Thomson scattering in ionized hydrogen for an expansion parameter $\zeta \simeq 2000$ \citep{kas10}, although the probability of totally shielding the accretion disk is only $P\sim 8\times 10^{-5} \lambda^2 \beta M_6^{-1/2} m_*^{1/2}$. However, the timescale for the blob to cross and totally shield the accretion disk is $\Delta t_{\rm ec} \sim 11\, {\rm days} \beta^{1/2} M_6^{-1/6} m_*^{1/6} \left({\Delta t \over 27.7 \, {\rm days}}\right)$ in the object rest frame or 13~days in the observer frame, which is about twice the observed upper limit to the timescale of absence, $\leq 7\, {\rm days}$. Recent numerical simulations suggested that for $\beta <3$ the unbound stellar debris from the TDE remains self-gravitating and recollapses into thin streams \citep{gui13}. Therefore, the expansion parameter $\zeta$ is $ < 1$ and any blob in the stream is unable to fully shield the tidal accretion disk to form the extremely large dip in the light curve. If an optically thick inhomogeneous clumpy structure in an expanding, optically thin accretion-disk wind could form due to some unknown reason after the accretion has passed the peak accretion rate for some time, it may completely absorb the disk emission and form the dips. However, to fully cover the accretion disk, the clumpy structure must extend to as large as the accretion disk or the clumpy structure in the disk wind is global. Because the clump is optically thick and would radiate at the order of the Eddington luminosity with a temperature about $10^5$~K before it becomes optically thin \citep{str09}, it would emit a peak radiation at the UV and soft-X-ray bands and should have been detected with {\it XMM}. \subsubsection{Transient eclipses due to stars or an optically-thick dense molecular cloud infalling toward the central SMBHs} A giant star or a dense optically thick gas cloud infalling toward the central SMBHs with extent along the orbital plane $\Delta R \geq (21/7) 2 r_{\rm d} \approx 6 r_{\rm d}$ may transit and completely shield the accretion disk to form a full eclipse within seven days of 21 day duration, as was suggested for some AGNs \citep[e.g.,][]{mck98,gil12,bek13}. For a giant star with radius $R_* \simeq 100 R_\sun$, it requires a SMBH mass $M_{\rm BH} \leq 4.6\times 10^3 M_\sun (\beta/2)^3 r_*^{-3} m_*$ in order for the giant star to completely shield the accretion disk. For a falling dense gas cloud to cross the tidal accretion disk and form a total eclipse within $7/(1+z)$~days, the dense gas cloud should be at a distance from the central SMBH $r_{\rm gas} \la 1.6 \times 10^5 r_{\rm g} \beta^2 ({\Delta t \over 6\, {\rm days}})^2 M_6^{-2/3} r_*^{-2} m_*^{2/3}$ and have an extension along the orbital plane $\Delta R_\| > 6 r_{\rm d}$ and vertical to the orbital plane $\Delta R_\bot > 2 r_{\rm d}$. The dense gas cloud would subtend a solid angle toward the SMBH $\Delta \Omega \ga \Delta R_\| \Delta R_\bot / r_{\rm gas}^2 \approx 1.1 \times 10^{-6} \beta^{-6} r_*^6 m_*^{-2} ({\Delta t \over 6\, {\rm days}})^{-4}$, implying a probability $P \ga 9\times 10^{-8}$ for such a dense gas cloud to cross the l.o.s. by chance. The probability can increase significantly if the dense cloud has much larger size or the galactic nucleus is full of small dense clouds similar to those in the broad-line regions of AGNs. In both cases, the gas clouds should be ionized by the tidal flare and emit strong broad emission lines. However, these have not been detected in the optical spectra taken at 12 days and 11 months after the discovery of the TDE (S2012). \subsubsection{Blobby accretion near last stable orbit or other AGN-like variability} In rare cases, AGN light curves do show occasional rapid drops or flares by factors of a few or more. Therefore, whatever causes short-time variability in AGN accretion disks could potentially also be at work in any TDE source, like in SDSS J1201+30. However, it is clear that accretion disks in AGNs and tidal disruption events are significantly different: the accretion disk in AGNs can extend outward to several thousands of Schwarzschild radii or more, but the size of the accretion disk in TDEs can only be as large as a few dozens of Schwarzschild radii (i.e., hundreds of times smaller). Therefore, the characteristic timescales of the sources driving the variations in AGNs \citep{kel09,kel11,tan10} range from a few hours up to a few hundreds of years for AGNs, but are always less than the viscous timescale $2.8\, {\rm hr}\, \alpha_{-1}^{-1} (\beta/2)^{-3/2}$ in TDEs \citep[e.g.,][]{dec12}. The observational timescale of order of days for \sdss is much larger than the characteristic timescales of the driving sources in TDEs, which suggests stochastic variations driven by blobs or white noises superimposing on the mean luminosity as in AGNs \citep{kel09,kel11,tan10}, or in the tidal disruption event {\it Swift 1644+57} \citep{dec12}. If the fractional amplitude of the driving noises is consistent with the observations of SDSS J1201+30 from 2010 June 10 to June 28 and between 2010 October 24 and December 23, the probability that one can detect the consecutive three observations at the extreme quiescent state of the flare from 2010 July 7 to July 21 is $P\sim p_q^3 \la 10^{-15}$, where $p_q < 10^{-5}$ is the probability to observe a variability with larger than $5 \sigma$ standard errors. If such large random variability with a timescale less than a few thousand seconds did exist in the light curve of SDSS J1201+30, it must have already been detected in the {\it XMM-Newton} pointed observations with the exposure time ranging from 10 ks to 30 ks on 2010 June 22, November 23, and December 23, which, however, was not (S2012). \subsubsection{Lense-Thirring precession of an accretion disk misaligned with a spinning SMBH} If the central SMBH is spinning and the accretion disk is misaligned with the spin axis, the disk may precess about the total angular momentum of the black hole accretion disk system as a solid body due to the Lense-Thirring torque \citep{fra07}. The precession of the accretion disk would lead to quasi periodic oscillations in TDE light curves \citep{dex11,sto12b,she13a} and to a reduction of the observed flux up to about 50 times if the disk precesses from a face-on into edge-on phases \citep{ulm99}. For an accretion disk with surface density given by the Equation~(\ref{eq:surf_in}), the precession period is \begin{equation} T_{\rm prec} \simeq {8\pi G M_{\rm BH} (1+2n) \over a c^3 (5-2n)} {\left(r_{\rm d} /r_{\rm g}\right)^{5/2-n} \left(r_{\rm in} /r_{\rm g}\right)^{1/2+n} \left(1-(r_{\rm in} /r_{\rm d})^{5/2-n}\right) \over 1-(r_{\rm in} /r_{\rm d})^{1/2+n}} \label{eq:pre} \end{equation} \citep{fra07,sto12b,she13a}, where $a$ is the dimensionless black hole spin parameter with $0 \leq a < 1$. For a black hole mass $M_{\rm BH} = 10^7 M_\sun$ and typical disk parameters $n=1/2$, $r_{\rm in} \simeq 3 r_{\rm g}$, and $r_{\rm d} \simeq 2 r_{\rm t} \simeq 10 r_{\rm g}$, the typical disk precession period is $T_{\rm prec} \approx 2.84 \, {\rm days}\, a^{-1} M_7$, or in the observer frame, $T_{\rm prec, obs}= (1+z) T_{\rm prec} \approx 3.25 \, {\rm days}\, a^{-1} M_7 \ga 3.25 \, {\rm days} \, M_7$. While for a black hole mass $M_{\rm BH} = 10^6 M_\sun$ and typical disk parameters $n=1/2$, $r_{\rm in} \simeq 3 r_{\rm g}$, and $r_{\rm d} \simeq 2 r_{\rm t} \simeq 47 r_{\rm g}$, the typical precession period is $T_{\rm prec} \approx 5.2 \, {\rm days}\, a^{-1} M_6$, or in the observer frame, $T_{\rm prec, obs}= (1+z) T_{\rm prec} \approx 5.9 \, {\rm days}\, a^{-1} M_6$. If the large drop in the light curve of \sdss is due to the disk Lense-Thirring precession with period $T_{\rm prec, obs} \ga 3.25 \, {\rm days} \, M_7$, the observations with regular time intervals of $10\, {\rm days}$ between 2010 June 10 and June 30, and $7\, {\rm days}$ between 2010 July 7 and July 28 of S2012 suggest that the face- and edge-on phases should be, respectively, longer than 20 days and 21 days. Therefore, the observations obtained between 2010 June 10 and July 28 imply that the precession period should have $T_{\rm prec, obs} \geq 48 \, {\rm days}$. However, the observations of the TDE between 2010 October 24 and December 23 suggest a face-on phase longer than 60~days and thus a precession period $T_{\rm prec, obs} \ga 81 \, {\rm days}$. The observation of 2010 December 23 suggests $T_{\rm prec, obs} \geq 84.5 \, {\rm days}$, while the observation of 2010 October 24 indicates $T_{\rm prec, obs} < 88 \, {\rm days}$. In conclusion, if the large drop in the flux was due to the disk Lense-Thirring precession, the precession period would be $ 84.5 \, {\rm days} < T_{\rm prec, obs} < 88 \, {\rm days}$. The drop in flux by a factor 50 within seven days, or $\la 8\% $ of the precession period, is too steep to be consistent with the predictions of Lense-Thirring precession \citep{dex11,sto12b,she13a}. \subsection{Orbital parameters of the SMBHB system} \label{sec:para} All of our results were obtained with $\Delta E$ given by Equation~(\ref{eq:DEp}) with $l=2$. However, some numerical simulations \citep[e.g.,][]{sto12,gui12} suggest a weaker dependence of $\Delta E$ on $\beta$. To investigate the dependence of our results on the different relationships of $\Delta E$ and $\beta$, we have carried out test numerical scattering experiments with $l=0$. The test numerical simulations are only carried out for $M_{\rm BH} = 10^6 M_\sun$, because the present results obtained with $\Delta E \propto \beta^2$ show a large variation of $\beta$ with $1.2 \la \beta \la 5$ for $M_{\rm BH} = 10^6 M_\sun$ but nearly a constant $\beta$ with $1.3 \la \beta \la 1.6$ for $M_{\rm BH} = 10^7 M_\sun$. Similar to Figure~\ref{fig:M6}, our results show that the simulated light curves for \sdss and the obtained model parameters of the star and SMBHB systems are nearly the same as those obtained with $l=2$, which can be understood as follow: different relationships of $\Delta E$ and $\beta$ significantly change only $t_{\rm min}$, which is degenerate with the scaling free parameter $f_{\rm x}$ as discussed in Section~\ref{obs}. Meanwhile, although $\Delta E$ is independent of $\beta$ for $l=0$, the truncation and recurrence of the light curve sensitively depends on $\beta$. Therefore, we will not discuss the results obtained with $l=0$ any further. We have shown that the peculiar characteristics of the light curves of the TDE in \sdss can be naturally explained by the SMBHB model given by LLC09. In the SMBHB model, the orbital parameters of the disrupted star approaching with negligible initial total energy can be determined to be $\theta \sim 0.3\pi$, $\Omega \sim 0.2 \pi$, and $\omega \sim 1.5\pi$ independent of the detailed choices of the model parameters. By fully reproducing the X-ray light curve of the TDE with the model light curves of a SMBHB system, we have obtained that the orbit of the SMBHB in \sdss should be elliptical with moderate eccentricity $e_{\rm _b} \simeq 0.3$ (with $0.1 \la e_{\rm b} \la 0.5$) and typical orbital period $T_{\rm b} \simeq 150\, {\rm days}$ (with $140 \, {\rm days} \la T_{\rm b} \la 160 \, {\rm days}$) for a primary SMBH of mass $M_{\rm BH} = 10^7 M_\sun$. A SMBH with that value is preferred by observations (S2012). The orbital period of the SMBHB suggests a semi-major axis $a_{\rm b} \simeq 0.59 \, {\rm mpc} \simeq 620 r_{\rm g}$. The black hole mass ratio, the penetration factor of that star, and the initial orbital phase at disruption have typical values $q\simeq 0.08$, $\beta\simeq 1.3$, and $\phi_{\rm b} \simeq 1.5\pi$, respectively. Because the parameters $q$, $e_{\rm b}$, and $\beta$ are three important model quantities and the simulation results sensitively depend on their values, we have carried out a large amount of simulations in three-dimensional space. The results are given in the panels (a)-(l) of Figure~\ref{fig:all9}. In the simulations, we have adopted $\phi_{\rm b} = 1.5\pi$ for simplicity. The simulation results show that the model solutions to the X-ray light curve of the TDE consist only of a small domain in the four-dimensional space ($\beta$, $q$, $e_{\rm b}$, $T_{\rm b}$) with $T_{\rm b} \sim 150\, {\rm days}$. In panels (a)-(b) of Figure~\ref{fig:all9}, we show the results obtained with $T_{\rm b} = 140\, {\rm days}$ only for $e_{\rm b} = 0.1$ and 0.2, and $0.03 \leq q \leq 0.2$, although we have done simulations for $0.1 \leq e_{\rm b} \leq 0.9$ and $0.03 \leq q \leq 0.9$, because no model light curve obtained with parameters outside the ranges can reproduce the X-ray light curve of the TDE. In panels (c)-(l), we show the simulation results in the three-dimensional space ($\beta$, $q$, $e_{\rm b}$) for $T_{\rm b}=145, 150, 155, 160\, {\rm days}$. Because the model solutions are insensitive to the small change of the orbital period, we have only done the simulations for $0.1 \leq e_{\rm b} \leq 0.6$, $1.2 \leq \beta \leq 1.6$, and $0.03 \leq q \leq 0.09$. \begin{figure} \begin{center} \includegraphics[width=0.8\textwidth,angle=0.]{f3.eps} \caption {Simulation results for the TDE of \sdss in the ($e_{\rm b}$, $q$, $\beta$) space for which the model light curves have been simulated. Numerical simulations have been done in the ($e_{\rm b}$, $q$, and $\beta$) space with $0 \leq e_{\rm b} \leq 0.9$, $0.03 \leq q \leq 0.9$, and $1 \leq \beta \leq 6$ for $\mbh=10^6\msun$ or $1 \leq \beta \leq 2.5$ for $\mbh=10^7\msun$. For ellipticity, those values, for which no model light curve is consistent with the observations of the TDE, are not shown here. In the computed domain of the parameter spaces, the fraction marked with the red triangle can give model light curves consistent with the observations of the TDE, while the other (marked with black dots) cannot. Panels (a)-(l) are results for $\mbh=10^7\msun$ with $\phi_{\rm b}=1.5 \pi$: panels (a)-(b) for $e_{\rm b} = 0.1$ and 0.2 with $T_{\rm b} = 140 \, {\rm days}$; panels (c)-(e) for $e_{\rm b} = 0.2$, 0.3, and 0.4 with $T_{\rm b} = 145 \, {\rm days}$; panels (f)-(h) for $e_{\rm b} = 0.3$, 0.4, and 0.5 with $T_{\rm b} = 150 \, {\rm days}$; panels (i)-(j) for $e_{\rm b} = 0.4$ and 0.5 with $T_{\rm b} = 155 \, {\rm days}$; panels (k)-(l) for $e_{\rm b} = 0.4$ and 0.5 with $T_{\rm b} = 160 \, {\rm days}$. Panels (m)-(r) are for $\mbh=10^6\msun$ and $e_{\rm b} =0, 0.1,0.2,0.3,0.4$, and $0.5$, respectively. In the simulations, $T_{\rm b} = 140 \, {\rm days}$ for $e_{\rm b} =0$ or $T_{\rm b} = 150\, {\rm days}$ and $\phi_{\rm b} = 1.7\pi$ for $e_{\rm b} \ge 0.1$ are adopted. \label{fig:all9}} \end{center} \end{figure} However, the mass of the central black hole can be smaller. If the SMBH has a mass $M_{\rm BH} = 10^6 M_\sun$, we have shown that the X-ray light curve of the TDE can also be reproduced with the model light curves obtained with SMBHB systems of orbits either circular $e_{\rm b} = 0$ or elliptical $e_{\rm b} \la 0.5$. The fitted orbital period of the SMBHB depends weakly on the orbital eccentricities and has a typical value of $T_{\rm b} \simeq 140 \, {\rm days}$ (or $a_{\rm b} \simeq 0.26\, {\rm mpc}$) with $132\, {\rm days} \la T_{\rm b} \la 145\, {\rm days}$ if $e_{\rm b} = 0$ or $T_{\rm b} \simeq 150 \, {\rm days}$ (or $a_{\rm b} \simeq 0.28\, {\rm mpc}$) with $142 \, {\rm days} \la T_{\rm b} \la 156 \, {\rm days}$ if $e_{\rm b} = 0.2$. The fitted mass ratio of the SMBHB system in \sdss has a typical value $q \sim 0.1$ for any possible orbit with $e_{\rm b} \la 0.5$, but distributes in a range depending sensitively on the values of eccentricity and penetration factor. The panels from (m) to (r) of Figure~\ref{fig:all9} show the complex dependence among $q$, $e_{\rm b}$, and $\beta$ in the parameter space, which are adopted from our simulation results for $0 \leq e_{\rm b} \leq 0.9$ and $0.03 \leq q \leq 0.9$. In the simulations, we have taken $T_{\rm b} = 140\, {\rm days}$ for $e_{\rm b} = 0$ and $T_{\rm b} = 150\, {\rm days}$ and $\phi_{\rm b} = 1.7 \pi$ for $e_{\rm b} > 0$ for simplicity. Different orbital periods are adopted here for different types of orbits in order to give the largest domain of model solutions in the parameter space. Again, the results depend only weakly on the orbital periods, in the sense that the variation of the orbital period in a certain range only changes the boundaries, but not the shape of the domain of the model solutions in the parameter space. The model solutions of the observed X-ray light curve are obtained with the assumption that the disrupted star is a solar-type main-sequence star. The disrupted star may be a different type of star, with different internal structures, masses, and/or radii. The tidal disruption of stars with different internal structures would lead to different light curves with different peak luminosities, peak time $t_{\rm peak}$, and power-law indices other than $-5/3$ \citep{lod09,gui12}. Because the key features of the interruptions and recurrences in the model light curves do not change with the structure of the star, our conclusions regarding the model solutions and the parameters are robust. For a certain orbital pericenter, Equation~(\ref{eq:DEp}) suggests the maximum specific energy $\Delta E$ changes with the radius of the star. The differences in $\Delta E$ do not change our conclusions as discussed before. However, our results do sensitively depend on the orbital pericenter $r_{\rm p}$ or $\beta$ for a certain tidal radius $r_{\rm t}$. If we have the knowledge of the star, with the condition $r_{\rm p} \leq r_{\rm t}$ or from Equation~(\ref{eq:beta}) we may give some more strict constraints on $r_{\rm p}$ (or $\beta$) and thus the mass ratio $q$ (and probably $e_{\rm b}$), based on Figure~\ref{fig:all9}. Notice that in Figure~\ref{fig:all9} $\beta = \beta_\sun \equiv r_{\rm t, \sun} / r_{\rm p}$ with $r_{\rm t, \sun}$ the tidal radius of a solar-type star. We have carried out numerical simulations to scan a significant fraction of the large model parameter space, but it is still prohibitive for the present computing powers to cover the whole space of the parameters ($\theta$, $\Omega$, $\omega$, $\beta$, $T_{\rm b}$, $q$, $e_{\rm b}$, and $M_{\rm BH}$). From the first principles, the potential sphere of the restricted three-body systems consisting of the SMBHB and the stellar plasma elements is split into inner and outer regions by the SMBHB orbit. As argued for Newtonian potential analytically by \citet{mar07} and numerically by LLC09, the shell of the potential sphere centered on the SMBHB orbit is chaotic because of the nonlinear overlap of the multiple resonances due to the strong perturbations by the secondary SMBH. The fluid elements with orbits inside the chaotic shell regions are resonantly scattered off and thus the inner and outer boundaries of the chaotic shell regions determine, respectively, the interruption and recurrence time of the TDE light curve. For a circular SMBHB orbit, the orbit of the SMBHB binary roughly determines the centers of the chaotic regions, suggesting that the Keplerian orbital period of the SMBHB is roughly between the time of the interruption and recurrence. The BH mass ratio determines the strength of the resonant perturbation, the extent of the nonlinear overlap of multiple resonances, and how effectively the fluid elements with orbits inside or crossing the chaotic shell regions are scattered off on the timescale when they move inside the chaotic shell, deciding the duration and shapes (e.g., smooth or flickering) of the interruptions and the recurrent light curves. The orbital parameters of the star could modify the characteristics of the key features of the SMBHB system only moderately. The high-quality X-ray light curve obtained by S2012 did not only catch the time of the interruption, the recurrence, and the re-interruption of the TDE, but also constrains well the long durations of the phases of low and high flux. The long duration of the recurrence suggests that the resonant perturbation by the secondary BH should not be too strong and the merger should not be a major merger with $q \ga 0.3$, while the long duration of the interruption implies that the perturbation cannot be too weak and the merger should not have an extreme mass ratio $q \la 0.01$ irrespective to the detailed modeling of the light curve. Therefore, the solutions with $q \sim 0.08$ are certain. With a moderate small mass ratio $q\sim 0.08$, the duration of the recurrent flare should not be much longer than the observed one, suggesting that the time of recurrence should not be much earlier than the first detection of the recurrent flare and the SMBHB orbital period is about the time of recurrence. Therefore, the model solutions with $T_{\rm b} \sim 150 \, {\rm days}$ are robust, too. However, we have to notice that the orbital period of the SMBHB is the Keplerian period, but the return time of the bound stellar plasma elements is determined by the radial epicyclic frequency. The Keplerian and epicyclic frequencies are equal in Newtonian gravity, but the latter is smaller than the former in GR. The differences between the two frequencies become significant for tidal disruptions by the SMBH with $M_{\rm BH} \ga 10^7 M_\sun$ because the tidal radius for a solar-type star is $r_{\rm t} \la 5 r_{\rm g} M_7^{-2/3}$. Therefore, for the certain orbital period $T_{\rm b}$, the time of the interruption in the model light curves is delayed so much that it is significantly later than the date of the first upper limit, which, for a SMBHB system with circular orbit, is hardly compensated by adjusting the other parameters. To significantly shift the time of interruption to an earlier date, we need an elliptical orbit for the SMBHB system. For the SMBHB system with the given orbital period, the moderate eccentricity decreases significantly the pericenter and thus the inner boundary of the chaotic shell region, resulting in the appearance of the interruption before the first upper limit on 2010 July 7 and after the last detection on 2010 June 30. Therefore, we expect that the solution for $M_{\rm BH} = 10^7 M_\sun$ with $e_{\rm b} \sim 0.3$ is robust. \subsection{Gravitational wave emission} \label{sec:gw} Upon final coalescence, SMBHB systems like the one in \sdss are prime sources for future space-based GW missions like {\it eLISA}. However, in its current state of evolution, it would be challenging to detect the GWs from this system. It would radiate GW emission at a frequency $f_{\rm obs} = 2 /T_{\rm b} (1+z) \simeq 0.13\, {\rm {\mu}Hz} \left(T_{\rm b} /150 \, {\rm days}\right)^{-1}$ in the observer frame, and with a characteristic strain in an observation of duration $\tau_{\rm obs}$ \begin{equation} h_{\rm c} = h_{\rm r} \sqrt{f_{\rm obs} \tau_{\rm obs}} , \end{equation} with $h_{\rm r}$ is the strain amplitude at the object rest frequency, $f_{\rm b} = 2/T_{\rm b}$ \begin{equation} h_{\rm r} = {8\pi^{2/3} \over 10^{1/2}} {G^{5/3} M^{5/3} \over c^4 r(z)} f_{\rm b}^{2/3} , \end{equation} where $M = (M_1 M_2)^{3/5} /(M_1+M_2)^{1/5} = M_{\rm BH} q^{3/5} / (1+q)^{1/5}$ is the ``chirp mass'' of the SMBHB and $r(z)$ is the comoving distance. The frequency $f_{\rm obs} \simeq 0.13 \, {\rm {\mu}Hz}$ is in the range observable with PTAs, but much smaller than that of {\it eLISA}. For a five-year PTA observation, the expected characteristic strain of the binary is \begin{eqnarray} h_{\rm c} \approx 1.7\times 10^{-20} \left({T_{\rm b} \over 140 \, {\rm days}}\right)^{-7/6} \left({\tau_{\rm obs} \over 5\, {\rm yr}}\right)^{1/2} M_6^{5/3} {q_{-1} \over (1+q)^{1/3}} \nonumber \\ \approx 6.0 \times 10^{-19} \left({T_{\rm b} \over 150 \, {\rm days}}\right)^{-7/6} \left({\tau_{\rm obs} \over 5\, {\rm yr}}\right)^{1/2} M_7^{5/3} {(q/0.08) \over (1+q)^{1/3}} , \end{eqnarray} which is about four orders of magnitude smaller than the detection limit of PTA at the frequency $f_{\rm obs}$ \citep[e.g.,][]{ell12}. If GW radiation was the only contribution to the orbital shrinkage, the lifetime of the system is \begin{equation} \tau_{\rm gw} \simeq 1.0\times 10^8 \, {\rm yr}\, \left({T_{\rm b} \over 140\, {\rm days}}\right)^{8/3} M_6^{-5/3} q_{-1}^{-1} f^{-1} (1+q)^{1/3} \label{eq:lfgw} \end{equation} \citep{pet63}, where $f$ is a function of the eccentricity $e_{\rm b}$ \begin{equation} f = \left(1 + {73 \over 24}e_{\rm b}^2 + {37 \over 96} e_{\rm b}^4\right) \left(1-e_{\rm b}^2\right)^{-7/2} . \end{equation} For a SMBHB system with $M_{\rm BH} = 10^7 M_\sun$ and typical parameter values $T_{\rm b} = 150\, {\rm days}$, $q=0.08$, and $e_{\rm b}= 0.3$, the life time is $\tau_{\rm gw} \simeq 1.9 \times 10^6 \, {\rm yr}$, while for a SMBHB system with $M_{\rm BH} = 10^6 M_\sun$ and the parameter values $T_{\rm b} = 140\, {\rm days}$, $q=0.1$ and $e_{\rm b}= 0$, the life time is longer, with $\tau_{\rm gw} \simeq 1.0\times 10^8 \, {\rm yr}$. However, a longer life time $\tau_{\rm gw}$ does not necessarily imply that the $10^6\msun$ fit is favored, nor that TDE light curve searches for SMBHBs are biased toward systems with larger separations and smaller SMBH masses for a given observed binary period. This is because of the biases in event detection in any (X-ray, transient) survey, which preferentially selects for the most luminous, most frequent events. In particular, X-ray surveys are biased toward SMBHs of higher mass $M_{\rm BH} \approx 10^7 \msun$ because of their higher peak luminosities. Further, the TDE rate $N_{\rm TDE}$ is a function of $a_{\rm b}$. A preliminary estimation suggests that $N_{\rm TDE}$ is a complicated function of $a_{\rm b}$ and does not change significantly for $10^{-3} \, {\rm pc} \la a_{\rm b} \la 1 \, {\rm pc}$ \citep{che11,liu12}. Thus, for a given observed $T_{\rm b}$ in an X-ray transient survey, a SMBHB system with higher SMBH mass $M_{\rm BH} \sim 10^7 \msun$ and smaller separation within the range of $10^{-3} \, {\rm pc} \la a_{\rm b} \la 1 \, {\rm pc}$ would be likely favored. \subsection{Frequency of SMBHBs among known TDEs} \label{sec:freq} Approximately 20 to 25 TDEs and candidates have been identified from the observations \citep[see][for a recent review]{kom12}, including the X-rays \citep[e.g.,][]{kom99}, UV \citep{gez08}, optical and emission lines \citep{kom08b,van11}, and gamma-rays \citep[e.g.,][]{bur11,blo11,cen12}. We have inspected these light curves, with the exception of the two jetted TDEs, in order to search for similar features as seen in SDSSJ1201+30. None are clearly present. This might have several reasons. It could be due to the gaps in the light curves of the TDEs (and so escaped detection). Alternatively, the orbital timescales of the SMBHBs can be longer or shorter, and so their effects would be undetectable on the timescales observed so far. Currently, this then makes SDSS J1201+30 the only good SMBHB candidate among the known TDEs. In summary, we conclude that the SMBHB model for SDSS J1201+30 is a viable model that naturally explains the abrupt dips and recoveries of the X-ray light curve of the event. Future sky surveys are expected to detect TDEs in the thousands. Analysis of their light curves will then provide a powerful new tool of searching for SMBHBs in otherwise non-active galaxies. | 14 | 4 | 1404.4933 |
1404 | 1404.4875_arXiv.txt | We present observations of extended, 20-kpc scale soft X-ray gas around a luminous obscured quasar hosted by an ultra-luminous infrared galaxy caught in the midst of a major merger. The extended X-ray emission is well fit as a thermal gas with a temperature of \emph{kT}$\approx 280$ eV and a luminosity of $L_{\rm X}\approx 10^{42}$ erg~s$^{-1}$ and is spatially coincident with a known ionized gas outflow. Based on the X-ray luminosity, a factor of $\sim 10$ fainter than the \oiii\ emission, we conclude that the X-ray emission is either dominated by photoionization, or by shocked emission from cloud surfaces in a hot quasar-driven wind. | Black hole (BH) ``feedback'' is often invoked to regulate massive galaxy formation \citep[e.g.,][]{springeletal2005}, but definitive examples of radiation from the quasar accretion disk driving powerful outflows are difficult to find \citep[e.g.,][]{moeetal2009}. While clear evidence exists that powerful radio jets entrain warm gas and carry significant amounts of material out of their host galaxies \citep[e.g.,][]{nesvadbaetal2006,fustockton2009}, the situation is far less clear for radio-quiet targets, which dominate the active galactic nucleus (AGN) population. In the past few years, we have identified a number of radio-quiet quasars with high intrinsic luminosities ($M_B < -26.9$ mag) that show outflowing ionized gas on $\sim 15$ kiloparsec (kpc) scales \citep{greeneetal2011, greeneetal2012, liuetal2013a,liuetal2013b, hainlineetal2013}. In this paper, we present observations of hot X-ray gas that is aligned with a known 20-kpc--scale ionized gas bubble in the radio-quiet quasar SDSS J135646.10+102609.0 (SDSS J1356+1026 hereafter). SDSS\,J1356$+$1026 is an on-going merger and ultra-luminous infrared galaxy (ULIRG) located at $z$=0.123 ($D_L = 568$ Mpc). The Northern nucleus hosts a luminous ($L_{bol}\simeq 10^{46}$ erg s$^{-1}$) obscured quasar that was originally discovered in the Sloan Digital Sky Survey \citep[SDSS;][]{yorketal2000} based on its \oiii$~\lambda 5007$ emission \citep{zakamskaetal2003,reyesetal2008}. The source was also flagged as a possible dual active nucleus, because of the presence of multiple velocity components in the SDSS spectrum, although that classification has been questioned \citep{liuetal2010,fuetal2012}. Our interest here lies in the $\sim$20 kpc outflow that we discovered in long-slit observations with Magellan \citep[][Paper I hereafter]{greeneetal2009,greeneetal2012}. In our Magellan spectrum, we detect the line splitting that is characteristic of an expanding ``bubble'' (Figure \ref{fig:xrayimage}). The shell region extends $\sim 10$ kpc ($\sim 4$\arcsec) to the South of the quasar hosted by the Northern nucleus. Equidistant from the Northern nucleus to the North are clumps of \oiii\ emission with comparable observed velocities to the bubble. We thus propose that we are observing an expanding bipolar super-bubble similar to those observed in many star-forming galaxies both with and without AGNs \citep[e.g.,][]{heckmanetal1990,rupkeveilleux2013}. | We find a total soft X-ray luminosity of $5-9\times 10^{41}$~erg~s$^{-1}$ with a best-fit temperature of $\sim 280$ eV, and a total \oiii\ luminosity in the extended component of $\sim 10^{43}$~erg~s$^{-1}$. Thus the extended X-ray emission is roughly an order of magnitude fainter than the extended \oiii\ emission. We discuss below the possible origins of the overwhelmingly soft extended X-ray emission. The prime suspects, in order from least to most probable, are electron scattering, superwind-driven shocks, and photoionization. We note that \citet{mcdowelletal2003} also suggest merger-driven shocks as the heating mechanism of the X-ray emitting gas in Arp 220 \citep[see also][ for similar arguments about NGC 6240]{nardinietal2013}. However, as pointed out by \citet{grimesetal2005}, non-starbursting mergers do not appear to show similar X-ray halos, strongly suggesting winds over mergers as the heating mechanism. \subsection{Electron scattering} Electron scattering of the AGN continuum could provide X-ray photons, but cannot account for the observations. For one thing, scattering would not change the hard spectral slope intrinsic to the AGN, so cannot explain the very soft extended X-rays. Secondly, the scattering efficiency is too low to account for the observed luminosity. If we assume that the intrinsic UV luminosity is $\sim$ twice that of the infrared bump in Paper I \citep[e.g.,][]{richardsetal2006}, we can estimate an intrinsic $\nu L_{\nu}$[2000~\AA$]=3\times 10^{45}$ erg~s$^{-1}$. Assuming that all UV emission is due to electron-scattered light from the nucleus places an upper limit on the electron-scattering efficiency of 3\% (much less so if there is a contribution from dust). Since electron-scattering is wavelength independent and dust scattering is negligible at X-ray wavelengths, and given the luminosity of the North nucleus $L_{\rm X} = \ee{(9 \pm 3)}{41}$~erg~s$^{-1}$, an upper limit to the scattered X-ray luminosity is $\ll 3\% \times (9 \pm 3) \times 10^{42}$ erg~s$^{-1}$, or $L_{\rm X}/L_{\rm [OIII]} \ll 0.003$, much lower than the observed X-ray luminosity. Finally, the amount of scattering is constrained by the amount of line emission. From \citet{zakamskaetal2005}, if we take $n_e \sim 100$~cm$^{-3}$ and $d \sim 5$~kpc, we expect $L_{\rm X}/L_{\rm [OIII]} \approx 0.005$, also lower than the ratio of $\sim 0.1$ that is observed. \subsection{Superwind} Perhaps the most exciting possibility is that we are detecting shocked gas associated with a wide-angle, quasar-driven wind \citep[e.g.,][]{fauchergiguerequataert2012,choietal2013}. Such a super-wind would have similar properties to those blown by starbursts, but the gas would be heated by the accreting black hole rather than star formation. To estimate the expected luminosity in the soft X-rays from a superwind, we follow \citet{heckmanetal1996} and assume that the expanding bubble of hot gas behaves like a supernova remnant, with negligible radiative losses, in order to translate our estimated mechanical luminosity of $L_{\rm mech} \approx 10^{44}-10^{45}$~erg~s$^{-1}$ into an expected X-ray luminosity \citep[see also][]{chevalierclegg1985}. Their derived relationship is: \begin{equation} L_{\rm X} \approx 3.1 \times 10^{40} L_{\rm mech, 43}^{33/35} \, n_{e,-2}^{17/35} \, t_7^{19/35} \, {\rm erg\, s^{-1}}, \end{equation} where $L_{\rm mech}$ is in units of $10^{43}$~erg~s$^{-1}$, $n_{e,-2}$ is the density in units of $10^{-2}$~cm$^{-3}$ and $t_7$ is the estimated age of the bubble in units of $10^7$ yr. The observed X-ray luminosity has $L_{\rm X} \approx f \, n_e \, n_H V \epsilon$, with APEC calculating the emissivity $\epsilon$, $f$ the volume filling factor, $n_e \approx n_H$, and the volume $V$ assumed to be a cylinder with length 20 kpc and radius 2 kpc. From the APEC spectral model, we find a best-fit electron density of $n_e \approx 0.002$~cm$^{-3}$. We emphasize that the normalization is poorly constrained from these data (Figure \ref{fig:showfit}, but it is interesting to perform this estimate nevertheless. Taking $t \approx 10^{7}$ yr and the range of mechanical luminosity from Paper I, we find $L_{\rm X} \approx 2 \times 10^{41} - 10^{42}$~erg~s$^{-1}$, in agreement with what we observe. The corresponding X-ray emitting gas mass is $M_{\rm X} \approx 10^{10} f^{1/2}$~\msun, with a total thermal energy of $E = PV = 2 n_e kT V \approx 1.3 \times 10^{58}\,f^{1/2}$ erg, or $\dot{E} = 3 \times 10^{43}\, f^{1/2}$~erg~s$^{-1}$. The uncertainties in these calculations are quite large, due to the uncertainties in the spectral fitting and the unknown volume and volume filling factor. However, the kinetic luminosity needed to power the X-ray outflow is within a factor of three of what we inferred from the ionized gas outflow. On the other hand, models of superwinds suggest that the wind is powered by far more tenuous and hotter gas than we observe here, $\sim 10^7$~K for starbursts \citep{stricklandstevens2000} and perhaps even hotter for AGN \citep[e.g.,][]{zubovasking2012}. In that case, the soft X-rays may come from the surfaces of clouds as they are shocked by the wind, and the X-ray luminosity cannot be inferred directly from the mechanical energy estimates. However, we can still phenomenologically compare the X-rays that we observe with other known superwinds. Most of the bolometric luminosity of starbursts and obscured quasars is radiated at infrared wavelengths. Therefore, it is useful to compare extended soft X-ray to total infrared flux ratios for a variety of wind-driving systems. In starburst galaxies over a wide range in mass, including ULIRGs, \citet{grimesetal2005} find $f_{\rm X}/f_{\rm FIR} \approx 10 ^{-4}$. The ratio in \bub\ is consistent with this value. Likewise the size scales as one might naively expect from the infrared luminosity. The one way in which the X-ray gas observed here differs significantly from that observed in starbursts is the temperature. Most of the ULIRGs in the Grimes et al.\ sample have temperatures of \emph{kT}$\approx 600-800$ eV, as compared with the \emph{kT}$\approx 280$ eV observed here. Based on our fitting, we rule out a temperature of 600 eV at greater than 10~$\sigma$ confidence. This low inferred temperature may be a clue that we are instead seeing photoionized gas. \subsection{Photoionization} Since we know that the central AGN is photoionizing gas on large scales, and because of the correspondence in morphology between the soft X-ray and warm ionized gas, we lastly consider the possibility that what appears as X-ray continuum at our low spectral resolution is actually composed of photoionized line emission. Detailed analysis of the extended X-ray emission around local Seyfert galaxies has found strong evidence that the soft X-ray emission is dominated by photoionization on large scales \citep[][]{bianchietal2006,wangetal2011} and comprised predominantly of line emission \citep[e.g.,][]{sambrunaetal2001}, although on galaxy scales collisional ionization is also important \citep[e.g.,][]{paggietal2012,wangetal2014}. Based on these works, the $L_{\rm X}/L_{\rm [OIII]}$ ranges from $0.1-0.3$, and is fairly constant with radius. The relatively low temperatures of \emph{kT}$\approx 280$ eV are consistent with the temperatures that result from thermal fits to other Seyfert galaxies. Also, the observed ratio of X-ray to \oiii\ luminosity of $0.05-0.1$ is consistent with expectations from photoionized gas (and is identical to that seen in NGC 4051 by Wang et al. 2011). Furthermore, the orientation of the X-ray emission (N-S) aligns with the direction of quasar illumination inferred from the position angle in polarimetric observations (Paper I). | 14 | 4 | 1404.4875 |
1404 | 1404.7271_arXiv.txt | We investigate structure of self-gravitating disks, their fragmentation and evolution of the fragments (the clumps) using both analytic approach and three-dimensional radiation hydrodynamics simulations starting from molecular cores. The simulations show that non-local radiative transfer determines disk temperature. We find the disk structure is well described by an analytical model of quasi-steady self-gravitating disk with radial radiative transfer. Because the radiative process is not local and radiation from the interstellar medium cannot be ignored, the local radiative cooling would not be balanced with the viscous heating in a massive disk around a low mass star. In our simulations, there are cases in which the disk does not fragment even though it satisfies the fragmentation criterion based on disk cooling time ($Q \sim 1$ and $\Omega t_{\rm cool}\sim 1$). This indicates that at least the criterion is not sufficient condition for fragmentation. We determine the parameter range for the host cloud core in which disk fragmentation occurs. In addition, we show that the temperature evolution of the center of the clump is close to that of typical first cores and the minimum initial mass of clumps to be about a few Jupiter mass. | \label{intro} Stars form in gravitationally collapsing molecular cloud cores. Since molecular cloud cores have angular momentum \citep{1993ApJ...406..528G,2002ApJ...572..238C}, a circumstellar disk forms around the protostar. According to recent theoretical studies of the gravitational collapse of molecular cloud cores, the protostar is surrounded by a circumstellar disk early in its evolutionary phase in the case without magnetic field, \citep{1998ApJ...508L..95B,2010ApJ...724.1006M,2011MNRAS.416..591T} and with magnetic field \citep{2010ApJ...718L..58I,2011ApJ...729...42M}. As \citet{2010ApJ...718L..58I} pointed out, a circumstellar disk can be gravitationally unstable during its early evolution. When the protostar forms, its mass is only $10^{-2}$ to $10^{-3}~M_{\odot}$. In contrast, the first-core that is the precursor to the circumstellar disk \citep{2006ApJ...645..381S,2010ApJ...724.1006M} has an initial mass of $\sim 0.1~M_{\odot}$. Therefore, in the formation epoch of the protostar, the disk has a mass that is significantly greater than that of the protostar. Observations also suggest that massive disks can form in the main accretion phase \citep{2009ApJ...707..103E}. In such massive disks, gravitational instability (GI) can develop. The Toomre's $Q$ value, \begin{eqnarray} Q=\frac{\kappa_{\rm ep} c_s}{\pi G \Sigma}, \end{eqnarray} is a well-known indicator for GI \citep{1964ApJ...139.1217T}. When $Q\lesssim 1.5$, the disk is gravitationally unstable against non-axisymmetric perturbations and develops spiral arms \citep{1994ApJ...436..335L}. The spiral arms readjust the mass and angular momentum of the disk, promoting mass accretion onto the protostar. They also heat the disk gas. By readjusting the surface density and the disk heating, the $Q$ value increases, and the disk is stabilized. This self-regulative nature is an important aspect of GI. To maintain GI, additional physical processes such as radiative cooling or mass accretion from the envelope are necessary. With these effects, the disk can also fragment and gravitationally bound gaseous objects (which we call ``clumps") form. Disk fragmentation is a candidate mechanism for the formation of wide-orbit planets \citep{2010ApJ...714L.133V,2011ApJ...729...42M,2013ApJ...768..131V}. Wide-orbit planets are planets separated from the central star by more than 10 AU \citep{2008Sci...322.1348M,2009ApJ...707L.123T, 2009A&A...493L..21L,2010Natur.468.1080M,2010ApJ...719..497L}. Furthermore, it has been suggested that disk fragmentation can explain the formation of brown dwarfs \citep{2009MNRAS.392..413S,2011MNRAS.413.1787S} and multiple stellar systems \citep{2008ApJ...677..327M,2010ApJ...708.1585K}. Effects of radiative cooling on GI and disk fragmentation has been investigated in \citet{2001ApJ...553..174G} with two dimensional local shearing box simulations. To model radiative cooling, he employed a simplified cooling law (see right hand side of equation (\ref{sec2_cooling0})). In his simulations, the disk is initially unstable against GI ($Q =1$) and GI immediately develops and heats the disk. When radiative cooling is not so strong, it balances the heating by GI, and the disk settles into a quasi-steady state. This quasi-steady state also realizes in three dimensional global disk simulations \citep{2004MNRAS.351..630L}. On the other hand, when radiative cooling is sufficiently strong, such a quasi-steady state can not be realized and the disk fragments. In the simulations of \citet{2001ApJ...553..174G}, disk fragmentation occurred when disk cooling time $t_{\rm cool}$ is comparable to the orbital timescale, $t_{\rm cool} \sim t_{\rm orbit}$ (or $\Omega t_{\rm cool}\sim O(1)$). The fragmentation condition are also confirmed by three dimensional global disk simulations \citep{2003MNRAS.339.1025R} but the simplified cooling laws are also used. Since \citet{2001ApJ...553..174G} and \citet{2004MNRAS.351..630L} employed the simplified cooling law, they implicitly assumed that radiation just acts as the cooling process to decrease the local gas energy (we call this the assumption of local radiative cooling). However, this assumption is not necessarily true. For example, irradiation from the protostar and that from the inner disk region can heat the disk. Thus, in reality, incoming radiation flux, in addition to outgoing radiation flux and local GI heating, should be considered. Furthermore, the interstellar medium has a typical temperature of about 10 K and it is almost impossible to cool the disk gas below 10 K because of radiation flux from the ambient interstellar medium. Therefore, it is not clear that, in realistic situations, the local balance between radiative cooling and viscous heating is achieved or not as in \citet{2001ApJ...553..174G}. Whether the balance is achieved is very important because the structure of quasi-steady self gravitating disk can be determined by the energy balance. Another important issue is applicability of the fragmentation criterion found by \citet{2001ApJ...553..174G}, $Q \sim 1$ and $\Omega t_{\rm cool} \sim 1$, in realistic situations. Gammie pointed out that, in realistic systems, fragmentation realizes when the external irradiation quickly diminishes and when the gas quickly cools. Thus, he regarded the fragmentation criterion can be applicable in very limiting cases. On the other hand, \citet{2003MNRAS.339.1025R} interpreted this criterion as ``almost isothermal conditions are necessary for fragmentation". When the cooling timescale of the disk is small, the gas evolves isothermally during GI growing and pressure repulsion becomes weak compared to the adiabatic evolution case (or inefficient cooling case). \citet{2003MNRAS.339.1025R} suggested that such almost isothermal evolution in non-linear evolution phase of GI is necessary for fragmentation. According to this interpretation, how the disk becomes $Q\sim 1$ or the energy balance within it is not important because whether fragmentation realize or not depends on the thermal behavior of the gas in the non-linear evolution of GI. The criterion seems to be regarded as a necessary condition in this interpretation. In the previous works using analytic approach, however, the criterion is used as if a sufficient condition for fragmentation \citep{2005ApJ...621L..69R,2011MNRAS.417.1928F,2011ApJ...740....1K,2013MNRAS.432.3168F}. As just described above, the interpretation of the criterion is ambiguous and its applicability in the realistic situation is still not clear. Another mechanism that makes a disk gravitationally unstable is mass loading from the envelope \citep[e.g.,][]{2003ApJ...595..913M,2010ApJ...718L..58I,2010ApJ...708.1585K, 2010ApJ...714L.133V,2011ApJ...729...42M, 2011MNRAS.416..591T,2011MNRAS.417.2036B,2011ApJ...730...32S,2013MNRAS.436.1667T,2013MNRAS.428.1321T}. This mechanism is efficient in the early phase of disk evolution during which the protostar and disk are embedded in a massive envelope. With mass accretion from the envelope, the $Q$ value of the disk decreases due to the increase of the surface density. When the mass accretion onto the disk is sufficiently high, the disk eventually fragments, and planetary mass clumps form. In this process, whether fragmentation occurs depends on envelope (or cloud core) parameters such as thermal energy or rotational energy. The parameter range in which fragmentation occurs has already been investigated in our previous studies \citep{2011MNRAS.416..591T,2013MNRAS.428.1321T}; however, in those studies, the effects of radiative transfer were approximated. Radiative transfer could also play important roles during the early phase of disk evolution; therefore, a parameter survey of disk fragmentation with radiation hydrodynamics simulation is necessary. Initial properties and the evolution of fragments (or clumps) are other important issues. The ultimate fate of clumps depends on their orbital and internal evolutions. For example, if the radial migration timescale is very short, clumps quickly accrete onto the protostar and disappear. If the radial migration timescale is sufficiently long and the clumps survive in the disk maintaining its mass in the range of planetary masses ($\lesssim 10 M_{\rm Jupiter}$), the clumps evolve into the wide orbit planets \citep{2010ApJ...714L.133V,2011ApJ...729...42M}. If the mass of the clumps quickly increases, disk fragmentation can be regarded as the formation process for brown dwarfs and binary or multiple stellar systems \citep{2009MNRAS.392..413S}. In spite of its importance, only a few studies have focused on the orbital and internal evolution of clumps in circumstellar disks. \citet{2011MNRAS.416.1971B} investigated the orbital evolution of massive planets in a gravitationally unstable disk under the assumption of local radiative cooling. They showed that massive planets rapidly migrate inward in a type I migration timescale \citep{2002ApJ...565.1257T}. By adopting an analytical approach or three-dimensional smoothed particle hydrodynamics (SPH) simulation, \citet{2010MNRAS.408.2381N} and \citet{2012MNRAS.427.1725G} investigated the internal evolution and the collapse timescale of an isolated clump. The gravitational collapse (the second collapse) occurs in the clump when the central temperature reaches $\sim 2000$ K, at which the dissociation of molecular hydrogen begins, and the gas pressure can no longer support the clump against its self gravity. These authors suggested that the timescale for the second collapse after clump formation is in the range of several thousand years to several $10^4$ years. However, they ignored further mass accretion from the disk onto the clumps. \citet{2013MNRAS.436.1667T} investigated the orbital and internal evolution of clumps permitting realistic gas accretion from the disk onto clumps with three-dimensional radiation hydrodynamics simulation. They showed that although most of the clumps rapidly migrate inward and finally fall onto the protostar, a few clumps can remain in the disk. They also showed that clumps are convectionally stable ($\gamma>\gamma_{\rm eff}$). The central density and temperature of a surviving clump rapidly increase, and the clump undergoes a second collapse within $1000$ -- $2000$ years after its formation. However, in this works, only one simulation was performed. The evolution process of clumps may change under different initial conditions. For example, the central entropy of the clump would become small when fragmentation occurs in the outer relatively cold region of the disk. Since the central entropy of the clump determines its initial mass and radius of the clump, fragmentation in different disk environments changes the nature of the clumps. It is also expected that the mass accretion from the disk onto clumps becomes small when fragmentation occurs in the outer region where the disk surface density is small at $Q=1$. In this study, we investigate the structure of self-gravitating disks, fragmentation of the disk, and evolution of clumps using both an analytic approach and radiation hydrodynamics simulations starting from molecular cloud cores. This paper is organized as follows. In \S 2, we analytically derive the structure of the self-gravitating steady disk using various energy balance relations. It would be insightful to understand the general structure of self-gravitating disks. The numerical method and initial conditions for the simulations are described in \S 3. Results and discussions are divided into two parts (\S \ref{self_grav_disks} and \S \ref{fragment_section}). In \S \ref{self_grav_disks}, we mainly investigate the structure of a self-gravitating disk that formed in the radiation hydrodynamics simulations. The simulation results for disk evolution are presented in \S \ref{results_disk}. In this section, we show that radiation can transfer energy within the disk and can heat the outer region of the disk. Therefore, the assumption of local radiative cooling is not valid in the disk. In \S \ref{self_grav_disk_discussion}, we discuss the consequences of the results obtained from our numerical simulations and their implications in interpreting previous work. In \S \ref{fragment_section}, we investigate disk fragmentation and the evolution of clumps. In \S \ref{fragment_simulation_results}, simulation results are shown. The parameter range of the molecular cloud core in which fragmentation occurs is determined, and the orbital and internal evolutions of clumps are investigated. In \S \ref{fragment_simulation_discussion}, we discuss the results reported in \S \ref{fragment_simulation_results} and derive the minimum initial mass of clumps. Finally, we summarize our results and discuss future perspectives in \S \ref{summary_future}. | \subsubsection{Temperature profile determined by radial radiative transfer in an optically thick disk} \label{section5_temp} The results in \S \ref{results_disk} shows that the temperature profile of the disk formed in our simulation is $T \propto r^{-1.1}$. This is significantly shallower than the disk in which local heating balances local cooling $T\propto r^{-2.2}$ (see, Fig. \ref{radial_profile}) and steeper than the passively irradiated disk $T\propto r^{-\frac{3}{7}}$. In this subsection, we analytically derive the profile $T\propto r^{-1.1}$. The right bottom panel in Fig. \ref{radial_profile} shows that the vertical optical depth is greater than unity over almost the entire region. Thus, we can use the diffusion approximation to derive the disk temperature profile. Under the assumptions that disk is steady, viscous heating is negligible, and that the radiation temperature is equal to the gas temperature, the energy equation can be expressed as \begin{equation} \label{flux} \nabla \cdot \mathbf{F}_{\bm r}=0. \end{equation} Figure \ref{faceon_Tgas} and \ref{rz_map} shows that the temperature distribution can be regarded as axisymmetric and vertically isothermal. Thus, we can assume that $F_r \gg F_z,~F_\phi$. Under the assumption that $F_r \gg F_z,~F_\phi$, (\ref{flux}) becomes \begin{equation} \label{flux_fr} \frac{1}{r}\frac{ \partial (r F_r)}{\partial r} =0. \end{equation} Around the mid-plane, the diffusion approximation is justified, and (\ref{flux_fr}) becomes \begin{equation} r \frac{\sigma T^3}{\kappa \rho}\frac{\partial T}{\partial r}={\rm const.}. \end{equation} Using the relation $ \Sigma=\rho c_s/\Omega $, we have \begin{equation} \label{flux_n} 2.5~ n_T - n_\Sigma -n_\Omega =0. \end{equation} Using (\ref{sec2_dynamics}), (\ref{sec2_qvalue}), $n_\Omega=-1.1$ and (\ref{flux_n}), we obtain \begin{equation} \begin{split} \alpha\propto r^{1.65},~\Sigma\propto r^{-1.65},~T\propto r^{-1.1}. \end{split} \end{equation} This agrees very well with the simulation results (see, the thin lines (simulation results) and thick solid lines (theoretical estimate) in Fig. \ref{radial_profile}). \subsubsection{Importance of non-local radiative transfer} As pointed out in \S \ref{intro}, the locality of radiative cooling has been assumed in many previous simulations \citep[e.g.,][]{2003MNRAS.339.1025R,2005MNRAS.358.1489L,2005MNRAS.364L..56R,2012MNRAS.420.1640R, 2011MNRAS.416L..65P} and in many analytical studies \citep{2005ApJ...621L..69R,2009MNRAS.396.1066C,2011ApJ...740....1K} to investigate the nature of GI and the conditions of disk fragmentation with radiative cooling. In contrast, our simulations show that radiation can transfer significant energy in the radial direction even in the absence of the stellar irradiation. Consequently, the temperature profile becomes $T \propto r^{-1.1}$ in our simulation and is significantly shallower than $T \propto r^{-2.2}$, which is expected under the assumption that local viscous heating balances local radiative cooling. Thus, the local energy balance between radiation and viscous heating is not satisfied in the disk formed in our simulations. This indicates that the assumption of local radiative cooling is not necessarily valid in a massive disk around a low mass star. The radial profiles of the surface density and the viscous $\alpha$ parameter are consistent with a self-gravitating quasi-steady disk model with a given rotation profile and $T \propto r^{-1.1}$. Thus, the disk is in the quasi-steady state with an energy balance that is not local. Therefore, we conclude that the local treatment of radiative cooling is not suitable approximation to investigate massive disk around low mass star. We only calculated disk evolution just about $ 10^4$ years after protostar formation and the disk and the protostar were still embedded in a massive envelope (Class 0 phase). One might think that non-local radiative transfer does not play the role in later evolutionary phase. However, with two-dimensional radiation hydrodynamics simulation, \citet{1993ApJ...411..274Y} showed that an almost isothermal temperature distribution in vertical direction also realize in the late evolutionary phase of disk at which 95 \% of initial cloud core has already accreted onto the protostar or disk. Thus, we expect that non-local radiative transfer also plays an important role for the temperature structure of disks in the later evolutionary phase. Note that a large simulation box in which the boundary is far from disk photosphere is crucial to investigate the effects of non-local radiative transfer, otherwise radiation flux is easily affected by the boundary conditions. We could not find evidence that the non-local energy transport of GI suggested by \citet{1999ApJ...521..650B} plays an important role because GI heating is itself small compared to radiation energy transfer in the outer region of the disk. \subsubsection{Applicability of fragmentation criterion based on disk cooling time} \label{application_fragmentation_criterion} In Fig. \ref{tcool_profile}, we show that the cooling time of disk corresponds to $\Omega t_{\rm cool}\lesssim 1$ in outer region and our disk apparently satisfies the fragmentation criterion based on disk cooling time ($Q \sim 1$ and $\Omega t_{\rm cool}\sim 1$). Because the cooling time is very short compared to the orbital period, the gas evolves almost isothermally during GI growing in outer region. However, the disk does not fragment. In our disk, the most unstable wave-length of GI is relatively large and the global spiral arms develop. The spiral arms readjust the surface density and the disk is stabilized. Such a readjustment is also observed in previous works \citep{1994ApJ...436..335L,2010ApJ...708.1585K}. Especially, \citet{2010ApJ...708.1585K} shows that the disk fragmentation is suppressed by the readjustment even with isothermal equation of state. Because such a stabilizing process also play the role in the realistic disk, we conclude that at least the fragmentation criterion is not sufficient condition for fragmentation in realistic disk around low mass star. A significant difference between our disk and disks used in the previous works with local cooling law is the most unstable wave-length of GI. The disks used in previous studies using local cooling law \citep[e.g.,][]{2003MNRAS.339.1025R,2012MNRAS.427.2022M} have very small value of the most unstable wave-length and the spiral arms formed in these simulations are not geometrically thick and have large azimuthal mode numbers $m$. It is expected that the efficiency of the readjustment promoted by such spiral arms is small compared to that promoted by global spiral arms which may form in realistic disk. Is the fragmentation criterion based on local cooling a necessary condition for disk fragmentation ? We think this is not true, either. Although the efficiency of the radiative cooling may affect the evolution of condensations formed by GI, cooling criterion is not necessary for the fragmentation of $Q \sim1$ disk. This can be understood from the previous works that employed the simplified equation of state. For example, \citet{2006ApJ...650..956V}, \citet{2010ApJ...718L..58I}, \citet{2011MNRAS.416..591T}, and \citet{2011MNRAS.413.2767M} employed barotropic equation of state and the gas evolves adiabatically when $\rho \gtrsim 10^{-13} \cm$ (the condensation exceeds this density at very early phase of its evolution). Even with such a stiff (or adiabatic) equation of state, fragmentation is observed. Therefore, we conclude that, in general, the fragmentation criterion based on disk cooling time ($Q \sim 1$ and $\Omega t_{\rm cool}\sim 1$) is not necessary nor sufficient conditions for fragmentation. One may think that our results appear very different from the previous results which show the disk fragmentation occurs when it satisfies the fragmentation criterion and does not occur when it does not satisfy the criterion \citep[e.g.,][]{2005MNRAS.364L..56R,2008A&A...480..879S,2009MNRAS.392..413S}. However, we emphasize that there is no contradiction. Logically speaking, there are four possible cases, \begin{enumerate} \item The disk satisfies ($Q \sim 1$ and $\Omega t_{\rm cool}\sim 1$) and the disk fragments, \item The disk does not satisfies ($Q \sim 1$ and $\Omega t_{\rm cool}\sim 1$) and the disk does not fragment, \item The disk satisfies ($Q \sim 1$ and $\Omega t_{\rm cool}\sim 1$) but the disk does not fragment, \item The disk does not satisfies ($Q \sim 1$ and $\Omega t_{\rm cool}\sim 1$) but the disk fragments. \end{enumerate} The previous works mentioned above show the cases of (i) and (ii). On the other hand, we point out there exist the cases of (iii) and (iv). Therefore, there is no contradiction. Note, however, that the finite number of examples of (i) and (ii) are not enough to prove the statement that ``ALL the disk fragments when it satisfies $Q \sim 1$ and $\Omega t_{\rm cool}\sim 1$" or ``ALL the fragmenting disk must satisfy $Q \sim 1$ and $\Omega t_{\rm cool}\sim 1$" because we cannot prove non-existence of the exceptions with finite number of the simulations. On the other hand, just one counter-example is enough to reject these statements. In this paper, we show there exists (iii) case and this is a counter-example for the statement, ``ALL the disk fragments when it satisfies $Q \sim 1$ and $\Omega t_{\rm cool}\sim 1$". Therefore, the fragmentation criterion is not sufficient condition. On the other hand, the previous works we mentioned above show that there exists (iv) case. This is a counter-example for the statement ``ALL the fragmenting disk must satisfy $Q \sim 1$ and $\Omega t_{\rm cool}\sim 1$". Therefore, the fragmentation criterion is not necessary condition. Have we emphasize that the discussions above is based on the azimuthally averaged quantities (see \S \ref{diff_frag}). \begin{figure*} \includegraphics[width=50mm,angle=-90]{f4_1.eps} \includegraphics[width=50mm,angle=-90]{f4_2.eps} \includegraphics[width=50mm,angle=-90]{f4_3.eps} \includegraphics[width=50mm,angle=-90]{f4_4.eps} \includegraphics[width=50mm,angle=-90]{f4_5.eps} \includegraphics[width=50mm,angle=-90]{f4_6.eps} \caption{ Azimuthally averaged radial profiles of the disk of Model 1. Thin solid, dashed, dotted, and dashed-dotted lines correspond to profiles at the same epoch as in Fig.~\ref{faceon_sigma}{\it f}, {\it g}, {\it h}, and {\it i}, respectively. Top, middle, and bottom left panels show the angular velocity, Toomre's $Q$ value, and gas temperature, respectively. Top, middle, and bottom right panels show the surface density, $\alpha$ parameter, and vertical optical depth, respectively. Thick solid lines show power law profiles estimated from (\ref{sec2_dynamics}), (\ref{sec2_qvalue}), $T \propto r^{-1.1}$, and $\Omega \propto r^{-1.1}$. Thick dashed lines show power law profiles estimated from (\ref{sec2_dynamics}), (\ref{sec2_qvalue}), (\ref{sec2_cooling2}), and $\Omega \propto r^{-1.1}$. Thick dotted lines shows power law of Kepler rotation $\Omega\propto r^{-3/2}$. Thick dashed-dotted lines are fittings used for theoretical estimates. } \label{radial_profile} \end{figure*} \subsubsection{Resolution consideration for disk fragmentation simulations} \label{sec5_res} \subsubsection*{Resolution consideration of the simulations performed in this paper} Numerical resolution is considered to be an important factor in simulations of disk fragmentation. Recently, \citet{2012MNRAS.427.2022M} argued that the condition for disk fragmentation using local cooling law strongly depends on numerical resolution. Even though our simulation is based on a more realistic radiative transfer method and the disk structure is completely different from theirs, it is important to check whether the numerical resolution in our simulation was sufficient. As \citet{1997MNRAS.288.1060B} discussed, the SPH method cannot correctly simulate the fragmentation phenomenon if the minimum resolvable mass $M_{\rm min}=2 N_{n} m_{p}$ is greater than the Jeans mass $M_{\rm Jeans}$, where $N_{n}$ and $m_{p}$ are the number of neighbors and mass of the SPH particles, respectively. Here, according to \citet{1997MNRAS.288.1060B}, the Jeans mass is given by \begin{equation} \label{eq_Jeans_mass} M_{\rm Jeans} = \left( \frac{5 R_g T}{2 G \mu} \right)^{3/2} \left(\frac{4 \pi}{3} \rho \right)^{-1/2}, \end{equation} where $R_g$ is the gas constant. On the other hand, \citet{2006MNRAS.373.1039N} suggested that Toomre mass, \begin{equation} \label{eq_Jeans_mass} M_{\rm Toomre} = \frac{\pi c_s^4}{G^2 \Sigma}, \end{equation} is more appropriate mass scale for fragmentation in disk and it should be resolved with $6 N_n$. Furthermore he also suggested that the disk vertical scale height should be resolved at least $4 h_{\rm sml}$, where $h_{\rm sml}$ is the smoothing length. In Fig. \ref{resolution1}, we plotted azimuthally averaged Jeans mass (top left), $M_{\rm Jeans}/m_{p}$ (top right), $M_{\rm Toomre}/m_{p}$ (bottom left) and $ H/h_{\rm sml} $ (bottom right) for the same epochs as in Fig.~\ref{faceon_sigma}{\it f} (solid), {\it g} (dashed), {\it h} (dotted), and {\it i} (dashed-dotted). The Jeans mass of our disk is about $4 \times 10^{-3}~M_\odot$ over almost the entire region of the disk; this value is consistent with the initial clump mass that formed in model 2. As shown in top right panel, the Jeans mass is resolved by larger than $\sim 2000$ particles. In our simulations, we adopted the number of neighbors to be $N_{n}\sim 50$; hence, the mass resolution is about 20 times higher than that required by \citet{1997MNRAS.288.1060B}. The Toomre mass is resolved by larger than $\sim 10000$ particles and this is about 30 times higher than the resolution criterion suggested by \citet{2006MNRAS.373.1039N}. The bottom right panel shows that the vertical scale height $H$ is resolved by larger than $4 h_{\rm sml}$ and our simulation also satisfies the resolution requirement for vertical scale height. Therefore, we conclude that the numerical resolution in our simulation was sufficient to resolve fragmentation in the disk. \subsubsection*{Resolution consideration of the simulations with local cooling law} Why does the disk fragmentation criterion with local cooling law strongly depend on numerical resolution ? To answer this question, we investigate the resolution requirement of the disk used in \citet{2005MNRAS.364L..56R} and \citet{2012MNRAS.427.2022M} with the quasi-steady state structure. In \S 2, we investigated the steady state of the self-gravitating disk with local cooling law. As we pointed out, the temperatures of the disks used in \citet{2005MNRAS.364L..56R,2012MNRAS.427.2022M} are very small in the quasi-steady state. Therefore, we can expect that the requirement on numerical resolution for their disks which settled into quasi-steady states is very severe. In this subsection, we only consider the resolution requirement suggested by \citet{1997MNRAS.288.1060B}. In Fig. \ref{resolution2}, we show the Jeans mass (top) and the required particle number to resolve the Jeans mass, $N_{\rm req}=2 N_{n} M_{\rm disk}/M_{\rm Jeans}$ (bottom) as functions of the radius for a disk that has dimensionless parameters of $M_{\rm star}=1,~M_{\rm disk}=0.1,~r_{\rm in}=0.25,~r_{\rm out}=25$ and is in the quasi-steady state $\Sigma \propto r^{-\frac{3}{2}},~T \propto r^{0}, \alpha\propto r^{0}$. Here according to \citet{2012MNRAS.420.1640R}, we approximated $M_{\rm Jeans}=\pi \Sigma H^2$ for comparison and we assumed $N_{n}=50$. The Jeans mass is $M_{\rm Jeans} \lesssim 10^{-5} $. This corresponds to about 0.01 $M_{\rm Jupiter}$ if we regard the central star mass as $1 ~M_{\odot}$. This value of the Jeans mass is very small compared to that in our simulation and to the mass of wide orbit planets ($\sim 10~M_{\rm Jupiter}$). The bottom panel in Fig. \ref{resolution2} shows that a particle number of $N_{p} \gtrsim 10^7$ is required to resolve the Jeans mass. Note that, with $N_{p}<500,000$, the Jeans mass is not resolved over the entire disk region. \citet{2012MNRAS.427.2022M} showed that the convergence of the calculation around $N_{p} \gtrsim10^7$, and their results are consistent with our estimate. Our estimate is more severe than that of \citet{2012MNRAS.420.1640R} in the outer disk region. The difference is because \citet{2012MNRAS.420.1640R} assumed $\Sigma \propto r^{-1}$ instead of assuming the steady state as in (\ref{sec2_dynamics}). Therefore, they derived $T\propto r^{1/2}$ and found a larger $M_{\rm Jeans}$ in the outer disk region. Note, however, that such a disk is not realized with local cooling law because the surface density profile also changes because of the angular momentum transfer to realize the quasi-steady state structure \citep[see Fig. 1 of][]{2011MNRAS.416.1971B}. Note also that the resolution requirement is estimated using the initial total disk mass and initial cutoff radii, $r_{\rm in}$ and $r_{\rm out}$. As the disk evolves, gas accretes onto the central star, and the disk radius increases. As a result, the surface density decreases, and the gas cools further to maintain $Q \sim 1$. In a disk with $Q=1$, the Jeans mass is proportional to \begin{equation} M_{\rm Jeans} \propto \Sigma^3 \Omega^{-4}. \end{equation} Therefore, as the surface density decreases, $M_{\rm Jeans}$ also decreases as $M_{\rm Jeans}\propto \Sigma^{3}$ and the resolution requirement becomes more severe as the disk evolves. We can ignore the change in $\Omega$ due to mass evolution of the central star because $M_{\rm star} \gg M_{\rm disk}$. In an isolated disk with the local cooling law and without a temperature floor, the disk cools infinitely to maintain $Q=1$, and the Jeans mass becomes infinitely small as the disk evolves (or as the surface density decreases). We must carefully monitor the Jeans mass during the simulations. On the other hand, in a realistic system, there exists an appropriate range of temperature or of the Jeans mass, depending on the system of interest. We emphasize that the nature of the gravitational instability depends not only on the value of $Q$ but also on the most unstable wave-length of GI, $\lambda_Q=\frac{2 c_s^2}{G \Sigma}$ ($\sim \lambda_{\rm Jeans}^2/H$), and different length scales give strikingly different outcomes for the nonlinear growth phase. For example, the widths of spiral arms and masses of fragments differ for different length scales \citep[compare the spiral pattern in Fig. \ref{faceon_sigma} with Fig. 1 in ][]{2005MNRAS.364L..56R}. We suggest that future self-gravitating disk simulations should use a disk model that has a realistic Jeans length. For example, the irradiated disk model \citep[e.g.,][]{2008ApJ...673.1138C} or a locally isothermal model seems to be more suitable for numerical simulations because we can limit the value of the most unstable wave-length to a realistic range. To construct appropriate initial conditions, the profiles derived in \S 2 would be useful. \subsubsection{Minimum central entropy of clumps} \label{minimum_entropy} An important finding in \S \ref{sec4_clump} is that the evolutionary paths of the central temperatures of clumps on the $\rho-T$ plane are close to that of the first-core even though the clumps form in the disk. This implies that the clump evolution after the fragmentation can be approximately regarded as spherically-symmetric. Therefore, in the same manner as in the case of the first-core, we can describe the evolution of the central entropy of the clump. Following \citet{1999ApJ...510..822M} and \citet{2005ApJ...626..627O}, the minimum entropy is calculated as follows. We assume the quasi-adiabatic evolution begins when the clump becomes opaque. If we assume the clump radius is the Jeans length $\lambda_{\rm Jeans}=\sqrt{\pi c_s^2/(G \rho)}$, the clump becomes opaque when \begin{equation} \label{omukai2} \tau_J=\kappa \rho \lambda_{\rm Jeans} \sim1, \end{equation} is satisfied. Because we are interested in the minimum central entropy, we neglect heating by the irradiation. In such a case, the clump evolves according to the energy balance between optically thin radiative cooling and compressional heating until it becomes opaque. The energy balance can be written as \begin{equation} \label{omukai1} \kappa \sigma T^4=\frac{c_s^2}{t_{ff}}, \end{equation} where $t_{ff}=\sqrt{3 \pi/(32 G \rho)}$ is the free-fall timescale. We assume the opacity is given as \begin{equation} \label{opacity} \kappa = \kappa_0 \left(\frac{T}{10 {\rm K}} \right)^2 ~ {\rm cm^2 ~g^{-1}}. \end{equation} Using equations (\ref{omukai2}), (\ref{omukai1}), and (\ref{opacity}), the density and temperature where the adiabatic evolution begins, $\rho_{\rm ad}$ and $T_{\rm ad}$ are given as \begin{eqnarray} \rho_{\rm ad} &=& 7.6 \times 10^{-14} \left(\frac{\kappa_0}{0.01~ {\rm cm^2 ~g^{-1}}}\right)^{-2/3} \cm, \\ T_{\rm ad} &=& 15 \left( \frac{\kappa_0}{0.01~ {\rm cm^2 ~g^{-1}}} \right)^{-4/15} {\rm K}. \end{eqnarray} The minimum value of entropy at the center of the clump is given by these values. Note that the minimum entropy does not depend on $\kappa_0$ when the ratio of heat capacities $\gamma$ is equal to $7/5$ because $ T_{\rm ad}/\rho_{\rm ad}^{\gamma-1} \propto \kappa_0^{3/2(\gamma - 7/5)}$ \citep{2005ApJ...626..627O}. Therefore, the evolution of the central region of the clump follows the same track in the $\rho-T$ plane irrespective of different $\kappa$. The property is the same as in the evolution of the protostars with various metallicities shown by \citet{2005ApJ...626..627O}. \subsubsection{Minimum initial mass of the clump} \label{minimum_entropy2} {\rm Based on the discussions in \S \ref{minimum_entropy}}, we can evaluate the minimum initial mass of a clump by assuming that the clump can be described by a polytropic sphere \citep[as we have shown in ][ the clump can be well described with polytropic sphere with $n\sim 3- 4$]{2013MNRAS.436.1667T}. the mass of the clump with polytropic index $n$ is calculated by \begin{equation} \begin{split} \label{critical_mass} M_{\rm min}=&(n+1)^{3/2} \left[ \frac{k_{\rm B}^3}{4\pi G \mu^3m_{\rm H}^3}\frac{T_c^3}{\rho_c}\right]^{\frac{1}{2}} \left[- \xi^2 \frac{d \theta}{d \xi} \right]_{\xi=\xi_n} \\ =&\left\{\ \begin{array}{c} 5.4 \times 10^{-3} ~(n=4) \\ 4.3 \times 10^{-3} ~(n=3) \end{array} \right\} \\ & \times \left(\frac{T_c}{15 {\rm K}}\right)^{\frac{1}{4}}\left(\frac{\rho_{{\rm ad}}}{7.6 \times 10^{-14} \cm}\right)^{-\frac{1}{2}}\left(\frac{T_{{\rm ad}}}{15 {\rm K}}\right)^{\frac{5}{4}} M_{\odot}, \end{split} \end{equation} where $T_c$, $k_{\rm B}$, and $\mu$ are the central temperature, Boltzmann constant, and mean molecular weight, respectively. In the estimate, the heat capacity at constant volume $c_v$ and the ratio of heat capacities, $\gamma$ ($=7/5$) are assumed to be constant for simplicity. {\rm The estimated initial mass is a few Jupiter mass}, which is consistent with the initial mass of the clumps formed in our simulation (see, Fig. \ref{time_mass_clump}). \subsubsection{Comparison with previous work} There are few studies about the evolution of the clumps with realistic accretion onto them and sufficient numerical resolution to resolve the central structure of clump \citep{2009MNRAS.400.1563S,2013MNRAS.436.1667T}. In this subsection, we compare our results with those in \citet{2009MNRAS.400.1563S}. \citet{2009MNRAS.400.1563S} investigated the evolution of the clumps with three-dimensional simulation starting from a massive isolated disk. In the disk, fragmentation immediately occurs and the clumps form. They show that the clump undergoes the second collapse when its mass reaches $\sim 10 M_{\rm Jupiter}$ and the timescale for the second collapse is several thousand years. They also points out that thermal evolution of the clump is consistent with the evolution of first-core \citep{2000ApJ...531..350M}. The evolution process of the clumps formed in our simulation is consistent with that found in their simulations. However, there are interesting differences between their results and ours. In their simulations, most of the clumps remained in the disk without falling onto the central protostar. On the other hand, in our simulation, a large fraction of clumps fell onto the central star and disappeared. This difference may come from the fact that the initial disk of \citet{2009MNRAS.400.1563S} is very massive ($0.7 M_\odot$) and unstable ($Q\sim0.9$). In such a massive disk, fragmentation immediately occurs and many clumps simultaneously form. Thus, many clumps reside in the disk at the same epoch and interact each other. On the other hand, in our simulation, only two or three clumps simultaneously exist in the disk at the same epoch because the disk is not so massive. The difference in the orbital evolution of the clump may come from the difference of the disk. Orbital evolutions of clumps depend more strongly on the condition of disk and further studies are needed on this issue. \subsubsection{Possible evolutionary path to realize the small mass clump} Our simulation results have shown that the central entropy of a clump cannot become significantly smaller than that of the first core. However, there is a possible path that can lead to a clump with an central entropy smaller than that of the first core. The above discussion relies on the clump evolution {\it after} disk fragmentation. Thus, the value of $Q$ in the disk has already become $Q\sim 1$. Once gravitational instabilities turns on, the surface density decreases by mass and angular momentum transfer by the spiral arms, or disk fragmentation occurs. As shown in \S \ref{sec4_clump}, the rapid evolution of the clump after fragmentation prevents temperature evolution which leads to smaller central entropy than that of the first core. However, when $Q$ is greater than unity, the disk surface density can monotonically increase by in-fall from the envelope without mass and angular momentum re-distribution or fragmentation by GI in the disk. The maximum mid-plane density of a gravitationally stable Keplerian disk ($Q\gtrsim1$) can be calculated from the condition $Q=1$ as \begin{equation} \rho_{\rm max}=\frac{c_s \Omega }{\pi G H } = 1.88 \times 10^{-10} \left( \frac{M_{\rm star}}{M_\odot} \right) \left( \frac{r}{10 {\rm AU}} \right)^{-3} \cm, \end{equation} where, $M_{\rm star}$ is the mass of the central star. The maximum mid-plane density is solely determined by the angular velocity. This indicates that a high mid-plane density can be achieved in the inner region of the disk. If the disk with such a high mid-plane density at the inner region and low temperature somehow fragments, a clump with small central entropy could can be created. For example, if a disk with a temperature of 50 K at 10 AU around $1 M_{\odot}$ fragments, adiabatic contraction of the clump begins from $\rho \sim 10^{-10} \cm$ and $~T=50 $ K. In such a case, the initial mass of clump is $\sim 0.7~ M_{\rm Jupiter}$. However, the realization of such a disk seems to require the inclusion of magnetic field \citep{2010ApJ...718L..58I,2011ApJ...729...42M}, which is beyond the scope of this paper. | 14 | 4 | 1404.7271 |
1404 | 1404.5042_arXiv.txt | We present new analytic theory and radiative transfer computations for the atomic to molecular (H{\small I}-to-H$_2$) transitions, and the build-up of atomic-hydrogen (H{\small I}) gas columns, in optically thick interstellar clouds, irradiated by far-ultraviolet photodissociating radiation fields. We derive analytic expressions for the total H{\small I} column densities for (one-dimensional (1D)) planar slabs, for beamed or isotropic radiation fields, from the weak- to strong-field limits, for gradual or sharp atomic to molecular transitions, and for arbitrary metallicity. Our expressions may be used to evaluate the H{\small I} column densities as functions of the radiation field intensity and the H$_2$-dust-limited dissociation flux, the hydrogen gas density, and the metallicity-dependent H$_2$ formation rate-coefficient and far-UV dust-grain absorption cross-section. We make the distinction between ``H{\small I}-dust" and ``H$_2$-dust" opacity, and we present computations for the ``universal H$_2$-dust-limited effective dissociation bandwidth". We validate our analytic formulae with {\it Meudon PDR code} computations for the H{\small I}-to-H$_2$ density profiles, and total H{\small I} column densities. We show that our general 1D formulae predict H{\small I} columns and H$_2$ mass fractions that are essentially identical to those found in more complicated (and approximate) spherical (shell/core) models. We apply our theory to compute H$_2$ mass fractions and star-formation thresholds for individual clouds in self-regulated galaxy disks, for a wide range of metallicities. Our formulae for the H{\small I} columns and H$_2$ mass fractions may be incorporated into hydrodynamics simulations for galaxy evolution. | The atomic to molecular hydrogen (H{\small I}-to-H$_2$) transition is of central importance for the evolution of the interstellar medium (ISM) and for star-formation in galaxies, from local environments in the Milky Way to distant cold gas reservoirs in high-redshift systems. Stars form in molecular gas, plausibly because H$_2$ formation enhances low-temperature cooling and cloud fragmentation, or perhaps simply because the molecular formation rates are elevated in the denser and more shielded components of the gravitationally collapsing regions. The atomic to molecular conversion is also the critical initiating step for the growth of chemical complexity in the ISM from large to small scales, e.g.~from diffuse clouds to dense star-forming cores to protoplanetary disks. Globally, the transition to H$_2$ appears to be associated with star-formation thresholds in galaxy-wide Kennicutt-Schmidt relations, and with the observed critical gas mass surface densities above which star-formation becomes probable. In this paper, we revisit the theory of the H{\small I}-to-H$_2$ transition and the build-up of atomic hydrogen gas layers in fully optically thick interstellar clouds irradiated by far-ultraviolet (FUV) radiation fields. Atomic (H{\small I}) gas produced by rapid stellar far-ultraviolet ``Lyman-Werner" (LW) photodissociation undergoes conversion to H$_2$ as the destructive radiation is absorbed. In steady-state, a mass of H{\small I} is maintained in the outer FUV irradiated photon-dominated regions (PDRs) of the dense molecular clouds. Much of the (cold) H{\small I} gas in galaxies may reside in such cloud boundary layers and envelopes, interspersed with the recently formed FUV-emitting OB-type stars. The study of interstellar H{\small I}-to-H$_2$ conversion has had a long and venerable history. Early theoretical discussions (e.g., \citealt{Spitzer_48, Gould_63, Field_66,Stecher_67,deJong_72}; followed by \citealt{Aaronson_74,Glassgold_74,Jura_74,Black_77,Federman_79,vanDishoeck_1986}) focussed on the competing processes of (grain-surface) molecule formation, photodissociation, and shielding, in predominantly atomic gas - the classical warm and cold neutral medium (WNM and CNM) and diffuse gas - showing that significant concentrations of H$_2$ could be expected in the Galactic ISM, especially in dusty dark clouds with high visual extinctions \citep{Meszaros_68,Hollenbach_71,Solomon_71,deJong_72}. This was confirmed observationally with the first direct (far-UV LW absorption line) detections of interstellar molecular hydrogen in diffuse clouds and the correlation of the H$_2$ with $E(B-V)$ color excess and dust extinction \citep{Carruthers_70,Spitzer_73,Savage_77}, and with the discovery of fully molecular clouds via proxy millimeter-wave carbon monoxide (CO) emissions \citep{Wilson_70,Rank_71}. Absorption line spectroscopy (Ly$\alpha$ for H{\small I}, and LW-band for H$_2$) has been carried out for H{\small I}-to-H$_2$ along many Milky Way sight-lines, through low-extinction diffuse-to-translucent gas in the disk, and into the infrared cirrus and high-velocity gas in vertical directions \citep{Savage_77,Bohlin_78,Richter_01,Liszt_02,Rachford_02,Rachford_09,Gillmon_06a,Gillmon_06b, Wakker_06,Liszt_07,France_13, Fukui_14, Rohser_14}. These studies probe systems in which the H$_2$ mass fractions range over many orders of magnitude, from $\lesssim 10^{-5}$ up to $\sim 50\%$ in highly reddened systems. Absorption line observations of damped- and sub-damped Ly$\alpha$ absorbers (DLAs) at high redshifts also directly reveal the partial conversion of H{\small I} to H$_2$ in optically thin media \citep{Levshakov_85,Foltz_88,Ge_97,Cui_05,Ledoux_06,Noterdaeme_10,Crighton_13, Albornoz_14}. In the early Universe, the formation of the first stars (Population III) was enabled by the partial conversion to H$_2$ via negative ion chemistry. The resulting H$_2$ rotational-line gas cooling rates were likely regulated by LW-photodissociation ``feedback" from the first stars and FUV sources \citep{Palla_83, Lepp_1984, Haiman_96, Haiman_97, Abel_97, Ciardi_00, Glover_03, Yoshida_03, Wise_07, Dijkstra_08, Ahn_09, Bromm_09, Miyake_10, Wolcott_11, Fialkov_12, Holzbauer_12, Safranek_12, Visbal_14}. In optically thick regions, 21~cm observations of very cold ($\lesssim 20$~K) narrow-line self-absorbed H{\small I} (the Galactic ``HINSA"; \citealt{Li_03}) in combination with CO, OH, and dust mapping for locating the H$_2$ clouds, reveal the presence of trace atomic hydrogen inside dark dusty and predominantly molecular clouds \citep{Bok_55,Heiles_69,Knapp_74,Burton_78,McCutcheon_78,Liszt_79,Mebold_82,vanderwerf_88,Li_03,Goldsmith_05,Krco_10}. Such clouds are fully shielded against externally incident photodissociating FUV radiation, and the conversion to H$_2$ is essentially complete. The residual atomic gas in the cloud cores is likely the product of impact-ionization by penetrating low-energy cosmic rays \citep{Spitzer_68, Webber_98, Dalgarno_06}. Somewhat warmer H{\small I} ($\sim 100$~K, so still ``cold") is also observed in dissociation zones surrounding Galactic H{\small II} regions associated with individual OB-type stars or clusters, and/or as H{\small I} PDRs in molecular cloud envelopes exposed to ambient interstellar radiation (e.g., \citealt{Sancisi_74,Myers_78,Read_81,Roger_81,Wannier_83,Elmegreen_87,vanderwerf_89,Wannier_91,Andersson_92,Gir_94,Reach_94,Williams_96,Gomez_98,Habart_03,Matthews_03,Roger_04,Lee_07}; Lee et al. 2012; \citealt{vanderwerf_13}). In nearby galaxies, H{\small I} has been mapped in spiral arms showing that the atomic gas likely traces outer photodissociated layers in the star-forming giant molecular clouds \citep{Allen_86,Shaya_87,Rand_92,Madden_93,Allen_97,Smith_00,Heyer_04,Knapen_06,Schuster_07,Heiner_09,Heiner_11}. By the 1980's a conceptual switch had occurred with the recognition that much of the hydrogen in galaxies is fully shielded H$_2$, and that in dense gas in star-forming regions the H{\small I} is often a surface photodissociation ``product", rather than being the dominant component within which some shielded H$_2$ may be present, as in the diffuse medium. Over the decades many model computations for the H{\small I}-to-H$_2$ transition in optically thick media have been presented, with varying degrees of sophistication in treating the critical roles of FUV dust absorption and scattering, and H$_2$ absorption line self-shielding. These include one-dimensional (1D) plane-parallel (slab) models assuming steady-state conditions with simplified (``isolated line") treatments of H$_2$ self-shielding (\citealt{Federman_79,deJong_80,Tielens_1985,Viala_86,Black_87,Sternberg_1988,Sternberg_1989,Burton_90,Spaans_94,Sternberg_99,Kaufman_99}), models incorporating ``exact" radiative transfer for the combined effects of multiple H$_2$ absorption-line overlap and dust absorption/scattering (\citealt{vanDishoeck_88,vanDishoeck_90,Viala_88,Abgrall_92,Draine_1996,Browning_03,Shaw_05,Goicoechea_2007,LePetit_2006}), spherically symmetric models (\citealt{Andersson_93,Diaz_98,Neufeld_96,Stoerzer_1996,SpaansNeufeld_97,Spaans_97,Krumholz_2008,Krumholz_2009,McKee_2010,Wolfire_10}), and also time-dependent models for the H$_2$ formation and destruction (\citealt{London_78,Roger_92,Goldshmidt_95,Hollenbach_95,Lee_96,Goldsmith_07}). More recently, sophisticated multidimensional (2D and 3D) radiative transfer codes have been developed for the atomic to molecular conversion, also incorporating hydrodynamics % (\citealt{Robertson_08,Gnedin_09,Glover_10,Bisbas_12,Christensen_12,MacLow_12,Dave_13,Offner_13,Thompson_14}), although the H$_2$ photodissociation rates and the implied H{\small I}/H$_2$ density ratios are generally still estimated using 1D shielding prescriptions for the individual hydrodynamic particles or cells. In recent years interstellar H{\small I}-to-H$_2$ conversion has become an important issue in the study of galaxy evolution on large scales, across entire galaxy disks, at both low- and high-redshifts, and for varying metallicities (e.g.,~\citealt{Wong_02,Boker_03,Blitz_04,Blitz_06,Bigiel_08,Leroy_08,Tacconi_10,Bolatto_11,Schruba_11,Welty_12,Genzel_12, Genzel_13, Tacconi_13}). Galaxy mapping surveys suggest that on global scales the star-formation efficiencies are determined, at least in part, by molecular gas fractions that may be sensitive to the varying mid-plane gas pressures and/or metallicities (e.g.,~\citealt{Hirashita_05,Fumagalli_10,Fu_10,Lagos_11,Feldmann_12, Kuhlen_13, Popping_13}). Remarkably, the observations of disk galaxies on large scales (e.g.,~\citealt{Leroy_08}), and individual Galactic molecular clouds on small scales (e.g.,~\citealt{Lee_12, Lee_14}), indicate that for solar metallicity the H{\small I}-to-H$_2$ conversion occurs for characteristic gas surface densities of $\sim 10$~M$_\odot$~pc$^{-2}$ (for ``ambient" FUV radiation fields). This surface density corresponds to an FUV dust optical depth $\sim 1$, for typical grain properties and dust-to-gas mass ratios, suggesting that dust absorption and hence metallicity is playing an essential role in setting the critical gas surface densities. An analytic theory for the H{\small I}-to-H$_2$ transition was presented by \cite{Sternberg_1988} (hereafter S88) % who derived a scaling-law for the growth of the H{\small I} column density and the associated FUV-excited infrared H$_2$ vibrational emission intensities produced in optically thick irradiated cloud surfaces, for application to Galactic emission-line sources (see also \citealt{Jura_74,Hill_78}, and \citealt{Elmegreen_93}). S88 included a general-purpose analytic formula for the total H{\small I} column density as a function of the FUV radiation intensity, the cloud gas density, and the metallicity-dependent H$_2$ formation rate coefficient and FUV dust attenuation cross section. S88 also identified the fundamental dimensionless parameter that controls the H{\small I}-to-H$_2$ transitions and the build-up of the atomic hydrogen columns. More recently, and motivated by the possible metallicity-dependence of molecular mass fractions in galaxy disks, \citealp{Krumholz_2008,Krumholz_2009} % and \cite{McKee_2010} (hereafter KMT/MK10) presented new models for the H{\small I}-to-H$_2$ transition, and for the associated metallicity dependent H$_2$ mass fractions and star-formation surface density thresholds. A novel feature of the KMT/MK10 study is their analytic focus on (idealized) spherical clouds embedded in ambient isotropic fields, as opposed to the (also idealized) planar geometry and beamed fields adopted in much of the earlier PDR literature, including S88. Our main goal and motivation in this paper is to reintroduce and extend the S88 theory, for applications to global galaxy evolution studies. In \S2 we elaborate on S88 and present a detailed overview and discussion of the basic theoretical ingredients and parameters controlling the H{\small I}-to-H$_2$ transition in FUV irradiated clouds. We rederive the fundamental S88 equation for the total H{\small I} column density produced for beamed radiation into a (one-dimensional) optically thick slab. We then extend the theory and consider irradiation by isotropic fields. This will enable our direct comparison to the more complicated (and more approximate) formalism for spheres. In \S 3 we present detailed numerical ({\it Meudon PDR-code}) radiative transfer computations for the H{\small I}-to-H$_2$ transitions and integrated H{\small I} columns for a wide range of interstellar conditions. The ratio of the free space FUV field intensity (or dissociation rate) to the gas density (or H$_2$ formation rate) is an essential parameter, as is the metallicity and dust-to-gas mass ratio. We present numerical computations for a verification of our analytic formulae for beamed and isotropic irradiation from the weak- to strong-field limits (gradual to sharp H{\small I}-to-H$_2$ transitions) and for low- to high-metallicity gas. In \S 4 we compare our planar formulae to the KMT/MK10 theory for spheres. This includes a discussion of the dimensionless parameters, a comparison of the expressions for the total H{\small I} columns, H$_2$ mass fractions, and star-formation thresholds, as functions of the metallicity. An important application and comparison is for ``self-regulated gas" in which the FUV-intensity to gas density ratio is set by the condition of two-phased equilibrium for the H{\small I}. We demonstrate that our simpler, more general, and fully analytic 1D formulae, predict H{\small I} columns and H$_2$ mass fractions that are essentially identical to results for spheres in the more restricted regime in which the spherical models are applicable (intense fields, sharp transitions, low-metallicity). This is a lengthy paper, and we develop the theory and present our comparisons, step-by-step, in a pedagogical style. In \S 5 we summarize and recap our basic analytic results for the H{\small I} column densities and molecular mass fractions in FUV irradiated clouds, including for self-regulated star-forming galaxies. A glossary of symbols is in the Appendix. | 14 | 4 | 1404.5042 |
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1404 | 1404.5618_arXiv.txt | We perform an \ap~test using stacked cosmic voids identified in the SDSS Data Release 7 main sample and Data Release 10 LOWZ and CMASS samples. We find $\sim$1,500 voids out to redshift $0.6$ using a heavily modified and extended version of the watershed algorithm {\tt ZOBOV}, which we call {\tt VIDE} (Void IDentification and Examination). To assess the impact of peculiar velocities we use the mock void catalogs presented in Sutter et al. (2013). We find a constant uniform flattening of 14\% along the line of sight when peculiar velocities are included. This flattening appears universal for all void sizes at all redshifts and for all tracer densities. We also use these mocks to identify an optimal stacking strategy. After correcting for systematic effects we find that our \ap~measurement leads to a preference of our best-fit value of $\Omega_{\rm M}\sim 0.15$ over $\Omega_{\rm M} = 1.0$ by a likelihood ratio of 10. Likewise, we find a factor of $4.5$ preference of the likelihood ratio for a \lcdm~$\Omega_{\rm M} = 0.3$ model and a null measurement. Taken together, we find substantial evidence for the \ap~signal in our sample of cosmic voids. Our assessment using realistic mocks suggests that measurements with future SDSS releases and other surveys will provide tighter cosmological parameter constraints. The void-finding algorithm and catalogs used in this work will be made publicly available at http://www.cosmicvoids.net. | Alternative cosmological probes offer complementary and orthogonal avenues for answering pressing questions such as the nature of dark energy and the growth of large-scale structure (for a recent review of traditional and alternative probes, see~\citealt{Weinberg2013}). One such alternative probe is the \ap~(AP) test~\citep{Alcock1979}, which instead of using standard candles such as Type Ia supernovae~\citep[e.g.,][]{AlderingGreg2002} or standard rulers such as baryon acoustic oscillations (BAO;~\citealt{Anderson2012}) relies on standard \emph{spheres} for a geometrical test of cosmological parameters. The principal concept underlying the AP test is simple: in a properly chosen cosmology, spheres will maintain a uniform ratio of line-of-sight to angular extent. Deviations from sphericity as a function of redshift thus reveal the true cosmology. Since the AP test relies only on statistical isotropy, it has been considered for --- and applied to --- a variety of systems and features, such as the Lyman-$\alpha$ forest~\citep{Hui1999, McDonald1999,EriksenK.A.2005}, the power spectrum of the epoch of reionization~\citep{Nusser2005}, galaxy cluster autocorrelation spectra~\citep{Kim2007a}, galaxy clustering in the WiggleZ survey~\citep{Blake2011}, galaxy pairs~\citep{Jennings2012}, and the BAO feature in the Sloan Digital Sky Survey~\citep{Reid2012}. Current successful applications of the AP test~\citep[e.g.,][]{Blake2011, Reid2012} are limited to large scales, fundamentally limiting their constraining power. A promising way to apply the AP test to smaller scales (thereby reducing statistical uncertainties) while still avoiding large systematics is to use cosmic voids~\citep{LavauxGuilhem2011}, the large underdense regions in the cosmic web~\citep{Thompson2011}. Voids offer potentially revolutionary potential:~in terms of statistical power \citet{LavauxGuilhem2011} predicted that the AP test applied with voids in the upcoming Euclid survey~\citep{Laureijs2011} will outperform BAO in constraining dark energy equation of state parameters by up to a factor of ten. The power of voids comes from two aspects. First, their small size compared to the BAO feature, down to $\sim$5~\hmpc~\citep{Sutter2012a}, gives them significant statistical weight. Second, since their evolution is in the linear or quasi-linear regime, systematic effects due to peculiar velocities will be highly suppressed and easy to model out. Even though the BAO feature is more linear than void features, voids are a collective phenomenon defined by many galaxies and so void profiles (and shapes) are a cross-correlation~\citep{Hamaus2013}, whereas the BAO relies on galaxy-galaxy auto-correlation. As we will see in this paper, the cross-correlation has potential to be less affected by peculiar velocities and other systematics than the auto-correlation. Put simply, voids are simple objects. For example,~\citet{Hamaus2014} discovered a single two-parameter density profile that describes voids of all sizes, and~\citet{Sutter2013a} applied this profile to reveal that voids in theory (e.g., in dark matter simulations) obey self-similar scaling relations to voids in observations (e.g., in galaxy surveys). Also, the merger tree analysis of~\citet{Sutter2014} found that voids essentially do not move and do not merge over their lifetimes; evolutionary dynamics do not overwhelm primordial cosmological information. Even though current galaxy redshift surveys are not optimized for finding large numbers of voids (due to their relative sparsity, low redshift, and complicated survey geometries), cosmological measurements with voids are still possible: for example, the largest publicly-available void catalog\footnote{http://www.cosmicvoids.net} ~\citep{Sutter2012a, Sutter2013c} has enabled observations such as the ISW effect~\citep{Planck2013b} and gravitational anti-lensing~\citep{Melchior2013}. Previously, we applied the AP test methodology described in~\citet{LavauxGuilhem2011} to voids found in the SDSS DR7 main sample and LRG catalogs~\citep{Sutter2012a}, but due to the small number of voids found no statistically significant result~\citep{Sutter2012b}. In this work we extend the void AP analysis to higher redshifts and to more voids using the BOSS Data Release 10 LOWZ and CMASS galaxy catalogs~\citep{Ahn2014}. We also use mock catalogs tuned to our observational surveys to examine the systematic impact of peculiar velocities noted in the pure $N$-body simulations of~\citet{LavauxGuilhem2011}. We use these mocks to find an optimal binning strategy to increase sensitivity to our potential signal and then use the resulting size bins on the data. In Section~\ref{sec:samples} we describe the galaxy samples and void catalogs to be used in the AP analysis. We discuss our method for measuring distortions in void shapes and the application to an AP test in Section~\ref{sec:method}. Section~\ref{sec:systematics} focuses on systematics due to peculiar velocities, while Section~\ref{sec:optimization} features an analysis of our strategy for optimizing the signal given the limited number of voids in our current void catalog. We present our AP results in Section~\ref{sec:results} and offer prospectives on future work in Section~\ref{sec:conclusions}. | \label{sec:conclusions} We have used $\sim$1,500 voids identified with the watershed transform code {\tt VIDE} in the SDSS DR7 main sample and BOSS DR10 LOWZ and CMASS samples to perform an \ap~test. We stacked voids to construct standard spheres and measured the ratio of their line-of-sight to angular extents, or \emph{stretch}. We used voids found in mock populations with realistic number densities and clustering properties to assess the impact of peculiar velocities and optimize the stacking to produce the most significant result. After correcting for systematic effects and measuring the void stretch from redshift $z=0.05$ to $0.6$ we translated our \ap~estimation into a constraint on $\Omega_{\rm M}$. We find a best fit value of $\Omega_{\rm M} ~\sim 0.15$, and our measurements prefer this value over $\Omega_{\rm M} = 1.0$ by a factor of 10. We find a likelihood ratio of 4.5 for our results to reject a null measurement. Taken together, we interpret these as a substantial detection of the \ap~test with our sample of cosmic voids. We have verified the uniform and constant systematic offset caused by peculiar velocities originally seen in the pure $N$-body simulations of~\citet{LavauxGuilhem2011} to also apply to realistic galaxy populations. This 14\% line-of-sight flattening appears universal for all void sizes studied (7-80~\hmpc), all redshifts studied ($z=0.0$-$1.2$), and all tracer densities studied ($3 \times 10^{-4}$ - $1.0$ particles per cubic~\hmpc). We observe this flattening regardless of the composition of the void stack, once a minimum threshold number of voids is met. Indeed, the AP measurement is quite binary: either no signal is obtained at all (if there are too few voids) or the measured signal has the expected uniform distortion. While we have some preliminary indication as to the source of this offset, we relegate a full analysis of the effects of peculiar velocities on voids found using {\tt VIDE} to a forthcoming paper. We used our mocks to find the minimum number of voids necessary in a stack to obtain a measurement and used these results to optimize our result in data. We did not perform an exhaustive search through the space of \emph{all} possible configurations (e.g., optimal number of redshift bins, volume-weighted samples, stacking configurations, etc.) which leaves open the possibility of a substantial improved measurement with current data. Our previous application of the AP test to cosmic voids~\citep{Sutter2012b} did not correct for systematic effects but did marginalize over potential bias values in the final likelihood analysis, which explains the very large uncertainty and preference for higher $\Omega_{\rm M}$ in that analysis. Based on dark matter simulations~\citet{LavauxGuilhem2011} predicted that in the full BOSS survey an AP analysis with voids would be competitive with BAO measurements from the same survey set. At this stage our Bayes factor of 4.5 presents substantial but not yet strong or decisive evidence for the AP effect in the current BOSS void sample. Several factors contribute to this difference. First, we do not yet have access to the full BOSS survey, which will include more galaxies within the same survey footprint, increasing the number density and hence accessing a much larger number of small voids. Second,~\citet{LavauxGuilhem2011} provided forecasts using a profile-based shape measurement technique. We found that this method results in far better ellipticity measurements but only when the number of voids in a stack exceeds a threshold of $\sim$100 for dense surveys and $\sim$300 for sparse surveys within relatively narrow radius bins --- otherwise the fit fails catastrophically with high probability. The redshift width of our volume-limited samples prevents us from forming stacks of the required number of voids. Finally, the earlier study used extrapolated abundances from voids found in the dark matter particle distribution rather than the more realistic simulations of voids found using dark matter halos or HOD galaxies as tracers~\citep[e.g,][]{Furlanetto2006, Jennings2013, Sutter2013a}. Our analysis of the AP test in void catalogs drawn from realistic mocks shows that the data quality is about to cross a threshold where the AP test based on stacked voids will yield competitive and complementary measurements to those based on BAO. All that is needed is more voids to enhance the signal-to-noise, add more independent stacks, and allow measurements at higher redshifts. The BOSS survey itself will provide more voids with upcoming data releases, and future spectroscopic surveys such as WFIRST~\citep{Spergel2013}, Euclid~\citep{Laureijs2011}, or the Square Kilometer Array~\citep{Jarvis2007} will dramatically increase the number of known voids from thousands to millions, allowing this analysis to move from detection of the effects to precision constraints and measurements of fundamental cosmological parameters. | 14 | 4 | 1404.5618 |
1404 | 1404.6530_arXiv.txt | We present optimal measurements of the angular power spectrum of the XDQSOz catalogue of photometric quasars from the Sloan Digital Sky Survey. These measurements rely on a quadratic maximum likelihood estimator that simultaneously measures the auto- and cross-power spectra of four redshift samples, and provides minimum-variance, unbiased estimates even at the largest angular scales. Since photometric quasars are known to be strongly affected by systematics such as spatially-varying depth and stellar contamination, we introduce a new framework of \textit{extended mode projection} to robustly mitigate the impact of systematics on the power spectrum measurements. This technique involves constructing template maps of potential systematics, decorrelating them on the sky, and projecting out modes which are significantly correlated with the data. Our method is able to simultaneously process several thousands of nonlinearly-correlated systematics, and mode projection is performed in a blind fashion. Using our final power spectrum measurements, we find a good agreement with theoretical predictions, and no evidence for further contamination by systematics. Extended mode projection not only obviates the need for aggressive sky and quality cuts, but also provides control over the level of systematics in the measurements, enabling the search for small signals of new physics while avoiding confirmation bias. | Quasars are bright, highly biased tracers of the large scale structure (LSS) of the universe, and are useful for testing cosmological models in large volumes and over extended redshift ranges. In particular, their bias can inform us about the abundance and mass of dark matter halos in which they form, opening new windows on galaxy formation and the astrophysics of active galactic nuclei (\eg \citealt{Fan:2005es}). In addition, they can be used to constrain primordial non-Gaussianity (PNG) which is predicted to enhance the bias of LSS tracers on large scales \citep{Dalal2008png, matarrese2008, 2009astro2010S158K, loverde2008}. However, these applications require accurate auto- and cross-correlation power spectrum measurements, which are complicated by the presence of significant systematics in the data, and the difficulty of creating large, deep quasar catalogues. Indeed, although quasar candidates are easily confirmed with spectroscopy, quasars are point sources, and most point sources in the sky are stars. Since acquiring high resolution spectra is a time- and resource-consuming process, the creation of large quasar catalogues is cumbersome and can only be realised by preselecting targets and scheduling them for spectroscopic follow-up. In optical frequencies, catalogues of photometric quasars were constructed from the Sloan Digital Sky Survey (SDSS, \citealt{Gunn2006}), and promising candidates were followed up using the SDSS spectrograph, yielding large catalogues of confirmed quasars such as the Baryon acoustic OScillations Survey (BOSS, \citealt{dawson2013boss}). While spectroscopic catalogues don't suffer from stellar contamination, photometric samples are larger and extend to fainter magnitudes, and can therefore yield more precise measurements of the clustering and the bias of quasars. However, photometric data are significantly contaminated by multiple sources of systematics, either intrinsic (\eg dust extinction), observational (\eg seeing, airmass), or instrumental (\eg instrument calibration), and star-quasar separation using only colour information is also nontrivial. These systematics affect the properties of the raw images in complex ways, propagate into the final quasar catalogues, and create spurious spatial correlations (spatially-varying star-quasar separation efficiency will induce a spurious clustering signal, see \eg \citealt{Huterer2012calibrationerrors}). Finally, some of these correlations may also be imprinted in spectroscopic catalogues, since the latter rely on targets selected from photometric quasars. Therefore, not just precise --- but also accurate --- cosmological inferences from quasar surveys require careful mitigation of systematics. The first studies of the clustering of quasars in optical frequencies used both spectroscopic (\eg \citealt{Outram20032dfqso, Shen2007specqso, Ross2009specqsodr5}) and photometric (\eg \citealt{Myers2006first}) catalogues from early SDSS data, and were used to constrain numerous cosmological and astrophysical quantities of interest, such as the quasar bias, PNG, and the quasar luminosity function \citep{Richards2006qlf, Serber2006, Myers2007one, Strandbrunner2008, SlosarHirata2008}. They exhibited power excesses on large and small scales \citep{Myers2007two}, which were even more significant in the DR6 photometric quasar catalogue \citep{Richards2008rqcat}. Although cuts to the data were not sufficient to remove this excess power, thus pointing to PNG \citep{Xia2009highzisw, Xia2011sdssqsocell, Giannantonio01112012, Karagiannis2013}, recent work has demonstrated that the excess power was due to systematics \citep{PullenHirata2012} and could be eliminated using mode projection \citep{Leistedt2013excessdr6}. Indeed, it is known that spatially-varying stellar contamination can combine with other systematics and generate such excess clustering power, mimicking significant levels of PNG \citep{Giannantonio2013png}. Alternatively, other studies have focused on using the cross-correlations of the photometric quasars with other data \citep{Giannantonio2013crosscmblss}, thus extracting some of the information they contain while avoiding the main systematics. The resulting PNG constraints were competitive with those obtained using normal galaxies (\eg \citealt{ross2012png}). The eighth data release of SDSS yielded a new catalogue of photometric quasars, XDQSO \citep{Bovy2010xdqso}, relying on the extreme deconvolution technique \citep{Bovy2011xd}; the latest spectroscopic data were used to provide an improved probabilistic selection of quasars, with greater control over completeness issues. XDQSO extends to fainter magnitudes, and was primarily used to select high redshift candidates scheduled for spectroscopic follow-up in the context of BOSS \citep{Ross2012dr9qsotarget}. Its extension, coined XDQSOz \citep{bovy2012xdqsoz}, provides estimates and probability density distributions for the photometric redshifts of the catalogued objects. XDQSOz was cross-correlated with the cosmic microwave background (CMB) lensing map from the Atacama Cosmology Telescope \citep{ACT2013} to constrain the quasar bias \citep{Sherwin2012qsolensing}. Constraints on PNG were also derived from clustering measurements \citep{agarwalho2013xdqsoz, hoagarwal2013xdqsoz}, but required significant cuts and corrections to exploit measured power spectra, and corrected for systematics using methodologies introduced in \cite{ross2011weights, ross2012systematics, ho2012cosmoweights, agarwalho2013sys}. Quasar clustering studies therefore remain suboptimal and limited due to cuts and corrections needed to address the high levels of spurious correlations created by systematics. Nevertheless, most of the potential systematics are actually known and can be mapped onto the sky. It is their complex impact on the data which is not known, and prevents the modelling of spurious correlations when estimating power spectra. Mode projection, however, can mitigate the impact of systematics in a robust manner, while minimising the need to throw out hard-won data through masking and cuts \citep{Tegmark:1997yq, THS1998future, SlosarSeljak2004modeproj, PullenHirata2012, Leistedt2013excessdr6}. The purpose of this work is to extend the standard mode projection approach by designing a generic methodology to mitigate the impact of large numbers of known systematics in a flexible and robust manner. We apply this technique to the XDQSOz catalogue in order to precisely control the level of the contamination and accurately measure the power spectrum on the largest scales, which is essential for constraining PNG. Next generation photometric surveys, such as the Dark Energy Survey\footnote{\url{www.darkenergysurvey.org}} (DES), will reach unprecedented precision and will require careful treatment of systematics. This {\it extended mode projection} approach will enable the full potential of such surveys to be exploited in the search for new physics. This article is organised as follows. In Sec. 2 we recall the definitions and properties of quadratic power spectrum estimators, and introduce the extended mode projection technique to mitigate systematics when estimating power spectra. In Sec. 3 we turn to the XDQSOz catalogue of photometric quasars. We present our data samples, theory predictions and power spectrum measurements, and discuss the ability of the extended mode projection, in combination with blind analysis techniques, to mitigate systematics. The discussion and conclusions are presented in Sec. 4. | Photometric quasar surveys are deep and span extended redshift ranges, which allows us to probe the largest scales of the universe, and therefore test physics which is not well constrained by galaxy surveys. In particular, they can be used to constrain PNG, which is expected to enhance quasar clustering on large scales and leave a characteristic scale-dependent signature in the quasar bias. However, this requires accurate power spectrum measurements, which are compromised by the presence of numerous observational systematics, creating spurious correlations which can mimic the signatures of new physics. We have introduced the {\it extended mode projection} technique to robustly mitigate the impact of large numbers of systematics when estimating angular power spectra, and applied it to the photometric quasars from the SDSS XDQSOz catalogue. This technique only relies on the ability to map known and potential sources of systematics on the sky, and cross-correlate them with the data of interest. Previous studies of XDQSOz data required stringent quality and sky cuts, and even the removal of band-powers in order to avoid excessive contamination by systematics. In our analysis, we have used minimal sky cuts, and applied the extended mode projection approach using a large number of systematics templates. Mode projection is equivalent to a Bayesian marginalisation over the amplitudes of the modes of the contamination model when estimating the power spectra. The base set of templates included $220$ potential systematics found in the SDSS database, and we have also included products of pairs of templates, leading to a total of $\sim 22,000$ systematics templates, yielding a non-linear model for the contamination signal. We have then decorrelated the systematics, and cross-correlated the resulting $\sim 3,700$ orthogonal modes with the quasar samples to carry out null tests and detect the modes which most likely create spurious correlations in the data. We have finally estimated clean quasar power spectra by projecting out the modes which yielded reduced $\chi^2>1$ for the cross-spectrum null tests. Our pool of systematics and resulting contamination model was very general, and the sky masks minimal; thus, the reduced $\chi^2$ cut is the only tuneable parameter in the extended mode projection approach. Our approach is therefore based on the principles of blind analysis, since projecting out modes with reduced $\chi^2>1$ is a simple and pre-selected criterion for the accepted level of correlation between the systematics and the maps, which does not depend on the intrinsic clustering of quasars. Using various settings for both the power spectrum estimation and the systematics mitigation, we have tested that the power spectrum measurements are robust to these choices, and consistent with the theoretical predictions. In a companion paper \citep{LeistedtPeiris:2014:XDQSO_png}, we show that these spectra, used in a combined likelihood function, yield stringent and robust constraints on PNG and on the bias of quasars. In particular, the constraints separately derived using the auto- and cross-spectra are consistent with each other, and robust to the underlying model and assumptions, for example to the uncertainties in the redshift distributions of the samples. This demonstrates that the remaining levels of correlations created by systematics are below the statistical uncertainties, and that the quasar power spectra are suitable for use in cosmological inferences. Future galaxy and quasar survey data will reach unprecedented precision, and will require accurate mitigation of large numbers of systematics. For instance DES, {\it Euclid} \citep{Amendola:2012ys}, and LSST \citep{Abell:2009aa} will observe hundreds of millions of objects, and probe extended redshift ranges and finer angular scales. This makes them very promising for testing new physics beyond the standard cosmological model, such as PNG, the neutrino sector, dark energy phenomenology, and modifications to General Relativity. At such precision levels, and given that these new physics signatures are typically small deviations from the standard model, power spectrum measurements will be highly sensitive to any systematics. The extended mode projection framework is a good candidate for mitigating such systematics in a robust and blind fashion, while extracting as much information as possible from the hard-won data. | 14 | 4 | 1404.6530 |
1404 | 1404.1917_arXiv.txt | The Orion--Eridanus superbubble, formed by the nearby Orion high mass star-forming region, contains multiple bright H$\alpha$ filaments on the Eridanus side of the superbubble. We examine the implications of the H$\alpha$ brightnesses and sizes of these filaments, the Eridanus filaments. We find that either the filaments must be highly elongated along the line of sight or they cannot be equilibrium structures illuminated solely by the Orion star-forming region. The Eridanus filaments may, instead, have formed when the Orion--Eridanus superbubble encountered and compressed a pre-existing, ionized gas cloud, such that the filaments are now out of equilibrium and slowly recombining. | \label{intro} The closest high-mass star-forming region to the Sun that is currently forming massive stars is the Orion star-forming region, which is located at a distance of 400 pc from the Sun \citep{Hirota07, Menten07, Sandstrom07}. The Orion star-forming region is surrounded by a highly elongated superbubble, with dimensions of 20$^\circ \times 45^\circ$ as seen in H$\alpha$ emission \citep{Bally08}, that is referred to as the Orion--Eridanus superbubble. The Eridanus side of the superbubble contains a very prominent hook-shaped H$\alpha$ feature that was first discovered on H$\alpha$ images and Palomar Observatory Sky Survey plates by \citet{Meaburn65, Meaburn67}. \citet{Johnson78} break this hook into three separate arcs, all of which are labelled in Fig. \ref{fig:dicicco}. Arc A is the eastern half of the hook, Arc B is the western half of the hook, and Arc C is the southern extension of the hook. For the remainder of this paper, we will refer to these three arcs collectively as the Eridanus filaments. In this paper, all references to north or south refer to increasing or decreasing declination and references to east or west refer to increasing or decreasing right ascension, unless otherwise specified. \begin{figure} \centering \includegraphics[width=3in]{fig1.eps} \caption{Orion--Eridanus superbubble as seen in H$\alpha$. Labels for the various major components of the bubble have been added to the image from \citet{DiCicco09}. Arcs A, B, and C are collectively referred to as the Eridanus filaments.} \label{fig:dicicco} \end{figure} The Eridanus filaments are clearly brighter, in H$\alpha$, than the superbubble wall in their vicinity. They are also remarkably bright, with H$\alpha$ intensities of the order of 25 Rayleighs, given that they are located almost 200 pc from the Orion star-forming region \citep{Haffner03}. In this paper, we examine the implications of the H$\alpha$ brightnesses and sizes of these filaments, with a particular eye towards whether the filaments are consistent with being in ionization equilibrium with the Orion star-forming region. The H$\alpha$ emission from a radiatively excited region is proportional to the amount of ionizing flux absorbed by that region, because the H$\alpha$ emission is generated from the recombination of bare protons and electrons. As such, information on the density and geometry of the emitting region, as well as the strength of the ionizing radiation field, can be obtained from H$\alpha$ intensities and distributions (e.g. \citealt{Reynolds79, Heiles99}). Strong dynamical events can also imprint their signatures into the H$\alpha$ emission from a gas cloud, such that ionization modelling can provide a window into the dynamical history of the H$\alpha$ emitting region. In Section \ref{properties}, we review and derive the general properties of the Eridanus filaments. In Section \ref{equilibrium}, we examine the criteria required for the Eridanus filaments to be in ionization equilibrium with the Orion star-forming region, while in Section \ref{alternative models}, we examine alternative possibilities for the ionization state of the filaments. We briefly discuss the possible origins of the filaments in Section \ref{origin} and we summarize our primary findings in Section \ref{conclusions}. | \label{conclusions} The Orion star-forming region is the closest high-mass star-forming region currently forming stars and it has blown a large 20$^{\circ}$ by 45$^{\circ}$ superbubble into the ISM. The superbubble contains very prominent filaments on the Eridanus side, referred to as the Eridanus filaments. We find that the Eridanus filaments have gas densities between 1 and 6 cm$^{-3}$ and contain between 300 and 3000 M$_\odot$ of ionized gas. Based upon the widths and H$\alpha$ intensities of these filaments, we find that if these filaments are in ionization equilibrium with the Orion star-forming region, then either the filaments must be edge-on sheets, with depths of a factor of roughly 5 larger than their widths, or that the ionizing luminosity of the Orion star-forming region must be a factor of about 5 larger than previously determined. We suggest, as an alternative, that the Eridanus filaments are non-equilibrium structures that are currently in the process of recombining after being formed from the compression of a pre-existing gas cloud due to the expansion of the superbubble. | 14 | 4 | 1404.1917 |
1404 | 1404.3123_arXiv.txt | DF Hya is a contact system of W UMa-type with a period of 0.3306022$^d$. Various papers have been published for this system (cf. \cite{LI90};\cite{NI92};\cite{ZA09};\cite{XI09}) concerning both light curve and orbital period changes analyses. The system was observed during the night of January 17 2011 at the Gerostathopoulion Observatory in Athens University using a 40-cm Cassegrain telescope equipped with the CCD camera ST-10XME and B, V, R, I Bessell photometric filters. Differential magnitudes were obtained with the software MUNIWIN v.1.1.26 \cite{HR98}, while GSC 0225-0943 and GSC 0225-0731 were used as comparison and check stars, respectively. The light curves were analysed with the PHOEBE v.0.29d software \cite{PZ05}. Mode 3 (contact system) was chosen for fitting applications and the `q search method' was applied for an estimation of the mass ratio with a step of 0.1 in the range of 0.1-10. This value then was adjusted in the subsequent analysis. The temperature of the primary component was set as a fixed parameter (T1=6000 K; \cite{MA06}), while the temperature of the secondary was left free. The albedos A$_1$, A$_2$ and gravity darkening coefficients g$_1$, g$_2$ were given theoretical values according to the components' spectral types. The potentials $\Omega_1$, $\Omega_2$, the system's inclination \textit{i} and the fractional luminosity of the primary component $L_1$ were also adjusted. The limb darkening coefficients $x_1,~x_2$ were taken from the tables of \cite{VH93}. Given the evidence for third body existence in the system (\cite{ZA09}; \cite{XI09}) the third light parameter $l_3$ was trialed. Synthetic and observed light curves are shown in Fig. \ref{fig1} with corresponding parameters given in Table \ref{tab1}. The absolute parameters of the components were calculated (Table \ref{tab1}) and used for further study of their present evolutionary status. Two cases are considered: (\textbf{A}) The mass of the primary (hotter) and (\textbf{B}) the mass of the secondary (cooler) assigned values according to their spectral types as Main Sequence stars. The location of the components in a theoretical Mass-Radius diagram is illustrated in Fig. \ref{fig1} for both cases. \begin{figure}[h] \begin{tabular}{cc} \centering \includegraphics[width=7.5cm]{LC.eps}&\includegraphics[width=7.5cm]{M-R.eps} \end{tabular} \caption{Left panel: Observed (points) and synthetic (solid lines) light curves of DF~Hya. Right panel: The position of the system's components for Cases A and B. P and S refer to primary and secondary components, respectively. } \label{fig1} \end{figure} \begin{table}[h] \caption{Results of light curve analysis and absolute parameters of the components (comp.).} \label{tab1} \scalebox{0.7}{ \begin{tabular}{lcc lcc cc l cc cc} \hline \multicolumn{8}{c}{\bf Light curve parameters} & \multicolumn{5}{c}{\bf Absolute parameters} \\ \hline & & & & & & & & & \multicolumn{2}{c}{Case A}& \multicolumn{2}{c}{Case B}\\ \cline{10-13} \emph{Comp.:} & \emph{P}&\emph{S}&\emph{Filters:} &\emph{B} & \emph{V}&\emph{R}& \emph{I} &\emph{Comp.:} & \emph{P}&\emph{S}& \emph{P}&\emph{S} \\ \hline T [K] & 6000* &5620 (5)& $x_{1}$ & 0.709 & 0.572 & 0.490 & 0.411 &M [M$_{\odot}$] & 1.07* & 2.5 (2)& 0.39 (3)& 0.94* \\ g & 0.32* & 0.32* & $x_{2}$ & 0.764 & 0.623 & 0.537 & 0.452 &R [R$_{\odot}$] & 0.97 (2)&1.44 (2)& 0.70 (2)& 1.03 (2) \\ A & 0.5* & 0.5* & L$_1$/L$_T$ &0.445 (5)&0.373 (4)&0.365 (2) &0.357 (1)&L [L$_{\odot}$] & 1.10 (5)&2.41 (6)&0.56 (3) & 1.23 (3) \\ $\Omega$ & 5.68 (1) &5.68 (1)& L$_2$/L$_T$ &0.509 (2)&0.604 (2)&0.617 (1) &0.628 (1)&M$_{bol}$ [mag] &4.64 (2) &4.08 (2)&5.37 (2) & 4.81 (2) \\ i [deg]&\multicolumn{2}{c}{84.8 (2)}& L$_3$/L$_T$ &0.046 (8)&0.023 (7)&0.17 (3) &0.015 (3)&a [R$_{\odot}$] & 2.17 (6)& 0.91(3)&1.56 (5) & 0.66 (2) \\ q &\multicolumn{2}{c}{2.38 (1)}& & & & & &log$g$ [cm/s$^2$] &4.49 (2)&4.53 (5) &4.34 (4) & 4.39 (1) \\ \hline \multicolumn{13}{l}{*assumed, L$_T$=L$_1$ + L$_2$ +L$_3$, P=Primary, S= Secondary} \end{tabular}} \end{table} | New photometric study of the eclipsing binary DF~Hya was performed and new geometric elements of the system and absolute parameters of its components were derived. The system is of W-type, meaning that the primary component (hotter) is less massive and smaller than the secondary. The components' location in the M-R diagram (see Fig. \ref{fig1}) for Case A indicate that the secondary is a pre-Main Sequence star with a mass of 2.5 $M_\odot$, which is quite unusual for members of W~UMa systems. The second hypothesis (Case B) seems to be more likely as both stars lie inside the ZAMS-TAMS limits and therefore it is suggested as the most realistic one. The comparison between the present light curves and the ones given by \cite{NI92} shows that brightness changes occur in the system affecting both the minima and maxima. In order to check any brightness variation periodicities, long term monitoring of the system is required. For an accurate solution a third light was considered in the light curve analysis and a contribution of $\sim$2.5\% was found. According to the O-C analysis results of \cite{ZA09} (M$_{3,min}$=0.84 $M_\odot$), and assuming the MS nature of the tertiary component and taking into account the Mass-Luminosity relation for MS stars (L$\sim$M$^{3.5}$), the expected light contribution was found $\sim$25\%, which is much larger than the observed one. A possible explanation for this mismatch could be a binary star orbiting DF~Hya instead of a single one. On the other hand, the orbital period analysis of \cite{XI09} suggested a minimal mass of 0.21 $M_\odot$ for the additional component and mass transfer between the binary's members. This value does not satisfy also the observed light contribution, but if we assume a non coplanar orbit of the third body with an inclination of $\sim30^\circ$, then the result can be adopted. The Applegate mechanism was also tested for \cite{ZA09} results, but it was found that the quadrupole moment variation for both stars ($\Delta Q < 10^{50}~gr~cm^2$) cannot implicate the period changes \cite{LR02}. Hence, the third body existence remains as the most possible solution for the orbital period modulations of the system. Spectroscopic observations are needed in order to check the value of the present photometric mass ratio and provide the information for a more accurate determination of the absolute parameters. | 14 | 4 | 1404.3123 |
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1404 | 1404.4645_arXiv.txt | Linear time-distance helioseismic inversions are carried out for vector flow velocities using travel times measured from two $\sim 100^2\,{\rm Mm^2}\times 20\,{\rm Mm}$ realistic magnetohydrodynamic quiet-Sun simulations of about 20~hr. The goal is to test current seismic methods on these state-of-the-art simulations. Using recent three-dimensional inversion schemes, we find that inverted horizontal flow maps correlate well with the simulations in the upper $\sim 3$~Mm of the domains for several filtering schemes, including phase-speed, ridge, and combined phase-speed and ridge measurements. In several cases, however, the velocity amplitudes from the inversions severely underestimate those of the simulations, possibly indicating nonlinearity of the forward problem. We also find that, while near-surface inversions of the vertical velocites are best using phase-speed filters, in almost all other example cases these flows are irretrievable due to noise, suggesting a need for statistical averaging to obtain better inferences. | Time-distance helioseismology \citep{duvall1993} is one of the few tools available that allows us to peer beneath the photosphere to better understand the Sun's internal structure and dynamics. Through helioseismic inversions of wave travel-times measured at the solar surface, we can, in principle, better understand and characterize different kinds of subsurface perturbations (i.e. magnetic fields, density anomalies, flows, etc.) that may be present in the upper convection zone. This method has been used to study the near-surface structure of supergranulation \citep{gizon2003, zhao2003, jackiewicz2008, duvall2010, svanda2012} and sunspots \citep{zhao2001, couvidat2006, kosovichev2011a}. One way to test the accuracy of helioseismology is through comparisons with other helioseismic methods (i.e. comparing time-distance inversion results with those of ring-diagram analysis or helioseismic holography) \citep[e.g.,][]{gizon2009, kosovichev2011b}. However, these types of studies can be misleading as agreement among methods does not necessarily guarantee correctness (which may be especially true around active regions). Perhaps the best way to to test the validity of time-distance inversions is by inverting for specific features present in solar simulations. This approach is advantageous in that the inversion results can easily be compared directly with the known values taken from the simulation. Synthetic data also allow us to carry out additional testing that would otherwise be impossible if only real solar data were available (i.e. testing the effects of data filter choice on results, tests of kernel performance through forward-modeling, etc.). A small number of studies have been carried out previously to validate time-distance helioseismology by applying the method to simulated quiet-Sun data possessing varying degrees of realism. \citet{zhao2007} performed time-distance inversions of realistic convection simulations \citep{benson2006} in the ray approximation and found that the recovered horizontal flows agree well (correlation coefficients of $\sim$0.5--0.9) with those of the simulation in the upper 5~Mm of the domain, though the vertical velocities were anticorrelated at nearly every depth. \citet{svanda2011} used a snapshot of a convective simulation flow-field to produce forward-modeled travel-time maps, inverting them using the first Born approximation methods \citep{gb02} to validate their time-distance inversions. They found high correlation over the same range of depths for the horizontal flow components, and improved correlation for the vertical component. In some sense, however, both cases may be too idealized. In the case of \citet{zhao2007}, the work was based upon a simulation which contained no magnetic fields. The work of \citet{svanda2011} did indeed validate the inversion procedure, yet it was based on simplified measurements, as forward-modeled travel times of a frozen flow field may be too idealized in comparison to a full time-distance analysis of a Doppler time series. \begin{figure*}[t] \begin{center}$ \begin{array}{c} \includegraphics[width=1\linewidth,clip=]{f1a.eps} \\ \includegraphics[width=1\linewidth,clip=]{f1b.eps} \end{array}$ \end{center} \caption{The two simulations used in this study. Shown are time averages (over $\approx 20$~hr) of the $v_x$ velocity for half of the computation domain ($y\ge 0$) for QS1 (top) and QS2 (bottom). The horizontal slice at the top is taken at the $\tau_{500} =0.01$ ($z=0$) level. The color scale is the same in each image.} \label{fig:QS} \end{figure*} The goal of this work is to test current time-distance methods using the most realistic solar simulations available to us today. These magnetohydrodynamic simulations are fully convective and nonlinear in nature and contain large-scale supergranular-type flows. Such data, described in Section~\ref{sec:sim}, will allow us to test methods in a regime that is as close as possible to the real Sun. In Section~\ref{sec:filt} the data filtering is described where two methods are considered. The filtered data are used to measure a large set of travel times in two different ways as discussed in Section~\ref{sec:tt}. Sections~\ref{sec:kernels} and \ref{sec:inv} briefly review the forward and inversion problems in the first Born approximation. Also shown are comparisons of measured and forward-modeled travel times. Inversion results for the three vector flow components are given in Section~\ref{sec:results}. We discuss the results in the context of validation of these time-distance methods in Section~\ref{sec:dis}. This initial work is carried out with the more difficult goal of testing time-distance inversions near active regions in mind. The inversion procedure described here will be applied to a similarly realistic sunspot simulations to assess how capable or limited current linear time-distance inversions may be at recovering subsurface flows in these strong perturbation regimes. As sunspot helioseismology is an active area of research, such work should prove useful. | \label{sec:dis} Current time-distance analysis has been tested using two realistic magnetohydrodynamic quiet-Sun simulations. Measurements made using the GB02 and GB04 travel-time definitions are found to correlate very well with one another, varying linearly over a large range of distances. The travel-times computed using GB04 are on average $10\%$ larger than those of GB02 in terms of RMS variation. Correlation between measured and forward-modeled travel-times computed in the first Born approximation is generally high for filters $f, p_1-p_2$ and $\rm{td_1}-\rm{td_4}$, but is found to decrease rapidly for filters $p_3$ and $\rm{td_5}$. We possibly attribute this to inadequate modeling of the simulation power at higher phase-speeds and for higher-order modes. SOLA inversions were carried out using both travel-time definitions for several filtering schemes, including phase-speed, ridge, and combined phase-speed and ridge measurements to recover flows in the upper layers of both simulations. We find that horizontal flow maps correlate well ($\sim0.8$) with the simulations in the upper 3~Mm of the domains. At a depth of 5~Mm, correlation deteriorates significantly ($\sim0.6$), though some large-scale flow structure is still visible. Simply increasing the number of measurements used in the inversions would likely help to improve wave coverage at larger depths, but this is not a trivial undertaking due to current computational constraints. We find that even for our best inversions, we severely underestimate the flow velocities at every depth, possibly indicating non-linearity of the forward problem caused by the very strong ($>500~\rm{m\,s^{-1}}$) near-surface flows present in both simulation domains. Inversions employing phase-speed filtering alone seem to show an advantage in the upper 5~Mm when compared to the other filtering schemes. At larger depths, however, the combined ridge+phase-speed filtering produced a better match between averaging kernel and target function for a fixed inversion noise level. Ridge filtering was generally found to give the worst correlation values. Vertical flow inversions show poor correlation with the simulation over the full range of depths for QS1, but noticeably better results for QS2. Amplitude determination of these vertical velocities fails everywhere but the nearest surface layer, as noise dominates these inferences. While the inversion procedure to minimize the important cross-talk terms appears to work effectively in the inversion procedure itself, we do not accurately retrieve the vertical flows as was the case in \citep{svanda2011}. This is likely due to the differences in the simulation data we used, such as overall flow amplitudes, time-series length, and utilization of forward-modeled travel times. In summary, the large-scale flows present in these very sophisticated solar-like simulations are not adequately retrievable with current time-distance techniques, and these results cause us to hesitate to invert for real solar features. Improvements to forward and inverse modeling may need to be made for studying individual structures over short time scales. Longer data sets can be used, but this eliminates the possibility of determining individual supergranule vertical flow profiles as their lifetimes are on average only $1-2$~days. However, these findings suggest that perhaps the most promising way to proceed is the statistical averaging scheme developed in \citet{duvall2010} and \citet{svanda2011} for supergranule-type flows. We have quantified the level of discrepancy between the seismic inferences and the known answer for these simulations, and a forthcoming study attempts a similar analysis for the flows in sunspot simulations. \begin{table*} \centering\footnotesize \caption{Parameters for each set of inversions presented in the text.} \label{tab1}\medskip \begin{threeparttable} \begin{tabular}{c c c c c c c c c c c} % \hline % inversion & sim & filter & depth & FWHM$_{\rm{h}}$ & FWHM$_{\rm{z}}$ & $\mu$ & $\nu$ & $\epsilon$ & noise % \\ & & & & [Mm] & [Mm] & [$\rm{s^2\, m^{-2}}$] & [$\rm{Mm^{3}}$] & [$\rm{s^4 \,m^{-2}}$] & [$\rm{m\,s^{-1}}$] \\ [0.5ex] % \hline % set 1 $(v_x, v_y)$ & QS1, QS2 & all & 1 Mm & 10 & 2 & (0.4--1.8)$\times$10$^{-8}$ & 1 & 1.0$\times$10$^{-6}$ & $\sim$35\\ & & & 3 Mm & 12 & 2 & (0.4--1.8)$\times$10$^{-8}$ & 1 & 1.0$\times$10$^{-6}$ & $\sim$35\\ \vspace{1ex} & & & 5 Mm & 14 & 2 & (0.4--1.8)$\times$10$^{-8}$ & 1 & 1.0$\times$10$^{-6}$ & $\sim$35\\ set 2 $(v_x, v_y)$ & QS2 & comb & 7 Mm & 16 & 3 & 4.6$\times$10$^{-10}$ & 1 & 1.0$\times$10$^{-6}$ & 64\\ & & & 9 Mm & 18 & 3 & 7.5$\times$10$^{-12}$ & 1 & 1.0$\times$10$^{-6}$ & 86\\ \multicolumn{1}{l}{set 3 $(v_z)$} & QS1 & ridge & 1 Mm & 12 & 2 & 7.2$\times$10$^{-9}$ & 80 & 3.2$\times$10$^{-6}$ & 18\\ & & & 3 Mm & 14 & 2 & 2.3$\times$10$^{-11}$ & 80 & 1.0$\times$10$^{-9}$ & 814\\ \vspace{1ex} & & & 5 Mm & 16 & 2 & 1.0$\times$10$^{-11}$ & 80 & 3.2$\times$10$^{-9}$ & 567\\ & & phase & 1 Mm & 12 & 2 & 3.7$\times$10$^{-8}$ & 80 & 1.0$\times$10$^{-5}$ & 10\\ & & & 3 Mm & 14 & 2 & 2.7$\times$10$^{-10}$ & 80 & 1.0$\times$10$^{-8}$ & 210\\ \vspace{1ex} & & & 5 Mm & 16 & 2 & 2.3$\times$10$^{-11}$ & 80 & 1.0$\times$10$^{-9}$ & 445\\ & & comb & 1 Mm & 12 & 2 & 3.7$\times$10$^{-8}$ & 80 & 1.0$\times$10$^{-5}$ & 12\\ & & & 3 Mm & 14 & 2 & 6.1$\times$10$^{-10}$ & 80 & 3.2$\times$10$^{-8}$ & 152\\ \vspace{1ex} & & & 5 Mm & 16 & 2 & 2.3$\times$10$^{-11}$ & 80 & 1.0$\times$10$^{-8}$ & 236\\ & QS2 & ridge & 1 Mm & 12 & 2 & 7.2$\times$10$^{-9}$ & 80 & 3.2$\times$10$^{-6}$ & 18\\ & & & 3 Mm & 14 & 2 & 1.0$\times$10$^{-11}$ & 80 & 1.0$\times$10$^{-9}$ & 814\\ \vspace{1ex} & & & 5 Mm & 16 & 2 & 1.0$\times$10$^{-11}$ & 80 & 1.0$\times$10$^{-9}$ & 567\\ & & phase & 1 Mm & 12 & 2 & 1.9$\times$10$^{-8}$ & 80 & 3.2$\times$10$^{-5}$ & 18\\ & & & 3 Mm & 14 & 2 & 1.4$\times$10$^{-10}$ & 80 & 1.0$\times$10$^{-8}$ & 210\\ \vspace{1ex} & & & 5 Mm & 16 & 2 & 1.2$\times$10$^{-11}$ & 80 & 3.2$\times$10$^{-9}$ & 445\\ & & comb & 1 Mm & 12 & 2 & 3.7$\times$10$^{-8}$ & 80 & 1.0$\times$10$^{-5}$ & 12\\ & & & 3 Mm & 14 & 2 & 2.7$\times$10$^{-10}$ & 80 & 3.2$\times$10$^{-8}$ & 152\\ \vspace{1ex} & & & 5 Mm & 16 & 2 & 5.2$\times$10$^{-11}$ & 80 & 1.0$\times$10$^{-8}$ & 236\\ [1ex] % \hline % \end{tabular} \begin{tablenotes}[para,flushleft] Columns from left to right are the inversion set number, the specific simulation, the type of filtering, target inversion depth, the horizontal target width, the vertical target size, the noise, cross-talk, and weight spread trade-off parameters, respectively, and the inversion noise level. \end{tablenotes} \end{threeparttable} \end{table*} \begin{table*} \centering\footnotesize \caption{Descriptive correlation statistics between inverted flows and corresponding simulation data.} \label{tab2}\medskip \begin{threeparttable} \begin{tabular}{c c c c c c c c c c c c c} % \hline % sim & fiter & depth & $v_x$ & $v_y$ & $v_z$ & $\rm{mag_h}$ & div & s$_{v_x}$ & s$_{v_y}$ & s$_{v_z}$ & s$_{\rm{mag_h}}$ & s$_{\rm{div}}$\\ [0.5ex] % \hline % QS1 & ridge & 1 & 0.87 & 0.74 &-0.37& 0.57 & 0.87 & 0.90 & 0.93 &-0.29& 0.64 & 1.20\\ & ridge & 3 & 0.80 & 0.66 &0.01& 0.45 & 0.78 & 0.63 & 0.67 &0.00& 0.41 & 1.08\\\vspace{1ex} & ridge & 5 & 0.58 & 0.53 &-0.03& 0.04 & 0.57 & 0.40 & 0.59 &0.00& 0.03 & 1.04\\ & phase & 1 & 0.92 & 0.70 &0.36& 0.58 & 0.86 & 0.97 & 0.82 &0.46& 0.68 & 0.95\\ & phase & 3 & 0.86 & 0.74 &0.34& 0.62 & 0.85 & 0.65 & 0.76 &0.02& 0.53 & 0.89\\\vspace{1ex} & phase & 5 & 0.69 & 0.62 &0.21& 0.23 & 0.69 & 0.73 & 0.88 &0.01& 0.32 & 1.46\\ & comb & 1 & 0.89 & 0.70 &0.28& 0.56 & 0.85 & 1.05 & 0.95 &0.33& 0.77 & 1.14\\ & comb & 3 & 0.85 & 0.72 &0.25& 0.57 & 0.83 & 0.57 & 0.67 &0.04& 0.44 & 0.80\\\vspace{1ex} & comb & 5 & 0.70 & 0.59 &0.12& 0.21 & 0.65 & 0.46 & 0.55 &0.01& 0.17 & 0.80\\ QS2 & ridge & 1 & 0.86 & 0.90 &0.50& 0.63 & 0.92 & 1.07 & 1.21 &0.65& 0.85 & 1.39\\ & ridge & 3 & 0.82 & 0.75 &0.39& 0.63 & 0.73 & 1.31 & 1.27 &0.01& 1.09 & 1.78\\\vspace{1ex} & ridge & 5 & 0.45 & 0.50 &-0.02& 0.26 & 0.33 & 0.99 & 0.98 &0.00& 0.51 & 1.30\\ & phase & 1 & 0.91 & 0.89 &0.81& 0.68 & 0.93 & 1.57 & 1.55 &0.67& 1.27 & 1.84\\ & phase & 3 & 0.86 & 0.84 &0.53& 0.65 & 0.88 & 0.92 & 0.97 &0.04& 0.77 & 1.27\\\vspace{1ex} & phase & 5 & 0.71 & 0.78 & -0.11& 0.54 & 0.81 & 0.97 & 1.09 &-0.01& 0.76 & 1.71\\ & comb & 1 & 0.89 & 0.90 &0.79& 0.65 & 0.92 & 1.25 & 1.20 &0.58& 0.92 & 1.30\\ & comb & 3 & 0.85 & 0.77 &0.49& 0.63 & 0.82 & 0.95 & 0.90 &0.06& 0.75 & 1.30\\\vspace{1ex} & comb & 5 & 0.65 & 0.71 &0.04& 0.43 & 0.74 & 0.83 & 0.83 &0.00& 0.53 & 1.53 \\[1ex] % \hline % \end{tabular} \begin{tablenotes}[para,flushleft] Columns 4-6 are the correlation coefficients for the given flow component. `${\rm mag_h}$' denotes $\sqrt{v_x^2+v_y^2}\equiv |\bm{v}_h|$, and `div' the horizontal divergence $\nabla_{\rm h}\cdot\bm{v}_{\rm h}$. The last 5 columns give the slope of the best-fit lines through the correlation plots for the same quantities. \end{tablenotes} \end{threeparttable} \end{table*} | 14 | 4 | 1404.4645 |
1404 | 1404.7470_arXiv.txt | {\sl K2}, the two-wheel mission of the {\sl Kepler} space telescope, observed the pulsating subdwarf B star EQ\,Psc during engineering tests in 2014 February. In addition to a rich spectrum of g-mode pulsation frequencies, the observations demonstrate a light variation with a period of 19.2\,h and a full amplitude of 2\%. We suggest that this is due to reflection from a cool companion, making EQ\,Psc the longest-period member of some 30 binaries comprising a hot subdwarf and a cool dwarf companion (sdB+dM), and hence useful for exploring the common-envelope ejection mechanism in low-mass binaries. | The hot subdwarf EQ\,Psc (=PB\,5450) was one of a number of stars discovered to show long-period pulsations likely to be due to opacity-driven gravity-modes \citep{green03}. Both gravity and pressure-mode pulsations are found amongst a significant fraction of hot subdwarfs, and offer the possibility to study the stellar interior using the methods of asteroseismology. During the first two-years of operation of the {\sl Kepler} spacecraft, some twenty pulsating hot subdwarfs were identified in the {\sl Kepler} field and observed for one or more quarters. The majority of these stars are primarily cool V1093 Her (g-mode) variables, one is a hybrid DW Lyn (p-mode + g-mode) variable and one is a low-amplitude V361 Her (p-mode) variable, although very-low amplitude p-modes are detected in a substantial fraction of the {\sl Kepler} V1093 Her variables \citep{kepler10.2,kepler10.3}. In addition to pulsation-driven light-variations, subdwarf B stars in binary systems can also show light variations caused by eclipses { and/or by reflection from} a companion (HW\,Vir variables) \citep{menzies86}, ellipsoidal deformation in a very short-period binary ({\it e.g.} KPD\,1930+2752) \citep{billeres00} and Doppler beaming ({\it e.g.} 2M\,1938+4603) \citep{barlow12}. Such phenomena are vital tools for interpreting the fundamental properties, internal structure and evolutionary origin of hot subdwarfs which, by several means, have become nearly-naked core-helium-burning stars \citep{heber86,han02}. Because of the rarity of hot subdwarfs and the significance of light variability for understanding them, it is natural that any such star which falls within a {\sl Kepler} pointing should, if possible, be observed. EQ\,PSc happened to fall in a field used for a nine-day engineering test at the start of 2014 to verify the stability of operations with two reaction wheels ({\sl K2}) \citep{howell14}. In this letter, we report observations which show a 19\,h periodic variation, which we interpret as being due to reflection from a cool stellar companion, as well as a rich g-mode pulsation spectrum. \begin{figure} \centering \includegraphics[width=0.47\textwidth,angle=0]{eqpsc_lcurve.ps} \caption{The {\sl K2} light curve for EQ\,Psc in relative flux units. Times in all figures are given as MJD - 56692.} \label{f:lc} \end{figure} \begin{table} \label{t:freq} \caption{Frequencies identified in the {\sl K2} power spectrum of EQ\,PSc.} \begin{center} \begin{tabular}{lrrrr} \hline & $f\, {\rm (d^{-1})}$ & P (s) & $a$ (ppt) & $\phi$~~~~~ \\ \hline $f_{\rm orb}$ & 1.2478 & 69242 & 10.218(107)& 0.494(02) \\ $2f_{\rm orb}$ & 2.4956 & 34621 & 1.300(108)& 1.240(14) \\ \hline $f_{\rm L+}$ & 8.0831 & 10697 & 0.569(110)& 0.098(31) \\ $f_{\rm L-}$ & 8.2256 & 10512 & 0.611(110)& 0.089(29) \\ $f_{\rm K}$ & 17.0468 & 5085.4 & 0.986(108)& 0.373(17) \\ $f_{\rm J}$ & 17.8751 & 4851.4 & 1.506(108)& 1.235(11) \\ $f_{\rm I}$ & 24.6959 & 3523.3 & 0.375(108)& 0.334(46) \\ $f_{\rm H}$ & 26.9578 & 3232.0 & 1.073(110)& 0.898(16) \\ $f_{\rm H-}$ & 27.0933 & 3216.1 & 0.321(110)& 0.423(54) \\ $f_{\rm G}$ & 29.2696 & 2981.1 & 0.943(108)& 0.286(19) \\ $f_{\rm F}$ & 33.8270 & 2587.3 & 0.360(108)& 0.912(48) \\ $f_{\rm E+}$ & 35.2728 & 2484.8 & 0.723(111)& 0.177(24) \\ $f_{\rm E}$ & 35.3638 & 2478.5 & 1.601(111)& 0.869(11) \\ $f_{\rm D}$ & 39.9094 & 2204.8 & 0.451(108)& 0.393(38) \\ $f_{\rm C}$ & 42.8191 & 2060.6 & 2.322(108)& 0.634(07) \\ $f_{\rm B+}$ & 46.6886 & 1897.2 & 6.573(381)& 0.557(09) \\ $f_{\rm B-}$ & 46.7061 & 1896.6 & 6.698(381)& 0.124(09) \\ $f_{\rm A}$ & 73.6477 & 1246.8 & 0.424(108)& -0.237(41) \\ \hline \end{tabular} \end{center} \end{table} \begin{figure*} \centering \includegraphics[width=0.9\textwidth,angle=0]{eqpsc_pspec.ps} \caption{Amplitude spectra obtained from the {\sl K2} light curve of EQ\,Psc. In all panels, black represents the power spectrum of the data shown in Fig.~\ref{f:lc}, and red represents the power spectrum of the data pre-whitened by the frequencies and amplitudes shown in Table~\ref{t:freq}. } \label{f:power} \end{figure*} \section[]{{\sl K2} observations and data reduction} The detector on board {\sl Kepler} is a shutterless photometer using 6\,s integrations and a 0.5\,s readout. The observations of EQ\,Psc were made in short cadence (SC) mode, where 9 integrations are summed for an effective 58.8 sec exposure. Observations were carried out in engineering mode from {MJD 56692.5411 to 56701.5306 } (2014 Feb 4th to Feb 13). The coverage was therefore 8.9 days in duration. During this time interval there were frequent corrections to the spacecraft pointing, with one significant shift occuring on MJD=56694.86 (or 2.3 days into the time series). A 50$\times$50 pixel array is downloaded from the satellite for each target. To extract a light curve of EQ Psc we used the {\tt PyKe} software (Still \& Barclay 2012){\footnote{http://keplergo.arc.nasa.gov/PyKE.shtml}} which was developed for the {\sl Kepler} mission by the Guest Observer Office. We experimented by extracting data from a series of different combinations of pixels. We found that a mask centered on EQ Psc consisting of 110 pixels gave the optimal results. If a smaller number of pixels are used we find that there are small discontinuities present in the light curve which are the result of small shifts in the position of the stellar profile over the CCD. We also experimented with subtracting the background (which increased in a nearly linear fashion over the course of the observations) in different ways. We found that using the median value of each time point to represent the background gave the best results. Finally we removed time points which were not flagged {\tt `SAP\_QUALITY==0'} (for instance during times of enhanced solar activity). The extracted and reduced light curve is shown in Fig.~\ref{f:lc} \begin{figure*} \centering \includegraphics[width=0.9\textwidth,angle=0]{eqpsc_lc_fit.ps} \caption{The adopted fit to the {\sl K2} light curve for EQ\,Psc shown in Fig.~\ref{f:lc}. Black dots are the {\sl K2} observations. The solid red curve shows the solution represented in Table ~\ref{t:freq}. } \label{f:fit} \end{figure*} \section[]{Light curve and frequency analysis} The {\sl K2} light curve for EQ\,PSc shows a strong modulation with an amplitude of about two per cent (0.022 mag) and a period close to 0.8 d (Fig.~\ref{f:lc}). Closer inspection shows additional variability on a timescale of half an hour with an amplitude of around one per cent. The periodic content of the light curve was investigated using a classical power spectrum analysis. An idea of the window function can be obtained from the lower-left panel in Fig.~\ref{f:power}. For a continuous run lasting 9\,d, the nominal frequency resolution is $0.22\,{\rm d^{-1}}$. Peaks in the power spectrum were identified in order of descending power, amplitudes and phases associated with each peak were measured using a multi-sine fit to the light curve, the light curve was pre-whitened by this fit, a new power spectrum was computed, the next-highest peaks were identified and added to the frequency table, and the cycle was iterated. A provisional list of frequencies in cycles per day, periods in seconds, semi-amplitudes in parts per thousand (ppt\footnote{Also referred to as {\it milli-modulation intensity} units, or mmi.}), and phases representing the {\sl K2} lightcurve of EQ\,Psc is presented in Table~\ref{t:freq}. {Phases refer to a zero-point at MJD 56692.0 and are given in cycles. Errors are shown in parentheses.} The multi-sine fit constructed from the data in this table is illustrated in Fig.~\ref{f:fit}. Frequencies have been labelled in alphabetical order of increasing period. Several low-frequency peaks were excluded from this analysis; with the exception of the dominant peak at $1.248\,{\rm d^{-1}}$, its first harmonic and their aliases, the power spectrum is dominated by red noise at $f<5\,{\rm d^{-1}}$. At $f>100\,{\rm d^{-1}}$, the power spectrum has the characteristics of all {\sl Kepler} SC data \citep{baran13}, including a peak at $\approx 390\,{\rm d^{-1}}$ and a picket fence of low-amplitude peaks just visible in the lower-right panel of Fig.~\ref{f:power}. None of these were considered to have a stellar origin. The highest-frequency signal $f_{\rm A}$ ($P_{\rm A}\approx21$\,m) is isolated from than the main group of g-mode frequencies. It may be a {\sl K2} artefact. There is a variable artefact at around $31 - 32\,{\rm d^{-1}}$ \citep{baran13}, but this is well clear of $f_{\rm F}$. $f_{\rm K}$ is close to a known broad feature at $16.98\,{\rm d^{-1}}$ in {\sl Kepler} SC data. There remain a number of significant peaks in the power spectrum after subtracting the 18-frequency solution shown here. These are all low-amplitude partners to much stronger peaks; examples include the base of the doublet at $46.7\,{\rm d^{-1}}$ and peaks at 27.1 and $29.3\,{\rm d^{-1}}$ Given the frequency resolution of our data, these may not be real. This is demonstrated by the large amplitudes in the fit to the $46.7\,{\rm d^{-1}}$ doublet, which do not reflect the height of the peaks in the power spectrum. The clue is in the phases, which are almost half a cycle different at the start of the run. Since the beat period between these two frequencies is some 57 days, the oscillations in the model are almost in anti-phase for the duration of the observations. As for other V1093\,Her variables, it will require a much longer observing run to fully resolve the g-mode oscillations in this star. In contrast to the sixteen or more pulsating sdB stars previously observed with {\sl Kepler} \citep{kepler10.6,kepler10.7}, the frequency resolution of the current data limits the information that can be extracted for asteroseismic analysis. It would be useful, for example, to identify series and multiplets with large and small period spacings, respectively, but this is not possible here. Where two frequencies in Table~\ref{t:freq} are identified with a spacing less than the nominal experimental resolution ($0.22\,{\rm d^{-1}}$), they have been marked B--, B+, etc. If one component is much stronger than the near-neighbour, the suffix is omitted from the strongest component. Frequencies $f_{\rm B} - f_{\rm L}$, corresponding to periods in the range 1800 - 11000\,s, are typical of periods commonly seen in V1093\,Her variables \citep{kepler10.6,kepler10.7}. \citet{green03} show 3\,h of R-band photometry for EQ\,PSc, which demonstrates variability on timescales of $\approx30$\, minutes. This corresponds well with the doublet $f_{\rm B-,B+}$. Despite the nominal resolution, this peak is clearly resolved in our power spectrum (Fig,~\ref{f:power}) with a separation $\Delta f = 0.018\,{\rm d^{-1}}$. We conclude that frequencies $f_{\rm B} - f_{\rm L}$ are associated with g-mode pulsations in EQ\,Psc. \begin{figure} \centering \includegraphics[width=0.47\textwidth,angle=0]{eqpsc_orbit2.ps} \caption{The {\sl K2} light curve for EQ\,Psc binned ($\delta\phi=0.005$, black squares: relative flux - 1) and the residual light curve (red squares) folded on the orbital frequency. The first element of the fit (Table\,\ref{t:freq}) is shown as a solid line. There is no evidence for an eclipse at either phase 0.0 (primary) or 0.5 (secondary). } \label{f:orbit} \end{figure} \begin{figure} \centering \includegraphics[width=0.47\textwidth,angle=0]{hwvir_pdist.ps} \caption{The orbital-period distribution for known sdB+dM binaries, distinguishing eclipsing (HW\,Vir: black) and non-eclipsing (grey) systems. } \label{f:periods} \end{figure} \section[]{Orbital reflection in a sdB+dM binary} EP\,Psc shows a strong periodic signal at 0.801\,d (19.2\,h) with a full {(peak-to-peak)} amplitude $>2\%$ of total light. The {\sl K2} data folded on this period are shown in Fig.~\ref{f:orbit}. The same data pre-whitened by the Table\,\ref{t:freq} solution and filtered to remove low-frequency (red) noise ($f < 3\,{\rm d^{-1}}$) are shown in the same figure. The presence of an harmonic shows that this is not perfectly sinusoidal. {Indeed, the roughly quarter-cycle phase difference between the orbital harmonics flattens the minimum and sharpens the maximum. } The lightcurve thus resembles those of hot subdwarf + M-dwarf (sdB+dM) binaries in which the heated surface of the M-dwarf facing the hot subdwarf reradiates (reflects) the incident energy. Fourteen sdB+dM binaries with periods in the range 0.069 -- 0.261\,d show such a reflection effect and also primary and secondary eclipses: these are true HW\,Vir-type sytems. Fifteen sdB+dM binaries with periods in the range 0.076 -- 0.75\,d show a reflection effect alone with amplitudes ranging up to 0.1 magnitudes. The prototype is XY\,Sex \citep{maxted02b}. {The longest-period system before EQ\,Psc was JL\,82 (0.75\,d) \citep{koen09}. } Since the 0.801\,d period is longer and the amplitude much larger than observed in any known g-mode in a pulsating sdB star, pulsation would seem to be a unsatisfactory explanation. Ellipsoidal deformation {of the hot star} due to rotation and tidal effects can be ruled out because the period is too long (by a factor 10) to account for the amplitude observed. Moreover, an ellipsoidal variation would have twice the period measured, with minima of unequal depth. We conclude that reflection from an M-dwarf or {otherwise unseen companion} is the most likely explanation for the 0.801\,d period in EQ\,Psc. Confirmation would make EQ\,Psc the longest-period sdB+dM binary known to date. In their paper reporting g-mode pulsations in EQ\,Psc, \citet{green03} write "\ldots we did find three low-amplitude variables with periods of several hours or more. Two are sdB stars exhibiting apparent reflection effects, having appropriately phased sinusoidal light curves the same length as their orbital periods ($\sim6$ and 12 hr)." The 19.2\,h modulation would have been difficult to identify from the 3\,h photometry reported for EQ\,Psc, so its omission at that time is understandable. During the preparation of this letter, the authors have been made aware, however, that subsequent ground-based photometry by Green et al. does show evidence for a low-amplitude reflection effect (Green, {\O}stensen, priv. comm.). Figure~\ref{f:orbit} shows no evidence for a primary eclipse, neither in the total flux, nor in the residual flux. A dip just before the expected position of secondary eclipes is consistent with being noise. Geometric considerations alone imply that longer-period sdB+dM binaries are less likely to eclipse, as indicated by the period distributions of eclipsing and non-eclipsing systems (Fig.~\ref{f:periods}\footnote{ {Periods for eclipsing (HW\,Vir) systems shown in Fig.~\ref{f:periods} were taken from: \citet{schaffenroth14} (SDSS\,J1622+4730: 0.0697\,d), \citet{drechsel01} (HS\,0705+6700: 0.096\,d), \citet{geier11} (SDSS\,J0820+0008: 0.096\,d), \citet{kilkenny98} (NY\,Vir: 0.101\,d), \citet{wils07} (NSVS\,14256825: 0.1104\,d), \citet{ostensen07.wd} (HS\,2231+2441: 0.1106\,d), \citet{menzies86} (HW\,Vir: 0.1168\,d), \citet{barlow13} (EC\,10246-2707: 0.1185\,d), \citet{polubek07} (OGLE BUL-SC16\,335: 0.1251\,d), \citet{ostensen10} (2M\,1938+4603: 0.126\,d), \citet{schaffenroth13} (ASAS\,102322-3737.0: 0.1393\,d), \citet{for10} (2M\,1533+3759: 0.162\,d), \citet{pribulla13} (FBS\,0747+725: 0.21\,d) and \citet{kilkenny78} (AA\,Dor: 0.261\,d). Periods for non-eclipsing (XY\,Sex) systems are from: \citet{maxted02} (XY\,Sex: 0.073\,d), \citet{kupfer14} (UVEX\,J0328+5035: 0.11017\,d), \citet{heber04} (HS\,2333+3927: 0.1718\,d), \citet{morales03} (PG\,1329+159: 0.2497\,d), \citet{ostensen13} (FBS\,0117+396: 0.252\,d), \citet{for08} (2M\,1926+3720: 0.2923\,d), \citet{geier14} (HS\,2043+0615: 0.3016\,d), \citet{green04} (PG\,1438-029: 0.3358\,d), \citet{latour14} (Feige\,48: 0.3438\,d), \citet{kepler10.2} (KIC\,11179657: 0.3944\,d and KIC\,2991403: 0.4431\,d), \citet{koen99b} (V1405\,Ori: 0.398\,d), \citet{pablo11} (B4\,NGC6791: 0.3985\,d), \citet{koen07b} (HE\,0230-4323: 0.4515\,d), \citet{koen09} (JL\,82: 0.75\,d) and this paper (EQ\,Psc: 0.801\,d). }} ). In crude terms, the amplitude of the reflection effect is a function of orbital separation $1/a$, cool dwarf diameter $r_{\rm dM}$ and orbital inclination $i$. Assuming that both components are typical of other sdB+dM binaries. the orbital period indicates a separation $a\approx3.0\pm0.2\Rsolar$, where the uncertainty indicates the spread in the period-separation relation for shorter-period systems. Assuming representative radii of 0.17\,\Rsolar\ for both stars {\citep{almeida12}}, we deduce a maximum inclination $i\lesssim84^{\circ}$ to avoid eclipses. The study of long-period sdB+dM binaries is important for stellar evolution theory and, in particular, for understanding the common-envelope ejection process. sdB+dM binaries are believed to originate in a system where an expanding red giant engulfs a low-mass main-sequence companion shortly before core helium ignition \citep{han02}. The spiral-in of the M dwarf leads to heating and ejection of the common-envelope surrounding the two stars. The final separation of the components is indicative of the amount of orbital binding energy required to remove the red-giant envelope. In the case of EQ\,Psc, the long period may be the result of a wider-than-typical orbital separation, {and possibly linked with a higher-than-typical mass } for the M dwarf. | Observations obtained during an engineering run with {\sl K2} in 2014 February have shown that thruster-assisted, two wheel operation, is sufficiently stable to obtain stellar photometry with high precision. The known pulsating subdwarf B star EQ\,Psc has been demonstrated to show a 2\% light modulation with a period of 19.2\,h. It is argued that this is most likely due to reflection of light from the hot subdwarf by a cool binary companion; an M dwarf is likely. The light curve also contains a rich spectrum of higher frequency oscillations with periods in the range 1800 - 10\,000\,s. Most of these are likely to be associated with g-mode pulsations, as identified by \citet{green03}. Spectroscopic studies of the binary orbit and of the hot star atmosphere are desirable. Opportunities to explore the g-mode pulsation spectrum in more detail should be pursued. | 14 | 4 | 1404.7470 |
1404 | 1404.2255_arXiv.txt | {Small molecular cloudlets are abundant in many \ion{H}{ii} regions surrounding newborn stellar clusters. In optical images these so-called globulettes appear as dark silhouettes against the bright nebular background.} {We aim to make an inventory of the population of globulettes in the Carina Nebula complex, and to derive sizes and masses for comparisons with similar objects found in other \ion{H}{ii} regions. } {The globulettes were identified from H$\alpha$ images collected at the Hubble Space Telescope.} {We have located close to 300 globulettes in the Carina complex, more than in any other region surveyed so far. The objects appear as well-confined dense clumps and, as a rule, lack thinner envelopes and tails. Objects with bright rims are in the minority, but more abundant than in other regions surveyed. Some globulettes are slightly elongated with their major axes oriented in the direction of young clusters in the complex. Many objects are quite isolated and reside at projected distances $>$~1.5 pc from other molecular structures in the neighbourhood. No globulette coincides in position with recognized pre-main-sequence objects in the area. The objects are systematically much smaller, less massive, and much denser than those surveyed in other \ion{H}{ii} regions. Practically all globulettes are of planetary mass, and most have masses less than one Jupiter mass. The average number densities exceed 10$^{5}$~cm$^{-3}$ in several objects. We have found a statistical relation between density and radius (mass) in the sense that the smallest objects are also the densest.} {The population of small globulettes in Carina appears to represent a more advanced evolutionary state than those investigated in other \ion{H}{ii} regions. The objects are subject to erosion in the intense radiation field, which would lead to a removal of any thinner envelope and an unveiling of the core, which becomes more compact with time. We discuss the possibility that the core may become gravitationally unstable, in which case free-floating planetary mass objects can form. } | \label{sec:intro} Optical images of galactic \ion{H}{ii} regions show a mix of bright and dark nebulosity. Foreground cold dust clouds obscure the bright background of warm and ionized gas. The warm plasma in these nebul\ae\ accelerates outwards through the interaction with radiation and winds from hot and massive stars. The molecular gas is swept up and forms expanding shells, which are sculpted into complex filamentary formations, like elephant trunks, pillars that point at O stars in the nebula. Blocks of cold gas can detach from the shells and trunks and may fragment into smaller clouds that appear as dark patches on optical images of these nebul\ae\ as noted long ago by Bok \& Reilly (\cite{bok47}) and Thackeray (\cite{tha50}). The clumps may be round or shaped like tear drops, some with bright rims facing the central cluster (Herbig \cite{her74}). A number of such \ion{H}{ii} regions have been subject to more detailed studies, and it has been found that many regions contain distinct, but very small clumps, extending over less than one to a few arcseconds. Several studies have focused on the so-called proplyds, which are photoevaporating discs surrounding very young stars (e.g. O'Dell et al. \cite{ode93}; O'Dell \& Wen \cite{ode94}; McCaughrean \& O'Dell \cite{mcc96}; Bally et al. \cite{bal00}; Smith et al. \cite{smi03}). In these studies small cloudlets without any obvious central stellar objects were also found, as also recognized by Hester et al. (\cite{hes96}) and Reipurth et al. (\cite{rei97, rei03}) from Hubble Space Telescope images of nebular regions. More systematic studies of such star-less cloudlets followed, and from the surveys of more than 20 \ion{H}{ii} regions by De Marco et al. (\cite{mar06}), Grenman (\cite{gre06}), and Gahm et al. (\cite{gah07}; hereafter Paper~1) it can be concluded that most of the objects have radii $<$10~kAU with size distributions that peak at $\sim$~2.5~kAU. In Paper~1 masses were derived from extinction measures indicating that most objects have masses $<$~13~M$_{J}$ (Jupiter masses), which currently is taken to be the domain of planetary-mass objects. This class of tiny clouds in \ion{H}{ii} regions were called {\it globulettes} in Paper~1 to distinguish them from proplyds and the much larger globules spread throughout interstellar space. We define globulettes as cloudlets with round or slightly elongated shapes with or without bright rims and/or tails. Some globulettes are connected by thin filaments to larger molecular blocks and it is then natural to assume that isolated globulettes once detached from shells and trunks. They may also survive in this harsh environment for long times, as concluded in Paper~1. Follow-up 3D numerical simulations in Kuutmann (\cite{kuu07}) predict lifetimes of $\sim$~$10^{4}$ years, increasing with mass. Owing to the outer pressure exerted on the globulettes from surrounding warm gas, and the penetrating shock generated by photoionization, it was found that many globulettes may even collapse to form brown dwarfs or planetary-mass objects before evaporation has proceeded very far. The objects are protected against rapid photoevaporation by a screen of expanding ionized gas (e.g. Dyson \cite{dys68}; Kahn \cite{kah69}; Tenorio-Tagle \cite{ten77}). Consequently, the objects are expected to develop bright rims on the side facing the cluster because of the interaction with stellar light. In addition, the models predict that dusty tails emerge from the cloud cores. It is therefore puzzling that most globulettes lack any trace of bright rims in H$\alpha$, and that most are round, or only slightly elongated, without any trace of tails. In a recent study by Gahm et al. (\cite{gah13}; hereafter Paper~2), based on NIR imaging and radio molecular line observations of globulettes in the Rosette Nebula, it was found that the objects contain dense cores, which strengthens the suggestion that many objects might collapse to form planetary-mass objects or brown dwarfs that are accelerated outwards from the nebular complex. The whole system of globulettes and trunks expands outwards from the central cluster with velocities of about 22 km s$^{-1}$. In the case where more compact objects are formed inside some globulettes, they will escape and become free-floating objects in the galaxy. In both the optical and radio/NIR surveys (Papers 1 and 2) it was concluded that the density is relatively high even close to the surface layers, which could explain why the objects lack extensive bright rims in H$\alpha$. Some of the optically completely dark objects were discovered to have thin rims manifested in P$\beta$ and H$_{2}$ emission. In a follow-up study of the NIR images, M\"akel\"a et al. (\cite{mak14}) found that some smaller globulettes are also crowned by thin bright rims that are not seen in H$\alpha$. The present study is an inventory of globulettes in the Carina Nebula (NGC 3372) based on images taken from the {\it Hubble Space Telescope} (HST) through a narrow-band H$\alpha$ filter. Basic parameters, like size and mass, are derived and we compare the results to surveys of similar objects in other nebulae. The Carina complex, with its extended network of bright and dark nebulosity, spans over several degrees in the sky and is one of the most prominent sites of star formation in the galaxy. More than 60 O-type stars and several young clusters (Tr 14, 15, and 16; Collinder 228 and 232; and Bochum 10 and 11) are located in the region, and more than a thousand pre-main sequence stars have been identified from optical, infrared, and X-ray surveys (e.g. Tapia et al. \cite{tap03}; Ascenso et al. \cite{asc07}; Sanchawala et al. \cite{san07a}, \cite{san07b}; Smith et al. \cite{smi10a}, \cite{smi10b}; Povich et al. \cite{pov11}; Gaczkowski et al. \cite{gac13}). The global properties of the nebular material was discussed in Smith et al. (\cite{smi00}), Smith \& Brooks (\cite{smi07}), and references to studies based on observations of selected areas can be found in the comprehensive review by Smith (\cite{smi08}). Additional surveys from the submm range (Preibisch et al. \cite{pre11}; Pekruhl et al. \cite{pek13}) and the far IR (Preibisch et al. \cite{pre12}; Roccatagliata et al. \cite{roc13}) have been made more recently. The Carina Nebula, in all its glory, is presented in multicolour mosaics found at the Hubble Space Heritage webpage. A number of small obscuring structures in the Carina Nebula were noted by Smith et al. (\cite{smi03}) from HST images, and were regarded as possible proplyds. However, the objects studied were found to be larger than the standard cases in the Orion Nebula (Bally et al. \cite{bal00}). More objects of this nature were recognized by Smith et al. (\cite{smi04}) who stated that their nature remains ambiguous: "analogues of Orion's proplyds, starless cometary clouds, or something in between?" Ascenso et al. (\cite{asc07}), however, concluded from near-infrared imaging that these candidates do not harbour any stars. Most of these objects are globulettes by our definition and are thereby included in our list of nearly 300 globulettes. Thus the Carina complex is the richest known with regard to total number of globulettes. A number of Herbig-Haro jets emanating from embedded young stars in the region were found by Smith et al. (\cite{smi10a}). Most of these are related to trunks or larger fragments. However, HH 1006 is related to an isolated cloud with an embedded jet-driving source (Sahai et al. \cite{sah12}; Reiter \& Smith \cite{reit13}). Tentative jet-signatures were also found for a few much smaller isolated clouds like HH 1011 and HHc-1. The distance to the Carina complex has been estimated in several investigations with rather different results. A distance of 2.3 kpc has been adopted as a kind of standard (Smith \cite{smi08}). Recently, Hur et al. (\cite{hur12}) concluded that the main stellar clusters Tr 14 and 16 are located at a distance of 2.9 kpc. We have adopted this value in the present investigation, but will discuss the implications if the complex is closer. The paper is organized as follows. We present the fields we have searched, the objects identified, and their measured properties in Section~\ref{sec:obs}. The results are analysed in Section~\ref{sec:results} and discussed further in Section~\ref{sec:disc}. We end with a summary in Section~\ref{sec:conclude}. \begin{figure}[t] \centering \resizebox{9cm}{!}{\includegraphics[angle=00]{HSTmap.jpg}} \caption{Image of the central region of the Carina Nebula, where the HST fields containing globulettes are marked. The locations of the star $\eta$~Carin{\ae} and four stellar clusters are marked. North is up and east to the left. The image spans 1.\degr3 x 1.\degr5 (credit: Nathan Smith, Univ. of Minnesota, NOAO, AURA, NSF).} \label{map} \end{figure} \begin{table} \caption[]{HST archive data used.} \label{HST} $$ \begin{array}{*{4}{p{0.1\textwidth}}} \hline \noalign{\smallskip} \ Field/Target & R.A. (J2000.0) \hfill{} & Dec. (J2000.0)& Images \\ \noalign{\smallskip} \hline \noalign{\smallskip} 1 / Pos 30 & 10:41:27 & -59:47:42 & J9dk09010 \\ 2 / Pos 30 & 10:41:38 & -59:46:17 & J9dk09020 \\ 3 / Pos 30 & 10:41:40 & -59:44:41 & J9dka9010 \\ 4 / Pos 19 & 10:42:23 &-59:20:59 & J9dk12010 \\ 5 / Pos 19 & 10:42:48 &-59:19:44 & J9dk32010 \\ 6 / Tr 14 & 10:43:07 & -59:29:34 & J900c1010 \\ 7 / Tr 14 & 10:43:23 & -59:32:06 & J900b1010 \\ 8 / Tr 14& 10:43:24 & -59:27:55 & J900c2010 \\ 9 / Tr 14 & 10:43:39 & -59:34:37 & J900a1010 \\ 10 / Tr14 & 10:43:41 & -59:30:17 & J900b2010 \\ 11 / Tr 14 & 10:43:47 & -59:35:53 & J90001020 \\ 12 / Tr 14 & 10:43:55 & -59:37:09 & J90001010 \\ 13 / HH 666& 10:43:58 & -59:54:39 & J900a9010 \\ 14 / Tr 14 & 10:43:59 & -59:32:38 & J900a2010 \\ 15 / Tr 14 & 10:44:00 & -59:28:05 & J900b3010 \\ 16 / HH 666 & 10:44:01 & -59:58:42 & J900b9010 \\ 17 / Tr 16 & 10:44:05 & -59:40:16 & J900c5010 \\ 18 / Tr 14 & 10:44:07 & -59:33:53 & J90002020 \\ 19 / Tr 14 & 10:44:15 & -59:35:09 & J90002010 \\ 20 / Tr 14 & 10:44:17 & -59:30:27 & J900a3010 \\ 21 / Tr 14 & 10:44:19 & -59:25:54 & J900b4010 \\ 22 / Tr 16 & 10:44:20 & -59:42:48 & J900b5010 \\ 23 / Tr 16 & 10:44:22 & -59:38:34 & J900c6010 \\ 24 / Tr 14 & 10:44:35 & -59:33:09 & J90003010 \\ 25 / Tr 16 & 10:44:36 & -59:45:19 & J900a5010 \\ 26 / Pos 27 & 10:44:40 & -59:59:46 & J9dk07010 \\ 27 / Pos 27& 10:44:43 & -59:56:34 & J9dk27010 \\ 28 / Tr 16 & 10:44:44 & -59:46:35 & J90005020 \\ 29 / Tr 16 & 10:44:49 & -59:37:35 & J900b7020 \\ 30 / Tr 16 & 10:44:52 & -59:47:51 & J90005010 \\ 31 / Tr 14 & 10:44:54 & -59:31:08 & J90004010 \\ 32 / Tr 15 & 10:44:58 & -59:26:50 & J9dka0010 \\ 33 / Tr 16& 10:44:58 & -59:38:47 & J900b7010 \\ 34 / Tr 16 & 10:45:12 & -59:45:51 & J90006010 \\ 35 / Tr 16 & 10:45:17 & -59:36:38 & J900b8010 \\ 36 / Tr 15 & 10:45:23 & -59:26:59 & J9dk10010 \\ 37 / Tr 16 & 10:45:44 & -59:40:34 & J90008020 \\ 38 / Pos 23& 10:45:53 & -60:08:16 & j90010010 \\ 39 / Pos 23 & 10:45:56 & -60:06:42 & J90010020 \\ 40 / Pos 22& 10:46:32 & -60:05:14 & J9dk23010 \\ 41 / Pos 21& 10:46:47 & -60:09:29 & J9dk22010 \\ 42 / Pos 20& 10:46:58 & -60:06:26 & J9dk01010 \\ 43 / Pos 20& 10:47:01 & -60:03:14 & J9dk21010 \\ \noalign{\smallskip} \hline \end{array} $$ \end{table} | \label{sec:conclude} We have made an inventory of globulettes in the Carina Nebula complex based on existing HST narrow-band H$\alpha$ images. A total of 288 globulettes were listed and measured for size, mass, and density. Most objects are either round or slightly elongated, and many of the latter are oriented in the direction of massive young clusters in the area. We discuss why only a minority have developed bright H$\alpha$ emitting rims and/or tails, and we note that there is no evidence so far of any embedded young stars. The Carina globulettes are, on the whole, much smaller and less massive than those recognized from HST surveys of a number of other \ion{H}{ii} regions. Practically all are of planetary mass, and most have masses less than one Jupiter mass. The corresponding mean densities are much higher than in other regions, exceeding number densities of 10$^{5}$ cm$^{-3}$ in several objects. We found a statistical relation between average density and size in the sense that the smallest globulettes are also the densest. Globulettes may detach from larger blocks of molecular gas, like isolated fragments, elephant trunks, and shell structures, after which their thinner envelopes evaporate and leave denser cores, which may become even more compressed with time. From virial arguments we conclude that the objects are not bound unless they contain a bit more mass than inferred from the derived mean mass. Most of the tiny objects are quite isolated and located at projected distances of $>$~1.5 pc from the closest larger molecular structures, which indicates that the objects can survive for long times in the nebula. We speculate that the objects might contain denser cores or even planetary-mass objects that already have formed in their interior. We suggest that the Carina globulettes are a more evolved state than the larger and less dense objects that are abundant in other \ion{H}{ii} regions. Globulettes in \ion{H}{ii} regions may be one source of the large number of free-floating planetary-mass objects that has been estimated to exist in the Galaxy. | 14 | 4 | 1404.2255 |
1404 | 1404.0120_arXiv.txt | We report estimated carbon-abundance ratios, \cfe{}, for seven newly-discovered carbon-enhanced metal-poor (CEMP) RR Lyrae stars. These are well-studied RRab stars that had previously been selected as CEMP candidates based on low-resolution spectra. For this pilot study, we observed eight of these CEMP RR Lyrae candidates with the Wide Field Spectrograph (WiFeS) on the ANU 2.3m telescope. Prior to this study, only two CEMP RR Lyrae stars had been discovered: TY Gru and SDSS~J1707$+$58. We compare our abundances to new theoretical models of the evolution of low-mass stars in binary systems. These simulations evolve the secondary stars, post accretion from an AGB donor, all the way to the RR Lyrae stage. The abundances of CEMP RR Lyrae stars can be used as direct probes of the nature of the donor star, such as its mass, and the amount of material accreted onto the secondary. We find that the majority of the sample of CEMP RR Lyrae stars is consistent with AGB donor masses of around $1.5-2.0$ M$_\sun$ and accretion masses of a few hundredths of a solar mass. Future high-resolution studies of these newly-discovered CEMP RR Lyrae stars will help disentangle the effects of the proposed mixing processes that occur in such objects. | Over the past few decades, it has become clear that a large fraction of stars with significant carbon enhancements exists among the populations of metal-poor stars in the Galactic halo. These carbon-enhanced metal-poor (CEMP) stars were originally defined as having metallicities \metal{} $\le-1.0$ and carbon-abundance ratios \cfe{} $\ge+1.0$ \citep{beers2005}. Recent studies of large numbers of metal-poor stars suggest that a more natural dividing line between the carbon-normal and carbon-enhanced populations is \cfe{} $\ge+0.7$ (see, for example, Figure 4 from Aoki et al. 2007 and Figure 4 from Carollo et al. 2012). We therefore define CEMP stars as having \metal{} $\le-1.0$ and \cfe{} $\ge+0.7$. The frequency of CEMP stars, among metal-poor stars in the Milky Way, increases with decreasing metallicity \citep{beers1992,norris1997,beers2005,cohen2005,marsteller2005,rossi2005,frebel2006,lucatello2006, norris2007,carollo2012,lee2013,norris2013,spite2013}, as well as with distance from the Galactic plane \citep{frebel2006,carollo2012,lee2013}. From the study of their elemental abundance patterns, one can begin to uncover details concerning the nature of their progenitor objects. There exist a number of different sub-classes of CEMP stars with specific abundance characteristics; these different sub-classes are suggestive of different sites of carbon production at early times \citep{beers2005}. CEMP-$s$ stars, which exhibit evidence of $s$-process-element enhancement, are the most common; around 80\% of CEMP stars exhibit $s$-process-element enhancements \citep{aoki2007}, including both the CEMP-$s$ and CEMP-$r/s$ sub-classes (the latter sub-class indicates stars for which the presence of both $r$- and $s$-process element enhancements are found). It is widely believed that these objects are the result of mass transfer from a companion asymptotic giant-branch (AGB) star, where the production of carbon and $s$-process elements occurs \citep{herwig2005,sneden2008}. About half of the CEMP-$s$ stars have been shown to be CEMP-$r/s$, suggesting formation from molecular clouds that had already been enhanced in $r$-process elements, opening the possibility that their carbon enhancements arose from more than one site. In any case, observational evidence suggests that the CEMP-$r/s$ stars (and other $r$-process-element rich stars) do not require a contribution of $r$-process elements from a binary companion (see Hansen et al. 2011b, 2013). Stars in the CEMP-no sub-class exhibit no neutron-capture element enhancements, and the source of the carbon enhancement for these stars is less certain. Current suggestions include the possibility that very massive, rapidly-rotating, mega metal-poor (\metal{} $< -6.0$) stars were very efficient producers of carbon, nitrogen, and oxygen, due to distinctive internal burning and mixing episodes followed by strong mass loss (Hirschi et al. 2006; Meynet et al. 2006, 2010). Another suggested origin is pollution of the interstellar medium (ISM) by so-called faint supernovae associated with the first generations of stars, which can experience extensive mixing and fallback during their explosions \citep{umeda2003,tominaga2007,kobayashi2011,ito2013,nomoto2013,Tominaga2013}. Recent observations of some of the lowest-metallicity RR Lyrae stars have revealed similarities between the abundance patterns of these stars and their non-varying counterparts in the halo of the Milky Way. For example, Hansen et al. (2011a) find that the elemental abundance patterns of two very metal-poor RR Lyrae stars (\metal{} $\sim-2.8$) match typical patterns of very metal-poor stars observed in the Galactic halo, and indeed, they can be compared to theoretical yields from the first generations of stars. Because a large fraction of the very metal-poor (VMP; [Fe/H] $< -2.0$) stars studied in the Galactic halo are CEMP stars, one would expect that a similar fraction of VMP horizontal-branch stars would exhibit carbon over-abundances. Prior to our observational program, only two CEMP RR Lyrae stars had been recognized \citep{preston2006,kinman2012}. Now, the sample size has increased by more than a factor of four, as we have identified seven new CEMP RR Lyrae stars. One clear advantage of the study of CEMP RR Lyrae stars, as opposed to CEMP stars in other evolutionary stages, is that the observed surface abundances are primarily influenced by the dilution of accreted material in the receiving star at first dredge up. When the receiving star is on the main sequence, it is unknown whether the observed surface composition is purely due to the makeup of the accreted material, or whether some non-convective process (such as rotation, e.g., Masseron et al. 2012, or thermohaline mixing, e.g., Stancliffe et al. 2007) has already led to dilution. By using more evolved objects we bypass this uncertainty. Detailed stellar models \citep{stancliffe2013} suggest that the surface composition of a CEMP star in the RR Lyrae phase is predominantly determined by the mass of material accreted, and the composition of the ejecta. This assumes that all evolved objects had a mass of around 0.8 M$_\sun$ at the main sequence turn-off, and consequently, their structures along the giant branch (particularly the depth that the convective envelope reaches during first dredge-up) are similar. The CEMP RR Lyrae stars may thus provide a constraint on the efficiency of wind accretion, which, although currently highly uncertain (Abate et al. 2013), potentially has an important impact on, e.g., Type Ia supernova progenitors. This paper is organized as follows. Section 2 describes the target selection, observing techniques, and details of the observations. Sections 3 and 4 describe the estimation of stellar parameters and carbon abundances. A discussion of the Oosterhoff classifications of our program stars, and their implications, is given in Section 5. Section 6 includes a description of the theoretical models used for comparison, and Section 7 contains a thorough discussion of the analysis of our measured \cfe{} abundances in terms of these theoretical scenarios. Our conclusions and plans for future work are provided in Section 8. | We have obtained moderate-resolution spectroscopy and estimated stellar parameters and carbon-abundance ratios, \cfe{}, for a sample of 8 RR Lyrae stars, resulting in the identification of seven new CEMP RR Lyrae variables. As there were previously only two such stars discovered, we significantly increase the sample size of these objects. Five of the stars are Oosterhoff II type variables and the remaining three are Oosterhoff I, based on their periods, $V$ amplitudes, and metallicities. Upon comparison to a sample of metal-poor RR Lyrae stars with sub-solar \cfe{}, we find a separation between pulsation period, suggesting that the presence (or lack) of sufficient carbon could have a physical effect on the dynamics of variability. However, larger sample sizes of both carbon-enhanced and carbon-weak RR Lyrae stars remain necessary to fully explore this claim. We compared the measured \cfe{} abundances in the CEMP RR Lyrae stars to new theoretical models of AGB binary mass transfer and subsequent evolution. We find that the majority of the are consistent with AGB donor masses of $\sim1.5-2.0$ M$_\sun$ and accretion masses of $\sim0.01-0.05$ M$_\sun$. Large accretion masses, on the order of 0.1 M$_\sun$ remain possible for a few objects. All eight stars are inconsistent with scenarios in which very low accretion masses of $\sim0.001$ M$_\sun$ are considered, which is to be expected, given the small contribution of carbon these donors provide and the large degree of dilution that this material undergoes. Future studies should include high-resolution spectroscopy of CEMP RR Lyrae stars, as well as other non-variable horizontal-branch stars, in order to explore more elements for theoretical comparison, in particular those associated with the $s$-process. With a larger set of high-precision abundance estimates, we can delve more deeply into the likely mixing history of these stars (by both convective and non-convective processes). Furthermore, we plan to expand the set of theoretical models to include those of different metallicities for a more complete set of donor masses and accretion masses. | 14 | 4 | 1404.0120 |
1404 | 1404.2914_arXiv.txt | Quasar damped Ly$\alpha$ (DLA) absorption line systems with redshifts $z<1.65$ are used to trace neutral gas over approximately 70\% of the most recent history of the Universe. However, such systems fall in the UV and are rarely found in blind UV spectroscopic surveys. Therefore, it has been difficult to compile a moderate-sized sample of UV DLAs in any narrow cosmic time interval. However, DLAs are easy to identify in low-resolution spectra because they have large absorption rest equivalent widths. We have performed an efficient strong-\MgII-selected survey for UV DLAs at redshifts $z=[0.42,0.70]$ using HST's low-resolution ACS-HRC-PR200L prism. This redshift interval covers $\sim1.8$ Gyr in cosmic time, i.e., $t\approx[7.2,9.0]$ Gyrs after the Big Bang. A total of 96 strong \MgII\ absorption-line systems identified in SDSS spectra were successfully observed with the prism at the predicted UV wavelengths of Ly$\alpha$ absorption. We found that 35 of the 96 systems had a significant probability of being DLAs. One additional observed system could be a very high $N_{\rm HI}$ DLA ($N_{\rm HI} \sim 2\times10^{22}$ atoms cm$^{-2}$ or possibly higher), but since very high $N_{\rm HI}$ systems are extremely rare, it would be unusual for this system to be a DLA given the size of our sample. Here we present information on our prism sample, including our best estimates of $N_{\rm HI}$ and errors for the 36 systems fitted with damped Ly$\alpha$ profiles. This list is valuable for future follow-up studies of low-redshift DLAs in a small redshift interval, although such work would clearly benefit from improved UV spectroscopy to more accurately determine their neutral hydrogen column densities. | Since the first spectroscopic survey for intervening quasar damped Ly$\alpha$ (DLA) absorption-line systems (Wolfe et al. 1986), it has been recognized that these gaseous regions with neutral hydrogen column densities $N_{\rm HI} \ge 2 \times 10^{20}$ atoms cm$^{-2}$ can be used to trace the neutral gas component of the Universe. DLA and related observations allow the Universe to be probed over about 90 per cent of its current age.\footnote{Throughout we assume a cosmology with H$_0$ = 70 km s$^{-1}$ Mpc$^{-1}$, $\Omega_{\rm M} = 0.3$, and $\Omega_{\Lambda} = 0.7$.} The most recent extensive results from low-redshift UV and high-redshift optical DLA surveys have been presented by Rao, Turnshek, \& Nestor (2006; hereafter RTN2006) and Noterdaeme et al. (2012), respectively. Relative to RTN2006 (41 DLAs in their statistical sample), Meiring et al. (2011) found a very high incidence of DLAs in a more recent HST COS UV blind survey (3 DLAs), which is counter to what Bahcall et al. (1993) found in the HST FOS UV QSO Absorption-Line Key Project blind survey (1 DLA), but both UV blind surveys suffer from small number statistics. Most recently, Noterdaeme et al. (2014) present a study of $\sim 100$ extremely strong high-redshift DLAs, with $N_{\rm HI} \ge 5 \times 10^{21}$ atoms cm$^{-2}$. Aside from statistical results on the DLA incidence (product of absorber cross-section and their comoving number density) and the cosmic mass density of neutral gas, many interesting facets of galaxy formation and evolution can be considered through follow-up studies of DLA metallicities, dust, molecular fractions, star formation, kinematics, associated galaxies, and clustering as a function of redshift. These topics in DLA research have been widely discussed in the literature, but it is not the purpose of this paper to summarize them (see Wolfe et al. 2005 for a past review). Here, we simply wish to emphasize that while follow-up studies of DLAs are providing a wealth of information about the neutral-gas-phase component of the Universe, reasonably accurate statistical measurements in any relatively narrow low-redshift interval have remained elusive. By low redshift we mean redshifts $z<1.65$, for which the Ly$\alpha$ line falls in the UV. For example, the low-redshift DLA survey of RTN2006 probed $z<1.65$. This redshift regime corresponds to $\sim$ 70 per cent ($\sim 9.6$ Gyrs) of the most recent history of the Universe, where significant evolution is known to have occurred. But since observation of a low-redshift Ly$\alpha$ line requires space-based UV spectroscopy, the number of confirmed DLAs remains relatively small in all narrow low-redshift intervals (e.g., in cosmic time intervals corresponding to $\sim 1$ to $2$ Gyrs). Even with the efficient strong-\MgII-selected DLA survey method used by RTN2006, only 9 DLAs have been previously confirmed at $z=[0.42, 0.70]$. This redshift interval spans $\sim1.8$ Gyr in cosmic time, $t\approx[7.2,9.0]$ Gyrs after the Big Bang. A number of years ago, when STIS had failed and COS was not yet installed on HST, we had the opportunity to perform a large strong-\MgII-selected survey for DLAs at $z=[0.42,0.70]$. This is a very efficient way to conduct a DLA survey since any biases can be accounted for if the statistics of \MgII\ absorption-line systems are well understood (RTN2006). This redshift interval was chosen because it is well-matched to the sensitivity of HST's low-resolution ACS-HRC-PR200L prism. To demonstrate this, Figure 1 shows the Ly$\alpha$ damping profiles for a range of DLA $N_{\rm HI}$ values within this redshift interval at full resolution and at the resolution of a prism spectrum. The prism has nonlinear dispersion so that a prism spectrum of a Ly$\alpha$ line at $z=0.42$ has resolution $\lambda$/$\Delta\lambda \approx 197$ (4.4 \AA\ pixel$^{-1}$ at 1726 \AA), while at $z=0.70$ it has $\lambda$/$\Delta\lambda \approx 97$ (10.6 \AA\ pixel$^{-1}$ at 2067 \AA). With this in mind, we undertook prism observations of the UV Ly$\alpha$ absorption lines in 109 strong-\MgII\ systems to determine if they exhibited an absorption profile with damping wings. The data collection on these 109 systems required 105 single-orbit observations since four of the quasars had two systems.\footnote{Note that during our program there were three one-orbit observations with target-acquisition failures. Repeat single-orbit observations were obtained for two of the failed observations; the observation of J003740.13-090810.0 was not repeated. Thus we lost one of the original strong-\MgII\ systems in our sample and it does not appear in our lists.} Of the 109 strong-\MgII\ systems in our sample that were observed with the prism, we found that only 97 of them had observations that were usable in our DLA search. We also obtained spectroscopy of three quasars with known DLAs (``DLA calibrators'') to confirm our ability to recognize and measure DLAs. In general, if a Ly$\alpha$ line does not exhibit a significant damping profile (i.e., if $N_{\rm HI}$ is too low in a \MgII\ system), it would be undetectable or nearly undetectable in its prism spectrum. Thus, prism observations offer a suitable method for distinguishing DLAs from non-DLAs. \begin{figure} \vspace{-0.4in}\centerline{ \includegraphics[width=1.0\columnwidth,clip,angle=0]{fig1.ps}} \caption{Simulation of expected HST ACS-HRC-PR200L prism spectra of DLAs at $z=0.44$ and $z=0.70$ for a low $N_{\rm HI}$ value of $2\times10^{20}$ atoms cm$^{-2}$ and a high $N_{\rm HI}$ value of $5\times10^{21}$ atoms cm$^{-2}$. The smooth red profiles (see online version) are the normalized theoretical DLA absorption-line profiles. The black profiles are the expected spectra at the resolution of the prism. Note the poorer resolution at higher redshift. Also, the redshift range of our usable observations is taken to be $z=[0.42,0.70]$, however at $z<0.44$ (see the top right panel) the short wavelength side of a high-$N_{\rm HI}$ DLA will begin to become impossible to measure reliably over the expected range in $N_{\rm HI}$ values since the prism calibration does not extend below $\sim 1700$ \AA.} \label{fig:spectrum} \end{figure} Below we describe the results of our HST observations with the primary goal of identifying new DLAs ($N_{\rm HI} \ge 2\times10^{20}$ atoms cm$^{-2}$) at $z=[0.42,0.70]$. Our method to achieve this was simply to examine the prism spectra at the predicted locations of the Ly$\alpha$ absorption lines in strong-\MgII\ absorption-line systems.\footnote{Strong-\MgII\ absorption lines usually means ones with observed \MgII$\lambda 2796$ rest equivalent widths $\ge 0.3$ \AA, however, the systems we study here generally have rest equivalent widths $>1$ \AA.} The outline of this paper is as follows. In \S2 we present the details of our observational program and data processing for the observed strong-\MgII\ systems. In \S3 we present $N_{\rm HI}$ results for the 36 systems which, based on the prism spectra, have a significant or an interesting probability of being DLAs, along with results on the three DLA calibrators. In \S4 we conclude with a short discussion of the significance of our results. The implications of these results for measurements of the incidence and cosmic mass density of neutral gas will be discussed in a future paper by Rao et al. | 14 | 4 | 1404.2914 |
|
1404 | 1404.0316_arXiv.txt | We present Spitzer/IRAC observations of nine $z'$-band dropouts highly magnified ($2\!\lesssim\!\mu\!\lesssim\!12$) by the Bullet Cluster. We combine archival imaging with our Exploratory program (SURFS UP), which results in a total integration time of $\sim\!30$~hr per IRAC band. We detect ($\gtrsim\!3\sigma$) in both IRAC bands the brightest of these high-redshift galaxies, with $[3.6]\!=\!23.80\pm0.28$~mag, $[4.5]\!=\!23.78\pm0.25$~mag, and $(H-[3.6])\!=\!1.17\pm0.32$~mag. The remaining eight galaxies are undetected to $[3.6]\!\sim\!26.4$~mag and $[4.5]\!\sim\!26.0$~mag with stellar masses of $\sim\!5\times10^{7}$~M$_{\odot}$. The detected galaxy has an estimated magnification of $\mu\!=\!12\pm4$, which implies this galaxy has an ultraviolet luminosity of $L_{1500}\!\sim\!0.3\;L^*_{z\!=\!7}$ --- the lowest luminosity {\it individual} source detected in IRAC at $z\!\gtrsim\!7$. By modeling the broadband photometry, we estimate the galaxy has an intrinsic star-formation rate of $\mbox{SFR}\!\sim\!\psiunlensedest~\mbox{M}_{\odot}$~yr$^{-1}$ and stellar mass of $M\!\sim\!\massunlensedest~\mbox{M}_{\odot}$, which gives a specific star-formation rate of ${\rm sSFR}\!\sim\!\ssfrestpergyr$~Gyr$^{-1}$. If this galaxy had sustained this star-formation rate since $z\!\sim\!20$, it could have formed the observed stellar mass (to within a factor of $\sim\!2$), we also discuss alternate star-formation histories and argue the exponentially-increasing model is unlikely. Finally, based on the intrinsic star-formation rate, we estimate this galaxy has a likely [\ion{C}{2}] flux of $\langle f_{[\mbox{C~{\tiny II}}]}\rangle\!=\!\aveciiflux$. | \label{sec:intro} Determining the details of cosmic reionization of hydrogen at high redshift is a central question to modern cosmology. Although the observed optical depth to Thompson scattering \citep{hinshaw} and complete Gunn-Peterson troughs \citep{bob} suggest that instantaneous reionization occurred around $z\!\sim\!10$ and was completed by $z\!\sim\!6$, the sources responsible for the ionizing radiation are far from clear. Although dwarf galaxies are sufficiently numerous and energetic to reionize the Universe \citep[e.g.][]{yan04,bou06,saw06,lem09}, it is uncertain how the ionizing photons escape such galaxies \citep[e.g.][]{shap06}. Consequently tracing the physical properties of the dwarf galaxy population into the neutral epoch is key in understanding cosmic reionization \citep[e.g.][]{font12}, and is a primary goal for the next-generation facilities and surveys. As the ionizing radiation is likely emitted by hot, young stars, the current star-formation rate (SFR) is of great interest \citep[e.g.][]{bou07}. However, the conversion from ultraviolet luminosity to SFR is complicated by an unknown an extinction corrections \citep[e.g.][]{bou10}, which can be mitigated to some extent with longer wavelength data \citep{fink10}. Although with the Infrared Array Camera (IRAC) on the Spitzer Space Telescope (\sst) observations redward of the 4000~\AA-break (in the restframe of high-redshift galaxies) are routinely available, new practical problems with source blending and confusion have arisen. After dealing with issues, it seems that high-redshift galaxies have $(H-[3.6])\!\sim\!0.6$~mag \citep[e.g.][]{gonz12}. Na\"{\i}vely, this suggests that the galaxies have strong 4000~\AA-breaks indicative of an evolved population \citep[e.g.][]{eyl07}, but such breaks seem unlikely given the age of the Universe at these redshifts \citep{rich11}. Instead this red color may point to a significant emission-line flux in the IRAC channels \citep{zack08}. Because both a 4000~\AA-break and optical emission lines are likely present, the IRAC photometry is a critical component in modeling the spectra and determining the stellar mass, age, and SFR of high-redshift galaxies \citep[e.g.][]{pap02}. Many of the previous interpretations of the IRAC data of $z\!\gtrsim\!7$ galaxies come from {\it stacking} fluxes of otherwise undetected, individual galaxies \citep[e.g.][]{labbe10a,gonz12,labbe12}. In such analyses, one selects objects of comparable properties (such as $H$-band magnitude), and combines the IRAC data to build up the ``average'' signal, effectively simulating deeper data. Despite the merits, this approach has three short-comings: First, extreme or exotic objects, which may challenge existing models or skew averages, may be excluded. Second, this method implicitly assumes that one obtains a homogeneous sample of galaxies by selecting on the $H$-band flux. However in the case of $H$-band flux, this is not guaranteed since this restframe wavelength is sensitive to both present star formation and extinction. Therefore these stacked samples are essentially selected on a combination of SFR and dust extinction, which complicates the interpretation of their ``average'' stellar populations. Finally, narrow emission lines can be smeared out by stacking galaxies of unknown (or imprecise) redshifts, which complicates the assessment of their ionizing budget. In contrast to stacking, one can use massive clusters of galaxies as {\it cosmic telescopes} and magnify background objects, which makes it possible to study intrinsically fainter individual objects for the same exposure time. Indeed this approach is quickly becoming a key tool in the study of high-redshift galaxies with the implementation of the Hubble Space Telescope (\hst) Frontier Fields program (HFF)\footnote{http://www.stsci.edu/hst/campaigns/frontier-fields/HDFI\_SWGReport2012.pdf}. In this paper, we present the first results from the {\it Spitzer UltRaFaint SUrvey: \surfsup}, a {\it Spitzer} Exploratory Program (PropID:~90009; PI:~M.~Brada\v{c}) approved in Cycle 9 during the Warm Mission \citep{bradac14}. This program adds $\sim\!25$~hr in both IRAC channels to the existing $\sim\!5$~hr for \nclust~strong-lensing galaxy clusters at $0.3\!\leq\!z\!\leq\!0.7$. Six of these clusters are part of the Cluster Lensing and Supernova Survey with Hubble program \citep[CLASH;][]{post12}, two are scheduled for Year~2 of the HFF (MACS J0717.5+3745 and MACS J1149.5+2223), and six are planned for the Grism Lens-Amplified Survey from Space (GLASS; PI:~Treu). Here we discuss $z'$-band dropouts lensed by the Bullet Cluster and identified by \citet{hall12}. This paper is organized as follows: in section~\ref{sec:obs} we discuss the \sst/IRAC data, in section~\ref{sec:phot} we describe our photometry and treatment of deblending, in section~\ref{sec:sed} we present the SED modeling, and in section~\ref{sec:disc} we give concluding remarks with comments for future work. We quote all magnitudes in the AB system and adopt a $\Lambda$CDM concordance cosmology ($\Omega_0\!=\!0.3$, $\Omega_{\Lambda}\!=\!0.7$, and $H_0\!=\!70$~km~s$^{-1}$~Mpc$^{-1}$). | \label{sec:disc} We have presented the first results from \surfsup\footnote{http://www.physics.ucdavis.edu/$\sim$marusa/SurfsUp.html}, a Spitzer Exploration Program to image \nclust\ strong-lensing clusters to $\sim\!100$~ks depth per channel. We have definitively detected one of the \ngal\ $z'$-band dropouts identified by \citet{hall12}. This galaxy is highly magnified by the Bullet Cluster ($\mu\!=\!12\pm4$) with an apparent magnitude of $J\!=\!25.43\pm0.22$~mag, which gives a far-UV luminosity of $M_{1500}\!=\!-18.9\pm0.42$~mag (accounting for both the photometric and magnification uncertainty). Therefore this galaxy has $L_{1500}\!\sim\!0.3\;L^*$ \citep[taking $M_{1500}^*\!=\!-20.14$~mag from][]{bou11}, and is the only {\it individual} dwarf galaxy at $z\!\gtrsim\!7$ detected so far by IRAC \citep[c.f.][]{yan12,labbe12}. This is the first direct detection of the kind of galaxy likely responsible for the cosmic reionization. From the SED modeling we infer a specific star-formation rate (sSFR) of ${\rm sSFR}\!\sim\!0.7$~Gyr$^{-1}$, which is lower than comparable galaxies \citep[e.g.][]{zheng12,zit12} or at low redshift \citep[e.g.][]{kai}. In contrast, the remaining eight galaxies have $\langle{\rm sSFR}\rangle\!\sim\!50$~Gyr$^{-1}$, similar to Lyman-break galaxies (LBGs) at $z\!\sim\!5$ \citep{nph12}, suggesting that this detected object may be an unusual member of the high-redshift galaxy population. It is intriguing to consider the SFHs that could yield a substantial stellar mass ($M_*\!\sim\!2^{+0.6}_{-0.9}\times10^9$~M$_{\odot}$) at this early epoch. The two inferences of stellar mass and SFR essentially constrain the integral and current value of the SFH, respectively. Assuming that galaxies begin to form around $z_{\rm form}\!\sim\!20$, then this galaxy must have acquired the observed stellar mass in $\lesssim\!650$~Myr\footnote{Although we estimate the age in \tab{tab:pop}, this age is predicated on an exponentially-declining SFH. To avoid circularity in the argument, we instead adopt a conservative estimate for the formation redshift.}. If it had constantly formed stars at the measured rate over this time, then it would have built up a stellar mass of $8.4\times10^8$~M$_{\odot}$. Although this constant SFR model is roughly consistent with the derived mass ($\sim\!1.5~\sigma$), it suggests that the SFR could not have been lower in the past without some corresponding period of increased star formation. Of course it is impossible to distinguish between a smooth, multi-component SFH \citep[e.g.][]{lee10,behroozi,pacifici} from a stochastic history punctuated by intense bursts. But, it does imply that the exponentially-increasing model \citep{mara10} can be ruled out, given its substantial stellar mass, modest SFR, and high redshift. If the actual formation redshift were lower than our conservative assumption, then the argument becomes stronger as the constant star-formation scenario cannot create enough mass by $z\!\sim\!7$. In the above we tacitly assumed that the stellar mass was created {\it in situ}, and that it had not experienced any type of merger. Although mergers would bring in stellar mass (and possibly enhance the star formation), they are not on frequent enough to change the mass significantly \citep{hopk10}. Using their merger rate calculator, we estimate that a galaxy with a stellar mass of $2\times10^9$~M$_{\odot}$ will have an average major merger rate of $\sim\!0.9$~mergers~Gyr$^{-1}$. In the $600-700$~Myr available to this galaxy (the range reflects the $\pm3\sigma$ uncertainty on the photometric redshift), there are only $0.5-0.7$~mergers of mass ratio $0.25\!<\!m_1/m_2\!<1$. Even if major mergers contributed to the observed stellar mass of this galaxy, this scenario raises the question of how two progenitors with stellar masses of $M_*\!\sim\!10^9$~$M_{\odot}$ formed --- the one galaxy is puzzling enough. While this galaxy may have had an exceptionally high merger rate, the major merger scenario seems unlikely, which leaves minor mergers or gradual accretion/inflow a possibility. Certainly gas inflow is an early prediction for the formation of the earliest galaxies \citep[e.g.][]{larson} and has even been observed in low-redshift star-forming galaxies \citep{rubin12}. Our broadband data are insensitive to the observational signatures of inflow \citep[such as redshifted resonance lines;][]{martin}, but it possible with the {\it The James Webb Space Telescope}. We estimate this galaxy has an observed $\mbox{SFR}\!=\!\psilensed\,\mu^{-1}$~M$_{\odot}$~yr$^{-1}$, and is a prime candidate for follow-up with the Atacama Large Millimeter Array (ALMA). Like the far-ultraviolet (FUV), the far-infrared (FIR) has many useful SFR indicators, particularly the [\ion{C}{2}] $\lambda157.7~\mu$m emission line and thermal continuum from warm dust. To predict the [\ion{C}{2}] flux, we use the SFR estimated in Section~\ref{sec:sed} and calibrations from \citet{delooze11}, to predict an integrated line flux of $F_{[\rm C~{\tiny II}]}\!\sim\!\ciiflux$. If we assume a Gaussian line profile (of width $\Delta v\!=\!100$~km~s$^{-1}$), the SFR gives an average flux density of $\langle f_{[{\rm C~{\tiny II}}]}\rangle\!=\!\aveciiflux$. Because our SED models imply a small amount of dust (see \tab{tab:pop}) and recent chemical evolution models find a sufficient amount of dust can be produced by $z\!\sim\!6$ \citep{vali09}, we estimate the FIR continuum flux (8--1000~$\mu$m) using the the \citet{kenn98} scaling relation. We predict this galaxy will have an integrated flux of $F_{\rm FIR}\!=\!\firflux$, which averaged over 8--1000~$\mu$m is $\left<f_{\rm FIR}\right>\!=\!\avefirflux$. All fluxes discussed in this paragraph include the magnification. These flux levels are readily achievable, even with the current ALMA facilities \citep[e.g.][]{wagg12}. Using standard tools and techniques we have robustly detected 1/9 $z'$-dropouts from \citet{hall12}. For the remaining eight galaxies that have gone undetected in \surfsup\ we performed a similar tweaking/re-fitting analysis described in section~\ref{sec:sed}. We tweak the IRAC upper limits for the eight undetected galaxies slightly deeper ($\sim\!0.25$~mag) and re-fit with \lephare. We find that either no combination of physical parameters could effectively characterize the tweaked photometry or that resulting best-fit models required extreme properties: very young ages ($\lesssim\!10$~Myr) or low stellar masses ($\lesssim\!10^8$~M$_{\odot}$~$\mu^{-1}$; where $\mu$ is the magnification). As such, we suspect that the IRAC limits quoted in \tab{tab:obs} for the remaining eight galaxies (where one is unobservable as discussed in section~\ref{sec:phot}) are close to their true brightnesses. As part of our on-going efforts with \surfsup\ we will continue to develop tools and techniques to deal with the unique challenges posed by this and similar datasets. | 14 | 4 | 1404.0316 |
1404 | 1404.2639_arXiv.txt | We discuss the absorption due to various constituents of the interstellar medium of M82 seen in moderately high resolution, high signal-to-noise ratio optical spectra of SN 2014J. Complex absorption from M82 is seen, at velocities 45 $\la$ $v_{\rm LSR}$ $\la$ 260 km~s$^{-1}$, for \ion{Na}{1}, \ion{K}{1}, \ion{Ca}{1}, \ion{Ca}{2}, CH, CH$^+$, and CN; many of the diffuse interstellar bands (DIBs) are also detected. Comparisons of the column densities of the atomic and molecular species and the equivalent widths of the DIBs reveal both similarities and differences in relative abundances, compared to trends seen in the ISM of our Galaxy and the Magellanic Clouds. Of the ten relatively strong DIBs considered here, six (including $\lambda$5780.5) have strengths within $\pm$20\% of the mean values seen in the local Galactic ISM, for comparable $N$(\ion{K}{1}); two are weaker by 20--45\% and two (including $\lambda$5797.1) are stronger by 25--40\%. Weaker than ''expected'' DIBs [relative to $N$(\ion{K}{1}), $N$(\ion{Na}{1}), and $E(B-V)$] in some Galactic sight lines and toward several other extragalactic supernovae appear to be associated with strong CN absorption and/or significant molecular fractions. While the $N$(CH)/$N$(\ion{K}{1}) and $N$(CN)/$N$(CH) ratios seen toward SN 2014J are similar to those found in the local Galactic ISM, the combination of high $N$(CH$^+$)/$N$(CH) and high $W$(5797.1)/$W$(5780.5) ratios has not been seen elsewhere. The centroids of many of the M82 DIBs are shifted, relative to the envelope of the \ion{K}{1} profile -- likely due to component-to-component variations in $W$(DIB)/$N$(\ion{K}{1}) that may reflect the molecular content of the individual components. We compare estimates for the host galaxy reddening $E(B-V)$ and visual extinction $A_{\rm V}$ derived from the various interstellar species with the values estimated from optical and near-IR photometry of SN 2014J. | \label{sec-intro} Supernovae in external galaxies provide rare, fleeting opportunities to probe the interstellar media of the host galaxies via absorption-line spectroscopy. In principle, such observations can reveal the behavior of various tracers of the ISM under somewhat different environmental conditions from those typically sampled in the local Galactic ISM. Differences in overall metallicity, specific elemental abundance ratios, dust-to-gas ratios, and radiation fields all can affect the structure and composition of interstellar clouds (e.g., Wolfire et al. 1995; Pak et al. 1998); in combination, the overall effects can be somewhat unexpected and counter-intuitive. Exploration of diverse environments, where those factors act in different combinations, thus can aid in disentangling the specific effects of each factor. It is particularly important to compare the behavior of the enigmatic diffuse interstellar bands (DIBs) in a variety of environments with the corresponding behavior of known atomic and molecular constituents of the ISM. Such comparisons should aid both in identifying the carriers of the DIBs and in calibrating the DIBs as diagnostics of the physical conditions in the ISM. Some of the typically strongest DIBs (in the local Galactic ISM) have therefore been measured toward a small number of stars in the Large and Small Magellanic Clouds (LMC and SMC; Vladilo et al. 1987; Ehrenfreund et al. 2002; Cox et al. 2006, 2007; Welty et al. 2006), toward a much larger set of stars in the 30 Dor region of the LMC (van Loon et al. 2013), and toward some stars in M33 (Cordiner et al. 2008b) and M31 (Cordiner et al. 2008a, 2011). A few DIBs have been detected in the host galaxies of extragalactic supernovae (D'Odorico et al. 1989; Sollerman et al. 2005; Cox \& Patat 2008, 2014) and in several damped Lyman-$\alpha$ systems (York et al. 2006; Ellison et al. 2008; Lawton et al. 2008); Phillips et al. (2013) have compiled measurements of the $\lambda$5780.5 DIB toward a number of recent Type Ia SNe. Examination of the behavior of the DIBs in the Local Group galaxies suggests that the DIB strengths can depend both on the overall metallicity and on local physical conditions (e.g., radiation field, molecular fraction). Certain DIB ratios (e.g., $\lambda$5797.1/$\lambda$5780.5) may provide information on the ambient radiation fields (e.g., Vos et al. 2011); the strengths of individual DIBs (e.g., $\lambda$5780.5) may yield useful estimates for the color excess $E(B-V)$ and the column density of atomic hydrogen $N$(H) where those quantities cannot be directly determined (e.g., Herbig 1993; Friedman et al. 2011; Phillips et al. 2013). The discovery of SN 2014J in M82 (Fossey et al. 2014) provided an opportunity to obtain moderately high resolution, high signal-to-noise (S/N) ratio spectra of a bright, nearby supernova at multiple epochs (both before and after maximum apparent brightness) -- enabling searches for weak interstellar features and for temporal variations in the absorption that might reveal changes in circumstellar material (e.g., Patat et al. 2007; Simon et al. 2009; Sternberg et al. 2011, 2013). As summarized by Goobar et al. (2014), analyses of the early photometry and optical spectra suggest that SN 2014J is a Type Ia, significantly reddened by intervening interstellar material located primarily within M82; estimates of $E(B-V)$ range from about 0.8 to 1.3 mag (Polshaw et al. 2014; Amanullah et al. 2014; Foley et al. 2014; Marion et al. 2014). Absorption from a number of known interstellar species and from many DIBs in M82 thus might be detectable in high-S/N ratio spectra of the supernova. Unfortunately, Type Ia SNe typically have very little UV flux below about 2600 \AA\ (e.g., Foley \& Kirshner 2011; Foley et al. 2014), making UV spectra impractical to obtain (particularly for appreciably reddened SNe) -- so that investigations of the intervening ISM will have to depend largely on interpreting the species observable in the optical and infrared. In this paper, we discuss the interstellar absorption features seen in multi-epoch, moderately high resolution, high-S/N ratio optical spectra obtained with the ARC echelle spectrograph (ARCES; Wang et al. 2003) at Apache Point Observatory (APO). Section 2 describes the observations and the processing of the raw spectral images. Section 3 presents the observed interstellar features, with some comparison to those seen toward several other SNe. Section 4 discusses some of the atomic and molecular species and several of the DIBs -- in the context of trends observed in the ISM of our Galaxy, the LMC, and the SMC -- yielding some insights into the behavior of the DIBs and the properties of the M82 ISM toward SN 2014J. Section 5 summarizes our results and conclusions. Two companion papers focus on the abundances and kinematics of the observed atomic and molecular species (Ritchey et al. 2014b) and on a more complete census of the DIBs detected toward SN 2014J (D. York et al., in preparation). | \label{sec-sum} We have discussed the interstellar absorption features found in moderately high resolution, high S/N ratio optical spectra of SN 2014J (in the nearby galaxy M82), obtained with the ARC echelle spectrograph at Apache Point Observatory between 2014 January 27 and March 04 (bracketing the maximum V-band brightness of the SN). Complex absorption from \ion{Na}{1}, \ion{K}{1}, \ion{Ca}{1}, and \ion{Ca}{2} is seen for LSR velocities between about $-$53 and +257 km~s$^{-1}$. The absorption at $v_{\rm LSR}$ $\la$ 30 km~s$^{-1}$ is due to gas in the Galactic disk and halo; the absorption at higher velocities arises in gas associated with M82. Absorption from CH, CH$^+$, and/or CN is seen for the strongest M82 components between 80 and 120 km~s$^{-1}$. Many of the diffuse interstellar bands are also detected, at velocities corresponding to gas in M82. Comparisons of the interstellar absorption in M82 with trends seen in the local Galactic ISM, in the lower metallicity Magellanic Clouds, and in other galaxies probed by SNe reveal both similarities and some intriguing differences. Overall, the $N$(\ion{K}{1})/$N$(\ion{Na}{1}) and $N$(CH)/$N$(\ion{K}{1}) ratios are very similar to those seen in our Galaxy; $N$(CN) is also quite consistent with the values seen locally, for comparable $N$(CH). The $N$(\ion{Ca}{1})/$N$(\ion{K}{1}) ratio is high, suggestive of relatively mild depletion of calcium in M82, particularly in the higher velocity components. The $N$(CH$^+$)/$N$(CH) ratio is very high -- significantly exceeded in the Galactic ISM only in several sight lines in the Pleiades. The moderate $N$(CN)/$N$(CH) and very high $N$(CH$^+$)/$N$(CH) suggest that the molecular material toward SN 2014J is unlikely to be in very cold, dense clouds. Of the ten DIBs considered in this paper, six ($\lambda\lambda$4963.9, 5487.7, 5780.5, 6196.0, 6203.6, 6283.8) have equivalent widths within $\pm$20\% of the mean Galactic values for the observed $N$(\ion{K}{1}); $\lambda$5705.1 and $\lambda$6379.3 are weaker by 20--45\%; and $\lambda$5797.1 and $\lambda$6613.6 are stronger by 25--40\%. The overall $W$(5797.1)/$W$(5780.5) ratio is thus fairly high ($\sim$0.7) -- suggestive of relatively weak ambient radiation fields and/or shielded environments. The combination of a high $N$(CH$^+$)/$N$(CH) ratio and a high $W$(5797.1)/$W$(5780.5) ratio is very unusual, as those two ratios exhibit a fairly tight anticorrelation in the Galactic ISM (and elsewhere). While $W$(5780.5) is moderately correlated with both $N$(\ion{K}{1}) ($r$ $\sim$ 0.71) and $E(B-V)$ ($r$ $\sim$ 0.82) in the Galactic ISM, the DIB is weaker than expected, relative to $N$(\ion{K}{1}) and/or $E(B-V)$, in a number of Galactic and extragalactic sight lines; the residuals (with respect to the mean Galactic trends) for $W$(5780.5) versus $N$(\ion{K}{1}) and $W$(5780.5) versus $E(B-V)$ are correlated. In general, the sight lines in which the $\lambda$5780.5 DIB appears to be weak also exhibit fairly high $N$(CN) and/or fairly high molecular fractions $f$(H$_2$). Similar behavior is exhibited by the other ''standard'' DIBs considered in this paper -- particularly the broader DIBs. Those DIBs appear weak, relative to $N$(\ion{K}{1} and/or $E(B-V)$, in sight lines with significant molecular fractions, at least in part because they trace primarily atomic gas, whereas \ion{K}{1} and $E(B-V)$ trace both atomic and molecular material. The $\lambda$4963.9 ''C$_2$-DIB'' is not weaker than expected in those sight lines, however, because the C$_2$-DIBs can be present (and enhanced) in molecular gas. The profiles of many of the M82 DIBs appear to be shifted in velocity, relative to the envelope of the \ion{K}{1} profiles toward SN 2014J, with different shifts for different DIBs. The DIB profiles toward SN 2014J may be modeled by combining ''intrinsic'' DIB profiles (derived from ARCES spectra of 20 Aql) for all the velocity components seen in \ion{K}{1}. Uniform weighting of the \ion{K}{1} components by $N$(\ion{K}{1}) yields a good match to the observed DIB profile only for the $\lambda$4963.9 C$_2$-DIB; heavier relative weighting of the weaker, higher velocity \ion{K}{1} components is required to fit the observed profiles of the other ''standard'' DIBs -- e.g., by factors of about 3 for the $\lambda$5797.1 DIB and about 7 for the $\lambda$5780.5 DIB. The differences in relative weighting [i.e., in $W$(DIB)/$N$(\ion{K}{1})] are suggestive of differences in local physical/environmental conditions in the stronger ''main'' M82 components and in the weaker, higher velocity components -- and of differences in the responses of the various DIBs to those local conditions. If standard Galactic relationships between $W$(5780.5) and $N$(H) and between $N$(CH) and $N$(H$_2$) are used to predict $N$(H) and $N$(H$_2$) in those two component groups, we estimate that the stronger main components would contain about 65\% of the total hydrogen in the sight line, with $f$(H$_2$) $\sim$ 0.75 and $W$(5797.1)/$W$(5780.5) $\sim$ 1.1 and the weaker, higher velocity components would contain about 70\% of the total atomic hydrogen, with $f$(H$_2$) $\sim$ 0.15 and $W$(5797.1)/$W$(5780.5) $\sim$ 0.45. The $\lambda$4963.9 C$_2$-DIB and (to a lesser degree) the $\lambda$5797.1 DIB are stronger in the main, largely molecular components, while the $\lambda$5780.5 and $\lambda$6613.6 ''standard'' DIBs are stronger in the higher velocity, primarily atomic components. The correlation between the residuals, relative to the mean Galactic trends, of $W$(5780.5) versus $N$(\ion{K}{1}) and $W$(5780.5) versus $E(B-V)$ suggests that comparisons of $W$(5780.5) with $N$(\ion{K}{1}) may be used to identify cases where estimates of $E(B-V)$ and $A_{\rm V}$ based on the measured $W$(5780.5) would be too small -- and then to refine those estimates for $E(B-V)$ and $A_{\rm V}$. Estimates of the reddening due to dust in M82 along the sight line to SN 2014J, derived from the equivalent widths of the ten DIBs considered in this paper (and Galactic trends of reddening versus DIB strength), yield $E(B-V)$ $\sim$ 0.71$\pm$0.11 mag -- consistent with the values estimated from $N$(\ion{Na}{1}) and $N$(\ion{K}{1}) and also with the lower end of the values inferred from photometry of the SN. Corresponding estimates of the visual extinction, $A_{\rm V}$ $\sim$ 1.9$\pm$0.2 (from the DIBs, \ion{Na}{1}, and \ion{K}{1}), are consistent with the most recent values inferred from the photometry. The explanation for the low $R_{\rm V}$ inferred toward SN 2014J (and many other Type Ia SNe) remains elusive. | 14 | 4 | 1404.2639 |
1404 | 1404.6060_arXiv.txt | We present the results based on $R$-band polarimetric follow-up observations of the nearby ($\sim$10 Mpc) Type II-plateau SN~2012aw. Starting from $\sim$10 days after the SN explosion, these polarimetric observations cover $\sim$90 days (during the plateau phase) and are distributed over 9 epochs. To characterize the Milky Way interstellar polarization (ISP$_{\rm MW}$), we have observed 14 field stars lying in a radius of 10$^\circ$ around the SN. We have also tried to subtract the host galaxy dust polarization component assuming that the dust properties in the host galaxy are similar to that observed for Galactic dust and the general magnetic field follow the large scale structure of the spiral arms of a galaxy. After correcting the ISP$_{\rm MW}$, our analysis infer that SN~2012aw has maximum polarization of 0.85\% $\pm$ 0.08\% but polarization angle does not show much variation with a weighted mean value of $\sim$138$\degr$. However, if both ISP$_{\rm MW}$ and host galaxy polarization (ISP$_{\rm HG}$) components are subtracted from the observed polarization values of SN, maximum polarization of the SN becomes 0.68\% $\pm$ 0.08\%. The distribution of $Q$ and $U$ parameters appears to follow a loop like structure. The evolution of polarimetric light curve (PLC) properties of this event is also compared with other well studied core-collapse supernovae of similar type. | \label{sec:introduction} Core-collapse supernovae (CCSNe) exhibit significant level of polarization during various phases of their evolution at optical/infra-red wavelengths. In general, the degree of polarization of different types of SNe seems to increase with decreasing mass of the stellar envelope at the time of explosion \citep[see][]{2000AIPC..522..445W, 2001ApJ...553..861L, 2001ApJ...550.1030W, 2005ASPC..342..330L}. Type II SNe are polarized at level of $\sim$1\% $-$ 1.5\%. However, Type Ib/c SNe (also known as stripped-envelope SNe as the outer envelopes of hydrogen and/or helium of their progenitors are partially or completely removed before the explosion) demonstrate significantly higher polarization in comparison to Type II SNe \citep[for more details, see][and references therein] {2001PASP..113..920L, 2002ApJ...580L..39K, 2003ApJ...593L..19K, 2003ApJ...591.1110W, 2006A&A...459L..33G, 2007ApJ...671.1944M, 2012A&A...545A...7P, 2012ApJ...754...63T, 2013MNRAS.433L..20M}. The higher polarization values observed in case of Type Ib/c SNe most probably arise due to extreme departure from the spherical symmetry \citep{1992SvAL...18..168C, 2001AIPC..586..459H, 2001AIPC..556..301K}. Theoretical modelling predicts that in general CCSNe show the degree of asymmetry of the order of 10\% $-$ 30\% if modelled in terms of oblate/prolate spheroids \citep[e.g.][]{1991A&A...246..481H}. Numerical simulations \citep[see][]{2006ApJ...651..366K, 2011MNRAS.410.1739D} indicate that in case of Type II SNe, the level of polarization is also influenced by SN structure (e.g., density and ionization), apart from their initial mass and rotation. The possible progenitors of Type IIP SNe are low-mass red/blue super-giants and their polarization studies are extremely useful to understand the SN structure in detail. In spite of being the most common subtypes among the known CCSNe, polarization studies of Type IIP SNe have been done only in a handful of cases \citep[e.g.][]{1988MNRAS.234..937B, 2001ApJ...553..861L, 2006Natur.440..505L, 2001PASP..113..920L, 2006AstL...32..739C, 2010ApJ...713.1363C, 2012AIPC.1429..204L}. In general, intrinsic polarization in these SNe are observed below 1\% but few exceptions exist in literature (for example \citet{2010ApJ...713.1363C} reported $\sim$1.5\% for SN~2006ov). Systematic polarimetric studies have been started, only after the observations of Type IIP SN~1987A \citep[see][]{1988MNRAS.231..695C, 1988ApJ...334..295M, 1991ApJS...77..405J}. \citet{1982ApJ...263..902S} first pointed out that polarimetry provides direct powerful probe to understand the SN geometry \citep[see also][]{1984MNRAS.210..829M, 1991A&A...246..481H}. Polarization is believed to be produced due to electron scattering within the SN ejecta. When light passes through the expanding ejecta of CCSNe, it retains information about the orientation of layers. In spherically symmetric scenario, the equally present directional components of the electric vectors will be canceled out to produce zero net polarization. If the source is aspherical, incomplete cancellation occurs which finally imprint a net polarization (see Fig. 1 of \citealt{2004cetd.conf...30F} and \citealt{2005ASPC..342..330L}). In addition to asphericity of the electron scattering atmosphere, there are several other processes which can produce polarization in CCSNe such as scattering by dust \citep[e.g.][]{1996ApJ...462L..27W}; clumpy ejecta or asymmetrically distributed radioactive material within the SN envelope \citep[e.g.][]{1995ApJ...440..821H, 2006AstL...32..739C}, and aspherical ionization produced by hard X$-$rays from the interaction between the SN shock front and a non-spherical progenitor wind \citep{1996ssr..conf..241W}. To diagnose the underlying polarization in SNe explosions, two basic techniques i.e. broad-band polarimetry and spectropolarimetry have been used. Both of these techniques have advantages and disadvantages relative to each other. One of the main advantages of spectropolarimetry of SNe with respect to broad-band polarimetry is its ability to infer geometric and dynamical information for the different chemical constituents of the explosion. Broad-band polarimetric observations construct a rather rough picture of the stellar death but require lesser number of total photons than spectropolarimetry. Hence broad-band polarimetric observations can be extended to objects at higher red-shifts or/and they allow to enhance the polarimetric coverage and sampling of the light curve (LC), especially at epochs far from the maximum when the SN is dimmer. The scope of this paper uses imaging polarimetric observations in $R$-band using a meter class telescope when the SN~2012aw was bright enough ($R$ $<$ 13.20 magnitude). \subsection{SN~2012aw} SN~2012aw was discovered in a face-on ($i$ $\sim$54.6$^\circ$, from HyperLEDA\footnote{http://leda.univ-lyon1.fr - \citet{2003A&A...412...45P}}), barred and ringed spiral galaxy M95 (NGC 3351) by P. Fagotti on CCD images taken on 2012 March 16.85 UT with a 0.5-m reflector \citep[cf. CBET 3054,][]{2012CBET.3054....1F}. The SN was located 60\arcsec\, west and 115\arcsec\, north of the center of the host galaxy with coordinates $\alpha = 10^{\rm h} 43^{\rm m} 53\fs73$, $\delta =+11\degr 40\arcmin 17\farcs9$ (equinox 2000.0). This SN discovery was also confirmed independently by A. Dimai on 2012 March 16.84 UT, and J. Skvarc on March 17.90 UT \citetext{more information available in \citealt{2012CBET.3054....1F}, CBET 3054; see also special notice no. 269 available at AAVSO\footnote{http://www.aavso.org/aavso-special-notice-269}}. The spectra obtained on March 17.77 UT by \citet*{2012CBET.3054....3M} with the Asiago Observatory 1.22-m reflector showed a very blue continuum, essentially featureless, with no absorption bands and no detectable emission lines. In subsequent spectra taken on March 19.85 UT \citep*{2012CBET.3054....2I} and 19.92 UT \citep{2012CBET.3054....4S}, the line characteristics finally led to classify it as a young Type II-P supernova. The explosion date of this event is precisely determined by \citet{2012ApJ...759L..13F} and \citet{2013MNRAS.433.1871B}. We adopt 2012 March 16.1 $\pm$ 0.8 day (JD 2456002.6 $\pm$ 0.8, taken from the later study) as time of explosion throughout this article. At a distance of about 10 Mpc \citep[cf.][]{2001ApJ...553...47F, 2002ApJ...565..681R, 2013MNRAS.433.1871B}, this event provided us a good opportunity to study its detail polarimetric properties. \begin{figure} \centering \includegraphics[scale = 0.11]{fig1.eps} \caption{ The $R$-band image of the SN~2012aw field around the host galaxy M95, observed on 17 April 2012 using AIMPOL with the 1-m ST, India. Each object has two images. The ordinary and extra-ordinary images of SN~2012aw and host galaxy are labeled as o and e, respectively. The galaxy is marked with a white arrow and the SN is located 60\arcsec\ west, 115\arcsec\ south of the center of M95 galaxy. North and East directions are also indicated.} \label{sn12aw_field} \end{figure} \begin{table*} \centering \caption{Polarimetric observation log and estimated polarimetric parameters of SN~2012aw. \label{sn2012aw_log}} \begin{tabular}{ccc|cc|cc|cc} \hline \hline UT Date &JD & Phase$^{a}$& \multicolumn{2}{c}{Observed} & \multicolumn{2}{c}{Intrinsic (ISP$_{\rm MW}$} subtracted) & \multicolumn{2}{c}{Intrinsic (ISP$_{\rm MW}$ + ISP$_{\rm HG}$} subtracted) \\ (2012) &2450000 &(Days) & $P_{R} \pm \sigma_{P_{R}}$ & $ \theta{_R} \pm \sigma_{\theta{_R}}$ & $P_{R} \pm \sigma_{P_{R}}$ & $\theta{_R} \pm \sigma_{\theta{_R}}$ & $P_{R} \pm \sigma_{P_{R}}$ & $\theta{_R} \pm \sigma_{\theta{_R}}$ \\ & & & ($\%$) &($^\circ)$ & ($\%$) & ($^\circ$) & ($\%$) & ($^\circ$) \\ \hline Mar 26 &6013.35& 10.75 &0.58 $\pm$ 0.46& 131.4 $\pm$ 22.9& 0.61 $\pm$ 0.46& 138.9 $\pm$ 21.6& 0.39 $\pm$ 0.46& 134.2 $\pm$ 33.4\\ Mar 28 &6015.23& 12.63 &0.56 $\pm$ 0.03& 132.0 $\pm$ 1.5& 0.60 $\pm$ 0.03& 139.6 $\pm$ 1.4& 0.38 $\pm$ 0.03& 135.1 $\pm$ 2.2\\ Mar 29 &6016.28& 13.68 &0.49 $\pm$ 0.08& 132.2 $\pm$ 4.6& 0.53 $\pm$ 0.08& 140.8 $\pm$ 4.3& 0.31 $\pm$ 0.08& 136.1 $\pm$ 7.3\\ Apr 16 &6034.18& 31.58 &0.24 $\pm$ 0.17& 132.0 $\pm$ 21.0& 0.30 $\pm$ 0.17& 147.8 $\pm$ 16.7& 0.07 $\pm$ 0.17& 150.5 $\pm$ 72.8\\ Apr 17 &6035.25& 32.65 &0.26 $\pm$ 0.01& 142.6 $\pm$ 1.0& 0.36 $\pm$ 0.01& 154.0 $\pm$ 0.8& 0.15 $\pm$ 0.01& 164.8 $\pm$ 1.8\\ May 15 &6063.05& 60.45 &0.87 $\pm$ 0.08& 123.8 $\pm$ 2.6& 0.85 $\pm$ 0.08& 129.0 $\pm$ 2.6& 0.68 $\pm$ 0.08& 123.3 $\pm$ 3.3\\ May 19 &6067.04& 64.44 &0.54 $\pm$ 0.01& 124.3 $\pm$ 0.5& 0.54 $\pm$ 0.01& 132.7 $\pm$ 0.5& 0.35 $\pm$ 0.01& 123.6 $\pm$ 0.8\\ May 21 &6069.08& 66.48 &0.43 $\pm$ 0.06& 112.3 $\pm$ 4.0& 0.37 $\pm$ 0.06& 122.7 $\pm$ 4.6& 0.28 $\pm$ 0.06& 103.4 $\pm$ 6.2\\ Jun 14 &6093.23& 90.63 &0.47 $\pm$ 0.14& 128.2 $\pm$ 8.5& 0.49 $\pm$ 0.14& 137.5 $\pm$ 8.2& 0.29 $\pm$ 0.14& 129.9 $\pm$ 14.1\\ \hline \end{tabular} \\ $^{a}$ with reference to the explosion epoch JD 2456002.6\\ \end{table*} The progenitor of this SN has been detected both in ground and space based pre-explosion images and its distinct characteristics are analyzed. In pre-SN explosion images obtained with {\it HST}\footnote{Hubble Space Telescope} + WFPC2\footnote{Wide-Field and Planetary Camera 2}, VLT\footnote{Very Large Telescope} + ISAAC\footnote{Infrared Spectrometer And Array Camera} and NTT\footnote{New Technology Telescope}+SOFI\footnote{Infrared spectrograph and imaging camera}, \citet{2012ApJ...759L..13F} found that the progenitor is a red super-giant (mass 14$-$26 M$_{\sun}$). An independent study by \citet{2012ApJ...756..131V} confirmed these findings (mass 15$-$20 M$_{\sun}$). However, \citet*{2012ApJ...759...20K} have a different view and have concluded that progenitor mass in earlier studies are significantly overestimated and that the progenitor's mass is $\textless$ 15 M$_{\sun}$. Immediately after the discovery, several groups have started the follow-up observations of this event in different wavelengths \citep[see, e.g.][]{2012ATel.3995....1I, 2012ATel.4012....1S, 2013ApJ...764L..13B, 2013NewA...20...30M, 2013arXiv1311.3568Y}. Early epoch (4 to 270 days) low-resolution optical spectroscopic and dense photometric follow-up (in $UBVRI$/$griz$ bands) observations of SN~2012aw has been analyzed by \citet{2013MNRAS.433.1871B}. In a recent study, \citet{2013arXiv1311.2031J}, have presented nebular phase (between 250 $-$ 451 days) optical and near-infrared spectra of this event and have analyzed it with spectral model calculations. Furthermore, the preliminary analysis of optical spectropolarimetric data of SN~2012aw, revealed that outer ejecta is substantially asymmetric \citep{2012ATel.4033....1L}. In this paper, we present Cousins $R$-band polarimetric follow-up observations of SN~2012aw. The observations and data reduction procedures are presented in Section~\ref{sec:obs_analy}. Estimation of intrinsic polarization is described in Section~\ref{sec:results_discussion}. Finally, results and conclusions are presented in Sections \ref{diss} and \ref{sec:conclusions}, respectively. \begin{table*} \centering \caption{Observational detail of 14 isolated field stars selected to subtract the interstellar polarization. Observations of all field stars were performed on 20 January 2013 in $R$ band with the 1.04 m ST. All these stars were selected with known distances and within 10$\degr$ radius around SN~2012aw. The distance mentioned in the last column has been taken from \citet{2007A&A...474..653V} catalogue. \label{tab:field_stars}} \begin{tabular}{lcccll} \hline \hline Star & RA (J2000) & Dec (J2000) & $P_{R} \pm \sigma_{P_{R}}$ & $ \theta{_R} \pm \sigma_{\theta{_R}}$ & Distance \\ id & ($^\circ$) & ($^\circ$) & $\%$ & ($^\circ$) & (in pc ) \\ \hline HD 99028$^{\dagger}$ & 170.98071& +10.52960 & 0.08 $\pm$ 0.00 & 167.9 $\pm$ 1.7 & 23.7 $\pm$ 0.5 \\ HD 88830$^{\dagger}$ & 153.73935& +09.21180 & 0.10 $\pm$ 0.01 & 116.8 $\pm$ 1.8 & 36.3 $\pm$ 3.8 \\ HD 87739$^{\dagger}$ & 151.78235& +08.76970 & 0.05 $\pm$ 0.01 & 99.9 $\pm$ 6.6 & 85.0 $\pm$ 8.3 \\ HD 97907$^{\dagger}$ & 168.96624& +13.30750 & 0.17 $\pm$ 0.05 & 59.6 $\pm$ 9.5 & 99.6 $\pm$ 12.1 \\ HD 88282$^{\dagger}$ & 152.72730& +07.69460 & 0.12 $\pm$ 0.01 & 79.1 $\pm$ 1.8 & 118.5 $\pm$ 10.0 \\ HD 87635$^{\dagger}$ & 151.57707& +07.94470 & 0.17 $\pm$ 0.00 & 89.0 $\pm$ 0.5 & 135.7 $\pm$ 19.9 \\ HD 87915$^{\dagger}$ & 152.08824& +07.57300 & 0.11 $\pm$ 0.01 & 86.4 $\pm$ 1.6 & 193.1 $\pm$ 34.7 \\ HD 87996$^{\dagger}$ & 152.20123& +06.71740 & 0.20 $\pm$ 0.04 & 62.5 $\pm$ 5.6 & 243.3 $\pm$ 91.2 \\ HD 88514$^{\dagger}$ & 153.15102& +07.67730 & 0.18 $\pm$ 0.03 & 90.5 $\pm$ 4.5 & 254.5 $\pm$ 82.9 \\ G 452 & 160.45186& +12.10886 & 0.10 $\pm$ 0.01 & 22.6 $\pm$ 2.4 & 261.1 $\pm$ 70.9 \\ BD+12 2250 & 161.08996& +11.33560 & 0.12 $\pm$ 0.08 & 100.1 $\pm$ 18.0 & 286.5 $\pm$ 91.1 \\ BD+13 2299 & 161.41026& +12.46724 & 0.20 $\pm$ 0.00 & 72.4 $\pm$ 0.8 & 314.5 $\pm$ 87.0 \\ HD 93329 & 161.65268& +11.18412 & 0.12 $\pm$ 0.03 & 144.8 $\pm$ 5.8 & 358.4 $\pm$ 118.2 \\ HD 92457 & 160.15550& +12.07868 & 0.05 $\pm$ 0.07 & 27.8 $\pm$ 41.3 & 460.8 $\pm$ 191.1 \\ \hline \end{tabular} \\ $^{\dagger}$ Stars with available $V$-band polarimetry from \citet{2000AJ....119..923H} catalogue. \\ BD+12 2250, BD+13 229, G 452, HD 93329 and HD 92457 are the stars within 2$\degr$ radius field around the SN. \\ \end{table*} | \label{sec:conclusions} We present results based on 9 epoch $R$ band imaging polarimetric observations of Type IIP supernova SN~2012aw. To the best of our knowledge, the initial three epoch polarimetric observations presented here are the earliest optical polarimetric data reported for this event. It was not possible to monitor the SN during the beginning of the nebular or post-nebular phase due to observational constraints, however present observations cover almost up to the end of the plateau phase ($\sim$90 days). The main results of our present study are the following: \begin{itemize} \item {The observed broad-band polarization for initial three epochs is $\sim$0.6\%, then decreases up to $\sim$0.3\% following a sudden increase up to $\sim$0.9\% on 15 may 2013 and at later epochs it seems to show a declining trend. However, the observed polarization angle is almost constant, superimposed with slight variations.} \item {To study the intrinsic polarization properties of SN~2012aw, we subtracted the contribution due to ISP$_{\rm MW}$ and ISP$_{\rm HG}$ from the observed $P$ and $\theta$ values of SN. The ISP$_{\rm MW}$ component was determined using the polarimetric observations of 10 field stars distributed within 10$\degr$ radius around SN and located beyond 100 pc distance. The estimated Stokes parameters of ISP$_{\rm MW}$ are found to be $<$$Q_{\it ISP_{\it MW}}$$>$ = $-$ 0.154 $\pm$ 0.002\% and $<$$U_{\it ISP_{\it MW}}$$>$ = 0.032 $\pm$ 0.002\% (equivalent to $<$$P_{\it ISP_{\it MW}}$$>$ = 0.157 $\pm$ 0.002 and $<$$\theta_{\it ISP_{\it MW}}$$>$ = 84.10$\degr$ $\pm$ 0.56$\degr$). We also estimated the degree of polarization (0.23\%) and polarization angle (147$\degr$) at the location of SN by using the extinction value from Schlegel map assuming that the host galactic dust follow the mean polarization efficiency and the magnetic field in the host galaxy follow the structure of the spiral arms.} \item {The intrinsic polarization parameters of SN~2012aw follow trends of the photometric LC which could be attributed to the small scale variations in the SN atmosphere or their interaction with the ambient medium.} \item{Polarimetric parameters of this SN are compared with other well studied Type IIP events. During the early phase ($\sim$10 $-$ 30 days), the ISP$_{\rm MW}$ subtracted PLC of SN~2012aw matches with that of SN~1987A whereas at later epochs ($\sim$30 $-$ 45 days) it matches to that of SN~2005af.} \end{itemize} | 14 | 4 | 1404.6060 |
1404 | 1404.3072.txt | We present a catalog of true edge-on disk galaxies automatically selected from the Seventh Data Release (DR7) of the Sloan Digital Sky Survey. A visual inspection of the $g$, $r$ and $i$ images of about 15000 galaxies allowed us to split the initial sample of edge-on galaxy candidates into 4768 (31.8\% of the initial sample) genuine edge-on galaxies, 8350 (55.7\%) non-edge-ons, and 1865 (12.5\%) edge-on galaxies not suitable for simple automatic analysis because these objects show signs of interaction, warps, or nearby bright stars project on it. We added more candidate galaxies from RFGC, EFIGI, RC3, and Galaxy Zoo catalogs found in the SDSS footprints. Our final sample consists of 5747 genuine edge-on galaxies. We estimate the structural parameters of the stellar disks (the stellar disk thickness, radial scale length, and central surface brightness) in the galaxies by analyzing photometric profiles in each of the g, r, and i images. We also perform simplified 3-D modeling of the light distribution in the stellar disks of edge-on galaxies from our sample. Our large sample is intended to be used for studying scaling relations in the stellar disks and bulges and for estimating parameters of the thick disks in different types of galaxies via the image stacking. In this paper we present the sample selection procedure and general description of the sample. | Edge-on galaxies provide a unique opportunity for studying the vertical structure of galactic components. Starting from early studies conducted mostly in the optical bands \citep{kormendybruzual78, burstein79, vdKS81a,vdKS81b,kylafisbahcall87} using simple photometric profile fitting, the studies of the vertical structure of galactic components evolved towards complex modeling based on the radiation transfer methods \citep{xilouris99,yoachim06,bianchi07,baes11,schechtman12,degeyter13} using multiple UV, optical and IR data \citep{popescu00,degeyter13}. Most of the structural studies employed limited samples of objects using high quality observations. Large surveys conducted during the last decade have made available benefits of observing large samples of interesting objects, which helps in statistical studies of the vertical structure of galactic disks, bulges, and thick disks \citep{zibetti04,bergvall10}. In this paper we describe our approach to selection of true edge-on galaxies from objects observed by Sloan Digital Sky Survey \citep[SDSS]{sdssDR8}. We identified about six thousand genuine edge-on galaxies with inclination angles not more than a few degrees different from perfect edge-on view. Our sample allows statistical studies of the vertical structure parameters of galactic components for the largest sample known to date. We also introduce an on-line catalog of processed SDSS images and of corresponding structural parameters, which will simplify further studies of edge-on disk galaxies in the optical bands. This paper describes our sample selection procedure and our approach to determination of the stellar disk parameters. The paper is focused mostly on the stellar disk parameters, while bulges will be considered in the next paper. | Careful selection of candidate galaxies from SDSS images allows us to create the largest modern sample (5747 objects) of edge-on galaxies ready for further analysis. Our sample is complete for all galaxies with major axis larger than 30 arcsec. The distribution of the the axial ratio shows that our sample size is reasonable, what also confirms its statistical completeness. We perform a 1-D radial and vertical profile analysis and infer the stellar disk's structural parameters. The results suggest that dust significantly biases the inferred parameters estimated from the optical band images. We also perform a simplified 3-D modeling of all our galaxies taking into account the presence of dust. Comparison between the structural parameters shows that more constrained modeling is needed to eliminate effects of dust in the galaxies. The catalog can be used for statistical studies of the properties of the thick disks using stacked co-adding images. Our large sample makes possible studying scaling relations for galactic stellar disks and bulges. | 14 | 4 | 1404.3072 |
1404 | 1404.2533_arXiv.txt | Recently, Duvall and Hanasoge ({\it Solar Phys.} {\bf 287}, 71-83, 2013) found that large distance $[\Delta]$ separation travel-time differences from a center to an annulus $[\delta t_{\rm{oi}}]$ implied a model of the average supergranular cell that has a peak upflow of $240\ms$ at a depth of $2.3\Mm$ and a corresponding peak outward horizontal flow of $700\ms$ at a depth of $1.6\Mm$. In the present work, this effect is further studied by measuring and modeling center-to-quadrant travel-time differences $[\delta t_{\rm{qu}}]$, which roughly agree with this model. Simulations are analyzed that show that such a model flow would lead to the expected travel-time differences. As a check for possible systematic errors, the center-to-annulus travel-time differences $[\delta t_{\rm{oi}}]$ are found not to vary with heliocentric angle. A consistency check finds an increase of $\delta t_{\rm{oi}}$ with the temporal frequency $[\nu]$ by a factor of two, which is not predicted by the ray theory. | Supergranulation, first seen as a 30 Mm cellular pattern of horizontal flows detected by Doppler shifts \cite{Hart54,Leighton62} in the solar photosphere, continues to puzzle investigators (see review by \opencite{Rieutord10}). Recent work attempts to understand supergranulation by revealing its subsurface structure by numerical simulations \cite{Stein06a} or by local helioseismology \cite{Gizon10}. Detailed radiative-hydrodynamic simulations of the outer convection zone and atmosphere show no excess flow signal at the supergranular scale in the photosphere, in contrast to the observational results \cite{Nordlund09}. These simulations, which match the observations of the solar granulation so well, would seem to have all of the ingredients required to reproduce supergranulation. In particular, the early suggestion of \inlinecite{Leighton62} that He {\sc II} ionization could give rise to supergranulation, is tested by the simulations with a null result. One possibility remaining to be tested is the simulation of magnetic field, which is known to be present along cell boundaries. Local helioseismology has been used extensively to study supergranulation (see review by \opencite{Gizon10}), although no consensus has emerged about fundamental questions such as the depth of the peak flow and the existence or not of counterflows at depth. Some efforts centered on making inversions of individual realizations of the supergranular flow field { \bf \cite{Duvall97,Zhao03,Woodard07,Jack08,Svanda11}. } In some of the work there is great difficulty in separating a horizontally diverging outflow from an upflow \cite{Zhao03,Dombroski13}, although in other work this may have been solved { \bf \cite{Svanda11}. } To make flow maps of individual supergranular realizations, it has been necessary to restrict the measurements to small separations $[\Delta < 5^\circ]$ for which the signal-to-noise ratio is large. To measure the general properties of supergranulation, a large number of cells needs to be examined (in the present work, $6\times10^4$ supergranules are analyzed). To increase the signal-to-noise ratio (S/N), spatial averages are made about cell locations determined from shallow signals such as peaks in the flow divergence. Such a method was first used by \inlinecite{Birch06} and subsequently by \inlinecite{Duvall10} and \inlinecite{Svanda12}. Weak signals can be separated cleanly from realization noise, although more attention to systematic errors is required. As noticed by \inlinecite{Svanda12}, the present method of defining cells is probably biased towards larger cells than the average. This might be corrected (in the future) by directly modeling the spatial autocovariance of the travel-time maps. The averaging of the signals from many cells makes it possible to use larger $\Delta$s (up to $24^\circ$ in the present study), which would normally not be feasible for a 12-hour observation because of the increased noise due to the amplitude reduction from the geometrical spreading of the wavefront \cite{Gizon04}. The separation of the horizontal and vertical flow signals is much better at larger $\Delta$, as the rays are more vertical in the critical near-surface region. \inlinecite{Duvall13} (hereafter Article I) found that the center-to-annulus travel-time difference $[\delta t_{\rm{oi}}]$ was roughly constant at $5.1$ seconds in the range $\Delta=10-25^\circ$. In a simple ray-theory interpretation, this requires a vertical upflow considerably larger than the $10\ms$ observed at the photosphere \cite{Duvall10} and in fact the best-fit model had a peak upflow of $240\ms$ at $z=-2.3\Mm$. Plots of this model and the bracketing models are shown in Figure~\ref{F-flowmodels}. That large vertical upflows are required was recently confirmed by the analysis of \inlinecite{Svanda12} by a considerably different formalism. The strategy for obtaining the best model was developed in Article I and is as follows: We assumed the simplest vertical-flow model that reduces to a $10\ms$ vertical flow at the surface and still approaches the $5.1$ seconds for the asymptotic behavior of the $\delta t_{\rm{oi}}$ signal at large $\Delta$. This is the gaussian with a single peak. For a particular choice of depth of the peak vertical flow $[z_0]$, the width of the gaussian and its amplitude are determined uniquely by the $5.1$ seconds $\delta t_{\rm{oi}}$ signal requirement and the $10\ms$ upward flow at the photosphere. With some reasonable choices for the horizontal parameters $k$ and $R$ (see Article I), the horizontal flow is then determined from the vertical flow and the continuity equation. Three models were examined that bracket the observations. These are distinguished by the height of the peak flow, $z_0=-1.15\Mm$, $z_0=-2.30\Mm$, and $z_0=-3.45\Mm$. The $\delta t_{\rm{oi}}$ signal is computed from the ray theory using both the vertical and horizontal flow components. We found that the $z_0=-2.30\Mm$ model was most similar to the observations. For the $z_0=-3.45\Mm$ model (and any with a deeper $z_0$), the horizontal component contributes significantly and leads to a behavior at large separations that is inconsistent with the observations. We conclude that if there is a deeper horizontal flow, it must have a small magnitude to not be observed in the $\delta t_{\rm{oi}}$ signal. In the present work, the efforts of Article I are extended to include quadrant analysis in Section~\ref{sec-quad}, an attempt to measure a heliocentric-angle (or center-to-limb) dependence in Section~\ref{sec-heliocen}, tests with simulations in Section~\ref{sec-sim}, and an attempt to measure a temporal-frequency $[\nu]$ dependence in Section~\ref{sec-nu}. We give some conclusions in Section~\ref{sec-dis}. \begin{figure} \centerline{\includegraphics[width=1.0\textwidth,clip=]{flowmodel_paper.eps}} \caption{ The flow models from Article I. (a) Velocity vectors for the best model. This is the model labeled {\sf g2} in Table 1 of Article I, with peak upward flow of $240\ms$ at $z=-2.3\Mm$ and peak horizontal flow of $700\ms$ at $z=-1.6\Mm$ and $x=7\Mm$. The cuts shown in (b) are taken at the location of the red dashed vertical line in (a). The cuts in (c) are taken at the location of the turquoise line in (a) at $x=7\Mm$. (b) Cuts of the vertical flow at cell center for the three models in Article I, model {\sf g1} (green; dashed), model {\sf g2} (blue; solid), and {\sf g3} (red; dot-dashed). (c) Cuts of the horizontal flow versus height at the location of the peak flow. Colors and line styles are the same as in (b). } \label{F-flowmodels} \end{figure} | \label{sec-dis} The bulk of the evidence in the present article continues to support a model of the average supergranulation cell as having an upflow with a velocity much larger than the surface upflow of $10\ms$, possibly as large as $240\ms$ and a peak flow $2$\,--\,$3\Mm$ below the surface as seen in the best model {\sf g2}. In Article I, center--annulus travel time differences $[\delta t_{\rm{oi}}]$ were shown to agree well with model {\sf g2}, while in the present article, the quadrant travel-time differences $[\delta t_{\rm{we}}$ and $\delta t_{\rm{ns}}]$ also agree mostly with this type of model. However, there is some disagreement that varies with $\Delta$ for the $\delta t_{\rm{qu}}$, suggesting that either the functional form of the model needs to be adjusted or the ray kernels are incorrect, or both. The apparent disagreement between the present work and the smaller flows seen before has largely disappeared with the work of \inlinecite{Svanda12}. That article does an analysis of average supergranules similar to the averaging done in the present article. He used $f$-modes and small separation p-modes and finds flows that largely confirm the present results. There may be a factor of two difference between the two results, which needs to be resolved. The lack of a center-to-limb variation of the $\delta t_{\rm{oi}}$ signal is useful for a general check of systematic errors. However, the $\nu$-dependence of the $\delta\tau_{\rm oi}$ signal as predicted by ray theory differs from observations, suggesting that ray theory may be inaccurate in near-surface layers. The errors may be due to unmodeled finite-frequency effects or possibly differences in the acoustic-cutoff frequency between the Sun and Model S (used in ray modelling here). That the acoustic-cutoff frequency may differ from that derived from Model S was shown by \inlinecite{Jefferies94}. In a model with the reflection point that is a significant function of frequency, the travel-time difference $[\delta t_{\rm{oi}}]$ could then also be a function of frequency. At a minimum, the variation in $\delta t_{\rm{oi}}$ by a factor of roughly two over the $\nu$-range observed would seem to make the suggested flows uncertain by a similar factor. The simulation results (Section~\ref{sec-sim}) show that the type of model considered (model {\sf g2}) does induce the kind of travel-time shifts observed. These are then seen by both the travel-time shifts measured from the simulation and by ray theory calculated with the model used. It is unfortunate that the modification to the solar model to stablize it has such a large effect on the resulting $\delta t_{\rm{oi}}$. Some of the earlier work finds the flow velocity peaking very near the surface with a monotonic decrease with depth \cite{Birch06,Woodard07}. These results would appear to be inconsistent with this article and Article I. It was suggested in Article I that the perturbations to the p-mode spectrum due to supergranulation are significant in $\ell$, the spherical-harmonic degree. The idea is that the supergranulation pattern, with a spectrum peaking near $\ell=120$ would induce a modulation of a $p$-mode ridge that would have a width in $\ell$ of at least twice this amount. To capture all of the supergranulation signal requires a filter of at least a full-width-half-max of $\Gamma_{\ell}=240$ and likely larger. This justifies the value chosen for the present work of $\Gamma_{\ell}=400$, which clearly captures all of the $\delta t_{\rm{oi}}$ signal at large $\Delta$. This conclusion is supported by Figure 4 of Article I. Of course, if the modeling is correct, one can use any filter. However, if much of the supergranulation signal is not being captured, one becomes much more sensitive to the modeling. In \inlinecite{Woodard07}, the filters are narrower than used here, particularly at low frequencies. Because the acoustic wavelength at the depth of the peak flow is larger than the depth of the peak flow, ray theory may show inaccuracies. To improve the quality of the flow model, it would therefore be useful to include finite-frequency effects \cite{Birch07}. Further, the functional dependence of travel times on the background-flow model may exceed the linear limit if flow speeds are indeed on the order of $700\ms$. Therefore a non-linear inversion for supergranular flow may be necessary to explain the measured travel times \cite{Hanasoge11}. \begin{acks} The data used here are courtesy of NASA/SDO and the HMI Science Team. We thank the HMI team members for their hard work. This work is supported by NASA SDO. \end{acks} | 14 | 4 | 1404.2533 |
1404 | 1404.5914_arXiv.txt | \noindent Highest energy neutrino events (contained) in cubic km ICECUBE detector resulted in last three years to be as many as $37-2=35$ signals (two of those having been recently discharged); these tens-hundred TeV (32 energetic events) up to rarest (only 3) PeV cascade showers, proved to have an extraterrestrial origin. Their flux exceeded, indeed, the expected atmospheric noise and clearly favored and tested the birth of a long waited $\nu$ astronomy. The UHE neutrino flavor transition from a $\nu_{\mu}$ atmospheric dominance (over $\nu_{e}$ showers at TeV energy), toward a higher energy shower cascade ($\nu_{e}$, $\nu_{\tau}$) events at few tens TeV up to PeV energy is a hint of such a fast extraterrestrial injection. The majority (28 out of 35) of all these events are spherical cascade showers and their exact timing in shower shining provided an approximate $\nu$ arrival direction, within about $\pm10^{\circ}$. However, their consequent smeared map is inconclusive: both because of such a wide angle spread signal of $\pm10^{\circ}$ and because of their paucity, is not yet allowable to define any meaningful source correlation or anisotropy. The additional rarest $9-2=7$ muon tracks, while being sharp in arrival directions, did not offer any correlated clustering nor any overlapping within known sources. Larger sample of UHE $\nu$ signals and their most accurate directionality is needed. We recently suggested that the highest energy (tens-TeV) crossing muon along the ICECUBE, mostly at horizons or upcoming, are the ideal tool able to reveal soon such clustering or even any narrow angle pointing to known (IR, X, Radio or $\gamma$) sources or self-correlation in rare doublet or triplet: a last hope for a meaningful and short-time $\nu$ Astronomy. Any crossing muons clustering along galactic sources or within UHECR arrivals might also probe rarest (possibly galactic, radioactive and in decay in flight) UHECR event made by nuclei or neutrons. Within three years of ICECUBE data all the non-contained crossing highest energy muons above few tens TeV may be several dozens, possibly around $54$, mostly enhanced along horizontal edges, painting known sources and/or self-correlating in doublets or rarest triplet, offering a first solution of the UHE neutrino source puzzle (if steady or transient nearby source are at sight). Recent preliminary ICECUBE presentation on crossing muons are consistent with our preliminary muon rate estimate. | The presence of Cosmic Rays, CR, their sources and their acceleration is presently an open problem in high-energy astrophysics. Cosmic rays are able to be accelerated because CR are charged particles. Unfortunately for the same reason CR charges suffer of relic (large scale) galactic and extragalactic magnetic field bending. Such a random walk in the magnetic field forest make smooth and homogeneous their arrival direction. Incidentally the same presence of such large scale magnetic fields test the absence in CR of any detectable magnetic monopole particle trace, the so called Parker bound; we know of such far magnetic fields presence by the consequent Faraday rotation of far polarized radio-sources. Therefore CR are smeared and do not offer any CR astronomy. The rarest Ultra High Energy Cosmic Rays, UHECR, above tens EeV, were expected to be less bent and to correlate with their nearby (Super-Galactic) sources because of their rigidity and straight directionality. This hope rose few years ago and it faded quite soon. No super-galactic imprint in UHECR maps has been found yet. Indeed, an additional variable generate confusion and smearing: the UHECR composition has been observed as heavy nuclei (AUGER) or light nuclei or protons (Hires-TA). Therefore CR are smeared. For a comparable reason the smeared CR while hitting the Earth atmosphere mimic the mess by producing a diffused rain of secondaries pions $\pi^{\pm}$, kaons $K^{\pm}$ and muons $\mu^{\pm}$, whose final traces in underground detectors are also smeared neutrinos: the so called atmospheric neutrinos. Therefore any eventual neutrino astronomy is drowned in such a smooth sea of atmospheric neutrino noise. Neutrinos have their own identities, or flavors: they do not behave at same way. In effect, the slow decay of muons respect to the $\pi^{\pm}$ one or the $K^{\pm}$ one, makes above few tens-hundred GeV the atmospheric $\nu_{e}$ flux more rare respect to the $\nu_{\mu}$ flux nearly by an order of magnitude. This implies a muon-rich signal at TeVs (long track traces) respect to rarer $\nu_{e}$ showers observed in Deep Core inside ICECUBE as small cascade showers. Therefore as soon as ICECUBE highest energy events have shown ruling cascades (mostly originated by $\nu_{e}$ or $\nu_{\tau}$ charged current, CC, interaction), then the atmospheric neutrino flux \cite{Gaisser02} \cite{Enberg08}, has been overcome by a new neutrino sky, mostly of extraterrestrial and astrophysical nature. Originally the ICECUBE attention was for the search of UHE neutrinos at EeV GZK cosmological edges \cite{za66}, but recent results are at lower PeV energy windows. Tau EeV neutrinos $\nu_{\tau}$, $\bar{\nu_{\tau}}$ might hit the Earth, produce and EeV $\tau$ lepton whose escape and decay in flight becoming observable (and searchable) as an horizontal fluorescence $\tau$ airshower \cite{Fargion02}; this probable event has not been observed yet \cite{AUGER13}. Neutrino oscillation \cite{Fargion-2012} and mixing \cite{Fargion-2011} from far galactic or extragalactic distance may overshadow most atmospheric neutrino flavor composition ruled by a final flavor ratio at TeV: $(\nu_{e}, \nu_{\mu}, \nu_{\tau})\div\left(\frac{1}{10}, 1, 0\right)$, into a more ``democratic" flavor composition above 30 TeV, as the observed one, approximately of $(\nu_{e}, \nu_{\mu}, \nu_{\tau})\div(1, 1, 1)$, also assuming the mild additional presence of neutral current cascades \cite{Vissani-2013}, \cite{DFPP14}. These signals might be born by a huge AGN flaring jets or by more abundant GRB precessing jets in competition with more conventional SNRs-microjets sources possibly origin of CR at lower (PeVs) energy edge. These extra-terrestrial events may be both of galactic and extragalactic nature. The CR and UHECR neutral parasite secondaries, $\gamma$, X, radio synchrotron signals suggest the AGN, BL Lac hypothesis for UHE $\nu$. The one-shoot GRB model is not well correlated up to our days with any observed UHE neutrino in ICECUBE. Some rare precursor event a few hour before the $\gamma$ burst might be correlated, but they call for a long life precessing gamma jet model \cite{Fargion99} often ignored respect to the (still) popular one shoot fireball model. More common AGN, Galactic Cluster, star forming clusters or extragalactic IR sources are the possible birth place of UHE neutrinos. Therefore we need a better view of the CR and possibly their related inner probe made by UHE neutrinos. UHECR were expected to produce (by scattering on BBR photons) an observable rate of photo-pions and EeV neutrino (the cosmogenic neutrinos). This scattering on relic photons lead to an opacity, the so-called GZK cut off in UHECR spectra, that is still experimentally unsettled because it might be in debt also of an intrinsic acceleration limit and/or to a changing mass composition role. Therefore the PeV neutrinos are not clearly related to such GZK EeV UHECR. \cite{DFPP14}. These UHECR cut off in GZK opacity, \cite{za66}, the consequent cosmo-genic neutrinos are possibly better observable soon as Tau airshower \cite{Fargion02} at EeV (also so called Earth-Skimming neutrinos \cite{Feng02}) in AUGER \cite{Fargion02}, \cite{Bertou2002}, HIRES, TA or ASHRA array telescopes; such a Tau airshower signal has not been yet revealed, although the time seem already mature, at least in ASHRA \cite{Aita2011} experiment tuned to PeV energies. The Tau airshower astronomy is a secondary tail of the \cite{doub_bang} Double Bang proposal, that might be observable also in ICECUBE by ellipsoidal or separate PeVs future events. However, in conclusion, the severe $\gamma$ BBR opacity to photons above galactic distances at PeV (10 kpc), suggest PeV neutrino of extragalactic origin. Let us remind that the recent ICECUBE spectrum near PeV is tailed and cut \cite{DFPP14} to avoid any (enhanced and also expected) resonant $\bar{\nu_{e}} + e\rightarrow W^{-}$ event at $6.3$ PeV \cite{glashow}. Therefore the novel extraterrestrial signal at PeV \cite{Science-2013} and below is fine-tuned to be suppressed at higher energies. As we mentioned in the introduction the contained events are mostly cascade showers whose angular resolution is poor: thus, any correlation with sources or other mass distribution become difficult. The absence of high angular resolution for cascades and the rareness (7) of contained $\nu_{\mu}$ events makes the ability to radically improve such contained UHE neutrino astronomy critical. | The discover of the highest energy neutrino astronomy require a high resolution probe. Recent $37-2=35$ ICECUBE highest energetic events are mostly $28$ cascade showers with poor arrival angle $\pm 10^{\circ}$, while $7$ muon tracks directions for contained events point to a much narrow angle as $\pm 1^{\circ}$, but they are rare; therefore muon track solid angle is more than two order of magnitude smaller and sharper by solid angle than cascade ones. The present spread shower signals in ICECUBE maps are not useful to address clearly to any smoking gun sources, nor to test large scale anisotropy. Clustering along a source, possibly along galactic regions (in analogy to the observed Cen-A UHECR multiplet events in AUGER maps or to the ARGO-MILAGRO anisotropy sky at TeVs CR), might favor also the presence of UHECR radioactive decay in flight, bent by magnetic fields \cite{Fargion-2011b}, whose decay secondaries could be $\gamma$ and also TeVs-PeV neutrinos. However the need for sharp neutrino maps is compelling. The abundant muon crossing at highest (tens TeV) tracks, tagged by their huge energy release, are self selected as extraterrestrial and they are a very rich key to discover by a sharp view the highest energy neutrino sky. A rare doublet may be not yet convincing; but two or above doublets and/or rare triplet within the expected $60$ events may make the steps into neutrino astronomy. Very recent presentation \cite{G.Hill14} , see Fig. \ref{Crossing} did show the preliminary crossing muons spectra (but not their map yet) corresponding to upgoing and horizontal crossing muons. Their rate for two years is nearly $40$ events, consistent with our recent \cite{Fargion-2014} and here reconfirmed estimate. \begin{figure}[h] \includegraphics[scale=0.33]{MUONS-HILL} \caption{The preliminary flux of crossing muons delivered only on second June 2014 at Boston-Neutrino14; their horizontal and upgoing rate in two years is consistent with the fraction of up-going foreseen in \cite{Fargion-2014}, (nearly $30-40$). } \label{Crossing} \end{figure} | 14 | 4 | 1404.5914 |
1404 | 1404.5639_arXiv.txt | {% A Central Laser Facility is a system composed of a laser placed at a certain distance from a light–detector array, emitting fast light pulses, typically in the vertical direction, with the aim to calibrate that array. During calibration runs, all detectors are pointed towards the same portion of the laser beam at a given altitude. Central Laser Facilities are used for various currently operating ultra-high-energy cosmic ray and imaging atmospheric Cherenkov telescope arrays. In view of the future Cherenkov Telescope Array, a similar device could provide a fast calibration of the whole installation at different wavelengths. The relative precision (i.e. each individual telescope with respect to the rest of the array is expected) to be better than 5\%, while an absolute calibration should reach a precisions of 4--11\%, if certain design requirements are met. Additionally, a preciser monitoring of the sensitivity of each telescope can be made on time-scales of days to years.} | Central Laser Facilities (CLF) have been used widely to calibrate fluorescence detectors, like HiRes~\cite{HiRes2006}, AUGER~\cite{auger2006,auger2011,auger2013} and the Telescope Array~\cite{ta2009,ta2012}. Such facilities employ a laser to emit fast light pulses of precisely monitored power, mostly in the vertical direction, although the more modern systems also incorporate a steerable beam option. The scattered laser light received by the photomultipliers of the detectors resembles that from fluorescing ultra high energy cosmic ray shower tracks and is used to calibrate the response of the photo-detector to these. CLFs are therefore ideal calibration devices for the fluorescence detectors, and are routinely run several times a night. In the case of Imaging Atmospheric Cherenkov Telescopes (IACTs)~\cite{weekes2005,buckley2008,hinton2009,holder2012,hillas2013}, a part of the laser path is seen as a track traveling across the focal plane of the camera, on micro-second time scales. IACTs consist nowadays of several telescopes and are optimized for the observation of Cherenkov light from air showers that are observed head-on and yield light pulses with full-width-half-maxima of typically few nanoseconds, with increasing pulse lengths, as the triggerable shower impact distance -- and hence the camera fields-of-view -- become larger. In extreme cases, several tens of nanoseconds pulse widths may be reached~\cite{cta}. The air shower images are then mainly (but not exclusively) used for gamma-ray astronomy in the energy range from tens of GeV to hundreds of TeV. Telescope calibration by a CLF is then only useful if the light pulses from CLF tracks are amplified and electronically transmitted and digitized in the same, undistorted way as the shorter Cherenkov light pulses. Moreover, the telescopes must be able to trigger on, and buffer, the much slower moving signals through the camera. In this case, a CLF can be used to monitor the sensitivity of each individual telescope, including mirrors and camera, and to cross-calibrate telescopes, or telescope types, between each other. Finally, an absolute calibration of the whole array can be attempted. Contrary to the already existing CLFs, we propose to operate a CLF at multiple wavelengths, allowing for a full spectral characterization of each telescope. The calibration could be carried out during selected very clear nights -- ocurring frequently at astronomical sites -- on time-scales of about once per month. Such a calibration scheme has the advantage to be fast and relatively cheap, as only one, or very few, devices are involved for the entire array. It cannot be used to equalize the gains of individual pixels of a camera, a task for which an individual light source for each telescope is better suited~\cite{gaug,hanna,aharonian,gaugphd,piron,rovero,puhlhofer}. VERITAS is the only IACT that has explored calibration of its Cherenkov telescopes with the help of a CLF~\cite{veritas2005,veritas2008}. A dedicated trigger and readout scheme has been developed there, which allows to read the signal of each pixel at different memory depths. While VERITAS has not yet published the precision of the achieved calibration, the AUGER collaboration has reached an absolute calibration precision better than 10\% using this technique~\cite{augerabsolute1,augerabsolute2}, and the Telescope Array cites 7.2\%~\cite{ta2012}. All installations make use, however, of other calibration devices and rely on their CLFs to yield redundant information. The AUGER experiment, moreover, uses different types of lasers to characterize the atmosphere and the fluorescence detectors. Given the experience of these installations, we now discuss a possible use of a CLF for the future Cherenkov Telescope Array (CTA)~\cite{cta,ctaconcept,ctamc}. The CTA will consist of a Southern installation, covering about 10~km$^2$ with telescopes, and a Northern one of about 1~km$^2$ extension. While the Southern array will contain at least three different telescope types, employing different mirror dish sizes and fields-of-view, the smaller Northern array is currently foreseen to consist of two types of telescopes. In both cases, large-size telescopes will be located in the center, surrounded by medium-size and small-size telescopes, the latter only for the Southern array. The aim of this paper is to predict the foreseen precision with which the sensitivities of individual telescopes can be monitored and calibrated against each other, as well as the absolute calibration precision for the entire observatory. | This study shows that a Central Laser Facility can be a solution for a fast calibration of the CTA, if certain design requirements for the CTA cameras are met. These must provide either externally triggered individual readout windows for each pixel or a pixel-cluster trigger configurable in such a way that the laser beam image subsequently triggers small units of pixels on its path through the camera. Accordingly, the minimum accessible memory depth must be correspondingly large, at least 1~$\mu$s, and the readout must be able to reconstruct pulses of up to 120~ns length without distortion due to the internal AC-couplings of the readout and amplification chain. In this case, the laser facility can calibrate all telescopes at the same time, on a time scale which is mainly limited by the movement of the telescopes towards the individual pointing toward the laser beam. Such a calibration can be run every night, although very clear nights are favored to reduce systematic uncertainties due to the aerosol contribution to the scattering process and the subsequent extinction of the scattered light on its way to the telescope cameras. A CLF can then be used to monitor the sensitivity of each telescope, to calibrate the telescopes among each other as well as to achieve a relative calibration between the different telescope types, a task which is difficult to achieve by other means. Especially appealing is the possibility to use different laser wavelengths to calibrate the spectral sensitivity of the array. Finally, an absolute calibration with a precisions ranging from 4--11\% seems possible, depending on the adaptation of the telescope hardware and if additional atmospheric monitoring devices, such as a LIDAR, are operated together with the CLF. | 14 | 4 | 1404.5639 |
1404 | 1404.5313_arXiv.txt | We compare the dynamical masses of dwarf galaxies in the Local Group (LG) to the predicted masses of halos in the ELVIS suite of \lcdm\ simulations, a sample of 48 Galaxy-size hosts, 24 of which are in paired configuration similar to the LG. We enumerate unaccounted-for dense halos ($\vmax \gtrsim 25~\kms$) in these volumes that at some point in their histories were massive enough to have formed stars in the presence of an ionizing background ($\vpeak > 30~\kms$). Within 300 kpc of the Milky Way, the number of unaccounted-for massive halos ranges from 2 -- 25 over our full sample. Moreover, this ``too big to fail" count grows as we extend our comparison to the outer regions of the Local Group: within 1.2 Mpc of either giant we find that there are 12-40 unaccounted-for massive halos. This count excludes volumes within 300 kpc of both the MW and M31, and thus should be largely unaffected by any baryonically-induced environmental processes. According to abundance matching -- specifically abundance matching that reproduces the Local Group stellar mass function -- all of these missing massive systems should have been quite bright, with $\mstar > 10^6\msun$. Finally, we use the predicted density structure of outer LG dark matter halos together with observed dwarf galaxy masses to derive an $\mstar-\vmax$ relation for LG galaxies that are outside the virial regions of either giant. We find that there is no obvious trend in the relation over three orders of magnitude in stellar mass (a ``common mass" relation), from $\mstar \sim 10^8 - 10^5 ~\msun$, in drastic conflict with the tight relation expected for halos that are unaffected by reionization. Solutions to the too big to fail problem that rely on ram pressure stripping, tidal effects, or statistical flukes appear less likely in the face of these results. | \label{sec:intro} Numerical simulations of structure formation have emerged as a standard technique for making and testing predictions of the \lcdm\ model of hierarchical galaxy formation \citep{Davis1985,Frenk1988,Warren1992,Gelb1994,Cen1994, Hernquist1996,Gross1998,Jenkins2001,Wambsganss2004,Springel2005,Boylan-Kolchin2009,Klypin2011}. These studies have been remarkably successful at reproducing the large-scale properties of the Universe, but disagreements have periodically emerged on smaller scales. The smallest dwarf galaxies (stellar mass $\mstar \lesssim 10^8\msun$) can be detected and studied best locally, and thus many of these small-scale problems have been identified by comparing observations of Milky Way (MW) satellites with subhalos of simulated MW-size hosts. For example, the ``missing satellites problem" \citep{Kauffmann1993,Klypin1999,Moore1999,Bullock2010}, points out that although dark matter (DM)-only simulations predicted a wealth of collapsed substructure around the MW, only $\sim10$ bright satellite galaxies are known. Though the known count of MW satellites has more than doubled in the past ten years, all of these new satellites have been of fairly low mass \citep[e.g.][]{Willman2005,Belokurov2006,Belokurov2007}. Moreover, even allowing for these new detections in the overall count, one must still assume that only a small percentage of subhalos are populated by luminous galaxies in order to explain the discrepancy. It is typical to assume that the brightest ``classical" dwarf spheroidal (dSph) galaxies are hosted by the largest subhalos typical of MW-size hosts ($\vmax\sim30~\kms$). The idea that the most luminous galaxies reside in the most massive halos is reinforced by the success of the abundance matching (AM) technique, which accurately reproduces clustering statistics and luminosity functions for $\mstar > 10^8\msun$ galaxies \citep{Kravtsov2004,Vale2004,Conroy2006,BehrooziAM,Moster2013}. Specifically, AM provides an $\mstar-M_{\rm halo}$ relation by matching DM halo mass functions from cosmological simulations with stellar mass functions from large-volume surveys, implicitly assuming that the most luminous galaxies reside in the largest dark matter halos. If one extrapolates AM to the dwarf scale, the resultant satellite stellar mass functions agree well with those of the MW and M31 satellites for $\mstar\gtrsim10^5\msun$ \citep{Koposov2009,Busha2010,Kravtsov2010,Lunnan2012,MBK2012,Brook2013,ELVIS}. Below $\mstar \sim 10^5 \msun$, the abundance of galaxies may become more strongly suppressed than expected in power-law AM extrapolations because the smallest subhalos ($\vpeak < 30~\kms$) may not have formed stars because of reionization \citep{Bullock2000,Somerville2002,Sawala2014}. As discussed in \citet{ELVIS}, surveys like LSST will test this possibility. With the advent of the zoom-in technique \citep{Katz1993,Onorbe2013}, which focuses the majority of the computational power of a cosmological simulation on a small high-resolution region, simulations can now test whether these largest subhalos are indeed compatible with the luminous MW dSphs, as AM predicts. \citet{MBK2011,MBK2012} used the zoom-in simulations of the Aquarius Suite \citep{Aquarius}, which includes six ultra-high resolution MW-size hosts, to compare the internal kinematics of the massive subhalos of MW hosts to the brightest MW satellites (those with $\mstar > 10^5\msun$). They discovered that measurements of the stellar velocity dispersions, $\sstar$, indicate systematically lower central mass estimates than simulations predict for large subhalos~--~that is, the MW dSphs are systematically less dense than the subhalos expected to host them, a problem that has been dubbed ``Too Big to Fail" (TBTF). While possibly related to the missing satellites problem, in that the largest subhalos may not have been found, TBTF is a distinct problem related to the internal structure of subhalos, rather than strictly their abundances. However, it could be alleviated by the discovery of several new high-density dwarf satellites. TBTF may also be tied to the shapes of the inner density profiles of dwarf halos. Collisionless simulations predict cuspy central regions, whereas measurements by \citet{Walker2011}, \citet{Jardel2012}, \citet{Agnello2012}, and \citet{Amorisco2013} indicate cored matter distributions in the larger dSphs (Fornax and Sculptor), similar to the cusp-core problem in slightly more massive low surface brightness galaxies \citep{Flores1994,Moore1994,KuziodeNaray2008,Trachternach2008,deBlok2010,KuziodeNaray2011}. The slope of the central density profiles are still under debate, however~--~\citet{Breddels2013} found that it is unlikely that Fornax, Sculptor, Carina, and Sextans are hosted by cored dark matter halos. The TBTF problem is independent of the inner slope, however, as it is phrased in terms of the integrated mass within the half-light radii of dwarfs, quantities that are much more robustly determined observationally than density profile slopes. There have been a number of suggestions proposed for resolving TBTF. Some authors have pointed out that self-interactions in the dark matter naturally lead to $0.5-1$~kpc cores in dwarf subhalos \citep{Vogelsberger2012,Rocha2013,Elbert2014}, though there are indications that the self-interaction cross section must be velocity dependent to satisfy other constraints \citep{Zavala2013}. Others have investigated whether TBTF may be a result of the underlying cosmology of the Aquarius simulations, where TBTF was first identified, such as the adopted values of $\sigma_8$ and $n_s$ \citep{Polisensky2013} or the assumed coldness of the dark matter \citep[][and references therein]{Anderhalden2013,Lovell2013}. Others have argued that TBTF is a result of the mass of the targeted halos, pointing to simulations that indicate that smaller hosts, $\mvir\sim8\times10^{11}~\msun$, do not typically contain these large, dense subhalos \citep{diCintio2011,Wang2012,Vera-Ciro2013}. It may also be that a fraction of the MW-size halos in the Universe do not host these dense subhalos \citep{Purcell2012}, though the statistical study of \citet{Rodriguez2013} found that the TBTF problem is typical of MW-size hosts. Many authors have also noted that TBTF was first identified in collisionless simulations, which do not account for baryonic forces, and that it is therefore possible that these missing physics, such as supernova feedback, ram pressure stripping, and tidal interactions, may account for the discrepancy \citep[e.g.][]{Pontzen2012,Zolotov2012,Arraki2012,BrooksZolotov2012,DelPopolo2012,Brooks2013,Gritschneder2013,Amorisco2013feedback,DelPopolo2014}. Although energetic arguments indicate that the former is unlikely in most cases \citep{Penarrubia2012,Garrison-Kimmel2013}, there is ample evidence that dwarfs are strongly affected by their environment~--~for example, there are only two galaxies within 300~kpc of the MW with detected gas (the Magellanic Clouds); conversely, there are only two known gas-free field dwarfs within $\sim1~\mpc$ of the MW \citep[Cetus and Tucana;][]{Grcevich2009,McConnachie2012}. Thus far, work on TBTF has focused largely on the subhalos and dSph satellites of the MW, while \citet{Tollerud2014} have shown the same issue is seen around M31. To eliminate the uncertain effects introduced by environment, however, one should study galaxies beyond the virial radii of the MW and M31, where ram pressure and tidal stripping are minimal. Isolated dwarf galaxies in the Local Field (a term we will use to refer to the region within $1.2~\mpc$ of either the MW or M31, but more than $300~\kpc$ from both) do not appear to be denser than the MW dSphs \citep{Kirby2013}, but predictions for halo properties in the Local Field have thus far been sparse. In this paper, we examine both satellite and field dwarf halos around the hosts of the Exploring the Local Volume in Simulations (ELVIS) Suite \citep[][hereafter GK14]{ELVIS}, a set of zoom-in simulations focused on LG-like environments that resolve $\sim3~\mpc$ regions without contamination from low resolution particles, for the TBTF problem. Specifically, we count the number of ``massive failures"~--~large halos ($\vpeak > 30~\kms$) that do not have luminous counterparts~--~both within $300~\kpc$ of the 48 MW-size hosts and in the fields surrounding the % LG analogs. Because the ELVIS Suite adopts cosmological parameters from the WMAP-7 results \citep[$\sigma_8 = 0.801$, $\Omega_m = 0.266$, $\Omega_\Lambda = 0.734$, $n_s = 0.963$, and $h = 0.71$;][]{Larson2011}, which includes a significantly lower value of $\sigma_8$ than the WMAP-1 parameter set adopted for the Aquarius simulations, we will also test whether an updated cosmology alleviates the problem. As we show below, however, we predict that there are many such unaccounted-for dense halos throughout the Local Volume. If these halos preferentially host low-luminosity or low-surface brightness galaxies, then future surveys may detect them. This paper is organized as follows. In \S\ref{sec:sims}, we briefly describe the simulations and analysis pipeline used in this work. In \S\ref{sec:rmaxvmax}, we present empirical scaling relations between the structural parameters of subhalos and field halos and explicitly compare the properties of small halos near isolated hosts with those in paired environments. \S\ref{sec:fails} presents the counts of massive failures around each host both within $300~\kpc$ of each host (\S\ref{ssec:rvirfails}) and in the field surrounding the Local Group analogs (\S\ref{sssec:fieldfails}), as well as a discussion of incompleteness (\S\ref{sssec:incompleteness}). We conclude with an analysis of the relationship between $\mstar$ and $\vmax$ for the known dwarfs in the Local Field in \S\ref{sssec:mstarvmax}. Our results are summarized in \S\ref{sec:conclusions}. | \label{sec:conclusions} In this paper, we have analyzed the structural properties of the small halos in the ELVIS Suite~--~both those within the virialized volumes of the two giant halos and those in the fields surrounding them. Our results indicate that the Too Big to Fail problem, the discrepancy in central masses between the large subhalos of simulated MWs and the dSphs surrounding the MW, is an issue not only within $300~\kpc$, where environmental physics may be able to resolve the disagreement, but also in the Local Field, where such effects should be small. Specifically, we find that \begin{itemize} \item For NFW-like density profiles, nearly all of the ELVIS hosts contain at least one ``strong massive failure"~--~satellite halos that are too dense to host any of the classical dSphs. The median number of strong massive failures per host is highly dependent on the assumed density profile, varying between 2 and 10, and would change dramatically if a dwarf much denser than Draco is discovered. \item The number of ``massive failures," $\vpeak > 30~\kms$ halos that remain dense at z = 0 and cannot be accounted for with the known census of dSphs, is much less dependent on the assumed profile. All of the ELVIS hosts contain at least one massive failure for the profiles considered in the work, with a median varying between 8.5 and 13. Unlike the count of strong massive failures, a newly discovered high-density dwarf would only alter these numbers by one. \item Though there are typically no strong massive failures in the Local Field (i.e. more than $300~\kpc$ from both giants in the LG), the overall discrepancy between known galaxies that appear to live in dense (typically high mass) halos and the number of these halos predicted is even stronger. Most simulated LFs contain $\gtrsim15$ more of these dense halos than can be accounted for observationally. \item If the discrepancy is to be resolved by discovering new galaxies, and \emph{if} the stellar mass of a galaxy scales in a reasonable way with $\vmax$, then the abundance matching technique predicts that there should be $\sim2-10$ undiscovered galaxies with $\mstar>10^7\msun$ within the LF, though there have been none found since 1958. However, perhaps more puzzlingly, the stellar masses of the known field galaxies do not appear to correlate with the apparent $\vmax$ of their host halos, as estimated from $\vhalf$, suggesting either that the density profiles of the dwarfs vary strongly or that the scaling of $\mstar$ with $\vmax$ breaks down at low luminosities. \end{itemize} The results presented in this work do not necessarily indicate the need to move beyond the standard \lcdm\ model with collisionless dark matter. They can largely be viewed as predictions for results from future surveys, such as LSST and DES. However, if these missing dense galaxies are not discovered as we probe the nearby Universe to an increasing depth, these large dark matter halos must somehow be explained. \vskip1cm \noindent {\bf | 14 | 4 | 1404.5313 |
1404 | 1404.4899.txt | We discuss complete theory of spin-1/2 electron-positron quantum plasmas, when electrons and positrons move with velocities mach smaller than the speed of light. We derive a set of two fluid quantum hydrodynamic equations consisting of the continuity, Euler, spin (magnetic moment) evolution equations for each species. We explicitly include the Coulomb, spin-spin, Darwin and annihilation interactions. The annihilation interaction is the main topic of the paper. We consider contribution of the annihilation interaction in the quantum hydrodynamic equations and in spectrum of waves in magnetized electron-positron plasmas. We consider propagation of waves parallel and perpendicular to an external magnetic field. We also consider oblique propagation of longitudinal waves. We derive set of quantum kinetic equations for electron-positron plasmas with the Darwin and annihilation interactions. We apply the kinetic theory for the linear wave behavior in absence of external fields. We calculate contribution of the Darwin and annihilation interactions in the Landau damping of the Langmuir waves. We should mention that the annihilation interaction does not change number of particles in the system. It does not related to annihilation itself, but it exists as a result of interaction of an electron-positron pair via conversion of the pair into virtual photon. A pair of the non-linear Schrodinger equations for electron-positron plasmas including the Darwin and annihilation interactions. Existence of conserving helicity in electron-positron quantum plasmas of spinning particles with the Darwin and annihilation interactions is demonstrated. We show that annihilation interaction plays an important role in quantum electron-positron plasmas giving contribution of the same magnitude as the spin-spin interaction. | In classical plasmas the model of electron-positron plasmas does not differ from model of electron-ion plasmas. Electrons, positrons, and ions are involved in the electromagnetic interaction between charges. Some interesting effects exist in classic electron-plasmas due to the equality of masses and module of charges of both species. Considering quantum plasmas we include spin of particles \cite{Maksimov Izv 2000}-\cite{Andreev Asenjo 13}. Quantum nature of particles requires us to include the Darwin interaction as well \cite{Ivanov Darwin}, \cite{Asenjo NJP 12}. This interaction has weakly-relativistic (semi-relativistic) nature \cite{Landau 4}, hence it is neglected in most of the papers on quantum plasmas. Quantum model of electron-positron requires to consider extra interaction, which does not exist between electrons or between ions. This is, so called, the annihilation interaction \cite{Pirenne 1947}-\cite{Berestetski ZETP 49 b}, see also Ref. \cite{Landau 4} section 83. It is not annihilation of electron-positron pairs itself. However it is the semi-relativistic trace of electron-positron interaction, when an electron-positron pair transforms in the virtual photon, which splits back into the electron-positron pair. Studying of the annihilation interaction in electron-positron quantum plasmas is an essential part of understanding of the quantum and relativistic properties of plasmas \cite{Ruyer PP 13}-\cite{Uzdensky arxiv review 14}. The quantum hydrodynamic model for electron-plasmas with the annihilation interaction is one of main topics of the paper. We derive the model and we use it to study spectrum of small amplitude collective excitations in magnetized electron-positron plasmas. We should mention that classical relativistic properties of electron-positron plasmas, as well as quantum properties of electron-positron and electron-positron-ion plasmas have been under consideration in last years. For instance thermal-inertial effects on magnetic reconnection in relativistic pair plasmas \cite{Luca Comisso arXiv 14}, self-modulation of nonlinear waves in a weakly magnetized relativistic electron-positron plasma with temperature \cite{Asenjo PRE 12}, and nonlinear Alfven waves in a strongly magnetized relativistic electron-positron plasma \cite{Lopez PRE 13} have been studied on the path of research of classic relativistic electron-positron plasmas. In these papers a hydrodynamic model of relativistic quantum plasmas with temperature \cite{Mahajan 03} was applied. Before speaking of quantum properties of electron-positron plasmas, we should present a brief description of the field of quantum plasmas of spinning particles. Method of description of quantum plasmas was developed in 1999-2001 in Refs. \cite{Maksimov Izv 2000}, \cite{MaksimovTMP 2001}, \cite{MaksimovTMP 1999}. This method arises as a representation of the many-particle Schrodinger equation with the charge-charge Coulomb and spin-spin interactions in terms of collective variables. The collective variables are the microscopic observable variables suitable for description of many-particle systems. They are the particle concentration $n$, the momentum density $\textbf{j}=n\textbf{v}$, the pressure $p$, the magnetic moment (spin) density $\mbox{\boldmath $\mu$}$, the energy density $\varepsilon$, the spin-current (magnetization flux) $J^{\alpha\beta}$, etc. These variables are determined via the many-particle wave function, or wave spinor for spinning particles. Evolution of the wave function obeys the many-particle Schrodinger equation. Hence, applying the Schrodinger equation we can derive equations of evolution of collective variables. The particle number evolution (the continuity equation), the momentum balance equation (the Euler equation), the energy balance equation, the magnetic moment evolution equation were derived for many-particle systems in 2000-2001. This set equation is a generalization of the five moment approximation ($n$, $\textbf{v}$, and $\varepsilon$) for spinning particles appearing as the eight-moment approximation ($n$, $\textbf{v}$, $\mbox{\boldmath $\mu$}$, and $\varepsilon$). This set of equations in not closed set of equations. It is a long chain of equations, which should be truncated. Truncation is making of an approximation, but this is also an "explanation" to our method of properties of the system under consideration. Generalization of the eight-moment approximation were developed in Ref. \cite{Andreev spin current}, where the spin-current evolution equation were derived to get richer information on the spin evolution properties. Terms describing interparticle interaction in hydrodynamic equations contains two-particle functions containing two-particle correlations. Main attention of Refs. \cite{Maksimov Izv 2000}, \cite{MaksimovTMP 2001}, \cite{Andreev RPJ 07}, \cite{MaksimovTMP 1999}, \cite{Andreev spin current}, \cite{Andreev PRB 11} were focused on the self-consistent field approximation, when two-particle functions appears as products of two corresponding one-particle functions. Nevertheless, quantum correlations related to the exchange Coulomb and spin-spin interactions were also considered in Refs. \cite{MaksimovTMP 2001}, \cite{MaksimovTMP 1999}. Since then various wave phenomenon have been studied for spin-1/2 quantum plasmas \cite{Andreev VestnMSU 2007}, \cite{Marklund PRL07}, \cite{Andreev AtPhys 08}, \cite{Andreev Asenjo 13}, \cite{Maksimov VestnMSU 2000}-\cite{Asenjo PL A 12}. Presence of spin induces the spin-spin interaction via the magnetic field created by magnetic moments \cite{MaksimovTMP 2001}. Spin also causes the spin-current interaction, i.e. interaction of the magnetic moments and electric currents via the magnetic field. These interactions change dispersion of plasma waves in compare with the spinless case. Spin evolution leads to extra waves in plasmas. These new spin-plasma waves were found in several papers, see Refs. Vagin et al \cite{Vagin Izv RAN 06}, Andreev and Kuz'menkov \cite{Andreev VestnMSU 2007}, Brodin et al \cite{Brodin PRL 08} for the spin-plasma waves propagating perpendicular to an external magnetic field, see Refs. Misra et al \cite{Misra JPP 10}, Andreev and Kuz'menkov \cite{Andreev IJMP 12}, \cite{pavelproc} for the spin-plasma waves propagating parallel to an external magnetic field, spin waves in quantum plasmas propagating due to perturbations of magnetic field with no contribution of electric field in the wave propagation were considered in Refs. \cite{Andreev VestnMSU 2007}, \cite{Andreev IJMP 12}, new branches of wave related to spin-current evolution were found in Refs. \cite{Andreev spin current} and \cite{Trukhanova 1403}. Equality of masses of electrons and positrons changes dispersion dependencies of spin-plasma waves. It happens with usual, spinless, plasma wave. It also affects plasmas of spinning particles. Let us also mention that the Karpman-Washimi magnetization and the Karpman-Washimi interaction for plasmas of spinning particles were considered in Ref. \cite{Dae PP 13}. An interesting application of quantum hydrodynamics to vorticity of spinning particles was suggested in Refs. \cite{Mahajan PRL 11} and \cite{Braun PRL 12}. Reviews of some topics studied for quantum plasmas are presented in Refs. \cite{Shukla UFN 10} and \cite{Shukla RMP 11}. Electron-positron and electron-positron-ion spin-1/2 quantum plasmas and their wave properties have been under consideration in recent years \cite{Bains PP 10}-\cite{Brodin PRL 10}. Hydrodynamic representation of the Schrodinger equation for a single particle in an external field was made by Madelung in 1926 \cite{Madelung}. Equations obtained by Madelung for a single particle look similar to hydrodynamic equations for many-particle systems of classic particles. This similarity was used by Rand in 1964 \cite{Rand PF 64} for quantum hydrodynamic description of quantum plasmas. The method of many-particle quantum hydrodynamics suggested by Kuz'menkov et al 1999-2001 \cite{MaksimovTMP 2001}, \cite{MaksimovTMP 1999} differs from the single particle one by the fair treating of the many-particle quantum dynamics. That opens a lot of possibilities for consideration of different physical systems (see for instance \cite{Andreev PRB 11} and \cite{Andreev PRA08}). This paper is organized as follows. Quantum hydrodynamic model for electron-positron quantum plasmas of spinning particles is developed in Sec. II. In Sec. III we consider dispersion of waves propagating parallel to the external magnetic field. We describe contribution of the annihilation interaction along with the spin-spin interaction in longitudinal and transverse waves including spin-plasma waves. We present contribution of the Darwin and exchange interactions in the longitudinal Langmuir wave. In Sec. IV we consider dispersion of waves propagating perpendicular to the external magnetic field. In Sec. V we pay special attention to the longitudinal waves. We consider oblique propagation of the longitudinal waves. In Sec. VI we present generalization of the theory developed in section II. From the first principles we develop set of kinetic equations for spinning electrons and positrons with the annihilation interaction. We apply kinetic theory to calculation of the Landau damping for the quantum Langmuir waves. In Sec. VII we present a pair of the non-linear Schrodinger equations for electron-positron plasmas including the Darwin and annihilation interactions. In Sec. VIII we derive equations for the vorticity evolution and show existence of conserving helicity in electron-positron quantum plasmas of spinning particles with the Darwin and annihilation interactions. In Sec. IX brief summary of obtained results is presented. | We have developed the quantum hydrodynamics for electron-positron plasmas. This model requires to include the annihilation interaction. It gives contribution in the Euler equations and the magnetic moment evolution equations. As consequence, contributions of the annihilation interaction in spectrum of plasma waves were found. We have found shifts of the eigen-frequencies of the transverse electromagnetic plane polarized waves, transverse spin-plasma waves, we have also included contribution of the quantum Bohm potential in dispersion of this branch of waves, longitudinal Langmuir waves. We do it for two limit cases of waves propagating parallel and perpendicular to the external magnetic field. We have also considered oblique propagation of longitudinal waves. It also contains contribution of the Fermi pressure, the Darwin interaction, and the quantum Bohm potential from the Euler equations. We have obtained corresponding set of two non-linear Schrodinger equations. These equations are another representation of the set of QHD equations for eddy-free motion. We have derived equations for the grand generalized vorticities for each species. We have applied these equations to demonstrate existence of conserving helicity in electron-positron quantum plasmas of spinning particles with the Darwin and annihilation interactions. We have generalized our model. We have derived the quantum kinetic equations from the many-particle Schrodinger equation. This kinetic theory is presented in the self-consistent field approximation. For simplicity of presentation we have shown interaction terms in the quasi-classic approximation. We applied the quantum kinetic equations to the Langmuir waves in absence of the external fields. We have found contribution of the Darwin interaction and spinless part of the annihilation interaction in frequency of the wave and in the collisionless Landau damping. These interactions decrease the real and imaginary parts of spectrum. Annihilation interaction may find its application in physics of quantum electron-ion plasmas. In this case the annihilation interaction reveals as result of virtual recombination of an electron and an ion, with subsequent ionization (since recombination is virtual). These models open possibilities to consider different linear and non-linear quantum effects with full interaction between spinning electrons and positrons. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | 14 | 4 | 1404.4899 |
1404 | 1404.7244_arXiv.txt | Low resolution ($\sim 4.5$ \AA) ESO VLT/FORS spectra of blue supergiant stars are analyzed to determine stellar metallicities (based on elements such as iron, titanium, magnesium) in the extended disk of the spiral galaxy NGC\,3621. Mildly subsolar metallicity (-0.30 dex) is found for the outer objects beyond 7 kpc independent of galactocentric radius and compatible with the absence of a metallicity gradient confirming the results of a recent investigation of interstellar medium \hii~region gas oxygen abundances. The stellar metallicities are slightly higher than those from the \hii~regions when based on measurements of the weak forbidden auroral oxygen line at 4363~\AA~but lower than the ones obtained with the R$_{23}$ strong line method. It is shown that the present level of metallicity in the extended disk cannot be the result of chemical evolution over the age of the disk with the present rate of in situ star formation. Additional mechanisms must be involved. In addition to metallicity, stellar effective temperatures, gravities, interstellar reddening, and bolometric magnitudes are determined. After application of individual reddening corrections for each target the flux-weighted gravity-luminosity relationship of blue supergiant stars is used to obtain a distance modulus of 29.07 $\pm$ 0.09 mag (distance $D=6.52\pm0.28$\,Mpc). This new distance is discussed in relation to Cepheid and tip of the red giant branch distances. | NGC\,3621 is a bulgeless isolated galaxy with a relatively regular spiral structure which extends out to at least two isophotal radii. The galaxy with its extended disk is imbedded into an envelope of neutral hydrogen gas (\citealt{koribalski04}). A recent study by \citet{bresolin12} analyzing the emission lines of \hii~region spectra reveals that the extended disk (beyond 0.8 isophotal radii) has no oxygen abundance gradient and shows an oxygen abundance distribution which is spatially flat at a relatively high level of -0.4 dex below solar oxygen abundance. While the flatness, though striking, does not seem to be a major issue and according to Bresolin et al. can be explained by the fact that the star formation efficiency is almost constant with radius in the extended disk, it is the high level of metallicity which poses a problem. Bresolin et al. estimate that with the large neutral hydrogen gas reservoir and the low-level of ongoing star formation the time required to enrich the interstellar gas to the observed level is 10~Gyr. While inner disks may have such an age, Bresolin et al. argue that outer disks are at least a factor of two younger, Thus, chemical enrichment of the interstellar medium through in situ star formation at the present level could have resulted only in a very low oxygen abundance with values smaller than -0.7 dex below the solar abundance. As possible mechanisms to explain the discrepancy Bresolin et al. discuss radial metal transport from the inner to the outer disk and gas accretion from the intergalactic medium by metal enriched galactic outflows. There are many galaxies with extended star forming disks and a flat oxygen abundance distribution, for instance M83 (\citealt{bresolin09b}), NGC\,4624 (\citealt{goddard11}), NGC\,1512 (\citealt{bresolin12}) and the thirteen mostly merging galaxies investigated by \citet{werk11}. However, NGC\,3621 appears to be the poster example for a galaxy with a well defined inner abundance gradient and a large outer extended disk with a flat metallicity distribution (see Figure 9 of \citealt{bresolin12}). In addition, NGC\,3621 is also the case where the discrepancy between expected and observed outer disk metallicity, as discussed above, is most significant. We have, thus, decided to reinvestigate the metallicity distribution in the disk of this galaxy using an independent alternative method, the spectral analysis of blue supergiant stars (BSGs). With absolute magnitudes up to $M_{V} \cong -10$ BSGs are the brightest star in the universe at visual light and perfect objects for quantitative stellar abundance studies beyond the Local Group. They are massive stars in the range between 15 and 40~\msun. At an age of $\sim$ 10 million years they have left the main sequence and cross the Hertzpsrung-Russell diagram to become red supergiant stars and then to explode as core collapse supernovae. \citet{kud08} in their study of metallicity in the Sculptor spiral galaxy NGC\,300 were the first to demonstrate how accurate metallicities based on elements such as iron, chromium, titanium etc. can be determined from low resolution spectra of individual BSGs using model atmosphere techniques. Since then a large number of galaxies has been studied (WLM -- \citealt{bresolin06}; \citealt{urbaneja08}; NGC\,3109 -- \citealt{evans07}, \citealt{hosek14}; IC\,1613 -- \citealt{bresolin07}; M33 -- \citealt{u09}; NGC\,55 -- \citealt{castro12}; M81 -- \citealt{kud12}; NGC\,4258 -- \citealt{kud13}). \begin{figure}[!] \begin{center} \includegraphics[width=0.45\textwidth]{fig1.eps} \caption[]{ Enlarged B, V, I composite HST ACS images of five of the observed BSG targets. The circle corresponds to 1 arcsec diameter. \label{targets} } \end{center} \end{figure} A particular motivation for this work is the systematic uncertainty inherent in \hii~region abundance studies. In most cases they are based on the use of the strongest nebular emission lines and using oxygen as a proxy for stellar metallicity. However, as shown, for instance, by \citet{kud08}, \citet{kewley08}, \citet{bresolin09a}, \citet{u09}, \citet{kud12} these ``strong-line methods'' are subject to systematic uncertainties as large as 0.6 dex. They are poorly understood and can severely affect the values of galaxy metallicities and abundance gradients. \citet{bresolin12} were aware of this uncertainty in their investigation of NGC\,3621 and used three different strong line calibrations. They all resulted in a flat oxygen abundance distribution over the outer extended disk, however the abundance level was different. Two calibrations yielded -0.44 dex lower than solar, whereas the third showed a much higher value, only -0.08 dex below and, thus, almost solar. In addition to the calibration dependent use of strong lines \citet{bresolin12} were also able to determine \hii~region electron temperatures from the detection of the weak auroral [OIII] 4363 line, which was detected in 12 of the observed 72 \hii~regions. Nebular oxygen abundance determinations based on the temperature information of this line are more reliable, as it can be used to calulate the excitation of the upper levels of the strong lines and thus their emission coefficient. For instance, in the case of the galaxy NGC\,300 excellent agreement has been found by \citet{bresolin09a} between \hii~region and BSG metallicities. On the other hand, the work by \citet{stasinska05}, \citet{bresolin05}, \citet{ercolano10}, and \citet{zurita12} indicates that also this method might be subject to uncertainties albeit much smaller than the strong line methods. An additional, more general problem of the oxygen abundances obtained from \hii~regions might be the depletion of oxygen through the formation of dust grains (for a discussion see \citealt{bresolin09a}). While the BSG abundance determination may certainly also be subject to systematic uncertainties, we see a double advantage in the investigation of BSG metallicties in the disk of NGC\,3621. First, it simply provides an independent measurement of metallicity using a well established accurate method. Second, it will give information about metallicity from elements other than oxygen and more relevant to ``metallicity'' in the sense of chemical evolution. We hope to use this advantage to develop improved constraints on the metallicity enrichment of the outer disks of star forming galaxies. \begin{figure} \begin{center} \includegraphics[scale=0.35,angle=90]{fig2a.ps} \includegraphics[scale=0.35,angle=90]{fig2b.ps} \caption{Top: Fit of observed Balmer line profiles (black solid) of target Slit 9 with model atmospheres of \teff=8750K and log g = 1.00 (red, solid) and 0.95 and 1.05 (both blue dashed), respectively. Bottom: Similar fit of target Slit 17 with \teff=8100K and log g =0.90 (red, solid) and 0.85, 0.95 (blue dashed). The gravities log g are given in cgs units. \label{balmfit_s9_s17}} \end{center} \end{figure} NGC\,3621 is not only interesting with regard to disk evolution and star formation. It is also an important galaxy for the determination of extragalactic distance scale. With an inclination angle of 65 degrees \citep{deblok08} and well ordered \hi~rotation it is an ideal galaxy for the calibration of the Tully-Fisher method. It is, thus, not surprising that it has been included in the Hubble Space Telescope Extragalactic Distance Scale Key Project (\citealt{freedman01}). Also the HST tip of the red giant branch (TRGB) study to calibrate type I supernovae as distance indicators by \citet{mould08} has included this important galaxy. Distance moduli determined over the last 13 years vary between 28.9 and 29.4 mag (see NED database http://ned.ipac.caltech.edu). Our BSG spectroscopic study provides an important alternative for distance determination through the use of the flux-weighted gravity -- luminosity relationship (FGLR). This technique, which uses the determination of stellar temperature and gravities to predict absolute bolometric magnitudes, has been introduced by \citet{kud03} and \citet{kud08} and has already been applied successfully in a variety of cases (WLM -- \citealt{urbaneja08}; NGC\,3109 -- \citealt{hosek14}; M33 -- \citealt{u09}; M81 -- \citealt{kud12}). \begin{figure} \begin{center} \includegraphics[scale=0.35,angle=90]{fig3.ps} \caption{Fit curve in the gravity-temperature plane for target Slit 9 along which the calculated Balmer line profiles agree with the observations. The fit point of Figure 2 (top) is indicated by the red square. \label{balmiso_s9}} \end{center} \end{figure} | 14 | 4 | 1404.7244 |
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1404 | 1404.0378_arXiv.txt | We study a sample of 23 Type II Plateau supernovae (SNe~II-P), all observed with the same set of instruments. Analysis of their photometric evolution confirms that their typical plateau duration is 100 days with little scatter, showing a tendency to get shorter for more energetic SNe. The rise time from explosion to plateau does not seem to correlate with luminosity. We analyze their spectra, measuring typical ejecta velocities, and confirm that they follow a well behaved power-law decline. We find indications of high-velocity material in the spectra of six of our SNe. We test different dust extinction correction methods by asking the following -- does the uniformity of the sample increase after the application of a given method? A reasonably behaved underlying distribution should become tighter after correction. No method we tested made a significant improvement. | Stars more massive than $\sim 8$~M$_{\odot}$ end their lives as core-collapse supernovae (CC~SNe). This is based on multiple lines of evidence, from their locations, in or near regions of star formation, to multiple progenitor identifications (see \citealt{Smartt:2009} for a review). The explosions of stars that have kept a large hydrogen envelope until their demise are observationally defined as Type II SNe, based on the presence of broad hydrogen lines in their spectra with line widths of several thousands km s$^{-1}$. The lines typically have P-Cygni profiles, formed by the expanding hydrogen-rich ejecta. Type II SNe are a diverse class, with a large range of observed luminosities, light-curve shapes, and spectroscopic features. These have been historically used to further subclassify these events. The optical light-curve shape has been used to separate those that decline linearly with time (II-L) from those that show a pronounced plateau (II-P; \citealt{Barbon:1979}). Later, two more classes were defined spectroscopically, SNe~IIn that have relatively narrow hydrogen emission lines attributed to interaction of the ejecta with circumstellar matter, and SNe~IIb that are spectroscopically intermediate between SNe~II-P and SNe~Ib (see \citealt{Filippenko:1997} for a review). SNe~Ib are interpreted as arising from stars stripped of their envelope, as indicated by their helium dominated, hydrogen-free spectra. SNe~IIb early-time spectra evolve from SN~II-P-like hydrogen-rich spectra, to SN~Ib-like \citep{Filippenko:1988}. Individual SNe~II-P have been well studied in the past thanks to their proximity. Examples include SN\,1999em (e.g., \citealt{Baron:2000}; \citealt{Leonard:2002a}; \citealt{Dessart:2006}), and SN\,1999gi \citep{Leonard:2002b}. Both objects have progenitor mass estimates -- a very tight restriction on the upper mass of the SN\,1999em progenitor was derived by \citet{Smartt:2009b}, who found 15~M$_{\odot}$, and for SN\,1999gi \citet{Smartt:2001} report an upper limit of 9$^{+3}_{-2}$~M$_{\odot}$. Another example of a nearby, well-studied event is SN\,2005cs (e.g., \citealt{Pastorello:2009}); it had a low luminosity and a low-mass progenitor. However, there are very few studies of samples of SNe~II-P. \citet{Hamuy:2002} and \citet{Hamuy:2003b} analyzed a sample of $\sim 20$ SNe~II-P, and found relations between plateau luminosity, ejecta velocities, and nickel abundances, as well as a useful luminosity-velocity relation which allows for distance measurements. This is an empirical application of the expanding photosphere method (EPM; \citealt{Kirshner:1974}; \citealt{Eastman:1996}; \citealt{Dessart:2005b}; \citealt{Dessart:2008}; \citealt{Jones:2009}). This method and its potential for cosmological distance measurements was further studied by \citet{Nugent:2006}, \citet{Poznanski:2009}, \citet{DAndrea:2010}, \citet{Poznanski:2010}, and \citet{Olivares:2010}. \citet{Maguire:2010b} examined its extension into the infrared. \citet{Arcavi:2012} analyzed a small sample of SNe~II-P, contrasting them with other SNe~II, and found that while they differ wildly in luminosity, they seem to have similar plateau durations, all near 100 days. While this paper was in final editing stages \citet{Anderson:2014} published an analysis of Type II SN photometry. They present a sample of more than 100 V-band light curves. Their results are consistent with some of our photometric findings, namely that these SNe seem to form a continuous class, with a range of luminosities, with a correlation between plateau duration and brightness. However, they consider a larger range of SNe, including objects that we would classify as II-L and analyze separately in a companion paper (Faran et al. 2014). Here we present a sample of 23 SNe~II-P, many of which have not been studied before, all observed by the Lick Observatory SN Search (LOSS; \citealt{Filippenko:2001}). All objects have high-cadence photometry in 3--4 bands, and between few and tens of optical spectra. This results in a dataset with 1574 photometric points and 152 spectra. We further use this sample to examine methods for dust-extinction correction\footnote{This paper is dedicated to the memory of our dear friend and colleague, Dr. Weidong Li, without whom these data would not exist.}. | Our photometric and spectroscopic analysis of a sample of 23 SNe~II-P reveals the following. \begin{itemize} \item The luminosity distribution of SNe~II-P seems continuous, spanning 3~mag, as indicated by \citet{Arcavi:2012}. \item Plateau durations are typically 100 days, as shown by \citet{Arcavi:2012}, but do get shorter for more luminous, energetic SNe, as expected from \citet{Poznanski:2013}. \item We do not find any indication for a correlation between rise time and plateau luminosity using a sample of 8~SNe, contrary to what was previously suggested by \citet{GalYam:2011} and \citet{Valenti:2013}. \item Three SNe show a post-plateau rebrightening, which is interpreted as being caused by helium recombination by \citet{Chieffi:2003}. \item We find that hydrogen and iron velocities follow well-behaved power laws, with little scatter, as shown by \citet{Nugent:2006}, though we derive a somewhat steeper decline using a much larger sample. \item Signs of interaction with CSM might be evident in the spectra of at least six events, where we find HV features in the blue wing of H$\alpha$ during the plateau phase. Corresponding absorption in H$\beta$ confirms that these are indeed HV lines associated with hydrogen and not metal lines. \item When studying SNe there are a multitude of methods used in the literature to correct for dust extinction: photometric methods based on comparison to low-extinction SNe, or spectroscopic ones using the Na~I~D doublet. With the availability of a sample we were given the opportunity to ask a simple question: Does the uniformity of the sample increase after the application of a given method? Any reasonably behaved underlying distribution should become tighter after correction. The uniform answer was negative; no method we tested made a significant improvement. This is likely due to a combination of the weakness of the methods (i.e., the intrinsic scatter they introduce) and modest typical extinction of SNe~II, of order $\sim 0.2$~mag. \end{itemize} | 14 | 4 | 1404.0378 |
1404 | 1404.6597_arXiv.txt | We present the results of our ALMA Cycle 0 observations, using HCN/HCO$^{+}$/HNC J=4--3 lines, of six nearby luminous infrared galaxies with various energetic contributions from active galactic nuclei (AGNs) estimated from previous infrared spectroscopy. These lines are very effective for probing the physical properties of high-density molecular gas around the hidden energy sources in the nuclear regions of these galaxies. We find that HCN to HCO$^{+}$ J=4--3 flux ratios tend to be higher in AGN-important galaxies than in starburst-dominated regions, as was seen at the J=1--0 transition, while there is no clear difference in the HCN-to-HNC J=4--3 flux ratios among observed sources. A galaxy with a starburst-type infrared spectral shape and very large molecular line widths shows a high HCN-to-HCO$^{+}$ J=4--3 flux ratio, which could be due to turbulence-induced heating. We propose that enhanced HCN J=4--3 emission relative to HCO$^{+}$ J=4--3 could be used to detect more energetic activity than normal starbursts, including deeply buried AGNs, in dusty galaxy populations. | Luminous infrared galaxies (LIRGs) and ultraluminous infrared galaxies (ULIRGs) emit very strong infrared (8--1000 $\mu$m) radiation with luminosity of $L_{\rm IR}$ $>$ 10$^{11}L_{\odot}$ and $>$10$^{12}L_{\odot}$, respectively \citep{sam96}. The strong infrared emission indicates that (U)LIRGs contain powerful energy sources hidden behind dust. The dust-obscured energy sources of (U)LIRGs may be either nuclear fusion reactions inside rapidly formed stars (starburst) and/or radiative energy generation by an accreting compact supermassive black hole (SMBH) with mass of $>$10$^{6}$M$_{\odot}$ (active galactic nucleus; AGN). Understanding the (U)LIRG's hidden energy sources is indispensable to clarify the nature of the (U)LIRG population. However, this is not easy because the powerful compact nuclear starbursts found in the bulk of (U)LIRGs are not clearly distinguishable from very compact AGN activity based on imaging observations alone at the distance of many (U)LIRGs of interest. Since (U)LIRGs are the dominant population at $z >$ 1 in terms of the cosmic infrared radiation density \citep{cap07,got10,mag11,mur11}, establishing a reliable method to differentiate the hidden energy sources of dusty (U)LIRG populations is useful to unravel the history of star formation and SMBH mass growth in the dust-obscured side of galaxy formation in the early universe. If AGNs are surrounded by toroidally distributed (torus-shaped) dusty medium, the so-called narrow line regions, which are photoionized by AGN radiation, should develop at 10--1000 pc along the torus axis, above the torus scale height \citep{ant93}. Since emission from the narrow line regions in AGNs is visible from all directions, such classical AGNs obscured by torus-shaped dusty medium are classified optically as Seyfert 2s, and are therefore distinguishable from starbursts through optical spectroscopic classification, based on optical emission line flux ratios \citep{vei87,kew01,kau03}. However, (U)LIRGs are major mergers of gas-rich galaxies and have large amounts of concentrated molecular gas and dust in their nuclei \citep{sam96}. The putative compact AGNs in (U)LIRG nuclei can be easily obscured by dust and gas in virtually all directions in the inner part of the surrounding obscuring material. Hence, optical detection of AGN signatures becomes very difficult, because the narrow line regions can be significantly underdeveloped. Understanding the energetic importance of such optically elusive {\it buried} AGNs is crucial to clarify the true nature of the (U)LIRG population, as well as the SMBH mass growth process during gas-rich galaxy mergers \citep{hop06}. To investigate buried AGNs in dusty (U)LIRG nuclei, it is essential to perform observations at wavelengths where dust extinction effects are small. The infrared 2.5--35 $\mu$m band is one such region. Systematic infrared 2.5--35 $\mu$m spectroscopy of nearby (U)LIRGs has allowed elucidation of the energetic role of buried AGNs in a quantitative manner \citep{ima06a,ima06c,ima07a,ima08,ima10a,ima10b,ima09a,nar08,nar09,nar10,vei09,lee12}. However, our understanding of distant ($z > 1$) (U)LIRGs is incomplete, because at $z > 1$, application of this infrared spectroscopy is limited to infrared 24 $\mu$m very bright sources only \citep{wee06,saj07,das09}, which are strongly biased toward AGNs \citep{pap07,don08,lee10}. No significant progress is expected until the SPICA satellite, which has high sensitivity in the infrared 10--200 $\mu$m range, becomes operational after 2020 \citep{nak12}. Starbursts (nuclear fusion) and buried AGNs (mass accretion onto SMBHs) have very different energy generation mechanisms. First, the radiative energy generation efficiency of a nuclear fusion reaction in a starburst is only $\sim$0.7\% of Mc$^{2}$ (where M is the mass of material used in the nuclear fusion reaction, and c is the speed of light). Thus, the emission surface brightness of a starburst region is modest and has both observational \citep{wer76,soi00} and theoretical \citep{tho05} upper limits of $\sim$10$^{13}$L$_{\odot}$ kpc$^{-2}$. An AGN, however, achieves high radiative energy generation efficiency (6\%--42\% of Mc$^{2}$, where M is the mass of accreting material) \citep{bar70,tho74}, and can produce high luminosity from a very compact region. A high emission surface brightness with $>$10$^{13}$L$_{\odot}$ kpc$^{-2}$ \citep{soi00} can be achieved in an AGN, and a large amount of dust in the close vicinity of the AGN can be heated to high temperatures (several 100 K). Second, while UV is the dominant energetic radiation in a starburst, an AGN emits strong X-rays in addition to UV radiation \citep{ran03,sha11}. Since it is predicted that these AGN-origin high dust temperatures and strong X-ray irradiation cause different chemical reactions for molecules compared to starbursts \citep{mei05,lin06,har10,har13}, different flux ratios of molecular rotational J-transition lines could be observed between AGNs and starbursts in the (sub)millimeter wavelength range. This difference may be used to distinguish the hidden energy sources of dusty galaxy populations, because of the negligible effects of dust extinction at (sub)millimeter wavelengths. Observational results of possibly different effects and feedback to the surrounding molecular gas between AGNs and starbursts have been reported, based on CO, HCN, HCO$^{+}$, and HNC rotational J-transition line observations of nearby bright starburst and Seyfert galaxies (modest luminosity AGNs) \citep{koh05,per07,kri08,cos11}. For example, it has been argued that AGNs show HCN J=1--0 (rotational transition) flux enhancement, relative to HCO$^{+}$ J=1--0 \citep{koh05,kri08}. However, the interpretation of these results is controversial, because observational data are sparse for sources for which the energetic contributions of AGNs are quantitatively well-constrained. In nearby Seyfert galaxies, modestly luminous AGNs are surrounded by starburst activity in nuclear regions \citep{ima02,ima03,rod03,iw04,oi10} and circum-nuclear regions in host galaxies \citep{cla00,wat08,woo12}. The AGN and starburst energetic contributions can vary markedly depending on the aperture size employed. Hence, a comparison among various observations at different wavelengths with different aperture sizes is not straightforward, which makes the discussion highly uncertain. Nearby ($z <$ 0.4) ULIRGs are energetically dominated by nuclear compact ($<$ a few 100 pc in physical scale, or $<$0$\farcs$5 at $z >$ 0.04) energy sources \citep{soi00,ima11a}, so that various observational data at different wavelengths (with different aperture sizes) must reflect the properties of nuclear emission, with minimum contamination from spatially extended ($>$kpc scale) star formation activity in host galaxies. The relative energetic contributions from starbursts and AGNs have also been estimated {\it quantitatively} and {\it consistently} for many nearby ULIRG nuclei through systematic infrared 2.5--35 $\mu$m spectroscopy \citep{vei09,ima10a,ima10b,nar10}. Nearby ULIRGs are thus excellent laboratories in which to create a template of molecular line flux ratio from AGNs and starbursts, and to scrutinize AGN effects and feedback on molecular rotational (J)-transition line flux ratios in a quantitatively reliable manner. Since ULIRG nuclear regions are dominated by dense molecular gas \citep{gao04}, observations with molecular lines with high critical densities (e.g., HCN, HCO$^{+}$, HNC), rather than the widely used low-J CO lines, are needed to properly probe AGN effects in ULIRG nuclei. Pre-ALMA interferometric observations using HCN and HCO$^{+}$ J=1--0 were performed for nearby bright ULIRGs at $z<$ 0.06 to probe their nuclear molecular gas properties. It was found that ULIRG nuclei classified as AGN-important based on infrared spectra tend to show higher HCN-to-HCO$^{+}$ J=1--0 flux ratios than starburst-classified nuclei \citep{ima04,ima06b,in06,ima07b,ima09b}, supporting the suggestion that enhanced HCN emission can be used to detect AGNs. With the advent of highly sensitive ALMA, this study is in principle applicable to fainter sources. However, at $z>$ 0.06, these J=1--0 lines will be redshifted beyond the frequency (wavelength) coverage of ALMA band 3, and hence will not be observable with the current specification of ALMA. It is particularly important to establish an energy diagnostic method using higher J-transition lines at higher frequencies (shorter wavelengths), which can be applied to distant ULIRGs using ALMA. For nearby sources, J=4--3 and J=3--2 transition lines of HCN, HCO$^{+}$, and HNC were observable in ALMA band 7 (275--373 GHz) and 6 (211--275 GHz), respectively, during ALMA Cycle 0, while J=2--1 lines were not. Earth's atmospheric background emission is smaller in band 6 than in band 7, and so observations in band 6 to cover J=3--2 transition lines of HCN, HCO$^{+}$, and HNC are easier. However, if excitation is thermal at up to J=4--3, the flux of J=4--3 is higher by a factor of 16/9 than that of J=3--2, largely compensating for the higher atmospheric background noise of Earth at J=4--3 in band 7. Given reasonable assumptions about the observing conditions, the ALMA sensitivity calculator showed that the required on source exposure times for the same detection significance (same S/N ratio) were similar between the J=3--2 and J=4--3 lines of HCN, HCO$^{+}$, and HNC, if the excitation is thermal at up to J=4--3. Given that the J=4--3 line energy diagnostic is applicable to higher redshift sources than that of J=3--2 using ALMA, we selected J=4--3 line as our initial choice, with the caution that the J=3--2 line could be better for detection if the excitation is significantly sub-thermal. We performed HCN J=4--3 (rest-frame frequency $\nu_{\rm rest}$ = 354.505 GHz), HCO$^{+}$ J=4--3 ($\nu_{\rm rest}$ = 356.734 GHz), and HNC J=4--3 ($\nu_{\rm rest}$ = 362.630 GHz) observations of nearby ULIRGs with well-calibrated energy sources. Since HCN, HCO$^{+}$, and HNC have similar dipole moments ($\mu$ = 3.0, 3.9, and 3.1 Debye, respectively) and similar frequencies for individual J transitions, it is likely that similar dense gas phases are probed by these molecular lines, making the interpretation straightforward. Throughout this paper, we adopt H$_{0}$ $=$ 71 km s$^{-1}$ Mpc$^{-1}$, $\Omega_{\rm M}$ = 0.27, and $\Omega_{\rm \Lambda}$ = 0.73 \citep{kom09}. | \subsection{Molecular Line Flux Ratio} Figure 10 shows a plot of the HCN-to-HCO$^{+}$ J=4--3 and HCN-to-HNC J=4--3 flux ratios in the four ULIRGs, together with the starburst-dominated LIRG, NGC 1614 \citep{ima13a}, and the AGN-starburst composite ULIRG, IRAS 20551$-$4250 \citep{ima13b}. The buried AGN-dominated ULIRGs, IRAS 08572$+$3915, 12127$-$1412, and 00183$-$7111, show higher HCN-to-HCO$^{+}$ flux ratios at J=4--3 than the starburst-dominated LIRG, NGC 1614. The AGN and starburst composite ULIRG, IRAS 20551$-$4250, is located between the buried AGN-dominated ULIRGs and a starburst-dominated LIRG, NGC 1614, on the ordinate, as expected ($\S$2). The starburst-classified ULIRG in the infrared spectrum, IRAS 22491$-$1808, shows a high HCN-to-HCO$^{+}$ J=4--3 flux ratio, which will be discussed in the next subsection. On the other hand, the HCN-to-HNC J=4--3 flux ratios in the abscissa are not clearly different between AGN-dominated and starburst-dominated sources. A high HCN-to-HCO$^{+}$ J=4--3 flux ratio could be an indicator of a luminous buried AGN, and could be used to distinguish AGNs from starbursts \citep{ima10c,ion13}. \subsection{Interpretation} We consider three possible mechanisms for the strong HCN J=4--3 emission in AGNs, relative to HCO$^{+}$ J=4--3. First, the HCN abundance enhancement is a natural explanation for the enhanced HCN emission. In an AGN, due to the high radiative energy generation efficiency of a mass-accreting SMBH, a larger amount of dust is heated to high temperatures (several 100 K) than in a starburst ($\S$1). It is predicted that the HCN abundance could be enhanced, relative to HCO$^{+}$ in high dust temperature chemistry \citep{har10}. In an AGN, the HCN abundance enhancement by strong X-ray radiation is also calculated by \citet{lin06}, but the HCN-to-HCO$^{+}$ abundance ratio under X-ray irradiation is also shown to be highly model-dependent \citep{mei05,har13}. Second, vibrationally excited HCN emission lines were detected in AGN-hosting galaxies \citep{sak10,ima13b}. Infrared radiative pumping \citep{aal95} by absorbing infrared $\sim$14 $\mu$m photons is the most natural mechanism for vibrational excitation, because vibrationally excited levels of HCN with $>$1000 K are very difficult to achieve with collisions \citep{sak10}. Since an AGN emits infrared 14 $\mu$m continuum emission much more strongly due to AGN-heated hot dust than a starburst, this infrared radiative pumping is expected to work more effectively in an AGN. This mechanism can increase the HCN J=4--3 flux at v=0 through a cascade process \citep{ran11} in comparison to collisional excitation alone. On the other hand, detection of the vibrationally excited HCO$^{+}$ emission line has not been reported to date in any AGNs. In fact, the HCN v$_{2}$=1--0 absorption features at infrared 14 $\mu$m were detected in several obscured AGNs, while the HCO$^{+}$ v$_{2}$=1--0 absorption features at infrared 12.1 $\mu$m were not \citep{lah07,vei09}. This may indicate that the necessary condition for the infrared radiative pumping is fulfilled more effectively for HCN than HCO$^{+}$. Thus, this infrared radiative pumping may be the reason for the enhanced HCN J=4--3 fluxes relative to HCO$^{+}$ J=4--3 observed in AGNs. Third, the higher HCN-to-HCO$^{+}$ J=4--3 flux ratios in AGNs compared to starbursts could be simply due to an excitation effect. As the critical density of HCN J=4--3 (n$_{\rm crit}$ $\sim$ 2 $\times$ 10$^{7}$ cm$^{-3}$) is higher than that of HCO$^{+}$ J=4--3 (n$_{\rm crit}$ $\sim$ 4 $\times$ 10$^{6}$ cm$^{-3}$) \citep{mei07}, HCO$^{+}$ J=4--3 is more easily excited than HCN J=4--3. The HCN-to-HCO$^{+}$ flux ratio at J=4--3 should be lower than that at J=1--0. AGN-heated hot dust could create large amounts of hot molecular gas, and more HCN J=4--3 excitation is expected in an AGN than a starburst. This can result in a higher HCN-to-HCO$^{+}$ J=4--3 flux ratio in an AGN than in a starburst, even without invoking HCN abundance enhancement and/or the flux enhancement of the HCN J-transitions at v=0 through the infrared radiative pumping mechanism. HCN and HNC have comparable critical densities \citep{mei07}, so their excitation is expected to be similar, as long as the same molecular gas phase is probed. The observational result that AGNs tend to show higher HCN-to-HCO$^{+}$ J=4--3 flux ratios than starbursts but similar HCN-to-HNC J=4--3 flux ratios suggests that excitation is an important factor. That is, the larger amount of hot molecular gas in an AGN may boost HCN J=4--3 excitation, relative to HCO$^{+}$ J=4--3, increasing the HCN-to-HCO$^{+}$ J=4--3 flux ratios compared to a starburst, but also increase the excitation of HCN and HNC up to J=4--3 in a similar manner, without changing the HCN-to-HNC J=4--3 flux ratio. It is also possible that the HCN abundance is enhanced relative to HCO$^{+}$ in AGNs due to AGN-related phenomena (high dust temperature and/or strong X-ray irradiation), but that the HNC abundance is similarly enhanced. Or, it may be that the HNC J=4--3 flux at v=0 is also enhanced through vibrational excitation by infrared radiative pumping \citep{cos13}, in a similar way to HCN, but the HCO$^{+}$ J=4--3 flux at v=0 is not. IRAS 22491$-$1808 shows an infrared spectrum whose observed flux can be explained solely by starburst activity, and yet shows a high HCN-to-HCO$^{+}$ J=4--3 flux ratio. As mentioned in $\S$2, the presence of a buried AGN in IRAS 22491$-$1808 is not precluded, due to the smaller observed PAH-to-infrared luminosity ratio compared to the known starburst-dominated, less infrared-luminous galaxies. However, the direct signature of such an AGN is also lacking. A notable feature of IRAS 22491$-$1808 is the very large molecular line widths, with $>$400--500 km s$^{-1}$ in full width at half maximum (FWHM) or $>$700 km s$^{-1}$ in full width at zero intensity (FWZI) for HCN and HCO$^{+}$ J=4--3 (Figure 6). These values are much larger than those for normal ULIRGs whose HCN and HCO$^{+}$ line widths are typically $\sim$200--300 km s$^{-1}$ in FWHM \citep{gao04,in06,ima07b}, and are as high as the values of the merger-induced shock-dominated highly turbulent luminous infrared galaxy NGC 6240 \citep{nak05}. The intensity-weighted velocity dispersion (moment 2) maps of HCN and HCO$^{+}$ J=4--3 of IRAS 22491$-$1808 in Figure 8 also show much larger peak values in the bulk of galactic areas than those of IRAS 08572$+$3915 (Figure 7), NGC 1614 \citep{ima13a}, and IRAS 20551$-$4250 \citep{ima13b}. This suggests that the high-density molecular gas in IRAS 22491$-$1808 is particularly turbulent compared to the majority of ordinary ULIRGs. A turbulent heating mechanism \citep{pan09} may produce large amounts of hot dust and molecular gas, and could (1) boost HCN J=4--3 excitation compared to normal starburst galaxies, (2) enhance HCN abundance under high dust temperature chemistry (see also Papadopoulos 2007), and (3) increase the effect of the infrared radiative pumping mechanism due to an increase in infrared 14 $\mu$m photons. If sufficient amounts of hot dust and molecular gas are created by a mechanism other than a luminous AGN, and if the enhanced HCN-to-HCO$^{+}$ J=4--3 flux ratios are due to phenomena related to hot dust and molecular gas (i.e., increased HCN J=4--3 excitation, HCN abundance increase by hot dust chemistry, and increased efficiency of infrared radiative pumping), then the high HCN-to-HCO$^{+}$ flux ratios could pick up not only luminous buried AGNs, but also starbursts with highly turbulent dense molecular gas. Although we obtained the molecular line data of the starburst-dominated LIRG NGC 1614 \citep{ima13a}, data on ordinary starburst-dominated ULIRGs that show usual dense molecular gas properties are lacking. Starbursts in ULIRGs could be more intense per unit volume than those in LIRGs, and could create different molecular gas excitation in such a way that HCN J=4--3 is excited to a greater extent in starbursts in ULIRGs than in the less infrared-luminous LIRGs. Molecular line data on starburst-dominated ULIRGs with normal dense molecular gas properties, if obtained in the future, would provide insight into the origin of the observed molecular line flux ratios in the highly turbulent ULIRG, IRAS 22491$-$1808. Observations of further well-studied (U)LIRGs are needed to better understand how molecular emission line flux ratios depend on the relative AGN and starburst energetic contributions, and other galaxy properties. Finally, we briefly mention some other possibilities that could affect the observed molecular line flux ratios. Emission line fluxes can be reduced by dust extinction. Since the frequencies of HCN, HCO$^{+}$, and HNC J=4--3 lines are $\sim$350 GHz ($\sim$850 $\mu$m) in the submillimeter wavelength range, flux attenuation of these molecular lines by dust extinction is usually not significant. \citet{mat09} estimated that in the nearby well-studied ULIRG, Arp 220, dust extinction may not be negligible even in the submillimeter wavelength. Even if dust extinction at $\sim$850 $\mu$m is not negligible in some of the observed (U)LIRGs, flux attenuation of HCN, HCO$^{+}$, and HNC J=4--3 lines should be comparable, due to their similar frequencies (wavelengths). Thus, molecular line flux ratios will not change significantly by possible dust extinction in the submillimeter wavelength. Line opacity could also have an effect on the observed molecular line fluxes. According to the wide-accepted standard scenario for molecular gas clouds in the Galaxy and external galaxies, molecular gas clouds consist of clumps with a small volume filling factor \citep{sol87}. The line opacity of each clump is thought to be larger than unity for CO \citep{sol87}. Emission from the other side of each clump is not completely probed from CO observations. Each clump has small molecular line widths by thermal broadening, but shows large random motion inside molecular gas clouds. Due to the velocity difference of each clump, line absorption by foreground clumps is insignificant, and clumps at the other side of the molecular gas clouds are observationally detectable. This model (the so-called mist model) can explain observed molecular gas properties very well \citep{sol87}. The detailed physical parameters of each clump are observationally not well-constrained. Thus, the physical properties of each clump are assumed to be uniform inside a molecular cloud, as well as among different galaxies. The optical depths of HCN J=4--3 lines in external galaxies could be larger than unity \citep{ngu92,sak10,jia11}. Even if each clump is optically thick for HCN, as long as the uniform physical properties of each gas clump is assumed, the enhanced HCN abundance results in an increased area filling factor of HCN emission in a molecular gas cloud, and so a higher HCN J=4--3 flux from a molecular gas cloud \citep{ima07b}, not changing our previous discussion. We should note that the unconstrained physical properties of each molecular gas clump could cause the largest uncertainty about the interpretation of the observed molecular line flux ratios. Summarizing, we regard that the proposed three scenarios (HCN abundance enhancement, infrared radiative pumping, and excitation effect) are the plausible mechanisms that could explain the variation of the observed molecular line flux ratios in (U)LIRGs with different AGN energetic contributions. If the excitation effect is important, the HCN-to-HCO$^{+}$ flux ratios are expected to systematically decrease at higher J-transition. On the other hand, in the case of HCN abundance enhancement, the HCN-to-HCO$^{+}$ flux ratios are not sensitive to J-transitions. Multiple J-transition molecular line observations are needed to differentiate physical mechanisms behind the observed molecular line flux ratios, with the aid of modeling \citep{van07}. For (U)LIRGs with small molecular line widths, vibrationally-excited HCN emission lines may be detectable, by separating from the nearby, much stronger HCO$^{+}$ emission lines at v=0 \citep{sak10,ima13b}. The strengths of the detected vibrationally-excited HCN emission lines can be used to understand the general role of the infrared radiative pumping for HCN excitation in AGN-hosting (U)LIRGs. \subsection{Implications} As mentioned in $\S$1, although the energy diagnostic method developed using the J=1--0 transition lines of HCN and HCO$^{+}$ \citep{koh05,ima04,in06,ima06b,ima07b,kri08,ima09b} is powerful, using ALMA it is applicable only to nearby galaxies with $z <$ 0.06. If we can establish a reliable energy diagnostic method using a higher J transition at higher frequency (shorter wavelength), the method could potentially be applied to more distant galaxies using ALMA. Furthermore, the HCN J=4--3 lines selectively trace dense molecular gas in the nuclear regions of galaxies where AGNs are expected to be present, with even less contamination from spatially extended galaxy-wide molecular gas than at lower J-transitions. Hence, the energy diagnostic method using HCN J=4--3 could be very sensitive to the presence of luminous AGNs. These were the primary reasons why we conducted our ALMA Cycle 0 program. In the case of thermal excitation, the flux of high-J transition lines increases proportional to the square of the frequency ($\propto$$\nu^{2}$), and so the J=4--3 flux can be 16 times higher than the J=1--0 flux. If realized, the high J=4--3 flux can keep the detection significance of molecular emission lines high, even under the higher Earth background noise at the frequency of J=4--3 compared to J=1--0. Given that the bulk of the infrared luminosity of nearby (U)LIRGs usually comes from the nuclear regions ($\S$1), we may be able to relate the nuclear molecular gas emission properties with the IRAS-measured whole galactic infrared emission. Based on our pre-ALMA interferometric HCN J=1--0 observations of nearby (U)LIRG nuclei, the nuclear HCN J=1--0 peak flux and whole galactic infrared flux are found to be correlated (Figure 11; Left), where the actual data are summarized in Table 7. Therefore, we can empirically predict the emission peak flux of HCN J=1--0 line in the (U)LIRG nuclei from the IRAS-measured infrared flux, and can convert to the HCN J=4--3 emission peak flux assuming thermal excitation. Figure 11 (right) compares the HCN J=1--0 luminosities at (U)LIRG nuclei based on our pre-ALMA interferometric observations, with the IRAS-measured infrared luminosities from the whole galactic regions of (U)LIRGs. Our plots, particularly for the nuclei of ULIRGs with L$_{\rm IR}$ $\gtrsim$ 10$^{12}$L$_{\odot}$, roughly follow the ratio established for ULIRGs based on single-dish telescope data \citep{gra08}, supporting the scenario that the bulk of high-density molecular gas in ULIRGs is concentrated in the energetically-dominant nuclear regions and is recovered with our pre-ALMA interferometric data with $\sim$1 to several arcsec spatial resolution. Table 8 presents a comparison of the expected HCN J=4--3 peak flux for thermal excitation with the observed peak flux. It can be seen that the HCN J=4--3 emission peak is substantially smaller than that expected from thermal excitation, indicating that HCN is sub-thermally excited at J=4--3 even in our active ULIRG sample, often hosting luminous buried AGNs. Thus, lower J transitions (J=3--2 or 2--1) may be better in terms of the detection significance of HCN J-transition line per given observing time. It is necessary to find the best J transition lines with which we can reliably and efficiently separate deeply buried AGNs from the surrounding starbursts in a dusty ULIRG population. | 14 | 4 | 1404.6597 |
1404 | 1404.4247_arXiv.txt | Saturn's inner B-ring and its C-ring support wavetrains of contrasting amplitudes but with similar length scales, 100---1000 km. In addition, the inner B-ring is punctuated by two intriguing `flat' regions between radii 93,000 km and 98,000 km in which the waves die out, whereas the C-ring waves coexist with a forest of plateaus, narrow ringlets, and gaps. In both regions the waves are probably generated by a large-scale linear instability whose origin lies in the meteoritic bombardment of the rings: the ballistic transport instability. In this paper, the third in a series, we numerically simulate the long-term nonlinear evolution of this instability in a convenient local model. Our C-ring simulations confirm that the unstable system forms low-amplitude wavetrains possessing a preferred band of wavelengths. B-ring simulations, on the other hand, exhibit localised nonlinear wave `packets' separated by linearly stable flat zones. Wave packets travel slowly while spreading in time, a result that suggests the observed flat regions in Saturn's B-ring are shrinking. Finally, we present exploratory runs of the inner B-ring edge which reproduce earlier numerical results: ballistic transport can maintain the sharpness of a spreading edge while building a `ramp' structure at its base. Moreover, the ballistic transport instability can afflict the ramp region, but only in low-viscosity runs. | Planetary rings of low and intermediate optical depth are vulnerable to the ballistic transport instability (BTI) which issues from the continual bombardment of ring particles by hypervelocity micrometeoroids. Ejecta released via these impacts reaccrete on to the ring at various radii, and thus redistribute mass and angular momentum (Durisen 1984, Ip 1984, Lissauer 1984). A small positive perturbation in surface density will change the ring's local transport properties, and if the overdense region releases less material than it can absorb relatively, then it will grow and an instability results (Durisen 1995, Latter et al.~2012, hereafter Paper 1). The BTI favours long lengthscales $l_\text{th}\sim 10-10^3$ km and long timescales $t_e \sim 10^5-10^7$ yr. Thus the 100-km waves in the inner B-ring (between radii 93,000 and 98,000 km) and the 1000-km undulations in the C-ring (between 77,000 and 86,000 km) are possible manifestations of its nonlinear development (Figs 13.17 and 13.13 in Colwell et al.~2009, Charnoz et al.~2009 ). This is the third paper in a series exploring the dynamics of the BTI and its generation of wave-like structure. The first paper presented a convenient local model with which to study the problem and worked through the BTI's linear theory (Paper 1). The second paper established semi-analytically that the instability could sustain families of nonlinear travelling wavetrains (Latter et al.~2013, herafter Paper 2). For C-ring parameters, these waves saturate at low amplitude. For B-ring parameters, the ring exhibits bistability, with the system falling into one of two linearly stable states: the background homogeneous state (a `flat zone') or a large-amplitude wave state (a `wave zone'). Both results are consistent with Cassini data and strengthen the connection between the observed wave features and the BTI. In this paper, our earlier results are verified and extended with time-dependent simulations. Our numerical algorithm exploits the convolution form of the ballistic transport integrals and, as a result, can easily evolve the system on extremely long timescales $\sim 1000\, t_e$ and lengthscales $\sim 100\, l_\text{th}$. We subsequently calculate structure formation in three contexts: (a) low-optical depth models of the C-ring, (b) bistable models of the B-ring, and (c) the spreading and structure of a sharp edge. The low-optical depth simulations fulfil most of the expectations of Paper 2. After an initial period of wave competition, the system settles upon a linearly stable low-amplitude wavetrain that fills the domain. Our simulations, however, possess translational symmetry, a special constraint not shared by the C-ring. In order to eliminate its effects, we perform additional runs with `buffered' boundaries that work similarly to out-going wave conditions. Low-amplitude wavetrains dominate these simulations as well, but their dynamics is more complicated; in particular, wave activity can propagate out of the ring entirely leaving behind a state of very low amplitude and long wavelength. Concurrently waves suffer strong time-dependent inhomogeneities in their amplitude and phase. Both sets of simulations are consistent with Cassini observations of the very long C-ring undulations, and reinforce the attribution of these features to the BTI. Our second group of simulations probes the dynamics of hysteresis in models of the B-ring. As the system supports both a stable homogeneous state and a wave state, we set up an initial condition in which these two states occupy different regions within the computational domain. We find that the `wave zones' behave like wave packets, moving at the group velocity of their constituent waves. In addition, the wave packets spread, a nonlinear effect due to the variation of the group velocity through the packet. This behaviour agrees qualitatively with the observations, though interesting discrepancies exist which we discuss. Finally, exploratory runs of a spreading ring edge are presented. Starting from a step function in optical depth between very thin and thick regions, we confirm the finding of Durisen et al.~(1992, hereafter D92), that ballistic transport maintains the sharpness of an edge as it spreads, while building at its foot a `ramp' (i.e.\ a region with a shallow optical depth gradient). Lower viscosity runs, however, indicate that this ramp is unstable to the BTI, with growing modes reaching large amplitudes. As such structures are absent in the Cassini observations, it may be possible to roughly constrain ring properties from this result. The organisation of the paper is as follows. In Section 2 we summarise the mathematical details of our physical model as well as the numerical method with which we solve it. Section 3 presents simulations that approximate the C-ring, Section 4 deals with the B-ring simulations, while Section 5 contains our results on spreading ring edges. We draw our conclusions and point to future work in Section 6. | In this paper we have developed a reliable and efficient numerical tool with which to simulate the ballistic transport process in planetary rings. We have subsequently reproduced the nonlinear evolution of the BTI in models of both the C-ring and B-ring, in addition to the spreading of a ring edge. Both our B-ring and C-ring simulations validate the predictions of Paper 2's semi-analytic theory. C-ring simulations saturate by forming stable low-amplitude wavetrains within a narrow range of preferred wavelengths. But because of the translational symmetry of our local model this outcome is not a global solution to the real, radially structured, C-ring. In order to eliminate some of the unrealistic effects of the translational symmetry, additional simulations were conducted with buffered boundaries. Near marginality, as in the C-ring, BTI modes possesses low growth rates and yet retain relatively large group velocities and, as a consequence, the BTI's `convective' character becomes important. Our buffered simulations show that unstable disturbances can propagate out of the region of interest before their nonlinear dynamics develop and sustain appreciable amplitudes. Unless continually fed new perturbations, the BTI may saturate at a very low level of activity. It is possible that the C-ring has fallen into such a state. However, C-ring undulations compete with other features, such as plateaus, ringlets, and gaps that may interfere with their evolution, or alternatively help seed fresh BTI modes. Undoubtedly the dynamics are complicated in this region and more irregular than predicted by the local shearing sheet with pure periodic boundary conditions. Our simulations of the inner B-ring show that it is possible that the system splits into stable wave zones and stable homogeneous zones, in agreement with Cassini data. Moreover, the wave zones propagate through the homogeneous regions as independent wave packets while simultaneously spreading. Consequently, both the observed larger and smaller flat spots may evaporate in a time $\sim 100t_e \sim 10^7-10^9$ yr. However, as discussed in Paper 2, the morphologies of the theoretical and observed B-ring waves exhibit troubling discrepancies. The troughs of the former are too deep, while the mean $\tau$ in the former varies between flat and wavy zones. The disagreement could issue from the simple fact that the theoretical and observational profiles are measured in dynamical and photometric optical depths, respectively. But further work is needed to establish this directly. Finally, we conducted exploratory simulations of the inner B-ring edge. We find that ballistic transport does not arrest the viscous spreading of the edge, but resculpts it as it spreads. In particular, ballistic transport forms a ramp-like feature at its base, while maintaining the sharpness of the edge --- in agreement with previous simulations. We also find, in low viscosity runs, that the ramp structure is susceptible to BTI. But as the observed ramp does not exhibit wave (or any other) features, we conclude that the BTI is suppressed in this region by physics not captured in our fiducial simulations. In the future we hope to refine our physical model and conduct more detailed simulations, especially of spreading edges. There are two obvious improvements: the inclusion of a $\tau$-dependent viscosity, and an absorption probability $P$ that depends on $\tau$ at both the emitting and absorbing radius. Preliminary simulations indicate little qualitative change when $\mu$ is an increasing function of $\tau$. On the other hand, a better $P$ model may alter our results more significantly, not only for the C-ring dynamics but for conditions at the inner B-ring edge. Indeed, it may aid in the suppresion of the BTI in the ramp region. Unfortunately the more realistic $P$ precludes use of the convolution theorem and its many computational benefits. An intermediate model, however, need only incorporate the first few terms in an expansion of $P$ (i.e.\ the first few ejecta ring-plane crossings), and the convolution theorem could then be applied to each term. Simulations with the improved model may better reproduce, and help explain, the observed morphologies of spreading edges. They may also constrain the spreading time of the inner A-ring and B-ring by examining the widths of their ramp regions. Other targets for research include the C-ring plateaus. BTI does not generate these features and, being too narrow, nor does it emerge within them. But ballistic transport may sculpt their structure, and in particular sharpen their front and rear edges. Future numerical work here would complement previous investigations which used a descendent of the D92 code (Estrada \& Durisen 2010). It could also explore a possible connection between the C-ring plateaus and similarly sized narrow rings, such as the $\epsilon$ ring in the Uranian system. | 14 | 4 | 1404.4247 |
1404 | 1404.6768_arXiv.txt | We demonstrate a possibility of existence of a peculiar temperature-dependent composition $g$-modes in superfluid neutron stars. We calculate the Brunt-V$\ddot{\rm a}$is$\ddot{\rm a}$l$\ddot{\rm a}$ frequency for these modes, as well as their eigenfrequencies. The latter turn out to be rather large, up to $\sim 500$~Hz for a chosen model of a neutron star. This result indicates, in particular, that use of the barotropic equation of state may be not a good approximation for calculation of inertial modes even in most rapidly rotating superfluid neutron stars. | The aim of this note is to present some new results concerning the gravity oscillation modes ($g$-modes) in neutron stars (NSs). It is generally accepted (e.g., \citealt*{yls99}) that neutrons and protons in the NS cores become superfluid (SF) at temperatures $T \lesssim 10^8 \div 10^{10}$~K. Thus, here we concentrate on SF NSs. Until recently, all attempts to find g-modes in such stars were unsuccessful (e.g., \citealt*{Lee95,ac01,pr02}). However, as we have shown (\citealt*{gk13}), SF NS cores composed of neutrons (n), protons (p), and electrons (e) can harbour specific thermal $g$-modes, whose frequencies (which are, typically, no more than a few Hz) depend on $T$ and vanish at $T=0$. In this note we show that an admixture of additional particle species (e.g., muons) in the NS core leads to very peculiar {\it temperature-dependent} composition $g$-modes. We discuss their properties, calculate their eigenfrequencies, which appear to be of the order of hundreds of Hz, and demonstrate that, although they depend on $T$, they do not vanish in the limit $T=0$. | We showed that a specific composition $g$-modes can propagate in SF NS cores composed of npe-matter with admixture of muons (or some other non-SF particle species), {\it provided} that $\nabla x_{e\mu} \equiv \nabla (n_{\mu}/n_{\rm e}) \neq 0$. The most peculiar feature of these $g$-modes is that their eigenfrequencies $\nu$ (and the corresponding Brunt-V$\ddot{\rm a}$is$\ddot{\rm a}$l$\ddot{\rm a}$ frequency $\mathcal{N}$) are {\it strong functions} of temperature $T^\infty$. They depend on $T^\infty$ through the parameter $\sqrt{(1+y)/y}$, which is in turn a function of the temperature-dependent entrainment matrix $Y_{ik}$, see equation (\ref{y}). Since at $T^\infty \rightarrow 0$ this parameter is $\approx \sqrt{n_{\rm b}/n_{\rm p}}\sim 3$ (see Section 5), the frequencies $\nu$ (and $\mathcal{N}$) of SF NSs can exceed, in this limit, the corresponding frequencies of non-SF NSs {\it by a factor of few}. We illustrated our results by finding solutions to oscillation equations (\ref{1})--(\ref{4}) and (\ref{1nsf})--(\ref{2nsf}) for a particular SF NS with $M=1.4 M_{\odot}$ and APR EOS in its core. We found that in the limit $T^\infty \rightarrow 0$ ($T^\infty \ll T_{\rm cn}^\infty,\, T_{\rm cp}^\infty$) the eigenfrequency of the fundamental quadrupolar $g$-mode is indeed remarkably large, $\nu \approx 462$~Hz (i.e., larger by a factor of $2.43$ than the corresponding $\nu \approx 190$~Hz in a non-SF NS with npe$\mu$ core composition, and by a factor of $3.64$ than the corresponding $\nu \approx 127$~Hz in a non-SF NS with npe core composition). At finite $T^\infty$ the calculations were made for two models (I and II) of nucleon SF. In particular, for the more realistic model II we showed that $\nu$ first decreases with increasing $T^\infty$ but then, close to a temperature $T_{\rm cn \, max}^\infty$, at which neutron SF disappears, it starts to grow up reaching, at $T^\infty = T_{\rm cn \, max}^\infty$, the value of $\nu$ for ordinary composition $g$-modes, first discussed by \cite{rg92} (see Fig.\ \ref{Fig:eigenfr2}). We see four immediate applications of the results obtained in the present note. First, it was shown in \cite*{lai99} that $g$-modes can be unstable with respect to emission of gravitational waves (CFS instability). That reference analyzed composition $g$-modes in non-SF NSs and concluded that CFS instability is much more efficient for $r$-modes than for $g$-modes. Notice however, that eigenfrequencies of SF composition $g$-modes are severalfold higher than the corresponding eigenfrequencies in non-SF NSs. This could make SF g-modes more CFS-unstable. Obviously, a detailed analysis of this issue is highly desirable. The second application is related to resonant excitations of $g$-modes by tidal interaction in coalescing NS-NS or NS-black hole binaries. This mechanism was analysed in \cite*{lai94} and \cite*{hl99} neglecting baryon superfluidity, but it can also be relevant for composition $g$-modes in SF NSs. The peculiar SF $g$-modes discussed here can substantially modify gravitational wave signal from such binaries. The third application concerns explanation of coherent oscillations with a frequency of $\nu_{\rm osc}=249.332609$~Hz from the accreting $435$~Hz pulsar XTE J1751-305. As first argued by \cite{sm14} they are possibly related to non-radial $r$-mode or near-surface $g$-mode oscillations of the pulsar (see also \citealt*{ajh14} and \citealt{lee14}). We note that SF $g$-modes can have frequencies comparable to $\nu_{\rm osc}$ and hence can also be relevant for interpretation of these observations. Finally, as we showed, the frequencies of SF $g$-modes can reach values $\nu \sim 500$~Hz, i.e., they can be of the order of the spin frequencies of the most rapidly rotating NSs [e.g., NSs in low-mass X-ray binaries (LMXBs)]. This may have a strong impact on the properties of the so called inertial (or, more precisely, inertial-gravity) modes in rotating NSs (e.g., \citealt{phajh09}). As a result, the latter modes may be very different from their cousins in barotropic NSs (for which $\mathcal{N}=0$). This issue is especially important in view of the recent work by \cite*{gck13a,gck13b} on rapidly rotating NSs. These authors proposed a method for extracting an information about the oscillation spectra of rotating NSs in LMXBs from observations of their quiescent surface temperatures. This information can then be used to put stringent constraints on the properties of superdense matter. However, for this method to work one needs to calculate {\it realistic} oscillation spectra of rotating NSs. Our results indicate that an analysis of barotropic NSs may be inappropriate for this purpose. Another problem, for which the approximation of a barotropic NS can be too rough, is related to calculation of $r$-mode saturation amplitude (\citealt*{btw07}), resulting from the resonance interaction of $r$-mode with a couple of inertial modes. At the end we would like to note that, although in this paper we discussed SF composition $g$-modes in the context of NSs, they can, in principle, be observed in laboratory experiments (e.g., with ultra-cold atoms or with liquid He II), provided that one has a mixture of an SF and 2 non-SF species. | 14 | 4 | 1404.6768 |
1404 | 1404.0134_arXiv.txt | The symbiotic X-ray binary 4U~1954+319 is a rare system hosting a peculiar neutron star (NS) and an M-type optical companion. Its $\sim$5.4\,h NS spin period is the longest among all known accretion-powered pulsars and exhibited large ($\sim$7\%) fluctuations over 8 years. A spin trend transition was detected with \textit{Swift}/BAT around an X-ray brightening in 2012. The source was in quiescent and bright states before and after this outburst based on 60 ks \textit{Suzaku} observations in 2011 and 2012. The observed continuum is well described by a Comptonized model with the addition of a narrow 6.4 keV Fe K$\alpha$ line during the outburst. Spectral similarities to slowly rotating pulsars in high-mass X-ray binaries, its high pulsed fraction ($\sim$60--80\%), and the location in the Corbet diagram favor high $B$-field ($\gtrsim$$10^{12}$ G) over a weak field as in low-mass X-ray binaries. The observed low X-ray luminosity ($10^{33}$--$10^{35}\,\mathrm{erg}\,\mathrm{s}^{-1}$), probable wide orbit, and a slow stellar wind of this SyXB make quasi-spherical accretion in the subsonic settling regime a plausible model. Assuming a $\sim$$10^{13}$\,G NS, this scheme can explain the $\sim$5.4\,h equilibrium rotation without employing the magnetar-like field ($\sim$$10^{16}$\,G) required in the disk accretion case. The time-scales of multiple irregular flares ($\sim$$50$\,s) can also be attributed to the free-fall time from the Alfv\'en shell for a $\sim$$10^{13}$\,G field. A physical interpretation of SyXBs beyond the canonical binary classifications is discussed. | \label{Introduction} Symbiotic X-ray binaries (SyXBs) are a growing new subclass of X-ray binaries which consist of an X-ray bright neutron star (NS) and an M-type giant primary star. % Originally SyXBs were seen as a subclass of low-mass X-ray binaries (LMXB), where accretion typically is from a K-type optical counterpart with a mass $M_\mathrm{c}\lesssim 1\,M_\odot$. It took more than 30 years, however, to recognize that their properties are different from LMXB and also from those of high-mass binaries (HXMB), i.e., systems where the mass donor is an O- or B-type giant with $M_\mathrm{c}\gtrsim 10\,M_\odot$. SyXBs are now considered as a separate subclass of X-ray binaries. They are named in analogy to symbiotic binaries, which consist of a white dwarf and an M giant companion, but their nature has not yet been understood. Some SyXBs were known as famous X-ray sources since the early X-ray observations: GX~1+4 \citep{Davidsen1977ApJ, Makishima1988Nature, Chakrabarty1997ApJ}, 4U~1700+24 \citep{Garcia1983ApJ,Masetti2002A&A}, and Sct~X-1 \citep{Kaplan2007ApJ}. With the discovery of new sources such as IGR~J16194$-$2810, there are now nearly 5 SyXBs and some candidates in our Galaxy; e.g., 5 objects out of 10 candidates (Table~1 in \citealt{Lu2012MNRAS}) have been confirmed as SyXBs, while three were ruled out (see e.g., \citealt{Masetti2012A&A...544A.114M}). Observational features of the SyXB class are i) quite long orbital periods\footnote{For many SyXB, orbital period has not yet been known nor confirmed in long-term X-ray studies (e.g., \citealt{Corbet2008ApJ}).}, e.g., 1161\,d in GX~1+4. ii) long NS spin periods over $\sim$110--18300\,s as shown in Fig.~\ref{fig:period_distribution}, and iii) high X-ray variability ranging from short to long timescales ($\sim$1\,s to up to a year). SyXB X-ray spectra are in general well described by an absorbed power-law with a photon index $\Gamma$$\sim$0.5--2.0 and a high energy roll-over, which is often modified in the soft X-rays by strong absorption. This spectrum resembles that of X-ray pulsars in HMXBs, and thus, SyXBs have been interpreted in the literature as NSs with $\sim 10^{12}$ G field in HMXBs. As another interpretation, following the classical LMXB classification based on optical companions, SyXBs were also interpreted as NSs in the low luminosity low/hard state of LMXB as having weak magnetic field ($B$-field), e.g., $\lesssim 10^{10}$\,G \citep{Nagae2008,Kitamura2013PASJ}. In any of these cases, the NSs in SyXB are expected to have $B$-fields strengths of around $10^{12}$\,G or much lower (e.g., $\lesssim 10^{10}$\,G). The canonical $B$-fields implied by the spectral analogy with HMXB and LMXB, however, are in contradiction to the fields implied by their timing behavior. The slow NS pulsations in SyXBs are sometimes in spin equilibrium or show a large spin-up rate \citep{Makishima1988Nature, Gonzalez2012A&A...537A..66G}. If interpreted in terms of standard disk accretion torque theory \citep{Ghosh1979ApJ}, the slow rotation and torque reversals imply extraordinary strong dipole fields ($\sim$$10^{14-16}$\,G), which are close to or exceed the quantum critical field, $B_\mathrm{cr}=m_\mathrm{e}^2c^3/(e\hbar)=4.4\times 10^{13}$\,G. Such a magnetar scenario for binary systems has been proposed, e.g., to explain the 1.6\,h pulsation and the high spin-up rate of the SyXB IGR~J16358$-$4726 \citep{Patel2007ApJ}. Similar scenarios have also been discussed for slowly rotating X-ray pulsars in HMXBs such as 4U~0114+65 \citep{Li1999ApJ...513L..45L} or 4U~2206+54 \citep{Reig2012MNRAS}, highly variable supergiant fast X-ray transients (SFXTs; \citealt{Bozzo2008ApJ}), and some slowly rotating NSs in the Small Magellanic Cloud \citep{2014MNRAS.437.3664H, Klus2014MNRAS.437.3863K}. Except for the timing properties, however, no direct evidence for ultra-strong $B$-fields has been found so far. As shown by \citet{Shakura2012MNRAS} and \citet{2012arXiv1212.2841P}, the extremely strong fields can be avoided when one assumes that the accretion does not happen through an accretion disk but via quasi-spherical accretion. In these models matter is gravitationally captured, e.g., from the donor's stellar wind. For low mass accretion rates, $\dot{M}\lesssim 4\times 10^{16}\,\mathrm{g}\,\mathrm{s}^{-1}$, gravitationally captured matter subsonically accretes onto the NS forming an extended, quasi-spherical shell around the magnetosphere, where large scale convective motions and subsonic turbulence lead to accretion onto the NS. Contrary to the canonical high luminosity Bondi-Hoyle accretion, where matter supersonically accretes and the sign of angular momentum (prograde or retrograde) determines the spin behavior \citep{Perna2006ApJ}, for quasi-spherical accretion the spin-up/spin-down is determined by the specific angular momentum of matter at the magnetospheric boundary and the angular velocity of the NS. In this paper we discuss \textit{Suzaku} observations of the SyXB 4U~1954+319 hosting the slowest rotating NS in an X-ray binary system. This source was originally discovered by \textit{Uhuru} \citep{Forman1978ApJS}, and observed in the 1980s with \textit{Ariel} \citep{Warwick1981MNRAS}, \textit{EXOSAT}, and \textit{Ginga} \citep{Tweedy1989ESASP}. These observations suggested that the source was a wind accreting HMXB with a very inhomogeneous wind \citep{Tweedy1989ESASP}, although no optical counterpart was known at that time. The source had virtually been forgotten until, after twenty years of no observations, \textit{Chandra}'s localization of the source position allowed the optical identification of the donor, which was found to be an M4-5 III star ($M_{\rm c}\sim 1.2M_{\odot}$) at a distance of 1.7\,kpc \citep{Masetti2006A&A}. Therefore 4U~1954+319 was re-classified as a SyXB. Further progress in our understanding of the characteristics came with the discovery of a $\sim$5\,h periodicity in \textit{Swift}/BAT monitoring data by \citet{Corbet2006ATel, Corbet2008ApJ}. This period is strongly variable \citep{Marcu2011ApJ}. So far, no orbital period has been discovered, although \citet{Mattana2006A&A} argue that the lower limit of the orbital period is $\sim$400\,d. These parameters are incompatible with typical white dwarf systems, such that the compact object in 4U~1954+319 is likely a NS. As shown in Figure~\ref{fig:period_distribution}, the extremely long spin period makes 4U~1954+319 the slowest rotating accretion-powered NS system known to date\footnote{A long periodicity, $P\sim 6.67$ hour, was also detected from the central object 1E161348$-$5055 in the young shell-type supernova remnant RCW 103. This object, however, has not been confirmed as an accretion-powered pulsar.}, and a prominent example to understand the SyXB class. Currently, no consensus has yet been obtained on the accretion models for SyXBs, or the $B$-field of their NSs. Revisiting and developing the quasi-spherical model further requires the spectral and timing investigations of SyXBs. In this paper, we report on the broad-band timing and spectral properties of 4U~1954+319 and discuss a possible accretion model beyond the conventional HMXB and LMXB classification. | \label{conclusion} We analyzed two {\it Suzaku} data sets, obtained in 2011 and 2012, of the SyXB 4U~1954+319 consisting of the slowly rotating 5.4 h X-ray pulsar and a late type primary star (M4-5 III). Our main results are as follows; \begin{enumerate} \item We reconfirmed the slow rotation period and the large period fluctuations. We also identified several additional features of 4U~1954+319, including a hard continuum without a clear CRSF, a narrow Fe-K$_{\alpha}$ line, and sporadic flares. The continuum was harder when the source was brighter. \item From spectral and timing properties, 4U~1954+319 is suggested to have a strong $B$-field of $\gtrsim 10^{12-13}$\,G. This is supported by the high pulsed fraction of 60--80\%, the slow rotation, the hard featureless continuum, and the narrow Fe-K$\alpha$ line. \item The NS is expected to be close to equilibrium because of the four spin transitions and large period fluctuations. Such an evolution can be explained by a quasi-spherical accretion in a subsonic accretion regime which is considered to apply to 4U~1954+319 because of its low luminosity ($0.023-2.1\times 10^{35}$\,erg\,s$^{-1}$), presumably wide orbital period, and rather low wind velocity from the M-type giant. \item Recurrent irregular flares during the outburst have a typical time scale of $\sim$50\,s, which is interpreted as intermittent accretion from the Alfv\'en radius of the $\sim 10^{13}$\,G NS. The log-normal distribution of the light curve indicates an underlying multiplicative process (e.g., positive feedback) in the accretion. \item The extreme magnetar-like extreme $B$-field ($10^{16}$\,G) derived from the standard disk accretion in Eq.\,(\ref{eq:Ghosh}) is not required if we assume a low luminosity and quasi-spherical accretion. \item The presence of a system like 4U~1954+319 which is very likely to involve a high-field NS, provides another example which urges us to challenge the conventional classification of NS-binaries into LMXBs and HMXBs. \end{enumerate} | 14 | 4 | 1404.0134 |
1404 | 1404.7522_arXiv.txt | We continue the study of mild transient reductions in the speed of sound of the adiabatic mode during inflation, of their effect on the primordial power spectrum and bispectrum, and of their detectability in the Cosmic Microwave Background (CMB). We focus on the regime of {\it moderately sharp} mild reductions in the speed of sound during uninterrupted slow-roll inflation, a theoretically well motivated and self-consistent regime that admits an effective single-field description. The signatures on the power spectrum and bispectrum were previously computed using a slow-roll Fourier transform (SRFT) approximation, and here we compare it with generalized slow-roll (GSR) and in-in methods, for which we derive new formulas that account for moderately sharp features. The agreement between them is excellent, and also with the power spectrum obtained from the numerical solution to the equation of motion. We show that, in this regime, the SRFT approximation correctly captures with simplicity the effect of higher derivatives of the speed of sound in the mode equation, and makes manifest the correlations between power spectrum and bispectrum features. In a previous paper we reported hints of these correlations in the Planck data and here we perform several consistency checks and further analyses of the best fits, such as polarization and local significance at different angular scales. For the data analysis, we show the excellent agreement between the CLASS and CAMB Boltzmann codes. Our results confirm that the theoretical framework is consistent, and they suggest that the predicted correlations are robust enough to be searched for in CMB and Large Scale Structure (LSS) surveys. | The paradigm of inflation as the explanation for the origin of cosmic structures has entered a decisive new phase. The latest data releases by the Planck \cite{Ade:2013ktc} and WMAP \cite{Bennett:2012zja} collaborations point towards models of inflation that produce a slightly red-tilted primordial power spectrum and a negligible amount of \emph{scale-independent} bispectra, as predicted \cite{Mukhanov:1981xt,Acquaviva:2002ud,Maldacena:2002vr} by the simplest models of cosmological inflation\footnote{These are slow-roll inflation models involving a single neutral scalar field with a canonical kinetic term and in the Bunch-Davies vacuum.}, but with a mild deficit of power on large scales. There are also mild hints of \emph{scale-dependent} features in the CMB power spectrum \cite{Bennett:2012zja,Ade:2013uln} and in the primordial bispectrum \cite{Ade:2013ydc}. Besides this, the discovery of B-mode polarization by BICEP2 \cite{Ade:2014xna}, if it is confirmed to be result of primordial tensor modes, would have striking implications and put inflation on a much firmer footing. A large tensor-to-scalar ratio of $r\sim{\cal O}(0.1)$ suggests -- again, in the context of canonical models -- a high scale of inflation around $10^{16}\,\text{GeV}$, a Hubble parameter $H \sim 10^{14}\,\text{GeV}$ during inflation and a large, transplanckian excursion in field space for the inflaton \cite{Lyth:1996im}.\\ According to \cite{Smith:2014kka}, there is currently a ``very significant tension'' (around $0.1\%$ unlikely) between the Planck temperature ($r<0.11~95\%$c.l.) and BICEP2 polarization ($r=0.2^{+0.05}_{-0.07}$) results. The model-independent cubic spline reconstruction \cite{Hu:2014aua} result shows that the vanishing scalar index running (${\rm d n_s}/{\rm d}\ln k$) model is strongly disfavored at more than $3\sigma$ confidence level on the scales $k=0.0002$ Mpc$^{-1}$. Recently, several fundamental/phenomenological models with features in the primordial spectra, such as sharp transition in the slow-roll parameters \cite{Miranda:2014wga}, false vacuum decay \cite{Bousso:2014jca}, initial fast roll \cite{Hazra:2014aea}, a non-Bunch-Davies initial state \cite{Ashoorioon:2014nta}, or a bounce before inflation \cite{Xia:2014tda}, among others, were proposed to explain the observed power deficit on large angular scales by Planck experiments. Alternatively, the tension could be resolved with new data releases. \\ Another consequence of the BICEP2 results is that a large tensor-to-scalar ratio seems to indicate a high energy scale of inflation around the GUT scale. If confirmed, one would need to find a successful UV embedding of the theory, and also deal with the problem of mass hierarchies in the presence of multiple degrees of freedom. This is challenging, but not impossible, and it seems that the energy range available could in principle host the inflaton and the possible additional UV degrees of freedom, while preserving a manageable mass hierarchy for which an effective single field theory is still possible. The BICEP2 results also suggest that the inflaton field underwent a super-planckian excursion, which makes the theory very sensitive to higher dimensional operators. While we expect a (mildly broken) symmetry protecting the overall flatness of the potential, this also leaves room for the presence of transient phenomena happening along the inflationary trajectory.\\ Among other phenomena, transient variations in the speed sound of the adiabatic mode may occur in the presence of additional degrees of freedom during inflation. For instance, when an additional heavy field can be consistently integrated out \cite{Shiu:2011qw,Cespedes:2012hu,Achucarro:2012sm,Achucarro:2012yr,Burgess:2012dz,Castillo:2013sfa}, inflation is described by an effective single-field theory \cite{Burgess:2003zw,Cheung:2007st,Weinberg:2008hq,Shiu:2011qw,Achucarro:2012sm,Achucarro:2012yr} with a variable speed of sound. In particular, changes in the speed of sound result from derivative couplings\footnote{Or equivalently, turns in field space.} \cite{Tolley:2009fg,Achucarro:2010da,Baumann:2011su,Cespedes:2012hu,Achucarro:2012sm,Achucarro:2012yr,Pi:2012gf,Chen:2012ge,Gao:2012uq}. Transient variations in the speed of sound will produce \emph{correlated} features in the correlation functions of the adiabatic curvature perturbation \cite{Cheung:2007st,Nakashima:2010sa,Park:2012rh,Achucarro:2012fd,Saito:2013aqa,Bartolo:2013exa,Cai:2013gma,Gong:2014spa}. They are worth taking into account since we expect them to be very good model selectors.\\ The detection of transients poses some interesting challenges. The effects of a feature in the potential or a localized change in the speed of sound depend on its {\it location} (in time or e-folds), its {\it amplitude} and the {\it sharpness} (or inverse duration). If transients are too sharp, they can excite higher frequency modes that make the single-field interpretation inconsistent (see, for example, \cite{Cespedes:2012hu,Shiu:2011qw,Konieczka:2014zja}). Notably, the best fit found so far in the data for a step feature in the potential \cite{Ade:2013uln,Benetti:2013cja,Miranda:2013wxa} falls outside the weakly coupled regime that is implicitly required for its interpretation as a step in the single field potential \cite{Adshead:2014sga,Cannone:2014qna}. On the other hand, if the features are too broad, their signature usually becomes degenerate with cosmological parameters, making their presence difficult to discern. There is an interesting intermediate regime where the features are mild (small amplitude) and moderately sharp, which makes them potentially detectable in the CMB/LSS data, and also they remain under good theoretical control. This regime is particularly important if the inflaton field excursion is large and can reveal features in the inflationary potential and the presence of other degrees of freedom. At the same time, if slow-roll is the result of a (mildly broken) symmetry that protects the background in the UV completion, the same symmetry might presumably preclude very sharp transients.\\ In this paper we study \emph{mild and moderately sharp} features in the speed of sound of the adiabatic mode, that we define to be those for which the effects coming from a varying speed of sound are small enough to be treated at linear order, but large enough to dominate over the slow-roll corrections. This carries an implicit assumption of uninterrupted slow-roll\footnote{In the particular case of reductions in the speed of sound coming from turns along the inflationary trajectory, this has been shown to be a consistent scenario.}. We will show that this regime ensures the validity of the effective single-field theory, even though our analysis is blind to the underlying inflationary model.\\ In order to compare any model with data, it is important to develop fast and accurate techniques to compute the relevant observables of the theory, in this case, correlations functions of the adiabatic curvature perturbation. The calculation of correlation functions is often rather complicated and the use of approximate methods is needed. The study of transients often involves deviations from slow-roll and may be analyzed in the generalized slow-roll (GSR) formalism \cite{Stewart:2001cd,Gong:2001he,Choe:2004zg,Dvorkin:2009ne,Adshead:2011bw,Miranda:2012rm,Bartolo:2013exa,Adshead:2013zfa,Gong:2014spa}. This approach is based on solving the equations of motion iteratively using Green's functions. Although this formalism can cope with more general situations with both slow-roll and speed of sound features, one usually needs to impose extra hierarchies between the different parameters to obtain simple analytic solutions.\\ A notable exception that is theoretically well understood is a transient, mild, and moderately sharp reduction in the speed of sound such as would be found in effectively single-field models with uninterrupted slow-roll inflation, obtained by integrating out much heavier fields with derivative couplings that become transiently relevant. In this regime, an alternative approach is possible, that makes the correlation between power spectrum and bispectrum manifest \cite{Achucarro:2012fd}. The change in the power spectrum is simply given by the Fourier transform of the reduction in the speed of sound, and the \emph{complete} bispectrum can be calculated to leading order in slow-roll as a function of the power spectrum. Hence we name this approximation Slow-Roll Fourier Transform (SRFT). One of the aims of this paper is to compare the GSR and SRFT approaches. In order to do this, we develop simple expressions within the GSR approach and the in-in formalism for computing the changes in the power spectrum and bispectrum due to moderately sharp features in the speed of sound. These are new and extend the usual GSR expressions for very sharp features.\\ The other aim of this paper is to further scrutinize and validate the results of our previous work \cite{Achucarro:2013cva}, where we searched for moderately sharp features in the Planck CMB data. We reported several fits to the CMB power spectrum and gave the predicted, correlated, oscillatory signals for the primordial bispectrum. The functional form of the speed of sound was inspired by soft turns along a multi-field inflationary trajectory with a large hierarchy of masses, a situation that is consistently described by an effective single-field theory \cite{Achucarro:2010jv,Achucarro:2010da,Cespedes:2012hu,Achucarro:2012sm,Gao:2012uq,Gao:2013ota}.\\ In the first part of this paper we study the intermediate regime of moderately sharp features in the speed of sound during uninterrupted slow-roll, in which both the SRFT and GSR approaches can give accurate results. More precisely: \begin{itemize} \item In \S IIA we review the SRFT results for the power spectrum and bispectrum, and in \S IIB we develop a simple formula within the GSR formalism that reduces to the SRFT result for nearly all scales and is valid for arbitrary functional forms of the speed of sound within the regime we study. \item In \S IIC, by comparing both results with a numerical solution for the power spectrum, we show that the SRFT method correctly captures the effect of \emph{all} the terms in the equation of motion in a very simple way, while the GSR method requires the inclusion of higher derivatives of the speed of sound to match the numerical result. Nevertheless, there is excellent agreement between both results with the numerical solution. \item Then we turn to the bispectrum. In \S IID we compute the features in the bispectrum using the in-in formalism, and we take into account the effect of additional operators with respect to previous results \cite{Bartolo:2013exa}. We show that, for transient reductions of the speed of sound, the contributions arising from the operators proportional to the amount of reduction and to the rate of change are of the same order, \emph{independently of the sharpness} of the feature. In addition, because we study the not-so-sharp regime, we compute the linear correction to the approximation that other quantities do not vary during the time when the feature happens. \item In \S IIE we compare the bispectra obtained with the SRFT approach and with the moderately sharp approximation, finding remarkable agreement for several functional forms of the speed of sound. \end{itemize} In the second part of this paper we perform a number of additional consistency checks regarding the theoretical framework and the statistical analysis carried out in a previous paper \cite{Achucarro:2013cva}. In particular: \begin{itemize} \item In \S IIIA we explain the choice of parameter space used for our statistical search of transient reductions of the speed of sound in the Planck data, which was designed to be theoretically consistent. In \S IIIB we check that adiabatic and unitary regimes are respected, and therefore the fits found in the data can be consistently interpreted as transient reductions in the speed of sound. \item In \S IIIC we analyze the implications of the BICEP2 results for the consistency of an effective single-field description of inflation. We conclude that, even with a inflationary scale at the level of the GUT scale, a single-field description may be possible, and we argue that moderately sharp reductions of the speed of sound are completely consistent with an adiabatic evolution, i.e. an effective single-field regime. \item In \S IIID we review the main results of our previous work \cite{Achucarro:2013cva} and make an independent consistency check using two different Boltzmann codes and MCMC samplers, namely \class\unskip$+$\montepython versus \camb\unskip$+$\cosmomc, finding great agreement. We explicitly give the (small) degeneracy of the cosmological parameters with the parameters of our model. Last, we also show the polarization spectra and the local improvement of our fits to the CMB power spectrum as a function of the angular scale. \end{itemize} Finally, we leave \S IV for conclusions and outlook. | A detailed understanding of the origin and detectability of transient features in the primordial (and observed) correlation functions is now more important than it was before the BICEP2 results \cite{Ade:2014xna}. A large transplanckian field excursion should detect any features present in the scalar potential as well as changes in the dispersion relation of the adiabatic mode, if they are there, and arguably there were hints of both in the Planck data \cite{Ade:2013uln,Ade:2013ydc}. At the same time, a high inflationary scale leaves less room for mass hierarchies in the UV completion, that would be needed to justify the single-field effective low energy description. This is a problem for very sharp features, as they tend to excite any higher frequency modes coupled to the inflaton. We have argued that the regime of moderately sharp features is particularly interesting. Most likely these cannot be detected in any particular dataset and have to be searched for in {\it correlations} between different data sets.\\ In this regime, the effect of a transient reduction in the speed of sound can be calculated with the simple SRFT approximation \cite{Achucarro:2012fd}, in which the correlations between power spectrum and bispectrum are manifest. We emphasize that the simple expressions \eref{eq:deltappfourier} and \eref{bispectrumana} hold provided ${\cal O}(\epsilon, \eta)\ll \text{max}\(|1-c_s^{-2}|,\, |\dot c_s/(Hc_s)|\)\ll 1$ and $c_s=1$ before and after the feature.\\ In this work we have presented an alternative way to calculate both the power spectrum and bispectrum, by consistently applying an approximation for moderately sharp features, both to the GSR power spectrum (eq. \eref{eq:gsr3}) and to the in-in calculation of the bispectrum (eq. \eref{completebi}). Within this regime, we have extended existing GSR calculations of the power spectrum to less sharp and arbitrary shapes of the speed of sound, and found excellent agreement with the SRFT approximation in the regime where both methods apply.\\ Given that the regimes of validity of the two methods are not entirely coincident, we are now equipped with a robust machinery that will allow us to describe features in the speed of sound for a broader region of the parameter space. Broad features can be calculated with the SRFT approach, while sharp features can be calculated using GSR for the power spectrum (eq. (\ref{eq:gsr3})) and the in-in approach for the bispectrum (eq. (\ref{completebi})).\\ In a previous paper \cite{Achucarro:2013cva} we performed a search for such correlated features assuming moderately sharp, mild reductions in the speed of sound of the adiabatic mode during uninterrupted slow-roll inflation. We reported several fits to the Planck CMB temperature spectrum data and predicted the correlated signatures in the complete primordial bispectrum. We qualitatively compared with the bispectrum search by Planck when possible and found reasonable agreement. We have performed additional tests to the results of our search in \cite{Achucarro:2013cva}. Namely, we have repeated it using independent codes and found practically equal results; we have studied more explicitly the small degeneracies among the cosmological and feature parameters, and proposed the CMB TE and EE polarization spectra as a way to break degeneracies among the latter; and finally we have investigated at which multipoles each of our fits describe the CMB temperature data better than the baseline \lcdm model.\\ The ability to make predictions in a wider region of the parameter space of features is of particular relevance, since new data sets may allow us to explore it. Besides, since different experiments generally have different foregrounds and systematics, a joint analysis could reduce the contamination of the primordial signal on the overlapping scales. In particular, we plan to extend our search to large scale structure surveys \cite{features3}. \subsection | 14 | 4 | 1404.7522 |
1404 | 1404.2241_arXiv.txt | We give an analytical form for the weighted correlation function of peaks in a Gaussian random field. In a cosmological context, this approach strictly describes the {\it formation bias} and is the main result here. Nevertheless, we show its validity and applicability to the {\em evolved} cosmological density field and halo field, using Gaussian random field realisations and dark matter N-body numerical simulations. Using this result from peak theory we compute the bias of peaks (and dark matter halos) and show that it reproduces results from the simulations at the ${\mathcal O}(10\%)$ level. Our analytical formula for the bias predicts a scale-dependent bias with two characteristics: a broad band shape which, however, is most affected by the choice of weighting scheme and evolution bias, and a more robust, narrow feature localised at the BAO scale, an effect that is confirmed in simulations. This scale-dependent bias smooths the BAO feature but, conveniently, does not move it. We provide a simple analytic formula to describe this effect. We envision that our analytic solution will be of use for galaxy surveys that exploit galaxy clustering. | One of the biggest challenges of large-scale structure surveys is to infer the properties of the dark matter density field from observables such as galaxies or clusters. Galaxies, and the dark matter halos they inhabit, are not perfect tracers of the underlying dark matter distribution, but it is the statistical properties of the dark matter distribution that are most robustly predicted by theory. Modelling of the clustering properties of the dark matter halos, or more precisely, modelling of the halo bias, has received recently renewed attention (e.g., \citet{Baldauf/etal:2013, Paranjape/etal:2013, Desjacques:2013,Castorina/Sheth:2013,Musso/Paranjape/Sheth:2012,Elia/etal:2011,Elia/etal:2012}) but pioneering work dates back to the 1970s-1980s (e.g., \cite{Doroshkevich:1970a,Doroshkevich:1970b,Kaiser84,JensenSzalay86}) as we will review below. Modelling the halo bias is particularly interesting for several reasons: the clustering of halos is driven only by gravity and thus in principle is completely specified by the initial conditions; it is virtually unaffected --at least on scales significantly larger than the size of the halos, ${\cal O}(Mpc)$-- by poorly known baryonic physics and physics of galaxy formation (which instead drive galaxy bias). It is also a crucial intermediate step to a full modelling of galaxy bias, if, for example, a halo occupation distribution model is used to describe how galaxies populate halos (e.g., \cite{Seljak:2000, Peacock/Smith:2000, CooraySheth02}). In principle a galaxy survey could be engineered so that the selected galaxies trace dark matter halos, for example by targeting bright luminous red galaxies which are typically central halo galaxies (e.g., \cite{Mandelbaum/etal:2006}). In practice, successful attempts have been made to reconstruct the halo density field from a real galaxy survey \citep{reid/spergel:2008, reid/spergel/bode:2009, reid/etal:2009}. Clusters of galaxies also are believed to trace the spatial distribution of (high mass) dark matter halos, and many forthcoming surveys promise to provide cluster correlation properties. It is well known that bias depends on halo properties, and in general halo bias is expected to be complicated, non-linear, non-local and scale-dependent. However, an accurate understanding of its behaviour is crucial to extract precise cosmological information from large scale structure clustering. For example, the shape and amplitude of the matter power spectrum, or equivalently its correlation function, are sensitive to cosmological parameters such as neutrino masses. Also, the primordial power spectrum slope and shape, and the precise location of the Baryon Acoustic Oscillation (BAO) can provide a direct probe of the Universe's expansion history. Future galaxy surveys will probe an appreciable fraction of the observable universe, reducing the statistical errors on these quantities and making the scale-dependence and non-linearity of halo bias a source of systematic error that cannot be ignored. The halo bias could be studied and modelled, in principle, solely via N-body numerical simulations (e.g., \cite{Seljak/Warren:2004, Paranjape/etal:2013,Elia/etal:2012}). However in practice the calculations needed to obtain the desired accuracy and error estimation far exceed the amount of CPU time available (see e.g., \cite{Dodelson/Schneider:2013,Morrison/Schneider:2013}). Having an analytic expression would be highly valuable: it could be used for example to model the halo bias scale dependence and/or the cosmology dependence, thus having to rely on N-body simulations only for calibrating and validating the analytic expressions. Further, it is always much more insightful to obtain a physical understanding of phenomena, such as the clustering of dark matter halos with respect to the dark matter field. In fact while N-body simulations have confirmed the non-linearity, non-locality, stochasticity and scale-dependence of halo bias, the origin of these effects remain unclear (see e.g., \citet{Porciani:2013} and references therein). In this paper we show how, using peak theory, we can derive an analytic expression for the correlation properties of the dark matter peaks which, we argue, can largely be identified with dark matter halos; our expression depends on the power spectrum of the dark matter field. This approach does not model the bias itself, however it provides a description of the observable quantity (the correlation properties of peaks/halos) from which a ``bias" can be obtained from e.g., the ratio of the relevant power spectra. The rest of the paper is organised as follows: In \S \ref{sec:review-and-approach} we review the current knowledge on halo bias and present the aim and goals of our approach. In \S \ref{sec:method} we present our derivation and the analytic expression for the halo bias. We also discuss the unavoidable approximations involved and their possible limitations. Sec. \ref{sec:validation} validates the approximations made and evaluates the performance of the formula comparing with simulations and in \S \ref{sec:BAO} we present the consequences and possible applications of our findings especially for Baryon Acoustic Oscillations studies. Finally we conclude in \S \ref{Conclusions}. | \label{Conclusions} The bias of dark matter tracers (be it galaxies or, more simple objects like halos or density peaks) is a very complicated, non-linear, non-local function that relates the density of tracers to the density of dark matter. A lot of effort is going into understanding and modelling the bias. Here we approached a simpler problem: that of modelling the correlation properties of tracers. In particular we present an analytic expression for the (N-point) correlation function of extrema in random gaussian fields, weighted by $1/|\det w|$. The results are valid in any number of dimensions, but we focus on the two-point function in three dimensions, which is of most practical relevance. Our main result is thus Eq.~\ref{eq:corrana}. In order to be able to arrive at a fully analytic result we had to assume that observations could be suitably weighted. Since most extrema above practically all interesting thresholds ($> 2\sigma$) are peaks, we find that one can identify the clustering of extrema with the clustering of peaks. Because, for a high enough threshold, dark matter halos correspond to peaks of the initial field (and vice versa), we argue that this provides also an analytic description for the clustering of dark matter halos. On the other hand the clustering properties of peaks may be of interest by themselves, for observations that produce directly density maps (e.g., weak lensing). We find that the presence of non-zero derivatives in the underlying power spectrum introduce scale-dependent features in the bias which would otherwise be constant in peak theory. We identify two scale-dependent features, one broad-band which is most affected by the choice of weighting and evolution bias and a localised one, which is expected to be robust to these effects. The localised, scale-dependent feature in the bias coincides with the location of the baryon acoustic feature (BAO). Its effect is to smooth the BAO feature but, conveniently, it does not move it and we provide a simple analytic formula to describe it. We have tested that the analytic formula we present describes accurately the clustering properties of peaks in a suite of Gaussian realisations. We find that the evolution bias appears to be relatively small, in other words clustering properties of peaks in the low redshift, highly non-linear field are very similar to those of the high-redshift Gaussian field. Given the fact that halos are identified with density peaks, this opens up the possibility to use our findings to describe halo clustering. We have started exploring this possibility although to get a detailed, quantitative description the choice of the weighting scheme used is crucial. In addition for halos the correspondence between actual threshold and the theoretical one might not be straightforward. We have explored the performance of out initial ansatz for an inverse halo mass halo weighting scheme, which we find encouraging. | 14 | 4 | 1404.2241 |
1404 | 1404.2288_arXiv.txt | The first detection of high-energy astrophysical neutrinos by IceCube provides new opportunities for tests of neutrino properties. The long baseline through the Cosmic Neutrino Background~(C$\nu$B) is particularly useful for directly testing secret neutrino interactions~($\nu$SI) that would cause neutrino-neutrino elastic scattering at a larger rate than the usual weak interactions. We show that IceCube can provide competitive sensitivity to $\nu$SI compared to other astrophysical and cosmological probes, which are complementary to laboratory tests. We study the spectral distortions caused by $\nu$SI with a large s-channel contribution, which can lead to a dip, bump, or cutoff on an initially smooth spectrum. Consequently, $\nu$SI may be an exotic solution for features seen in the IceCube energy spectrum. More conservatively, IceCube neutrino data could be used to set model-independent limits on $\nu$SI. Our phenomenological estimates provide guidance for more detailed calculations, comparisons to data, and model building. | \label{sec:Introduction} Neutrinos are mysterious. The discovery of neutrino mass and mixing established physics beyond the standard model. With rapid improvements in experimental sensitivity, neutrinos might soon reveal more dramatic new physics. This could include signatures that depend on neutrino mass, e.g., neutrino decay, neutrino magnetic moments, or neutrinoless double beta decay. The weak interactions of neutrinos make them unique messengers for studying astrophysical systems. The extreme scales of astrophysics allow tests of neutrino properties far beyond what is possible in the laboratory, and may reveal new interactions that shed light on the origin of neutrino mass and other important questions. The term ``secret neutrino interactions"~($\nu$SI) indicates new physics that couples neutrinos to neutrinos. A wide variety of models have already been considered, and some have implications for neutrino masses. A way to characterize these models is by their mediator mass. For massless mediators, such as in Majoron models~\cite{Chikashige:1980ui, Gelmini:1980re, Georgi:1981pg, Gelmini:1982rr, Nussinov:1982wu}, there is at least one stable new particle. For very heavy mediators, one can use an effective theory to study the phenomenology of a class of models~\cite{Kolb:1987qy, Bilenky:1992xn, Bilenky:1994ma, Bilenky:1999dn}. In between, the mediator mass is more moderate, and could induce resonances~\cite{Chacko:2003dt, Chacko:2004cz, Davoudiasl:2005ks, Goldberg:2005yw, Baker:2006gm, Wang:2006jy, Gabriel:2006ns}. In some models, the neutrinos also interact with dark matter~\cite{1992hena.conf..173W, Fayet:2006sa, Barenboim:2006dj, Mangano:2006mp, Lindner:2010rr, Palomares:2011xx, Aarssen:2012fx, Shoemaker:2013tda, Dasgupta:2013zpn, Bringmann:2013vra, Farzan:2014gza}. It is challenging to directly test $\nu$SI through neutrino-neutrino scattering. Sufficiently high flux or volume densities of neutrinos for any interactions to occur only exist in astrophysical systems. Even there, the difficulty is revealing (using neutrinos!)~the signatures of such interactions. So far, only $\nu$SI interactions much stronger (in a sense explained below) than weak interactions have been constrained. Given the difficulty of probing $\nu$SI in the laboratory, it is therefore interesting to consider more model-independent probes, such as those from astrophysics and cosmology. One direct probe of $\nu$SI uses astrophysical neutrinos as a beam and the Cosmic Neutrino Background (C$\nu$B) as a target. Kolb and Turner~(hereafter KT87)~\cite{Kolb:1987qy} utilized the detection of astrophysical neutrinos from SN 1987A. The agreement of the detected signal with the standard expectation of no neutrino scattering en route yields robust constraints on $\nu$SI. KT87 established a phenomenological approach by considering general interactions with mediator masses either much smaller or much larger than the interaction energy. Their constraints could be applied to many possible $\nu$SI models. The first detection of astrophysical neutrinos since SN 1987A is the 37 events detected by IceCube~\cite{Aartsen:2013bka, Aartsen:2013jdh, Aartsen:2014gkd}. One expects a steady stream of more events in the near future, so the precision will improve quickly. The angular distribution of the events suggests that most, if not all, of them are extragalactic in origin. Compared to the SN 1987A neutrinos, the IceCube neutrinos have a much longer baseline through the C$\nu$B, making them more sensitive to $\nu$SI; they have much higher energies, making them more powerful probes for massive mediators; and they have a diffuse (many-source) origin, thus averaging out the uncertainties for individual sources. We take advantage of this new opportunity and explore the sensitivity of IceCube to $\nu$SI. With minimal assumptions about the interaction to reduce model dependence, we show that there are regions of parameter space where $\nu$SI could cause significant distortions to the neutrino spectrum. Because the flux is diffuse and the shape and normalization without interactions are not known, we must look for distortions to the spectrum that have characteristic shapes. This favors interactions with strong energy dependence, especially due to a resonance. Our method generalizes earlier work, going beyond the pure attenuation considered in KT87 and Refs.~\cite{Keranen:1997gz, Hooper:2007jr} as well as the simplified treatment of regeneration considered in Refs.~\cite{Goldberg:2005yw, Baker:2006gm}. We improve upon these by using the propagation equation to describe the interaction of a neutrino beam with the C$\nu$B in the presence of strong $\nu$SI. Besides attenuation, this properly takes into account regeneration as well as multiple scattering of the parent and daughter neutrinos, i.e., a cascade. In Sec.~\ref{sec:nusi}, we consider existing $\nu$SI constraints. In Sec.~\ref{sec:nucnub}, we discuss the effects of $\nu$SI on astrophysical neutrino spectra. We conclude in Sec.~\ref{sec:conclusion}. Throughout, we use cosmological parameters for which the matter density fraction is $\Omega_{M} = 0.3$, the cosmological constant density fraction is $\Omega_{\Lambda} = 0.7$, and the Hubble function is $H(z) = H_{0} \sqrt{\Omega_{\Lambda}+\Omega_{M}(1+z)^{3}}$, where $H_{0} = 70 \; {\rm km\;s^{-1}\; Mpc^{-1}}$. | \label{sec:conclusion} Neutrinos may still hold surprises, and $\nu$SI are among the possibilities. Their effects can be probed directly through neutrino-neutrino scattering --- provided that we have detected neutrinos from astrophysical sources traveling through the C$\nu$B. Until recently, this was only possible with the SN 1987A data~\cite{Kolb:1987qy}. The detection of high-energy neutrinos by IceCube has opened a new frontier in neutrino astronomy, which provides new opportunities for probing $\nu$SI. Because the IceCube sources appear to be extragalactic, the column density of neutrino targets is much greater than for SN 1987A; because the energies are much larger, a wider range of $\nu$SI parameters can be probed; and, because the observed flux is diffuse, that averages out the peculiarities of individual sources. The observed IceCube spectrum contains interesting features, which include a gap at moderate energies, a possible excess near 1 PeV, and a cutoff at slightly higher energies~\cite{Aartsen:2013jdh, Aartsen:2013bka, Aartsen:2014gkd}. Given the current statistics, these features are consistent with standard model expectations with simple astrophysical assumptions~\cite{Laha:2013lka, Chen:2013dza, Anchordoqui:2013dnh}. It is, however, interesting to consider exotic explanations such as $\nu$SI, pseudo-Dirac neutrinos~\cite{Esmaili:2012ac}, or Lorentz-invariance violation~\cite{Gorham:2012qs, Anchordoqui:2014hua}. We perform the first study of $\nu$SI in the context of the detected IceCube spectrum and its features. Using a phenomenological approach for the interactions, we show that IceCube is sensitive to an interesting range of $\nu$SI parameters that evades the most robust of the laboratory limits and is more sensitive than other astrophysical or cosmological techniques. We provide an improved calculation using the propagation equation, the first for high-energy neutrinos to take into account $\nu$SI through attenuation, regeneration, and multiple scattering. Solving the propagation equation numerically, we show $\nu$SI could generate spectral distortions such as a dip, bump, or cutoff large enough to mimic the features seen in the IceCube spectrum. Although $\nu$SI might be able to explain some features of the observed data, it is too soon to draw such conclusions. We expect the IceCube spectrum will become more precise in the near future by improved statistics and analysis. With that, more detailed phenomenological studies and associated model-building will be possible. An expected --- but not yet observed --- source of high-energy astrophysical neutrinos is produced through the energy losses of ultra-high-energy cosmic rays propagating through the CMB~\cite{Greisen:1966jv, Zatsepin:1966jv}. Once these cosmogenic neutrinos~\cite{Beresinsky:1969qj} are observed, it will be possible to test $\nu$SI using calculations similar to those presented here. Although the cosmogenic neutrino spectrum is not a simple power law, its shape is reasonably well predicted. For an energy of $\sim 10^{10} {\rm\ GeV}$, a resonance with the C$\nu$B would probe mediator masses near $M \sim 10^3$ MeV, which are not well constrained (see Fig.~\ref{fig:constraint}). We do not show the curves for optical depth $\tau$ for this case; their shape is similar to that for PeV neutrinos, but displaced to larger mediator masses and couplings (for a heavy mediator, the sensitivity is $g/M\sim0.4/\left(10^{3}\,{\rm MeV} \right)$). Could $\nu$SI explain the non-observation of cosmogenic neutrinos? While pushing their spectrum to lower energies could be consistent with IceCube data, the required coupling is relatively large, $g\sim 1$. Our calculations are for a diffuse flux, which is consistent with IceCube data. If point sources are observed, the effects of deflection and delay should be noted (these are irrelevant for the diffuse flux). The Lorentz factor $\gamma$ of the center of momentum frame is $\sim 10^{8}$ for 1 PeV neutrinos scattering on neutrinos of mass 0.1 eV. For one scattering, the deflection is $\Delta \theta \sim10^{-8} \, (10^{8}/\gamma)$, which is tiny, and the time delay is $\Delta t \sim 10 {\rm\ s} \,(10^8/\gamma)^2$, which might not be negligible in some cases. These effects would be increased by multiple scattering, ultimately washing out transient and point sources into a steady diffuse flux. For reasonable couplings, these effects are not relevant for the PeV neutrinos. For low-energy neutrinos from a nearby supernova, these effects could be much more important. The delay is smaller by $\sim 10^6$ due to the closer distance but larger by $\sim 10^8$ due to the change in $\gamma^2$, making $\Delta t \sim 10^3 {\rm\ s}$. KT87~\cite{Kolb:1987qy} defined their constraint by changes in the energy due to energy loss, which requires assumptions about the total energy in neutrinos and the energy spectrum. The same constraint can be obtained by the simpler time delay argument, which only requires an assumption about the total energy in neutrinos. The IceCube neutrino telescope has opened a new age in neutrino astronomy, as well as providing a way to directly test $\nu$SI. Complementary constraints should also be developed for neutrinos in the early universe and core-collapse supernovae. In those settings, even weak-scale neutrino-neutrino collisions and mixing from the self-induced potential are important. The rapid advance of precision cosmology and perhaps a lucky detection of a Milky Way supernova might reveal more secrets about neutrinos. \medskip {\bf Note added:} As this paper was being completed, we learned of an independent study by Ioka and Murase~\cite{Ioka:2014kca}, which was submitted to arXiv simultaneously. | 14 | 4 | 1404.2288 |
1404 | 1404.4651_arXiv.txt | Measurements from the Solar Irradiance Monitor (SIM) onboard the SORCE mission indicate that solar spectral irradiance at Visible and IR wavelengths varies in counter phase with the solar activity cycle. The sign of these variations is not reproduced by most of the irradiance reconstruction techniques based on variations of surface magnetism employed so far, and it is not clear yet whether SIM calibration procedures need to be improved, or if instead new physical mechanisms must be invoked to explain such variations. We employ three-dimensional magneto hydrodynamic simulations of the solar photosphere to investigate the dependence of solar radiance in SIM Visible and IR spectral ranges on variations of the filling factor of surface magnetic fields. We find that the contribution of magnetic features to solar radiance is strongly dependent on the location on the disk of the features, being negative close to disk center and positive toward the limb. If features are homogeneously distributed over a region around the equator (activity belt) then their contribution to irradiance is positive with respect to the contribution of HD snapshots, but decreases with the increase of their magnetic flux for average magnetic flux larger than 50 G in at least two of the Visible and IR spectral bands monitored by SIM. Under the assumption that the 50 G snapshots are representative of quiet Sun regions we find thus that the Spectral Irradiance can be in counter-phase with the solar magnetic activity cycle. | Solar irradiance, the radiative energy flux the Earth receives from the Sun at its average orbital distance, varies along with magnetic activity, over periods of days to centuries and presumably even on longer time scales. The magnitude of irradiance variations strongly depends on wavelength. The precise measurement of irradiance over the spectrum is becoming more and more compelling, because of the increasing evidence of the effects of these variations on the chemistry of the \textbf{Earth's} atmosphere and terrestrial climate \citep[e.g.][ and references therein]{lockwood2012, ermolli2013}. However, absolute measurement of spectral irradiance variations, especially over time scales longer than a few solar rotations, is seriously hampered by difficulties in determining degradation of instrumentation in space. Therefore, calibrations of radiometric measurements have to rely significantly on inter-calibration with other instruments and/or reconstructions through models based on proxies of magnetic activity. In this context, recent measurements obtained with the Spectral Irradiance Monitor \citep[SIM;][]{harder2005} radiometers on board the Solar Radiation and Climate Experiment \citep[SORCE;][]{rottman2005}, which show an irradiance signal at Visible and IR spectral bands in \emph{counterphase} with the solar cycle \citep{harder2009}, have been strongly debated. This result was confirmed by \citet{preminger2011}, who found that variations in irradiance of solar and solar-like stars in red and blue continuum band-passes is in counter phase with their activity cycle. By contrast, recent results obtained from the analysis of \textbf{VIRGO/SOHO} \citep{frohlich1995} data at visible spectral ranges \citep{wehrli2013} show signals \emph{in phase} with the magnetic cycle.\textbf{ Theoretically, most of the irradiance reconstruction techniques which usually reproduce more than $90\%$ of variations of total solar irradiance (i.e., the irradiance integrated over the whole spectrum), produce irradiance variations at SIM Visible and Infrared bands that are in phase with the magnetic cycle \citep[see][for a review]{ermolli2013}. The Spectral and Total Irradiance REconstruction models for Satellite Era (SATIRE) produce a signal slightly in counter-phase in the IR \citep[e.g.][]{ball2011}. The only reconstructions that produce a signal in counter-phase with the magnetic activity cycle on both visible and IR bands are those obtained with the Solar Radiation Physical Modelling (SRPM) tools \citep{fontenla2012}, which, on the other hand, have been criticized for being explicitly constructed to reproduce SIM measurements.} Given the above controversy it is still an open question whether SIM finding of counter phase spectral variation in visible and IR bands is the result of a problem with internal calibration procedures% , or if instead current modeling is not adequate in reproducing irradiance variations at those spectral ranges. In particular the physical cause of long-term variations is still unclear having been attributed alternatively to changes in quiet Sun magnetism that is mostly hidden in full-disk observations \citep{fontenla2012}, or to a change of the temperature gradient in the solar atmosphere, most likely due to an increase of the magnetic filling factor over the cycle \citep{harder2009}. \textbf{Several irradiance reconstruction techniques, such as the SATIRE and the SRPM cited above, the reconstructions of the Astronomical Observatory of Rome \citep[OAR,][]{ermolli2011}, and those obtained with the Code for Solar Irradiance \citep[COSI,][]{haberreiter2008, shapiro2010} and with the Solar Modelling in 3D \citep[SOLMOD,][]{haberreiter2011}, are based on one-dimensional static atmosphere models.} Such models can be constructed to reproduce observed spectra very well, but their semi-empirical nature prevents them from being used to explore the underlying physics \citep{uitenbroek2011}. In this contribution we employ snapshots from 3-D magneto-hydrodynamic (MHD) simulations of the solar photosphere to qualitatively investigate whether an increase of the magnetic filling factor over the solar surface can produce a decrease of the disk-integrated solar radiative emission in the four visible and IR spectral bands monitored by SIM. Since the contribution of features as pores and sunspots is well known to be negative, this study is aimed at investigating the contribution of features like faculae and network. The paper is organized as follows: in Sect. 2 we describe the MHD snapshots employed and the spectral synthesis performed; in Sect. 3 we present our results and in Sect. 4 we draw our conclusions. \begin{figure*}[!] \includegraphics[width=16.5cm] {images2.eps} \caption{Vertical line of sight emergent radiation at 630 nm through MHD snapshots characterized by different amounts of average magnetic flux. From left to right: HD, 50 G, 100 G and 200 G.} \label{images} \end{figure*} | We employed snapshots from 3-D MHD simulations, characterized by different values of average vertical magnetic flux, to estimate solar irradiance variations at the visible and IR spectral ranges of SIM radiometers, stemming from contributions of patches of unresolved magnetic field. The results from our spectral synthesis confirm the fact the contribution of facular region to irradiance is strongly dependent on their location over the solar disk \citep[see also the discussion in][]{fontenla2012}. In particular, we find that the increase of the magnetic filling factor over the solar surface can produce a {\it decrease} of emitted radiation only for mostly vertical lines of sight and only for wavelengths below 500-700 nm (depending on the magnetic flux), or above 1500 nm (Fig. \ref{CLVs}). Integrating the intensity over the disk, even if we limit the contribution of magnetic regions to an activity belt, always renders the contribution of the magnetic elements to the irradiance positive (Fig. \ref{fluxesactivitybelt}). Nevertheless, if magnetic features are distributed over the activity belt, their contribution decreases at two of the SIM bands (namely at 400-691 and 1630-2423 nm) with the increase of the average magnetic flux. This suggests that, assuming that the relative number of features with larger magnetic flux increases with the increase of the magnetic activity, then the spectral irradiance at those SIM bands can decrease toward solar maximum. \textbf{Results shown in Fig. \ref{fluxesactivitybelt} also indicate that, if we take as reference the 50 G snapshots instead of the HD ones, then the contribution of facular regions to irradiance at the 400-691 and 1630-2423 nm SIM wavelength bands is always negative. We note that this is a more "realistic" assumption than taking the HD snapshots as reference, as previous works have shown that MHD simulations with average vertical magnetic field between 20 - 30 G best represent properties of magnetic field of the quiet Sun \citep{khomenko2005, danilovic2010}. Finally, we note that magnetic features tend to appear toward higher latitudes at the beginning of the cycle, migrate toward the equator as the magnetic activity peaks, and that then part of their flux, fragmented into lower magnetic flux features, tends to migrate toward the poles during the descending phase. Since, as we have shown, the contribution to irradiance of these features strongly depends on their position on the solar disk, we speculate that multiple peaks of the solar spectral irradiance could be observed. } Note that an average flux of 200 G, the maximum we considered, is modest for facular regions, as values up to 800 G are usually employed for reconstructions \citep[e.g.][and references therein]{ball2012}. On the other hand, from results shown in this work as well as from results obtained from numerical simulations by other authors \citep[e.g.][]{vogler2005}, and from observations \citep[e.g.][]{yeo2013, ortiz2002} it is clear that the center-to-limb variation of contrast increases with magnetic flux so that it is likely that our conclusions would be even stronger. Likewise, the inclusion of spectral lines in our calculations would have most likely increased the contrast between MHD and HD intensities, as spectral lines contribute opacity and raise the formation height of the spectral bands, causing them to sample slightly higher layers, where the differences between the average temperatures of the models with different field strength is larger. Nevertheless, we expect this effect to be larger for the lower magnetic flux simulations, where the average temperature gradient is steeper (and spectral lines are deeper), with respect to higher magnetic flux simulations, thus increasing the steepness of the relations in Fig. \ref{fluxesactivitybelt} for the 400-691 ans 1630-2423 nm bands, and decreasing the steepness of the curves of the other two bands. This effect too would thus strengthen our conclusions. \textbf{We therefore conclude that the spectral synthesis presented in this study are compatible with a negative contribution of facular regions to the irradiance in the SIM visible and IR bands with an increase in magnetic filling factor if as reference for quiet Sun we assume snapshots of 50 G average magnetic flux. } | 14 | 4 | 1404.4651 |
1404 | 1404.3247_arXiv.txt | We report the results of a $J$ band search for cloud-related variability in the atmospheres of 62 L4-T9 dwarfs using the Du Pont 2.5-m telescope at Las Campanas Observatory and the Canada France Hawaii Telescope on Mauna Kea. We find 9 of 57 objects included in our final analysis to be significantly variable with $>$99\% confidence, 5 of which are new discoveries. In our study, strong sinusoidal signals (peak-to-peak amplitudes $>$2\%) are confined to the L/T transition (4/16 objects with L9-T3.5 spectral types and 0/41 objects for all other spectral types). The probability that the observed occurrence rates for strong variability inside and outside the L/T transition originate from the same underlying true occurrence rate is excluded at $>$99.7\% confidence. Based on a careful assessment of our sensitivity to astrophysical signals, we infer that 39$^{+16}_{-14}$\% of L9-T3.5 dwarfs are strong variables on rotational timescales. If we consider only L9-T3.5 dwarfs with 0.8$<J-K_{\rm s}<$1.5, and assume an isotropic distribution of spin axes for our targets, we find that $80^{+18}_{-19}$\% would be strong variables if viewed edge-on; azimuthal symmetry and/or binarity may account for non-variable objects in this group. These observations suggest that the settling of condensate clouds below the photosphere in brown dwarf atmospheres does not occur in a spatially uniform manner. Rather, the formation and sedimentation of dust grains at the L/T transition is coupled to atmospheric dynamics, resulting in highly contrasting regions of thick and thin clouds and/or clearings. Outside the L/T transition we identify 5 weak variables (peak-to-peak amplitudes of 0.6\%-1.6\%). Excluding L9-T3.5 spectral types, we infer that $60^{+22}_{-18}$\% of targets vary with amplitudes of 0.5\%$-$1.6\%, suggesting that surface heterogeneities are common among L and T dwarfs. Our survey establishes a significant link between strong variability and L/T transition spectral types, providing evidence in support of the hypothesis that cloud holes contribute to the abrupt decline in condensate opacity and 1\,$\mu$m brightening observed in this regime. More generally, fractional cloud coverage is an important model parameter for brown dwarfs and giant planets, especially those with L/T transition spectral types and colors. | \label{sect:intro} Brown dwarfs (BDs) are objects thought to form similarly to stars, yet lack the required mass ($M \lesssim$ 0.07\,$M_{\odot}$) to burn hydrogen \citep{chabrier00}. Without a sustained energy source they spend their lives cooling. While young brown dwarfs may resemble the lowest mass stars, after the first $\sim$0.1-1 Gyr their atmospheres have cooled to sub-stellar temperatures ($\lesssim$2200\,K). The coolest brown dwarfs yet detected are reported to have temperatures as low as $\sim$300-400\,K \citep{liu11,cushing11,luhman12,dupuy13}, and represent the coolest atmospheres available to direct and detailed study outside of our solar system. As such, a detailed understanding of brown dwarf atmospheres is an important stepping stone toward the understanding of giant planet atmospheres---including those recently discovered \citep[e.g. HR8799 system;][]{marois08} and cooler objects to be found in the near future through campaigns such as GPI \citep{gpi} and SPHERE \citep{sphere}---for which we will collect comparatively fewer data of significantly lower quality. Direct spectra for hundreds of free-floating BDs in the solar neighborhood provide an unrivaled sample from which the majority of current knowledge about cool, cloudy atmospheres has been derived. The standard picture is as follows. As temperatures fall below $\sim$2200\,K refractory species---including iron, silicates, and metal oxide compounds---condense to form``dust'' clouds in substellar atmospheres \citep{burrows99,lodders99,burrows06}. The formation and thickening of dust clouds leads to progressively redder spectral energy distributions, and characterizes the L spectral sequence. However, at temperatures of $\sim$1200\,K dust opacity is observed to diminish abruptly, signaling the transition to cloud-free and methane-rich T spectral types. This transition from cloudy to cloud-free atmosphere is known as the ``L/T transition'' and is characterized by a dramatic spectral evolution (a blueward shift of $\sim$2 magnitudes in $J-K$, encompassing $\sim$L8-T5 spectral types), at near constant effective temperature \citep{golimowski04,stephens09}. The disappearance of dust as a major opacity source is thought to occur as dust grains gravitationally settle below the photosphere. For example, although we see prominent ammonia clouds in Jupiter's photosphere, thick iron and silicate clouds are thought to reside in its deep atmosphere, hidden from view \citep{lodders06}. However, the detailed physics governing the dissipation and settling of condensates remains poorly understood, with models generally predicting a much more gradual disappearance of clouds over a wider range of effective temperatures \citep{tsuji03,marley02,allard03}. The discrepancy between observations and models is perhaps best highlighted by the $\sim$1\,$\mu$m fluxes of L/T transition brown dwarfs, which counterintuitively brighten by a factor of approximately two-fold from L8 to T5 spectral types \citep{dahn02,tinney03,vrba04,dupuy12,faherty12}, whereas models predict monotonically decreasing fluxes. This discordant observation has led to the suggestion that, rather than uniformly settling below the photosphere, clouds are dynamically disrupted at L/T transition temperatures, opening up windows to the deep photosphere, which contribute to the abrupt decline in cloud opacity and resurgence of 1$\mu$m flux \citep{ackerman01,burgasser02_lt}. The cloud disruption hypothesis makes a testable prediction: patchy cloud coverage should produce rotationally modulated variability as cloud features rotate in and out of view \citep[typical rotation periods are $\sim$2-10\,hr;][]{reiners08}. Searches for cloud related variability have been ongoing for over a decade for a range of spectral types at both red optical \citep{tinney99,bailer-jones99,bailer-jones01,gelino02,koen03,koen05c,littlefair06,koen13} and infrared wavelengths \citep{artigau03,bailer-jones03,enoch03,koen04a,koen05a,morales-calderon06,lane07,clarke08,goldman08}, but have yielded mostly ambiguous results. Observations in the red optical have targeted mainly late-M to early-L dwarfs, due to a significant drop-off in optical flux for later type dwarfs. In the $I$-band, a rather high fraction of early L-dwarfs show some statistical evidence for variability \citep[as high as 30-80\%;][]{bailer-jones01,gelino02,koen03,koen04b,koen05b,koen05c}, although the fraction for which periodic variability has been claimed is at the lower end of this range ( $\sim$30\%). Typical peak-to-peak amplitudes of periodic variables are of the order of a few percent, and are often comparable to the photometric noise level. Complicating the interpretation of these results is that many of the claimed periodicities are inconsistent with rotation periods based on $v\sin{i}$ measurements \citep{kirkpatrick99,mohanty03,bailer-jones04,zapatero06,reiners08}. Despite the existing ambiguity, there are cases where optical periods can be matched to periodic radio pulsation \citep{lane07} or periodic variations in $H\alpha$ \citep{clarke03}, and likely correspond to rotation periods. Recent work by \citet{harding13} has shown that radio emitting late-M and L dwarfs are often periodic variables in the red optical, suggesting magnetism as an underlying cause for this subset of objects. Recent work by \citet{koen13} reporting short timescale $I$-band variability for 125 ultra cool dwarfs found variability to be more common for early spectral types: of 24 objects found to be significantly variable on timescales of 2-3\,hr, 18 had spectral types earlier than L2. Interestingly, this study included 5 objects with spectral types $>$L8 (and as late as T5.5) and 4 of them were found to show nightly changes in mean flux level, hinting at longer timescale variability in these objects. Thus, based on red-optical studies, variability in late-M, and early-L dwarfs is relatively common and may be related to magnetic spot activity, dust meteorology, or a combination of both. The work of \citet{koen13} hints at a re-emergence of $I$-band variability at later spectral types, possibly coincident with the L/T transition. While optical studies have been mostly confined to early spectral types, the L/T transition is one of the most interesting regimes to test for cloud related variability and weather due to the ability of cloud holes to explain observed properties of the transition. Due to a strong drop off in optical flux with increasing spectral type, a move to NIR wavelengths is required (wherein late-L and T-dwarfs are brightest). Since the atmospheres of late-L and T dwarfs are increasingly neutral, they are less likely to support cool magnetic spots \citep{gelino02,mohanty02}, making the interpretation of detected variability in this regime less ambiguous. However, in contrast to optical surveys, data obtained in the NIR is typically subject to larger amounts of correlated noise due to the bright IR sky, variable precipitable water vapor in Earth's atmosphere, and detector systematics. This makes the interpretation of NIR time series a challenging task \citep[e.g.][]{bailer-jones03,artigau06}, and can be a source of false-positives if not accounted for. There have been several surveys for variability of L and T dwarfs at NIR wavelengths. In a study of 18 L and T dwarfs, \citet{koen04b} found no significant evidence of variability in the $J$ band above the $\sim$20 mmag level nor in the $H$ or $K_s$ bands above $\sim$40 mmag, but find marginal evidence of periodic variability at lower peak-to-peak amplitudes with periods of $0.8-1.5$\,hr, for a few objects in their sample. Similarly, the $J$ band survey of \citet{clarke08} found variability to be confined to amplitudes $<15$\, mmag, reporting periodic variations for 2 of 8 late L and T dwarfs surveyed with amplitudes of 15 and 8 mmag and periods of 1.4~hr and 2~hr respectively. The work of \citet{girardin13} echoes these conclusions, finding all but one target to be non-variable above $5-15$\,mmag, and find evidence for periodic variability of a T0.5 binary at the $\sim$25-60\,mmag level, with a $\sim$3\,hr periodicity. In contrast to these studies, \citet{enoch03} found 3 of 9 L2-T5 dwarfs monitored in the $K_s$ band to be variable at the 10\%-20\% level (2 of which had low-significance periodicities of 1.5\,hr and 3.0\,hr). Similarly, \citet{khandrika13} found 4 of 15 L and T dwarfs to be variable in $J$ and/or $K_s$ with peak-to-peak amplitudes of 10\%-60\%, and find a significant periodicity for the T1.5 dwarf 2M2139$+$02, which was previously reported to be variable by \citet{radigan12}. Combined, these latter two studies find that 7 of 24 (or $\sim$30\%) of L and T dwarfs are high-amplitude variables in the NIR. It is notable that the detections in these latter studies are typically only 2-3 times the level of the photometric noise, and given the lack of detections in higher-precision surveys, this may suggest a large number of false positives due to correlated noise. Alternatively, it is possible that differences in target selection, filter choice (i.e. the use of a $K_{\rm s}$ filter instead of or in addition to $J$), and observing strategy (i.e. observations of the same targets at multiple epochs) differentiate the high-yield \citet{enoch03} and \citet{khandrika13} studies from others. The HST/WFC3 survey of \citet{buenzli14} report $\sim$40\,min spectral time series for 22 L5-T6 dwarfs and report significant variability (p$>$95\%) in at least one wavelength region from 1.1-1.7\,$\mu$m for six brown dwarf spanning the range of spectral types observed. Periods and amplitudes of the variability are not well constrained due to the short observation window of this study. Taken together, previous studies in the NIR do not find variability to be correlated with spectral type or color, and do not find evidence to support the hypothesis that variability may be more common at the L/T transition. The most compelling detections of brown dwarf variability to date in the NIR---those whose amplitudes greatly surpass the photometric noise, and/or have been repeated at multiple epochs---have been mostly reported as single object detections. The first such result was reported by by \citet{artigau09}, who found the T2.5 dwarf SIMP~J013656.57$+$093347.3 (SIMP0136+09) to be variable with a peak-to-peak amplitude of $\sim$50~mmag in $J$ and a period of 2.4\,hr (a 10-$\sigma$ detection). Since this benchmark finding, there have been three additional reports of large-amplitude variables in the NIR: the T1.5 dwarf 2MASS~J21392676$+$0220226 \citep{radigan12} which varies with an amplitude as high as 26\% in $J$ on a 7.72\,hr timescale\footnote{Although reported as a single object, this target was first detected as part of the variability survey presented in this work}, the T0.5 binary SDSS~J105213.51$+$442255.7, which was found to be variable by \citet{girardin13} with an amplitude as high 6\% and a period of 3\,hr, and the T2 secondary component of the Luhman AB system \citep{gillon13,biller13} which has been observed to have an amplitude as high as 13\% in the $H$ band and a $\sim$5\,hr period. These reports of high amplitude variables, all of which have early T spectral types, hint that large-amplitude variability may be more common in the L/T transition despite the lack of evidence in previous survey work. Low sample sizes of early-T targets in previous studies may explain this discrepancy. Here we present results of the largest, most sensitive search for NIR variability in brown dwarf atmospheres to date, with the specific goal of testing whether L/T transition dwarfs are variable at $\sim$1\,$\mu$m wavelengths. Our survey, conducted over 60 nights using the 2.5-m Du Pont telescope at the Las Campanas Observatory, and the Canada France Hawaii Telescope on Mauna Kea is described in section \ref{sect:obs}. The analysis of light curves, detection limits, and our search sensitivity are described in section \ref{sect:lightcurves}. In section \ref{sect:results} we present our results, and demonstrate a statistically significant increase in variability for early T-dwarfs. Finally, in section \ref{sect:concl} we summarize the major conclusions of our study, and discuss their implications for our understanding of cloudy substellar atmospheres. | \label{sect:concl} This work reports the most extensive and sensitive survey of brown dwarf variability to date at NIR wavelengths. Of 57 targets included in our final statistical sample---monitored for variability in continuous sequences of $\sim$2-6\,hr---we detected significant variability ($p>$99\%) in 9 objects. Of these, 5 objects (including 2M2139$+$02, for which follow-up observations were reported in \citet{radigan12}) are reported to be variable for the first time here. For L9-T3.5 spectral types, 4/16 objects were found to be variable with peak-to-peak amplitudes ranging from 2.9\% to 9\%, while 5/41 targets outside the transition exhibit low-level variations with amplitudes ranging from 0.6\%$-$1.6\%. The major conclusions of this work can be summarized as follows: \begin{enumerate} \item We find a statistically significant increase in strong $J$-band variability (peak-to-peak amplitudes larger than 2\%) within the L/T transition (L9-T3.5 spectral types) at $>$99.7\% confidence. \item We infer that $39^{+16}_{-14}$\% of L9-T3.5 dwarfs are periodic variables with peak-to-peak amplitudes $>$2\%. \item In our sample, sinusoidal signals with peak-to-peak amplitudes $>$2\% are confined to a narrow region of the L/T transition consisting of early T-dwarfs with intermediate $J-K_{\rm s}$ colors. The flux contrast between clouds and clearings (or thick and thin cloud patches) may peak within this narrow range. \item Correcting for target inclinations, we infer that $80^{+18}_{-19}$\% of L9-T3.5 dwarfs with $0.8>J-K_{\rm s}>1.5$ would be variable if viewed edge-on. Azimuthal symmetry of cloud patches or binary contaminants may account for remaining non-variable objects. This is consistent with the majority of early L/T transition dwarfs having high contrast cloud patches in their atmospheres (see section \ref{sect:stats}). \item It follows from conclusion 4, that the development of spatially heterogeneous clearings or thin-cloud regions may contribute to the abrupt decline in cloud opacity and $J$-band brightening observed at the L/T transition. \item We identify a tentative correlation between strong variability and weak $H$-band CH$_4$ absorption for early T-dwarfs. Otherwise, the variable targets have rather unremarkable NIR spectra (see discussion in section \ref{sect:properties}). \item Outside the L/T transition we estimate that $60^{+22}_{-18}$\% of targets may vary with amplitudes of 0.5-1.6\%, suggesting that surface heterogeneities (e.g. cloud patches of lower contrast) are common among L and T dwarfs. \item The largest detections of variability outside the L/T transition were made for an unusually blue L6.5 dwarf (1.2\% peak-to-peak) and a somewhat red T6.5 dwarf (1.6\% peak-to-peak), suggesting that cloud patchiness (clearings in the former case, and residual clouds in the latter case) may influence emergent spectra for a wide range of spectral types. However, we also detect lower-level variability (0.6\%-0.9\%) in 3 T-dwarfs with unremarkable NIR colors. Further monitoring of will be required to determine the significance of any color trends outside the L/T transition. \item Finally, the detection of $J$-band variability in four mid-T dwarfs provides non-spectroscopic evidence for the persistence of clouds---potentially composed of salts and sulfides--- in late-type objects. Temperature perturbations may provide an alternate explanation, and multi-wavelength monitoring will be required to distinguish between variability mechanisms for late-type brown dwarfs for which silicate clouds are expected to have settled below the photosphere. \end{enumerate} For the first time here, we report a statistically significant correlation between high amplitude variability and L/T transition spectral types. This result suggests that cloud dispersal at the L/T transition proceeds in a spatially non-uniform manner, leading to localized regions of clouds and clearings (or alternatively thick and thin cloud patches). Our observations therefore support the longstanding hypothesis of \citet{ackerman01} and \citet{burgasser02_lt} that the development of cloud holes plays an important role in the transition from cloudy to clear spectral types, and may contribute to puzzling properties of the transition such as $J$-band brightening. This implies that substellar models of the L/T transition must include at minimum a multi-component surface model, and in the idealized case a fully 3D radiative hydrodynamical treatment. First steps in this direction have been made by \citet{freytag10}, \citet{marley10}, \citet{showman13}, and \citet{xi14}. More generally, fractional cloud coverage has been established as an additional parameter that may influence the emergent colors of brown dwarfs, and by extension directly imaged planets, especially those with L/T transition spectral types such as HR8799c \citep{marois08,oppenheimer13}. Variable brown dwarfs, and notably the new population of high-amplitude variables at the substellar L/T transition, provide novel opportunities to constrain cloud properties and dynamics in cool atmospheres. Surface variations in cloud thickness produce a chromatic variability signature, providing an unprecedented opportunity to probe cloud structure via multi-wavelength monitoring as in \citet{radigan12}, \citet{buenzli12}, \citet{apai13}, \citet{heinze13}, and \citet{biller13}. And finally, mapping the evolution of features over multiple rotations will provide a way to study atmospheric dynamics in the high-gravity, non-irradiated regime. \clearpage \appendix | 14 | 4 | 1404.3247 |
1404 | 1404.4521_arXiv.txt | {} {Besides its major objective tuned to the detection of the stellar galactic population the Gaia mission experiment will also observe a large number of galaxies. In this work we intend to evaluate the number and the characteristics of the galaxies that will effectively pass the onboard selection algorithm of Gaia.} {The detection of objects in Gaia will be performed in a section of the focal plane known as the Sky Mapper. Taking into account the Video Processing Algorithm criterion of detection and considering the known light profiles of discs and bulges galaxies we assess the number and the type of extra-galactic objects that will be observed by Gaia.} {We show that the stellar disk population of galaxies will be very difficult to be observed. On the contrary the spheroidal component of elliptical galaxies and bulges having higher central surface brightness and steeper brightness profile will be more easy to be detected. We estimate that most of the 20 000 elliptical population of nearby galaxies inside the local region up to 170 Mpc are in condition to be observed by Gaia. A similar number of bulges could also be observed although the low luminosity bulges should escape detection. About two thirds of the more distant objects up to 600 Mpc could also be detected increasing the total sample to half a million objects including ellipticals and bulges. The angular size of the detected objects will never exceed 4.72 arcsec which is the size of the largest transmitted windows.} {An heterogeneous population of elliptical galaxies and bulges will be observable by Gaia. This nearby Universe sample of galaxies should constitute a very rich and interesting sample to study their structural properties and their distribution.} | The Gaia satellite experiment was launched in December 2013 as part of a mission to produce an all sky survey with unprecedented angular resolution in the spectral range 330-1000 nm. The selected objects will first pass through the Sky Mapper (SM) section of the focal plane responsible for filtering those objects that in the sequence should be observed in the Astrometric Field (AF). The expected software defined magnitude limit of the observable targets in the Gaia photometric system is estimated to be $G=20$ mag for point source objects. The satellite is also equipped with two low resolution spectro-photometers operating in the blue spectral region 330-680 nm (BP) and in the red 640-1000 nm (RP) with a typical resolution of 3-27 nm per pixel for the BP photometer and 7-15 nm per pixel for RP. All the observed objects will have their spectral energy distribution evaluated by these instruments. Moreover an additional radial velocity spectrograph (RVS) instrument will measure the radial velocity in the Calcium triplet region (847-874 nm) for a fraction of the brightest objects with a resolution R=11500. The evaluation of the accurate position, distance and radial velocity for an enormous number of stellar objects will provide an extremely useful material to improve our understanding of our Galaxy (Perryman, \cite{Perryman2001}). Although the mission is focused on the detection of galactic stellar objects Gaia will also deliver a huge number of detections of non stellar objects such as quasars and particularly interesting data set of galaxies. In the case of nearby galaxies in the local group it is expected that their brightest stars will be also resolved providing an invaluable information for studying their stellar population and their dynamics. The more distant galaxies will be detected through their diffuse brightest regions mostly concentrated in their central regions. A natural question to ask in this scenario is related to the potential impact of the sample of detected non-resolved galaxies for our comprehension of this subject. It is clear that the sample of these non-resolved galaxies observations by Gaia will be limited to their very central and bright regions for nearby objects. In each passage of the telescope trough these galaxies, the on board satellite software will sample an small strip of pixels covering the information gathered from a region of $0.59$x$1.77$ arc sec (along scan vs. across scan) in the SM section. This region is used to estimate the magnitude of the object and to analyse if the object should be transferred to the Earth. An important point however is that the SM window send to Earth is larger and will cover an sky size of 4.72x2.12 arcsec. Since nowadays most of the morphological information occurring in the disks and bulges of nearby galaxies comes mainly from the observation of regions on much larger angular scales, its clear that the observed light distribution will be invaluable for morphological studies of the central region of galaxies. This sample will be a complementary set of observations to those that can be obtained from lower resolution Earth based facilities. However, it is important to mention that these data have reduced spatial resolution, reduced depth and increased noise since the integration time is $2.9$ s, instead of the usual $4.4$ s adopted for the AF field. Moreover, the SM window that reaches ground is composed of samples of 2x2 binned pixels for $G < 16$ mag. For $G > 16$ mag an on-board binning of four 2x2-pixel will be applied resulting in an increase of the total noise. As we will show in the next sections most of the unresolved galaxies should have $G > 16$ mag and therefore the SM Gaia observation of these objects will suffer from these limitations. Due to its orbital characteristics the satellite will observe regularly the same region of the sky each time at different scanning directions. Therefore, it is possible to apply some numerical reconstruction method to obtain estimated two dimensional images for the observed objects, even though such approaches usually present severe reconstruction artefacts (see Dollet et al., \cite{Dollet2005} , Harrison, \cite{Harrison2011}, and references therein). Nevertheless the best angular resolution of Gaia's AF is 59 mas in the scanning direction and therefore we should expect that the its measurements of the central region of nearby galaxies will be available with a very good resolution, quite probably comparable with those available from the HST data and resulting in a larger dataset. One possible way to evaluate the impact of Gaia observations is through the simulation of a complete distribution of objects in the Universe including solar system objects, galactic stellar sources and extragalactic sources like galaxies, QSOs and supernovae (Robin et al, \cite{Robin2011}). This could be a valuable approach for point-like objects, because the detection of such objects by the Gaia onboard software will be unbiased. Nonetheless, for extended sources, such as other galaxies, this large scale approach is infeasible, as it would required that images of all targets to be simulated and afterwards passed through the video processing algorithms. In Robin et al., 2011, simulation, a total of 38 million extragalactic objects were generated with integrated magnitudes $G \leq 20$ mag, obeying the observed luminosity functions. This figure could be considered as an upper limit of the possible number of detections by Gaia. In the present work we explore a complementary view of the extra-galactic science that Gaia may produce focusing in the analysis of the possible structural components of galaxies that might be observed by Gaia. The two major components that we study are the disk and the bulge spheroidal components. Each of these two basic blocks have been extensively studied in the past decades having their own structural photometric properties well understood. Given the results discussed in the literature we then ask the question of what are the characteristic properties of these two components that might be more suited to be detected and selected for transmission to the ground selected for detection by the satellite. In section 2 we present some general characteristics of the detection parameters adopted by Gaia that will be more relevant for the observation of galaxies. Section 3 discuss the implications for the detection of galaxies constituted by pure stellar disks assuming that those objects are dominated by an exponential surface brightness. Most of the stellar disks have a relatively low surface brightness distribution that will be hard to be detected by Gaia. In section 4 we analyse the detections of the spheroidal population located in ellipticals and bulges of spiral galaxies. This component is known to have a much higher central surface brightness and will probable be the major component to be detected by Gaia. In section 5 we describe the results of a numerical simulation of galaxies obeying the nearby observed brightness profiles. A population of these objects were distributed in a uniform space distribution and their simulated images pass trough a software emulating the same detection procedure adopted by Gaia. In section 6 we evaluate the effect of increasing the distance in the detection of more distant objects that should be affected by the fixed pixel aperture sampling and cosmological dimming. In section 7 we present our major conclusions. | Based on the present status of Gaia mission our main conclusions are: \begin{itemize} \item It is quite unlikely that the stellar disks could be detected except if we consider the population of objects harbouring AGN's and those presenting strong nuclear star forming episodes. \item The major fraction of detections will be quite probably constituted by normal ellipticals and bulges of S0-Sb galaxies having steeper brightness profiles and S\'ersic indices $n=3-5$ or larger. A crude estimate indicate that the possible number of elliptical detections in the nearby 170 Mpc is situated around 19 000 objects and could be doubled by the inclusion of S0-Sa bulges. The population of very bright ellipticals present a relatively lower central surface brightness and some of them could escape detection. \item More distant objects, in the range 170-600 Mpc, could be observed but the evaluation of the total number of possible detections is more uncertain. If most of the population is represented by a S\'ersic profile $n=4$ then about 2/3 of them could be detected increasing the total number of source to half a million objects. \item Ellipticals having soft brightness profiles , $n<3$, will be more difficult to be detected and the same is valid for spheroidal galaxies. \item This scenario is supported by numerical simulations of the detection at the sky mapper level. These simulations were performed by the Gaia Instrument and Basic Image Simulation and the video processing algorithm prototype using nominal parameters. \end{itemize} At first glance we could think that the predicted number of detections is too small in comparison with the huge expectations of Gaia in the stellar area. However, it is useful to remember that the present number of observed spheroidal objects having similar image resolution is less than one hundred objects. Therefore, if our expectations reveal to be true Gaia will provide a massive sample of new nuclear observations of ellipticals and bulges of early type galaxies in the nearby Universe. Due to the characteristics of the Gaia mission the same object will be observed several times with different scanning directions. All detected objects will have in each scanning passage a collection of the AF high resolution images as well as the lower resolution SM data. At the end this collection of data along each direction may be processed at Earth to reconstruct the estimated images. It is conceivable that some loss of resolution could result from the reconstruction process, and also that reconstruction artefacts might exist. Nevertheless it is also conceivable that the sample of Gaia observations will be of great importance for our understanding of the central structure of spheroids and their distribution in the local Universe, from its one-dimensional data alone. In the past ellipticals were considered relaxed systems that evolved passively due to little or no gas reservoir, formed from a monolithic collapse scenario, in a single burst of intense star formation. Nowadays this picture was completely changed due to recent photometric and kinematic studies that have revealed an huge complexity in their dynamical structure, star-formation history and assembly history. These studies have been showing that ellipticals can be classified in three groups according with their luminosity. The photometric and kinematic properties of each group are very different and depend of their luminosity (Mo et al., \cite{Mo2010}; Blanton \& Moustakas, \cite{Blanton2009}). Therefore the high resolution Gaia observations in the central region of ellipticals could be very useful to test these different scenarios by using an homogeneous sample of objects. An important fraction of the observed sample of nearby galaxies brighter than $G_{RVS}=17$ mag should also be detected in the spectrophotometer and due to its characteristics the same object will be observed several times along different angle directions. Another interesting issue is that the detected objects should also be observed in the blue (BP) and red (RP) photometers. This would be an invaluable information for the stellar population studies in the central regions of galaxies. One interesting issue is the discussion of the scientific impact of changing the limiting detection magnitude of Gaia to $G=21$ mag. Such a change will obviously impact the quantity of data processing and is a matter under discussion by the mission control board. If this change could be consolidated we might ask on its impact in the detection of galaxies. In the case of the disks it is conceivable that this change will not modify the scenario discussed in section 3. As we can see from figure \ref{Mu0ReDisk} a variation of one magnitude in the detection limit magnitude will not be able to include the population of normal stellar disks. On the other hand that change will include a significant higher fraction of local spheroids as we can observe from figure \ref{Mu0ReSph}. Perhaps more importantly it will include a fraction of local spheroids with a soft surface brightness profile similar to those found in some of the local spheroidal ellipticals as well as a fraction of the spheroidal bulges of late spirals observed by MacArthur et al (\cite{MacArthur2003}). In the case of normal $n=4$ ellipticals the upgrade to $G=21$ mag will include in the detection list a large fraction of the objects more distant than 170 Mpc. If we consider an object with with $log r_e(kpc)=1.5$ obeying the Kormendy relation, corresponding therefore to a very luminous elliptical with $M_{abs}=-23.19$ mag, it will have at $d=600$ Mpc a total corrected magnitude in the SM window of G=21.00 mag and therefore will be include in the list of detected objects. Therefore the limiting distance for completion will triplicate expanding our number estimate approximately by a factor of 30. | 14 | 4 | 1404.4521 |
1404 | 1404.6524_arXiv.txt | Quenched central galaxies tend to reside in a preferentially quenched large-scale environment, a phenomenon that has been dubbed {\em galactic conformity}. Remarkably, this tendency persists out to scales far larger than the virial radius of the halo hosting the central. Therefore, conformity manifestly violates the widely adopted assumption that the dark matter halo mass $\mvir$ exclusively governs galaxy occupation statistics. This paper is the first in a series studying the implications of the observed conformity signal for the galaxy-dark matter connection. We show that recent measurements of conformity on scales $r\sim1-5$ $\mpc$ imply that central galaxy quenching statistics cannot be correctly predicted with the knowledge of $\mvir$ alone. We also demonstrate that ejected (or `backsplash') satellites cannot give rise to the signal. We then invoke the age matching model, which is predicated on the co-evolution of galaxies and halos. We find that this model produces a strong signal, and that central galaxies are solely responsible. We conclude that large-scale `2-halo' conformity represents a smoking gun of {\em central galaxy assembly bias,} and indicates that contemporary models of satellite quenching have systematically over-estimated the influence of post-infall processes. | \label{sec:intro} The well-established connection between galaxies and dark matter halos forms the basis of a very broad class of models of galaxy evolution that we will loosely refer to as halo occupation models. Such models exploit the ability of contemporary N-body simulations to calculate the abundance, spatial distribution, and internal structure of dark matter halos with exquisite precision. Armed with this knowledge, halo occupation models make predictions for the observed galaxy distribution by specifying, in a statistical sense, how galaxies populate dark matter halos. The Halo Occupation Distribution \citep[HOD, e.g.,][]{seljak00, berlind02, zheng05} and the closely related Conditional Luminosity Function \citep[CLF, e.g.,][]{yang03, vdBosch13} are the two most prevalent classes of halo occupation models in the literature. In the HOD, the galaxy-halo connection is formalized by the quantity $P(\ngal|\mvir),$ the probability that a halo of mass $\mvir$ hosts $\ngal$ galaxies brighter than some luminosity (or stellar mass) threshold. In the CLF, the quantity $\Phi(\mathrm{L}|\mvir)$ plays the central role by specifying the mean abundance of galaxies of luminosity $L$ found in dark matter halos of mass $\mvir.$ These well-studied formalisms have both proven to be very powerful theoretical tools to constrain both the galaxy-halo connection \citep[see, for example,][and references therein]{magliocchetti03, yang03, zehavi05a, cooray06,zheng07, vdBosch07, zheng09, skibba_sheth09, simon_etal09, ross10, zehavi11, watson_powerlaw11, tinker_etal13} and the fundamental parameters in cosmology \citep{vdBosch03cosmo, tinker05, leauthaud11a, more_etal13, cacciato_etal13}. All of the above results concerning both cosmology and galaxy evolution are predicated upon the assumption that the mass $\mvir$ of a dark matter halo entirely determines the statistical properties of its resident galaxy population. Yet, it is well established that the spatial distribution of dark matter halos depends on halo properties besides mass \citep{gao_etal05, wechsler06, gao_white07, wetzel_etal07, dalal_etal08, li_etal08, lacerna11, lacerna12}. Here we will collectively refer to the dependence of halo clustering upon additional halo properties besides $\mvir$ as {\em halo assembly bias}. Of course, if galaxy occupation statistics depend only on $\mvir,$ then halo assembly bias only contributes random noise in halo model predictions for the galaxy distribution. Because halo occupation models such as the HOD and CLF have generally been very successful at fitting observations of galaxy clustering statistics, the possibility that the galaxy-halo connection requires dependence on additional parameters besides $\mvir$ is generally not considered. However, it has recently been shown in \citet{zentner_etal13} that this assumption has the potential to introduce significant systematic errors in halo occupation modeling of the two-point clustering of luminosity threshold galaxy samples. \citet{zentner_etal13} showed that these systematics can be even more severe when color cuts comprise part of the selection function, such as, for example, in halo occupation modeling of color-dependent clustering \citep[e.g.,][]{zehavi11}. In what follows, we will generically refer to any dependence of the mapping between galaxies and halos upon halo properties besides $\mvir$ as {\em galaxy assembly bias}. In particular, our focus in this paper will be the potential correlation of galaxy color/star formation rate with halo properties besides $\mvir.$ In the context of assembly bias, galaxy group catalogs constructed from large redshift surveys, such as the Sloan Digital Sky Survey \citep[SDSS:][]{york00a,DR7_09}, have proven to be particularly rich datasets. For example, in \citet[][hereafter W06]{weinmann06b}, the authors used the halo-based group-finding algorithm of \citet{yang_etal05} to divide their SDSS galaxy sample into {\em central} galaxies residing at the center of the dark matter halo of the group, and {\em satellite} galaxies orbiting around the central within the potential well of the group's halo. W06 found that both the $g-r$ color and star formation rate (SFR) of satellite galaxies depends on the color/SFR of the group's central galaxy {at fixed halo mass},\footnote{Of course the true dark matter halo mass of a galaxy group is not directly observable, and so in W06 the authors use total group luminosity as their halo mass proxy. The role played by this choice and other details associated with this conformity measurement will soon appear in Campbell et al., in prep.} a phenomenon the authors dubbed {\em galactic conformity}.\footnote{See also \citet{phillips_etal14} for measurements of this phenomenon in a sample of satellites of isolated Milky Way-mass galaxies.} If correct, this observation manifestly violates the assumption that galaxy assembly bias is zero, as the properties of the satellites were explicitly shown to have an additional dependence upon some property besides $\mvir$ (in particular, satellite color/SFR evidently also depends on the color/SFR of the central). In a recent, closely related paper, \citet[][hereafter K13]{kauffmann_etal13} used SDSS data to demonstrate that correlations between star formation indicators of central galaxies and their neighboring galaxies persist out to several $\mpc,$ far outside the virial radius of the host halos of the centrals. Although K13 also used the term ``conformity'' to refer to the signal they measured, from the perspective of the halo model \citep[e.g.,][]{Cooray02,mo_vdb_white10} the W06 and K13 measurements are qualitatively distinct: the former refer to SFR correlations between galaxies occupying the same dark matter halo, while the latter considers galaxies in distinct halos. Hence, in what follows we refer to the conformity signals detected by W06 and K13 as ``1-halo'' and ``2-halo'' conformity, respectively. This paper is the first in a series investigating the implications of galactic conformity for halo occupation statistics and for the physics of galaxy formation (in particular galaxy quenching). In this paper we argue that {\em central} galaxy assembly bias is required for any galaxy-halo model to produce non-zero 2-halo conformity. In a companion paper to the present work (Paper II), we will show that 1-halo conformity can naturally be encoded in a generalized HOD formalism, and demonstrate that the W06 measurements indicate that this signal is strong enough to significantly impact small-scale clustering. Each of these two ``theory papers'' will be accompanied by its own follow-up paper providing new measurements of the corresponding conformity signal. In the observational follow-up to the present paper (Paper III), we will quantitatively compare our updated K13 measurements to predictions from both empirical and semi-analytic models (SAMs) of galaxy formation, and seek to identify the ingredients necessary to bring theoretical predictions into accord with the observations. Finally, in Paper IV, we will conduct a likelihood analysis using the generalized HOD model developed in Paper II to provide quantitative constraints on the co-evolution of central and satellite galaxies, as well as other signatures of galaxy evolution that have been previously neglected in HOD modeling of SFR-dependent galaxy clustering. This paper is organized as follows. We provide an overview of the conformity measurement in \S\ref{sec:twohaloconf}. In \S\ref{sec:halomodel} we outline the various formulations of the galaxy-halo connection we use to model the galaxy distribution. Our primary results are presented in \S\ref{sec:twohaloconfmockobs}, and we discuss the implications of our findings in \S\ref{sec:discussion}. Throughout the paper we assume a flat $\Lambda$CDM cosmological model with $\Omega_{\mathrm{m}}=0.27$ and Hubble constant $H_0=70$ km s$^{-1}$ Mpc$^{-1}$. | \bit \item[] {\bf Mock 1:} {\em Standard HOD model.} Quenching of both centrals and satellites depends only on $\mvir.$ \item[] {\bf Mock 2:} {\em Delayed-then-rapid model.} Quenching of centrals depends only on $\mvir.$ Quenching of satellites and backsplash galaxies depends on both $\macc$ and $(t-\tacc)$. \item[] {\bf Mock 3:} {\em Age matching model.} Quenching of centrals and satellites depends on both $\mvir$ and (sub)halo formation time. \eit \subsection{Model Comparison} \label{subsec:modelcomparison} We conclude this section by comparing some statistics of the three mocks introduced above. For mock galaxies with $\mstar > 10^{9.8} \msun,$ Fig.~\ref{fig:modelcomparisons} shows the HODs, $\meanm{\ngal}$, in the left-hand panels, and two-point correlation functions, $\xi(r)$, in the right-hand panels. Results are shown for all galaxies (upper panels), star-forming galaxies (middle panels), and quenched galaxies (lower panels). All three mocks have, by construction, the same stellar mass function, but differ in the way the mock galaxies were split into quenched and star forming sub-populations. Although none of the mocks has been tuned to reproduce the observed clustering, or to agree with the clustering of any of the other mocks, they have halo occupation statistics and clustering properties that are remarkably similar. This indicates that both of these one- and two-point functions, which are commonly used to quantify halo occupation statistics, are largely insensitive to the differences between these three mock galaxy distributions. This is despite the fact that they represent radically different perspectives on the physical processes that drive galaxy quenching. These results are especially noteworthy because, as we will see, 2-halo conformity brings the differences between these models into sharp relief. \begin{figure} \begin{center} \includegraphics[width=8cm]{./FIGS/standard_HOD.eps} \includegraphics[width=8cm]{./FIGS/two_halo_wetzel_0327.eps} \caption{ In each panel, the vertical axis shows the mean quenched fraction of all galaxies neighboring samples of ``isolated primaries'' selected in the same manner as in \citet{kauffmann_etal13}. Horizontal axes are the 3D distance from the primary. The {\em top} panel shows the 2-halo conformity signal around isolated primaries with $10^{10}\msun < \mstar < 10^{10.5}\msun$ as predicted by the standard HOD quenching model described in \S\ref{subsubsec:tradhodquenching}. Standard HOD models predict that the SFR of galaxies occupying distinct halos are uncorrelated, giving rise to zero 2-halo conformity, in contrast to the relatively strong signal measured in K13 (see their Figs. 2 $\&$ 3). The {\em bottom} panel is the same as the top panel, only here we show the prediction of the ``delayed-then-rapid'' model described in \S\ref{subsubsec:wetzelmodel}. There is little-to-no signal, again in contrast with the K13 measurements. This demonstrates that satellite backsplashing alone cannot account for the observed level of 2-halo conformity, and furthermore implies that the role of post-infall processes on satellite quenching has been over-estimated in this and related models. See \S\ref{subsec:wetzeltwohalo} and \S\ref{subsec:thenewjam} for further discussion. } \label{fig:hodcentralconformity} \end{center} \end{figure} \label{sec:discussion} \subsection{2-Halo Conformity as an Assembly Bias Marker} \label{subsec:assembias} The results in \S\ref{sec:twohaloconfmockobs} support the conclusion that the K13 measurements of 2-halo conformity constitute a detection of {\em central galaxy assembly bias.} We use this term to mean that central galaxy SFR is significantly correlated with some halo property in addition to halo mass $\mvir.$ The evidence for this conclusion is straightforward. First, in the top panel of Fig.~\ref{fig:hodcentralconformity}, we have shown that standard HOD models of galaxy quenching, in which there is no assembly bias of any kind, predict that 2-halo conformity should be zero in the stellar mass range where it has been observed with high statistical significance ($10^{10}\msun < \mstar < 10^{10.5}\msun$). Although Fig.~\ref{fig:hodcentralconformity} only shows that this is the case for a particular choice of HOD parameters, we find that this conclusion holds regardless of the fiducial values of the parameters. The K13 signal is not easily computable within the analytical framework of the halo model, necessitating this mock catalog-based approach. Second, we have shown that 2-halo conformity is also zero in two very different quenching models in which the galaxy assembly bias is limited to satellites. The first is the delayed-then-rapid model put forth in \citet{Wetzel_Tinker_Conroy12}, and shown in the bottom panel of Fig.~\ref{fig:hodcentralconformity}. In the second case, we consider an alteration to the age matching model \citep{HW13A} wherein we scramble the SFRs of {\em central} galaxies, at fixed halo mass. Both of these models produce essentially zero 2-halo conformity for scales $1 \mathrm{Mpc/h} \lesssim R \lesssim 5 \mathrm{Mpc/h}$. However, when we then test a mock in which {\em satellite} galaxy SFRs have been scrambled in the age matching model (bottom right panel of Fig.~\ref{fig:agematchingconformity}), the signal is nearly as strong as it is in the unscrambled age matching mock (top panel of Fig.~\ref{fig:agematchingconformity}). This directly implies that central galaxy assembly bias is responsible for the 2-halo conformity signal predicted by this model. Although we acknowledge that these results do not conclusively rule out a relationship between 2-halo conformity and satellite SFR, simply because our exploration of satellite-based models has been far from exhaustive, the fact that centrals dominate the abundance of galaxies at all stellar masses of interest clearly supports the notion that any 2-halo conformity is likely to be driven by central galaxies rather than satellites. Detections of central galaxy assembly bias have been reported in a growing body of literature. For example, numerous studies of SDSS galaxy samples \citep[e.g.,][]{yang_etal05, yang_etal06a, wang_etal08, wang_etal13} have employed galaxy group finders to demonstrate that the clustering of central galaxies (or the clustering of the groups themselves) depends on star formation indicators even after controlling for halo mass. The results presented in \S\ref{sec:twohaloconf} complement these previously reported detections with a method that has no reliance on a group-finding algorithm: both the K13 measurements and the above group-finder based methods support the notion that the statistics describing the quenching of galaxies are not solely a function of halo mass $\mvir$ alone. \subsection{2-Halo Conformity as a New Probe of Galaxy Evolution} \label{subsec:newprobe} The delayed-then-rapid model presented in \citet{Wetzel_Tinker_Conroy12} attaches unique physical significance to the virial radius $\rvir$ of the dark matter halo: central galaxy quenching statistics are exclusively governed by the mass $\mvir$ enclosed by the virial radius, and the SFR of satellites only begins to differ from centrals some time after $\tacc,$ when the satellite first passes within $\rvir$ of a larger halo. This model can be tuned to accurately reproduce a number of well-studied statistics based on galaxy group catalogs, such as the quenched fraction of satellites as a function of group mass, and the radial quenching gradients of satellites \citep{wetzel_etal13}. Moreover, we have shown in Fig.~\ref{fig:modelcomparisons} that the two-point correlation functions predicted by this model are in close agreement with the predictions of the age matching model, which itself accurately fits data from the SDSS \citep{HW13A, hearin_etal13b, watson_etal14}. Hence, we conclude that the shortcomings of the delayed-then-rapid model are not revealed by conventional statistics, but only become apparent when using the 2-halo conformity signal. This demonstrates that this new statistic possesses heretofore untapped constraining power for models of galaxy evolution.\footnote{See also \citet{cohn_white14} for an extensive investigation of the information content contained in alternative statistics to two-point clustering at $z \sim 0.5$.} Another example supporting the notion that the information content of 2-halo conformity is largely independent from that of more traditional statistics is the SAM presented in \citet{guo_etal11b}. This model reproduces reasonably well the observed clustering of galaxies as a function of stellar mass and color, as well as the distribution of galaxies within rich clusters. And yet, as shown explicitly in K13, this model predicts little-to-no 2-halo conformity. In K13, the authors speculate that 2-halo conformity may arise under a modification to the Guo et al. SAM in which there is ``pre-heating'' of the inter-galactic medium (IGM) at early times. This possibility is intriguing in light of the recent results presented in \citet{lu_etal14}, who showed that pre-heating of the IGM may play an important role in establishing numerous scaling relations of disk galaxies. \subsection{Toward a New Picture of Satellite Quenching} \label{subsec:thenewjam} The significant levels of 2-halo conformity measured in K13 suggest a different picture of galaxy evolution than the one offered by the prevailing paradigm. In particular, this signal indicates that contemporary models of satellite quenching have systematically over-estimated the significance of post-infall physical processes on attenuating the SFRs of satellite galaxies. This conclusion derives from the following chain of reasoning. First, the results of this work together with the K13 measurements strongly suggest that the large-scale environment ($R\sim 1-5$ $\mpc$) of a central galaxy is correlated, {\em at fixed $\mvir$}, with processes influencing the star formation history of the central. And so if satellites evolve as centrals for most of cosmic time, just as subhalos lead most of their lives as host halos, then these same processes should also be at work in quenching the satellites.\footnote{See \citet{watson_conroy13} for further empirical justification of the notion that satellites do indeed evolve as centrals for most of cosmic history.} Second, at fixed $\mstar$, galaxies that end up as satellites are far more likely to evolve in a dense large-scale environment. Therefore, the quenching mechanisms that correlate with large scale environment at fixed $\mvir$ will have had a statistically greater influence on the present-day satellite population, which will tend to produce preferentially quenched satellites {\em even in the complete absence of post-infall specific processes}. Models of galaxy quenching that ignore the above fact about structure growth in CDM are left with little choice but to rely too heavily on post-infall processes in order to reproduce the observed excess quenched fractions of satellites relative to centrals of the same $\mstar$. We conclude that careful comparisons to 2-halo conformity measurements (and other unambiguous markers of galaxy assembly bias) should henceforth be considered an essential component of modeling and constraining the star formation histories of galaxies. | 14 | 4 | 1404.6524 |
1404 | 1404.4085_arXiv.txt | Interaction of supernova (SN) ejecta with the optically thick circumstellar medium (CSM) of a progenitor star can result in a bright, long-lived shock-breakout event. Candidates for such SNe include Type IIn and superluminous SNe. If some of these SNe are powered by interaction, then there should be a specific relation between their peak luminosity, bolometric light-curve rise time, and shock-breakout velocity. Given that the shock velocity during shock breakout is not measured, we expect a correlation, with a significant spread, between the rise time and the peak luminosity of these SNe. Here, we present a sample of 15 SNe~IIn for which we have good constraints on their rise time and peak luminosity from observations obtained using the Palomar Transient Factory. We report on a possible correlation between the $R$-band rise time and peak luminosity of these SNe, with a false-alarm probability of 3\%. Assuming that these SNe are powered by interaction, combining these observables and theory allows us to deduce lower limits on the shock-breakout velocity. The lower limits on the shock velocity we find are consistent with what is expected for SNe (i.e., $\sim10^{4}$\,km\,s$^{-1}$). This supports the suggestion that the early-time light curves of SNe~IIn are caused by shock breakout in a dense CSM. We note that such a correlation can arise from other physical mechanisms. Performing such a test on other classes of SNe (e.g., superluminous SNe) can be used to rule out the interaction model for a class of events. | \label{sec:Introduction} A supernova (SN) exploding within an optically thick circumstellar medium (CSM) may have several unique characteristics. First, if the Thomson optical depth in the CSM is larger than $c/v_{{\rm s}}$, where $c$ is the speed of light and $v_{{\rm s}}$ is the shock velocity, then the shock breakout will occur in the CSM rather than near the stellar surface. This will lead to shock-breakout events that are more luminous and longer than those from normal supernovae (SNe; e.g., Falk \& Arnett 1977; Ofek et al. 2010; Chevalier \& Irwin 2011; Balberg \& Loeb 2011). In a CSM with a slowly decreasing radial density profile (e.g., a wind profile with density $\rho\propto r^{-2}$, where $r$ is the radial distance), the radiation-dominated shock will transform to a collisionless shock, generating hard X-ray photons and TeV neutrinos (Katz et al. 2011; Murase et al. 2011, 2013; Ofek et al. 2013a). While the collisionless shock traverses regions in which the Thomson optical depth, $\tau$, is above a few, the hard X-ray photons can be converted to visible light (e.g., via comptonization; Chevalier \& Irwin 2012; Svirski et al. 2012). We refer to this as the optically thick interaction phase. In most cases, emission of visible light from the optically thick interaction phase will last on the order of ten times the shock-breakout time scale (e.g., the time it takes the shock to evolve\footnote{In a wind-profile CSM ($\rho_{{\rm CSM}}=K r^{-2}$) the optical depth is inversely proportional to the radius.} from $\tau \approx 30$ to $\tau \approx 3$). Svirski et al. (2012) showed that the optically thick interaction phase is characterized by bolometric emission with a power-law or broken power-law light curve, with specific power-law indices. A recent example for such behavior was demonstrated by Ofek et al. (2013d) for SN\,2010jl (PTF\,10aaxf; see also Moriya et al. 2013; Fransson et al. 2013). However, in most cases the shock-breakout time scale may be less than several days, and the optically thick interaction phase will thus be short and hard to distinguish in the optical band. It is possible that later, when the interaction is moving into the optically thin region, the hard X-ray photons traveling inward toward optically thick regions (e.g., the cold dense shell; Chevalier \& Fransson 1994) will be partially converted to optical photons. Svirski et al. (2012) and Ofek et al. (2013d) showed that for SNe having light curves that are powered by interaction, there should exist a specific relation between the shock-breakout time scale, the SN luminosity, and the shock velocity at shock breakout. For various reasons the shock velocity is hard to measure. Ignoring the shock velocity will introduce considerable scatter into this relation. However, we still expect a correlation, with a significant spread, between the SN rise time (i.e., a proxy for the shock-breakout time scale; Ofek et al. 2010) and peak luminosity. Type IIn SNe (e.g., Filippenko 1997) are characterized by intermediate-width emission lines which are presumably emitted by shock interaction and/or recombination in optically thin gas in the CSM due to the SN radiation field (e.g., Chevalier \& Fransson 1994; Chugai 2001). Furthermore, it was suggested that hydrogen-poor superluminous SNe are powered by interaction (Quimby et al. 2011; Chevalier \& Irwin 2011; see a review by Gal-Yam 2012), as well as some other rare types of SNe (e.g., Ben-Ami et al. 2013). Here we perform a simple test of the interaction model for SNe~IIn, by searching for a correlation between the rise time and peak luminosity. Indeed, we find a possible correlation between these properties. However, we stress that other models that can produce this correlation cannot yet be ruled out. We present our SN sample and observations in \S\ref{sec:Observations}, and review the predictions in \S\ref{Pred}. The data are analyzed in \S\ref{Analysis}, and we discuss the results in \S\ref{Disc}. | \label{Disc} There is a growing line of evidence that SNe~IIn are embedded in a large amount of CSM ejected months to years prior to their explosions (e.g., Dopita et al. 1984; Weiler et al. 1991; Chugai \& Danziger 1994; Smith et al. 2008; Gal-Yam \& Leonard 2009; Kiewe et al. 2012; Ofek et al. 2013c). In some cases we probably see optical outbursts associated with these mass-loss events (e.g., Foley et al. 2007; Pastorello et al. 2007; Mauerhan et al. 2012; Corsi et al. 2013; Fraser et al. 2013; Ofek et al. 2013b; 2014b). This CSM is likely to be optically thick and lead to luminous and long shock-breakout events (Ofek et al. 2010; Chevalier \& Irwin 2011). For some SNe the early-time light curve is powered by shock breakout in a dense CSM followed by conversion of the kinetic energy to optical luminosity via shock interaction in optically thick regions. In such cases, Svirski et al. (2012) and Ofek et al. (2014a) predicted a relation between the shock-breakout time scale ($t_{{\rm bo}}$), velocity ($v_{{\rm bo}}$), and the SN peak luminosity $L_{{\rm max}}$. Based on a sample of 15 SNe~IIn from PTF/iPTF, we show that there is a possible correlation between their rise time and peak luminosity. Interpreting this correlation in the context of the relation predicted by Ofek et al. (2014a), the deduced lower limits on the shock velocity are consistent with the expected shock velocity from SNe (i.e., on the order of $10^{4}$\,km\,s$^{-1}$). Our findings support the suggestion made by Ofek et al. (2010) and Chevalier \& Irwin (2011) that the early-time light curves of some SNe~IIn are powered by shock breakout in a dense CSM. However, we note that the light curves may be contaminated by additional sources of energy (e.g., radioactivity), adding additional spread into the expected relation. Furthermore, our observations cannot yet be used to rule out other alternatives (at least not without a detailed model in hand). In Figure~\ref{fig:IIn_PeakL_RiseTime} there is a puzzling deficiency of objects around $L_{0} \approx 10^{45}$\,erg\,s$^{-1}$, and maybe also some concentration of events with $L_{0}\approx 4\times10^{44}$\,erg\,s$^{-1}$. We note that comparison of the $L_{{\rm max}}$ distribution of our sample and that of 11 SNe~IIn reported by Kiewe et al. (2012) suggests that this feature may be caused by small-number statistics (Fig.~\ref{fig:te_Lp_corr}). Finally, we propose that application of this test to other classes of SNe can be used to rule out the hypothesis that they are powered by interaction of their ejecta with a dense CSM. | 14 | 4 | 1404.4085 |
1404 | 1404.6339_arXiv.txt | Depolarizing collisions are elastic or quasielastic collisions that equalize the populations and destroy the coherence between the magnetic sublevels of atomic levels. In astrophysical plasmas, the main depolarizing collider is neutral hydrogen. We consider depolarizing rates on the lowest levels of neutral and singly ionized alkaly-earths Mg~{\sc i}, Sr~{\sc i}, Ba~{\sc i}, Mg~{\sc ii}, Ca~{\sc ii}, and Ba~{\sc ii}, due to collisions with H$^\circ$. We compute {\em ab initio} potential curves of the atom-H$^\circ$ system and solve the quantum mechanical dynamics. From the scattering amplitudes we calculate the depolarizing rates for Maxwellian distributions of colliders at temperatures $T\leq $10000~K. A comparative analysis of our results and previous calculations in the literature is done. We discuss the effect of these rates on the formation of scattering polarization patterns of resonant lines of alkali-earths in the solar atmosphere, and their effect on Hanle effect diagnostics of solar magnetic fields. | Since the discovery of the linearly polarized component of the Fraunhofer spectrum observed close to the solar limb \citep{Stenflo+83a, Stenflo+83b}, much effort has been devoted to understand the physical mechanisms involved in its formation, which is dominated by scattering in the continuum and spectral lines \citep[][]{Stenflo94, Stenflo97, TrujilloLandi97, FluriStenflo99, Trujillo+02b, Innocenti:04}. Special attention has received, observationally and theoretically, the influence of weak or tangled magnetic fields on resonance line polarization through the Hanle effect \cite[][]{MoruzziStrumia91}, which has opened a new diagnostic window for the magnetism in the solar atmosphere \cite[e.g., ][]{Stenflo82, Stenflo91, Leroy89, Bommier+94, Faurobert93, Faurobert+95, Lin+98, Trujillo01, TrujilloManso02, LopezAristeCasini05, Trujillo+05}. By contrast, elastic depolarizing collisions have received relatively little attention in this context, a neglect motivated by their apparent lack of diagnostic value. However, collisions compete with magnetic fields to depolarize the atomic levels, which must be properly accounted for to calibrate Hanle effect diagnostic techniques; besides, by broadening the atomic energy levels, they modulate the magnetic field strength at which the Hanle effect is sensitive \citep{Lamb70}. Alkaline-earth metals, atomic and singly ionized, show some of the strongest resonant lines in the Fraunhofer spectrum and their resonance polarization patterns have proved remarkable too. Their interpretation has posed important theoretical challenges. Thus, the Ca~{\sc ii} infrared triplet and the Mg~{\sc i} $b$-lines \citep[][]{Stenflo+00} provided the first clear manifestation of the presence of atomic polarization in metastable levels in the solar chromosphere \citep[][{ consistently with our results here, see Section 4}]{MansoTrujillo03, Trujillo01}; the polarization pattern around the $H$- and $K$-lines of Ca~{\sc ii} \citep{Stenflo+80, Stenflo80}, and the $h$ and $k$-lines of Mg~{\sc ii} \citep{HenzeStenflo87}, arise from the interference between the upper ${}^2P$ levels \citep{Stenflo80, BelluzziTrujillo12}. { Resonance lines of alkali-earths have proved essential to diagnose} unresolved fields in the solar atmosphere. The remarkable scattering polarization signal in the Sr~{\sc i} at 460.7~nm \citep{Stenflo+80, Faurobert+01, BommierMolodij02}, in particular, has been extensively observed with the aim of diagnosing tangled magnetic fields in the solar atmosphere \citep{Stenflo82, Faurobert93, Faurobert94, Faurobert+95, Bianda+99, Trujillo+04}. Depolarizing collisions in alkali and alkaline earth atoms with a foreign noble gas have been throughly studied theoretically and experimentally \citep[see][and references therein]{LambterHaar71, Omont77, Baylis78}. However, in the solar atmosphere the most important depolarizing collider is neutral hydrogen \citep{Lamb70}. Rough estimates for the depolarizing rates can be obtained from a dipole-dipole van der Waals approximation for the atom-H$^\circ$ \citep[][see also Landi Degl'Innocenti \& Landolfi 2004]{LambterHaar71}. More recently, \cite{Derouich+03, Derouich+03b, Derouich+04, Derouich+04b, Derouich+05, DerouichBarklem07} used {\em ab initio} interaction potentials and a semi-classical approach using straight line trajectories at different impact parameters. \cite{Kerkeni+00, Kerkeni02, KerkeniBommier02, Kerkeni+03} have calculated depolarizing rates with neutral hydrogen with a fully quantum mechanical approach for the interaction Hamiltonian and dynamics. We follow a similar approach here. We computed {\em ab initio} potential curves of the atom-H$^\circ$ system and then solved the dynamics within the scattering matrix formalism. From them, we calculated the depolarizing collision rates for a Maxwellian distribution of colliders. The most important results of the present work are summarized in Table~\ref{depolarization-constants}, which gives the depolarizing rates for the lowest-lying energy levels of Mg~{\sc i}, Sr~{\sc i}, Ba~{\sc i}, Mg~{\sc ii}, Ca~{\sc ii}, and Ba~{\sc ii}. Figure~\ref{sunny} shows the relative importance of these depolarizing rates in the solar atmosphere as compared to the radiative (polarizing) rates in the main resonance lines of these atoms and ions (Figure~\ref{solar-transitions}). The next section introduces the general theoretical framework used and Section~3 details the calculations performed for each individual atom and ion considered. The impact on the formation of the scattering polarization patterns in the solar atmosphere is discussed in Section~4. \begin{figure}[t] \centering\includegraphics[scale=0.8]{fig1.ps} \caption{\label{solar-transitions} Partial Grotrian diagrams with the lowest energy levels of the most abundant alkaline earth metals. All levels (except the ${}^2S$ and ${}^2D$ terms of the Mg~{\sc i} at 8.6 and 8.8 ev) and resonance transitions between them considered in this work are represented. The fine structure energy splitting in Mg and Ca are exaggerated for clarity.} \vspace*{0.5cm} \end{figure} | The main results of this work are summarized in Table~\ref{depolarization-constants} and Figure~\ref{sunny}. Table~\ref{depolarization-constants} gives the effective depolarizing collisional rates averaged over a Maxwellian distribution of velocities for the colliders ($T\leq 10000$~K), for low lying levels of four neutral and singly ionized alkalines of astrophysical relevance. The $C^{(K)}(\alpha J'\leftarrow \alpha J )$ collisional rates needed to solve the master equations, Eq.(\ref{master-equation-densities}), with the radiative terms required for a complete treatment, have been fitted and the corresponding parameters are listed in the appendix. The cross-sections have been computed from interatomic potentials calculated using the most up-to-date {\it ab initio} methods using an adiabatic approach, and the rates using a quantum time-independent close coupling approach. For the excited electronic states there are many curve crossing with ionic states which introduce complicated features in the energy curves considered. At these crossings there are non-adiabatic couplings which may induce inelastic transitions among different $L,S_A$ manifolds. Because of the many crossings observed in this work, it is concluded that it is necessary to go beyond the adiabatic quantum {\it ab initio} method used here or the diabatic semiclassical method \citep{Brueckner:71,Anstee-Omara:95,Derouich+03} in order to incorporate inelastic transitions for these kind of systems, in order to get more realistic results. Figure~\ref{sunny} summarizes the relative importance of the depolarizing collisions and the (polarizing) radiative rates in the solar atmosphere. We have considered the effect of depolarizing collisions on the polarization pattern of resonance lines of the studied species. | 14 | 4 | 1404.6339 |
1404 | 1404.2206_arXiv.txt | We investigate the dependence of the Vainshtein screening mechanism on the cosmic web morphology of both dark matter particles and halos as determined by ORIGAMI. Unlike chameleon and symmetron screening, which come into effect in regions of high density, Vainshtein screening instead depends on the dimensionality of the system, and screened bodies can still feel external fields. ORIGAMI is well-suited to this problem because it defines morphologies according to the dimensionality of the collapsing structure and does not depend on a smoothing scale or density threshold parameter. We find that halo particles are screened while filament, wall, and void particles are unscreened, and this is independent of the particle density. However, after separating halos according to their large scale cosmic web environment, we find no difference in the screening properties of halos in filaments versus halos in clusters. We find that the fifth force enhancement of dark matter particles in halos is greatest well outside the virial radius. We confirm the theoretical expectation that even if the internal field is suppressed by the Vainshtein mechanism, the object still feels the fifth force generated by the external fields, by measuring peculiar velocities and velocity dispersions of halos. Finally, we investigate the morphology and gravity model dependence of halo spins, concentrations, and shapes. | The late time acceleration of the Universe is one of the most intriguing mysteries of modern cosmology. The acceleration could simply be caused by the cosmological constant, or alternatively, modifications to General Relativity (GR) on cosmological scales may account for the acceleration. The main problem of modified gravity models is that new degrees of freedom are introduced when GR is modified. These new degrees of freedom are generally scalar degrees of freedom, and they mediate the so-called ``fifth force,'' which is strongly constrained by the solar system experiments. There has been interesting progress in developing ``screening'' mechanisms to suppress scalar interactions on solar system scales. Screening mechanisms invoke non-linearity in the field equations and change the behaviour of the fifth force in high density regions. For example, the chameleon mechanism makes the mass of the field large in high density environments \cite{Khoury:2003rn} whereas the symmetron mechanism changes its coupling to matter \cite{Hinterbichler:2010es}. One of the oldest ideas to suppress the fifth force is the Vainshtein screening mechanism \cite{Vainshtein}, originally discovered in the context of massive gravity. Massive gravitons have five polarisations instead of the two in GR, and the helicity-0 mode mediates the fifth force. In a linear approximation, this helicity-0 mode does not decouple in the massless limit, leading to the so-called van Dam-Veltman-Zakharov discontinuity \cite{vanDam, Zakharov}. This problem can be solved by the Vainshtein mechanism. If the graviton mass is small, the derivative self-interactions of the helicity-0 mode become important at much larger distances compared with the Schwarzschild radius of a source, and they suppress the coupling of the helicity-0 mode to matter. The key feature of this mechanism is that derivative self-interactions of the scalars are responsible for hiding the fifth force. We do not require any particular form of the scalar potential and any couplings of the scalar to matter, unlike the chameleon and symmetron mechanisms. In a simple extension of the Fierz-Pauli massive gravity \cite{Fierz}, the non-linear interactions involve higher derivatives, and this leads to the Boulware-Deser ghost \cite{Boulware}. The non-linear interactions that give an equation of motion containing only up to second derivatives have been constructed imposing a Galilean symmetry \cite{Nicolis:2008in}, and this has led to the discovery of a Boulware-Deser \cite{Boulware} ghost-free massive gravity theory \cite{drgt}. The Vainshtein mechanism occurs not only in massive gravity \cite{Koyama:prd, Koyama:Vainshtein} but also in galileon cosmology \cite{Chow:2009fm, Silva:2009km} and braneworld models. Indeed it is in the braneworld model of Dvali, Gabadadze, and Porrati (DGP) \cite{Dvali:2000hr} that it has been best studied. See Ref.~\cite{Babichev:2013usa} for a review and references therein. Interestingly, these screening mechanisms are distinguished by how screened bodies fall in external fields \cite{Hui:2009kc}. As a consequence of universal coupling, all un-self-screened test bodies fall in the same way and obey a microscopic equivalence principle. In the chameleon and symmetron models, screened bodies do not respond to external fields while in the Vainshtein mechanism they do, as long as those fields have wavelengths long compared to the Vainshtein radius \cite{Hui:2012jb}. These differences arise because of the non-superimposability of field solutions. Also, the peculiar structure of the non-linear interactions in the Vainshtein mechanism implies that the screening depends on the dimensionality of the system. For example, the Vainshtein mechanism does not work at all in one-dimensional systems \cite{Brax:2011sv}. The potential dimensionality dependence of the Vainshtein screening mechanism motivates us to look for its signatures in the cosmic web of large scale structure. On very large scales, the distribution of matter in the present-day Universe forms into complex, interconnected, hierarchical structures composed of voids, walls or sheets, filaments, and halos or knots. While voids are underdense regions and halos are density peaks, it is now understood that density alone is not the salient feature that distinguishes these structures. Rather, it is the dynamics of the nonlinear gravitational collapse that fundamentally distinguishes between expanding voids, walls collapsing along one dimension, filaments collapsing along two, and halos collapsing along three orthogonal dimensions \cite{Zeldovich:1969sb, Klypin, Bond:1995yt, AragonCalvo:2007mk, Hahn:2006mk, Falck, Hoffman:2012ft}. While the chameleon mechanism has been found to depend on the density of the halo environment \cite{Zhao:2011cu}, the dimensionality dependence of the Vainshtein mechanism suggests it may depend instead on the morphology of the cosmic web. In this paper, we study how the Vainshtein mechanism operates to hide the fifth force in the cosmic web of large scale structure using cosmological $N$-body simulations. The most general effective theory in four dimensions without involving higher derivative operators was derived in Ref.~\cite{Koyama:2013paa}. Although there are many parameters in this effective theory, the stability condition around the spherically symmetric solutions significantly restricts the available parameter space. For this study, we focus on the simplest non-linear operator, the cubic Galileon term, which appears in the DGP braneworld and galileon models~\cite{Barreira:2013eea}. We consider the normal branch DGP model where the background expansion history is exactly the same as LCDM to disentangle the effects of different cosmological backgrounds and those of the Vainshtein mechanism. The paper is organised as follows. In section II, we introduce a normal branch DGP model and describe the evolution of the background cosmology and quasi-static perturbations. We provide spherically symmetric solutions for a dark matter halo described by the NFW profile~\cite{Navarro:1996gj}. Then we describe our $N$-body simulations in detail. In section III, we study the fifth forces acting on dark matter particles. We describe the ORIGAMI method of Ref.~\cite{Falck} to identify the morphology of dark matter particles and study the dependence of the Vainshtein mechanism on the morphology. In section IV, we study dark matter halos. We first identify dark matter halos using the ORIGAMI code, determine their cosmic web environment, and study the screening of dark matter halos. We then study velocity dispersions and peculiar velocities of halos to investigate how screened bodies respond to external fields. Finally, we study the morphological environment and screening dependence of various halo properties by cross-matching ORIGAMI halos with halos found using the AHF code~\cite{Gill:2004km,Knollmann:2009pb}. Section V is devoted to conclusions. | We have studied how the Vainshtein mechanism hides the fifth force in cosmological $N$-body simulations. By identifying the cosmic web morphology of dark matter particles with ORIGAMI, we showed that the Vainshtein mechanism operates effectively to screen halo particles while leaving filament, wall, and void particles unscreened, and this effect is independent of density. Since ORIGAMI morphology is defined according to the dimensionality of the dynamical collapse of individual particles, this means that dark matter particles collapsing along only two or one orthogonal axes feel the full fifth force even if they are in high density environments. This highlights a key difference between Vainshtein screening and chameleon or symmetron mechanisms. With the hope of finding an observable signature of the dimensionality dependence of the Vainshtein mechanism, we determined the cosmic web morphology of dark matter halos, which we found to be primarily situated in filaments and clusters. We calculated the ratio of the fifth force to Newtonian force, $\Delta_M$, both as a function of radius from halo centres and as a function of halo mass. Though most halo particles are screened and most filament particles are unscreened, the halos in filaments feel the same fifth force as the halos in clusters. For both cluster and filament halos, $\Delta_M$ is very close to zero until beyond the virial radius and is largest well outside, out to 10 times the virial radius, in good agreement with the theoretical prediction for a NFW halo profile. The average $\Delta_M$ for each halo shows no dependence on either halo mass or cosmic web environment, but it is larger for nDGP models that deviate more strongly from GR. Another interesting feature of the Vainshtein mechanism is how, in contrast with chameleon and symmetron screening mechanisms, a screened body can still feel the fifth force generated by external fields as long as its wavelength is long compared to the Vainshtein radius. We tested this by measuring the peculiar velocities of dark matter halos and velocity dispersions within the virial radius. We found that, consistent with theoretical expectations, the ratio of nDGP to LCDM peculiar velocities is enhanced by the linear fifth force induced by large scale structure, while the ratio of velocity dispersions is suppressed inside the halo by the Vainshtein mechanism. Finally, we studied the morphology and gravity model dependence of the concentrations, spins, and shapes of dark matter halos. We found that cluster halos below $\sim 10^{12}\,h^{-1}\,{\rm M}_{\astrosun}$ have slightly higher concentrations than filament halos of the same mass, but this difference is about the same for the LCDM and nDGP simulations. The uncertainties are large, and the morphology dependence of halo concentrations is not well understood even in LCDM. The distributions of halo spins suggest that cluster halos are slightly skewed toward having larger spin, though this effect is small and likely insignificant; additionally we found no significant difference between the spin distributions of LCDM and nDGP halos. We again find no significant difference, and large scatter, between LCDM and nDGP halo shapes; however, the mean values of the axis ratios suggest that cluster halos are slightly more spherical than filament halos. In all of these cases, measuring the halo properties is fraught with difficulties, from halo relaxation, to substructure, to methods of calculation, and the dependence of halo properties on their cosmic web morphology is not well understood even for LCDM simulations. When properties are measured in the inner regions of the halos, the screening mechanism is sure to come into effect such that deviations from GR are hard to identify. It is in the outer regions of the halo, beyond the virial radius and out to the caustic or turn-around radius, where modified gravity signatures have a better chance of being detected. Further studies of the morphological dependence of halo properties, both in LCDM and in modified gravity models with the Vainshtein mechanism, would benefit from a larger suite of high resolution, multiple realisation simulations for better statistics. While it is unfortunate that the morphology dependence of Vainshtein screening for dark matter particles does not appear to hold for dark matter halos, it may be possible to come up with ways of exploiting this feature by tracing along filaments found in the galaxy distribution. Though the galaxies themselves would live in screened dark matter halos, the filament itself may induce a lensing signature (see for example~\cite{Clampitt:2014lna, Higuchi:2014eia}), which may be affected by the enhanced gravity in the filaments in models with the Vainshtein mechanism. Another promising area of future work would be the effect of the Vainshtein mechanism on the properties of voids and of halos found in voids, which has been studied so far in $f(R)$ gravity models with the chameleon screening mechanism (see, e.g.,~\cite{Li:2011pj}). It has been found that there are significant differences in the distribution (by volume) of voids in LCDM and $f(R)$ models, and that halos in voids are significantly less screened. Studies of voids in simulations require large box sizes to accurately capture large voids, which are more likely to be observable than small voids, and studies of halos in voids require very high resolution to resolve these usually very small halos. With the types of simulations presented here, we will be able to disentangle the effect of the background expansion from the effect of Vainshtein screening mechanism on the properties of cosmic voids. The Vainshtein parameters for the simulations in this work were tuned such that they result in the same $\sigma_8$ as specific parameters in the Hu-Sawicki $f(R)$ model. This means that in addition to being able to separate the effects of the cosmological background from the screening, we can directly compare the Vainshtein simulations to simulations of models with the chameleon screening mechanism. The difference between how the Vainshtein and chameleon mechanisms depend on the cosmic web morphology and the environmental density of dark matter particles and halos could provide clues as to how to observationally distinguish between these two different ways of hiding the fifth force in modified gravity models. | 14 | 4 | 1404.2206 |
1404 | 1404.3799_arXiv.txt | We present scale-dependent measurements of the normalised growth rate of structure $f\sigma_{8}(k, z=0)$ using only the peculiar motions of galaxies. We use data from the 6-degree Field Galaxy Survey velocity sample (6dFGSv) together with a newly-compiled sample of low-redshift $(z < 0.07)$ type Ia supernovae. We constrain the growth rate in a series of $\Delta k \sim 0.03 h{\rm Mpc^{-1}}$ bins to $\sim35\%$ precision, including a measurement on scales $>300 h^{-1}{\rm Mpc}$, which represents one of the largest-scale growth rate measurement to date. We find no evidence for a scale dependence in the growth rate, or any statistically significant variation from the growth rate as predicted by the {\it Planck} cosmology. Bringing all the scales together, we determine the normalised growth rate at $z=0$ to $\sim15\%$ in a manner {\it independent} of galaxy bias and in excellent agreement with the constraint from the measurements of redshift-space distortions from 6dFGS. We pay particular attention to systematic errors. We point out that the intrinsic scatter present in Fundamental-Plane and Tully-Fisher relations is only Gaussian in logarithmic distance units; wrongly assuming it is Gaussian in linear (velocity) units can bias cosmological constraints. We also analytically marginalise over zero-point errors in distance indicators, validate the accuracy of all our constraints using numerical simulations, and demonstrate how to combine different (correlated) velocity surveys using a matrix `hyper-parameter' analysis. Current and forthcoming peculiar velocity surveys will allow us to understand in detail the growth of structure in the low-redshift universe, providing strong constraints on the nature of dark energy. | \label{sec:intro} A flat universe evolved according to the laws of General Relativity (GR), including a cosmological constant $\Lambda$ and structure seeded by nearly scale-invariant Gaussian fluctuations, currently provides an excellent fit to a range of observations: cosmic microwave background data (CMB) \citep{Collaboration:2013qf}, baryon acoustic oscillations (BAO) \citep{2013arXiv1303.4666A, Blake:2011kl}, supernova observations \citep{2011ApJS..192....1C, Freedman:2012bs,Ganeshalingam:2013kx}, and redshift-space distortion (RSD) measurements \citep{2011MNRAS.415.2876B, Reid:2012ij}. While the introduction of a cosmological constant term allows observational concordance by inducing a late-time period of accelerated expansion, its physical origin is currently unknown. The inability to explain the origin of this energy density component strongly suggests that our current understanding of gravitation and particle physics, the foundations of the standard model of cosmology, may be significantly incomplete. Various mechanisms extending the standard model have been suggested to explain this acceleration period such as modifying the Einstein-Hilbert action by e.g. considering a generalised function of the Ricci scalar \citep{RevModPhys.82.451}, introducing additional matter components such as quintessence models, and investigating the influence structure has on the large-scale evolution of the universe \citep{Clifton:2013kx,Wiltshire:2013vn}. Inhomogeneous structures in the late-time universe source gravitational potential wells that induce `peculiar velocities' (PVs) of galaxies, i.e., the velocity of a galaxy relative to the Hubble rest frame. The quantity we measure is the line-of-sight PV, as this component produces Doppler distortions in the observed redshift. Determination of the line-of-sight motion of galaxies requires a redshift-independent distance estimate. Such estimates can be performed using empirical relationships between galaxy properties such as the `Fundamental Plane' or `Tully-Fisher' relation, or one can use `standard candles' such as type Ia supernovae \citep{Colless:2001fk,Springob:2007zr, Magoulas:2009vn,Turnbull:2011qf}. A key benefit of directly analysing PV surveys is that their interpretation is independent of the relation between galaxies and the underlying matter distribution, known as `galaxy bias' \citep[][]{gbias1}. The standard assumptions for galaxy bias are that it is local, linear, and deterministic \citep{1993ApJ}; such assumptions may break down on small scales and introduce systematic errors in the measurement of cosmological parameters \citep[e.g.][]{Cresswell:2008dz}. Similar issues may arise when inferring the matter velocity field from the galaxy velocity field: the galaxy velocity field may not move coherently with the matter distribution, generating a `velocity bias'. However such an effect is negligible given current statistical errors \citep{Desjacques:2009fk}. Recent interest in PV surveys has been driven by the results of \citet{Watkins:2008kx}, which suggest that the local `bulk flow' (i.e. the dipole moment) of the PV field is inconsistent with the predictions of the standard $\Lambda$CDM model; other studies have revealed a bulk flow more consistent with the standard model \citep{Ma:2012vn}. PV studies were a very active field of cosmology in the 1990s as reviewed by \citet{willic} and \citet{kaiser88}. {Separate to the measurement of the bulk flow of local galaxies, a number of previous studies have focused on extracting a measurement of the matter power spectrum in $k$-dependent bins \citep[for example see,][]{1995ApJ...455...26J,Freudling:1999cr,2000ASPC..201..262Z,Zaroubi:2001dq, Silberman:2001ve,Macaulay:2011bh}. This quantity is closely related to the velocity power spectrum. Other studies have focused on directly constraining standard cosmological parameters \citep{Gordon:2007dq, Abate:2009ly}.} The quantity we can directly measure from the 2-point statistics of PV surveys is the velocity divergence power spectrum\footnote{Note in this analysis we will constrain the `velocity power spectrum' which we define as a rescaling of the more conventional velocity divergence power spectrum (see Section \ref{sec2}).}. The amplitude of the velocity divergence power spectrum depends on the rate at which structure grows and can therefore be used to test modified gravity models, which have been shown to cause prominent distortions in this measure relative to the matter power spectrum \citep{Jennings:2012zr}. In addition, by measuring the velocity power spectrum we are able to place constraints on cosmological parameters such as $\sigma_{8}$ and $\Omega_{\rm m}$ (the r.m.s of density fluctuations, at linear order, in spheres of comoving radius $8 h^{-1}{\rm Mpc}$; and the fractional matter density at $z=0$ respectively). Such constraints provide an interesting consistency check of the standard model, as the constraint on $\sigma_{8}$ measured from the CMB requires extrapolation from the very high redshift universe. The growth rate of structure $f(k,a)$ describes the rate at which density perturbations grow by gravitational amplification. It is generically a function of the cosmic scale factor $a$, the comoving wavenumber $k$ and the growth factor $D(k,a)$; expressed as $f(k,a) \equiv d \ln D(k,a) /d \ln a $. We define $\delta(k,a) \equiv \rho(k, a) /{\bar\rho(a)} -1$, as the fractional matter over-density and $ D(k,a) \equiv \delta(k,a)/ \delta(k,a=1)$. The temporal dependence of the growth rate has been readily measured (up to $z \sim 0.9$) by galaxy surveys using redshift-space distortion measurements \citep[][]{2013arXiv1312.4611B, 2011MNRAS.415.2876B, Torre:2013fu}, while the spatial dependence is currently only weakly constrained\footnote{ A scale dependent growth rate can be indirectly tested using the influence the growth rate has on the halo bias e.g. \citet{Parfrey:2010ys}.}, particularly on large spatial scales \citep[][]{2010PhRvD..81h3534B,2013JCAP...02..007D}. {The observations are in fact sensitive to the `normalized growth rate' $f(k,z)\sigma_8(z)$, which we will write as $f\sigma_8(k,z) \equiv f(k,z)\sigma_8(z)$.} Recent interest in the measurement of the growth rate has been driven by the lack of constraining power of geometric probes on modified gravity models, which can generically reproduce a given expansion history (given extra degrees of freedom). Therefore, by combining measurements of geometric and dynamical probes strong constraints can be placed on modified gravity models \citep{2005PhRvD..72d3529L}. A characteristic prediction of GR is a scale-independent growth rate, while modified gravity models commonly induce a scale-dependence in the growth rate. For $f(R)$ theories of gravity this transition regime is determined by the Compton wavelength scale of the extra scalar degree of freedom \citep[for recent reviews of modified gravity models see ][]{Clifton:2011nx,2010LNP...800...99T}. Furthermore, clustering of the dark energy can introduce a scale-dependence in the growth rate \citep{Parfrey:2010ys}. Such properties arise in scalar field models of dark energy such as quintessence and k-essence \citep{Caldwell:1998uq,Armendariz-Picon:2000fk}. The dark energy fluid is typically characterised by the effective sound speed $c_{s}$ and the transition regime between clustered and smooth dark energy is determined by the sound horizon \citep{Hu:2004fk}. The clustering of dark energy acts as a source for gravitational potential wells; therefore one finds the growth rate enhanced on scales above the sound horizon. In quintessence models $c_{s}^{2} =1$; therefore the sound horizon is equal to the particle horizon and the effect of this transition is not measurable. Nevertheless, in models with a smaller sound speed ($c_{s}^{2} \ll 1$) such as k-essence models, this transition may have detectable effects\footnote{ The presence of dark energy clustering requires some deviation from $w=-1$ in the low redshift universe.}. Motivated by these arguments we introduce a method to measure the scale-dependence of the growth rate of structure using PV surveys. Observations from PVs are unique in this respect as they allow constraints on the growth rate on scales inaccessible to RSD measurements. This sensitivity is a result of the relation between velocity and density modes $v(k,z) \sim \delta(k,z)/k$ which one finds in Fourier space at linear order \citep{Dodelson-Cosmology-2003}. The extra factor of $1/k$ gives additional weight to velocities for larger-scale modes relative to the density field. A further advantage arises because of the low redshift of peculiar velocity surveys, namely that the Alcock-Paczynsi effect -- transforming the true observables (angles and redshifts) to comoving distances -- only generates a very weak model dependence. A potential issue when modelling the velocity power spectrum is that it is known to depart from linear evolution at a larger scale than the density power spectrum \citep{Scoccimarro:2004ij, Jennings:2010ys}. We pay particular attention to modelling the non-linear velocity field using two loop multi-point propagators \citep{Bernardeau:2008fk}. Additionally, we suppress non-linear contributions by smoothing the velocity field using a gridding procedure. Using numerical $N$-body simulations we validate that our constraints contain no significant bias from non-linear effects. For our study we use the recently compiled 6dFGSv data set along with low-redshift supernovae observations. The 6dFGSv data set represents a significant step forward in peculiar velocity surveys; it is the largest PV sample constructed to date by a factor of $\sim 3$, and it covers nearly the entire southern sky. We improve on the treatment of systematics and the theoretical modelling of the local velocity field, and explore a number of different methods to extract cosmological constraints. We note that the 6dFGSv data set will also allow constraints on the possible self-interaction of dark matter \citep{Linder:2013ve}, local non-Gaussianity \citep{Ma:2013qf}, and the Hubble flow variance \citep{Wiltshire:2012bh}. The structure of this paper is as follows. In Section \ref{sec1} we introduce the PV surveys we analyse; Section \ref{sec2} describes the theory behind the analysis and introduces a number of improvements to the modelling and treatment of systematics effects. We validate our methods using numerical simulations in Section \ref{sec:sim}; the final cosmological constraints are presented in Section \ref{sec:results}. We give our conclusion in Section \ref{sec:con}. | \label{sec:con} We have constructed 2-point statistics of the velocity field and tested the $\Lambda$CDM cosmology by using low-redshift 6dFGSv and Type-Ia supernovae data. We summarise our results as follows: \begin{itemize} \item{We introduced and tested a new method to constrain the scale-dependence of the normalized growth rate using only peculiar velocity data. Using this method we present the {\it largest-scale} constraint on the growth rate of structure to date. For length scales greater than $\sim 300h^{-1}\rm{Mpc}$ ($k < 0.02h{\rm Mpc^{-1}}$) we constrain the growth rate to $\sim 30\%$. Specifically, we find for 6dFGSv, which provides our best constraints, $f\sigma_{8}(k<0.02h\rm{Mpc}^{-1}) = 0.72^{+0.17}_{- 0.23}$. This result is consistent with the standard model prediction of $f\sigma_{8}(z=0)= 0.4439$, albeit higher than expected.} \vspace{0.10cm} \item{Examining the scale-dependence of the growth rate of structure at $z=0$ we find the constraints $f\sigma_{8}(k_{i})=[ 0.79^{ {+0.21}}_{ {-0.25}}, 0.30^{ {+0.14}}_{ {-0.19}}, 0.32^{ {+0.19}}_{ {-0.15}}, 0.64^{ {+0.17}}_{ {-0.16}}, 0.48^{ {+ 0.22}}_{ {-0.21}}]$ using the wavenumber ranges $k_{1} \equiv [0.005,0.02]$, $k_{2} \equiv [0.02,0.05]$, $k_{3} \equiv [0.05,0.08]$, $k_{4} \equiv [0.08,0.12]$ and $k_{5} \equiv [0.12,0.150]$. We find no evidence for a scale-dependence in the growth rate, which is consistent with the standard model. All the growth rate measurements are consistent with the fiducial {\it Planck} cosmology.}\vspace{0.10cm} \item{Averaging over all scales we measure the growth rate to $\sim 15\%$ which is {\it independent} of galaxy bias. This result $f\sigma_{8}(z=0) = 0.418 \pm 0.065$ is consistent with the redshift-space distortion analysis of 6dFGS which produced a measurement of $f\sigma_{8}(z) = 0.423 \pm 0.055$ \citep{Beutler:2012fk}, increasing our confidence in the modelling of galaxy bias. In addition this measurement is consistent with the constraint given by \citet{2012ApJ...751L..30H} of $f\sigma_{8} = 0.400 \pm 0.07$, found by comparing the local velocity and density fields. In contrast to our constraint this measurement is sensitive to galaxy bias and any systematic errors introduced during velocity field reconstruction.}\vspace{0.10cm} \item{We also consider various other methods to constrain the standard model. We directly constrain the amplitude of the velocity power spectrum ${\mathcal P}_{v v}(k)\equiv {\mathcal P}_{\theta \theta}(k)/k^2$ for the same scale range as specified above; we find that the predictions from two loop multi-point propagators assuming the {\it Planck} cosmology gives an accurate description of the measured velocity power spectrum. Specifically, the derived amplitudes $A_{i}$ of the power spectrum of 4 bins are consistent with the fiducial cosmology at the $1\sigma$ level, and the largest scale bin is consistent at the $2\sigma$ level. We can also compare these constraints to those given by \citet{Macaulay:2011bh}. Similarly to our results they found the amplitude of the matter power spectrum, determined using the composite sample of PVs, to be statistically consistent with the standard $\Lambda$CDM cosmology. In addition they also find on the largest scales a slightly higher amplitude of the power spectrum that expected in the standard model\footnote{Note we cannot directly compare these sets of results given different bin ranges were used.}.}\vspace{0.10cm} \item{We show that when analysing PV surveys with velocities derived using the Fundamental Plane or the Tully-Fisher relation, one should perform the analysis using a variable that is a linear transformation of $x = \log_{10}\left( D_{z} / D_{\rm H} \right)$. We show the intrinsic scatter is not Gaussian for the PV and this can significantly bias cosmological constraints. We show how the analysis can be reformulated using the variable $\delta m$, which removes the bias.} \end{itemize} With a large number of upcoming PV surveys, the prospect for understanding how structure grows in the low-redshift universe is excellent. Future work will move beyond consistency tests by adopting specific modified gravity models and phenomenological parametrisations, including measurements of redshift-space distortions and by self-consistently modifying the growth and evolutionary history of the universe. This will allow a vast range of spatial and temporal scales to be probed simultaneously, providing a strong and unique test of the standard $\Lambda$CDM model, and perhaps even providing some insight on the so-far mysterious dark energy component of the universe. \begin{figure*} \centering \includegraphics[width=12cm]{mcmc_growth_Prob_dis.pdf} \caption{68\% confidence intervals for the normalized growth rate $f(k,z=0)\sigma(z=0)$ for the combined constraints (using no hyper-parameters). The prediction for the growth rate of structure assuming a fiducial {\it Planck} cosmology is given by the solid black line.} \label{plot:growth5_dis} \end{figure*} | 14 | 4 | 1404.3799 |
1404 | 1404.4493_arXiv.txt | \noindent From analytical studies of tidal heating, eclipses and planetary illumination, it is clear that the exomoon habitable zone (EHZ) - the set of moon and host planet orbits that permit liquid water on an Earthlike moon's surface - is a manifold of higher dimension than the planetary HZ. This paper outlines the first attempt to produce climate models of exomoons which possess all the above sources and sinks of energy. We expand on our previous 1D latitudinal energy balance models (LEBMs), which follow the evolution of the temperature on an Earthlike moon orbiting a Jupiterlike planet, by adding planetary illumination. We investigate the EHZ in four dimensions, running two separate suites of simulations. The first investigates the EHZ by varying the planet's orbit, keeping the moon's orbit fixed, to compare the EHZ with planetary habitable zones. In general, planetary illumination pushes EHZs slightly further away from the star. Secondly, we fix the planet's orbit and vary the moon's orbit, to investigate the circumplanetary inner habitable edge. We demonstrate that an outer edge can exist due to eclipses (rather than merely orbital stability), but this edge may be pushed outwards when the effect of the carbonate-silicate cycle is taken into account. | \noindent There are currently no confirmed detections of extrasolar moons (exomoons). The only moons known to humanity thus far are those which reside in our own Solar System. However, there are several proposed methods of detecting exomoons within the ability of current instrumentation, amongst which are: exoplanet transit timing and duration variations \citep{Simon2007, Kipping2009, Heller2014b}; microlensing \citep{Liebig2010}; and direct imaging, provided that the moon is strongly heated by tidal forces \citep{Peters2013}. The Hunt for Exomoons with Kepler team \citep{Kipping2012} are now attempting to make such a detection using transit data from the Kepler Space Telescope. Any first detection is likely to lie at the very edge of instrumental ability, and as such the primary objective of current missions is to establish upper limits on the occurrence rate of satellites in their samples (cf \citealt{Weidner2010,Montalto2012,Kipping2013a, Kipping2014}). As observers continue to reduce these upper limits, it is reasonable to expect that detections of exomoons will soon follow. If these exomoons are Earthlike, and the host planet orbits in the habitable zone (HZ) of their parent star, then it is possible that the moons themselves are habitable (given other factors which we will discuss below). The HZ concept was originally created to investigate planetary habitability \citep{Huang1959}. Assuming that a planet has Earthlike properties such as mass, atmospheric composition and surface water (amongst others), the HZ is calculated by modelling how stellar radiative flux interacts with the planet's atmosphere, and what equilibrium temperature that planet subsequently adopts. If the temperature is conducive to the surface water being liquid, that planet is said to be within the habitable zone. As it is determined in the first instance by radiative flux, the planetary HZ is a sensitive function of distance from the star, and is a spherical annulus. Planets beyond the inner edge of the HZ will generally suffer water loss by photolysis and hydrogen escape after a runaway greenhouse effect; planets beyond the outer edge of the HZ experience runaway glaciation as $CO_2$ clouds form (see e.g. \citealt{Kasting_et_al_93} and \citealt{Kopparapu2013} for more detail). Moons possess sources and sinks of energy that planets do not. If their orbit around the planet is eccentric, tidal forces can dissipate in the moon's interior, releasing heat. This mechanism allows icy Solar System moons such as Europa \citep{Melosh2004} and Enceladus \citep{plume_enceladus, Iess2014} to possess liquid oceans beneath ice crusts; equally, it can produce extensive volcanism, on moons such as Io \citep{Peale1979,Veeder2012}. The magnitude of such tidal heating, dependent on the gravitational field of the planet and the moon's interaction with it, has important consequences for habitability. The planet's radiation field also plays an important role. This includes both the thermal radiation the planet emits and the starlight reflected by the planet, thanks to its non-zero albedo. If the planet is tidally locked to the star, then the moon will experience a variation in the planet's thermal flux as it orbits it, periodically forcing the climate in ways that planets are unlikely to experience. The spectrum of the planet's radiation is also important - strong EUV or X-Ray radiation can result in catastrophic atmosphere loss \citep{Kaltenegger2000}. These processes are in turn linked to the planet's magnetic field, another factor that can either promote or destroy exomoon habitability depending on the magnetosphere's ability to shield the moon from high energy photons \citep{Heller2013a}. Finally, moons are likely to experience frequent eclipses of starlight due to the host planet, which act as an effective sink of energy. The extent to which eclipses screen stellar flux from the moon is a sensitive function of the moon's orbit about the planet \citep{Heller2012}. In short, it is clear that the planetary HZ and the equivalent lunar HZ will differ in their spatial extent, as well as in the factors that determine that spatial extent. \citet{Reynolds1987} demonstrated that Europa presented a viable niche for terrestrial marine life, and proposed a circumplanetary habitable zone determined by tidal heating. \citet{Williams1997b} considered potential sites for the first exomoons, albeit from the then-limited sample of known exoplanets, where they considered the risks of the moon becoming tidally locked, the potentially hazardous local radiation environment and the (over-)abundance of volatiles. \citet{Scharf2006} used a more populous exoplanet sample to consider potential habitable exomoon hosts. Estimating that around 30\% of the population could host icy moons amenable to subsurface oceans via tidal heating, the main consequence was an extension of the combined exoplanet/exomoon HZ by a factor of almost 2 (if one is willing to accept heating levels significantly larger than Io, which is likely to have other negative consequences). \citet{Heller2013} constructed models of the insolation received by an exomoon in orbit of a tidally locked exoplanet. These models calculated the flux as a function of moon surface longitude and latitude, taking into account direct stellar radiation, eclipses, planetary radiation and tidal heating, demonstrating that there is indeed an inner circumplanetary ``habitable edge'', beyond which moons are heated too strongly (either by tidal heating or planetary illumination) to avoid becoming uninhabitable. Later modelling \citep{Hinkel2013} has shown that, much as planets need not spend their entire orbit within the HZ to be habitable themselves \citep{Williams_and_Pollard_02,Kane2012,Kane2012c}, exoplanets hosting exomoons need not spend their entire orbit within the planetary HZ for the exomoon to be habitable, depending on the moon's heat redistribution efficiency. In a previous paper \citep{Forgan_moon1} we developed a latitudinal energy balance model (LEBM) that described the one-dimensional temperature evolution of an Earthlike moon in orbit of a Jupiterlike planet, which in turn orbits a Sunlike star. Rather than finding an equilibrium surface temperature through analytical calculation, we allow the temperature to evolve due to the radiative flux of the star, tidal heating, eclipses, the moon's albedo, the transfer of heat through the atmosphere, and its loss via infrared radiation. In this paper, we improve our LEBM, by including the planet's thermal blackbody radiation and starlight reflected by the planet. In section \ref{sec:LEBM} we describe the model and the improvements we have made. Section \ref{sec:results} describes the results of two separate suites of simulations, where we investigate the exomoon habitable zone (EHZ) in terms of \begin{enumerate} \item the planet semimajor axis and eccentricity, and \item the moon semimajor axis and eccentricity \end{enumerate} In section \ref{sec:discussion} we discuss the limitations of the model and the implications of the results, and in section \ref{sec:conclusions} we summarise the work. | \label{sec:conclusions} \noindent We have continued our work in 1D latitudinal energy balance models (LEBMs) of exomoon climates, adding in the extra radiation source that is the host planet. The model now incorporates stellar insolation, planetary insolation from thermal blackbody radiation and reflected starlight, tidal heating, eclipses of the star by the planet, diffusion of heat across latitudes and atmospheric cooling. It is the first climate model of its kind to contain all the primary sources and sinks of energy that dictate the radiative energy budget of exomoon systems. We have used this upgraded LEBM to explore the exomoon habitable zone (EHZ), in four dimensions: the planet semimajor axis $a_p$ and eccentricity $e_p$, and the moon semimajor axis $a_m$ and eccentricity $e_m$. In terms of $a_p$ and $e_p$, the EHZ overlaps most of the planetary habitable zone, but is extended marginally outward in $a_p$ by the effect of planetary illumination. In terms of $a_m$ and $e_m$, we find an inner circumplanetary ``habitable edge'' produced by tidal heating and planetary illumination, in line with previous studies \citep{Heller2013,Heller2013b}. However, we also find evidence for an outer circumplanetary habitable edge, defined by eclipses. This is found for large values of $a_p$, and exists at sufficiently low $a_m$ to be well within the orbital stability limit typically used as an outer habitability boundary. To summarise, these models suggest that exomoon climates exhibit even more complex behaviour than was originally believed, and more work is required to determine under what circumstances outer circumplanetary habitable edges exist. | 14 | 4 | 1404.4493 |
1404 | 1404.1080_arXiv.txt | { {We present results from a comprehensive survey of 70 radio galaxies at redshifts 1$<$$z$$<$5.2 using the PACS and SPIRE instruments on-board the \herschel\ {\it Space Observatory}. Combined with existing mid-IR photometry from the \spitzer\ {\it Space Telescope}, published 870\mum\ photometry and new observations obtained with LABOCA on the APEX telescope, the spectral energy distributions (SEDs) of galaxies in our sample are continuously covered across 3.6--870\mum. The total 8-1000\mum\ restframe infrared luminosities of these radio galaxies are such that they almost all are either ultra-(\lirtot$>$10$^{12}$ \lsun) or hyper-luminous (\lirtot$>$10$^{13}$ \lsun) infrared galaxies. We fit the infrared SEDs with a set of empirical templates which represent dust heated (1) by a variety of starbursts (SB) and (2) by an active galactic nucleus (AGN). We find that the SEDs of radio galaxies require the dust to be heated by both AGN and SB, but the luminosities of these two components are not strongly correlated. Assuming empirical relations and simple physical assumptions, we calculate the star formation rate (SFR), the black hole mass accretion rate (\mdotbh), and the black hole mass (\mbh) for each radio galaxy. We find that the host galaxies and their black holes are growing extremely rapidly, having SFR$\approx$100-5000\msunyr and \mdotbh$\approx$1-100\msunyr. The mean specific star formation rates (sSFR) of radio galaxies at $z$$\ga$2.5 are higher than the sSFR of typical star-forming galaxies over the same redshift range but are similar or perhaps lower than the galaxy population for radio galaxies at $z$$\la$2.5. By comparing the sSFR and the specific black hole mass accretion rate, we conclude that black holes in radio loud AGN are already, or soon will be, overly massive compared to their host galaxies in terms of expectations from the local \mbhgal\ relation. In order to ``catch up'' with the black hole, the galaxies require about an order-of magnitude more time to grow in mass, at the observed SFRs, compared to the time the black hole is actively accreting. However, during the current cycle of activity, we argue that this catching-up is likely to be difficult due to the short gas depletion times. Finally, we speculate on how the host galaxies might grow sufficiently in stellar mass to ultimately fall onto the local \mbhgal\ relation.} {}{}{}{} } | At high redshifts, deep sub-mm observations suggest that massive galaxies have high flux densities and vigorous, on-going star formation \citep[e.g.][]{Hughes1998, Barger1998, Stevens2003, Chapman2005, Wardlow2011, Swinbank2014}. The sensitivity of wide-field bolometer arrays limits these studies to only the brightest sub-mm emitters \citep[e.g.][]{Weiss2009}. Such bright sub-mm galaxies (SMGs) frequently appear to be highly disturbed, which favours gas inflows driven by mergers as the chief instigator for generating the high observed sub-mm fluxes \citep[e.g.][]{Somerville2001, Engel2010}. Whether these intense starbursts are indeed driven by mergers or by high rates of cold gas accretion is a question that is still actively debated \citep[e.g.][]{Noeske2007, Daddi2007a, Tacconi2008}. Often, vigorous star formation is accompanied by powerful active galactic nuclei \citep[AGN; e.g.][]{Hopkins2010,Wang2011,Seymour2012,Rosario2012}. The presence of AGN is revealed throughout the electromagnetic spectrum, from X-rays to radio, and in both continuum and line emission \citep[e.g.][]{Carilli1997, Hardcastle1999, Vernet2001, Alexander2005, Ogle2006, Nesvadba2008, Ivison2012,Wang2013}. How AGN are triggered remains one of the most challenging questions of contemporary extragalactic astrophysics \citep[see ][for a recent review]{Alexander2012}. Even if current solutions and simulations are not completely satisfying \citep[e.g.][]{Hopkins2010}, it is evident that the same material, cold molecular gas, is the reservoir out of which stars are formed and the AGN is fuelled \citep[e.g.][]{Hicks2009}. Interestingly, the expected correlation between AGN activity and star-formation rate is not obvious in observations, both locally and at high redshift \citep[e.g.][]{Netzer2009,Hatziminaglou2010,Asmus2011,Dicken2012,Bongiorno2012,Harrison2012,Rosario2012,Rosario2013,Feltre2013,Videla2013,Esquej2014,Leipski2014}. This may be due to high variability of AGN \citep{Hickox2011} or the differences in timescales it takes for gas to become unstable, collapse to form stars over kpc scales compared to the time it takes for gas to lose sufficient angular momentum to reach the inner central parsec of the galaxy \citep{Jogee2005}. Despite our difficulties in understanding how relationships between the host galaxy and super massive black holes come about, we observe a tight correlation between the black hole and the physical properties of their host galaxies in the local universe \citep[e.g.][]{Magorrian1998, Gebhardt2000, Ferrarese2000, Neumayer2004}. These relations suggest that both components of galaxies grew simultaneously \citep[e.g.][]{Hopkins2006p}. Nevertheless, some discrepancies have been observed from the local relation implying either an observational bias or a possible evolution of this relation with redshift \citep[e.g.][]{Lauer2007,Zhang2012}. Currently, there are no complete answers that reconcile all the observations \citep[][for a recent review]{Kormendy2013}. Observations of infrared emission plays a key role in disentangling the relative importance of star formation and AGN to the bolometric emission from galaxies. As the IR emission is a mixture of dust heated by both the stars and the AGN, the nature of the IR spectral energy distribution (SED) can be used to probe the relative growth of galaxies and supermassive black holes and how their growth rates are related (the ``AGN-starburst connection''). The short cooling time of the dust provides us with a snapshot of the heating rate of a galaxy due to the re-emission of absorbed UV and optical photons \citep[e.g.][]{Draine2003}. However, the peak of the IR SED, where both heating of dust grains by AGN and star formation make important contributions, was not completely covered with good sensitivity by \spitzer\ or by ground-based sub-mm photometry for distant galaxies \citep[e.g.][]{Archibald2001, Reuland2004, Cleary2007, DeBreuck2010, Rawlings2013}. \herschel\ now provides the first opportunity to explore the complete IR SED of high redshift AGN, and thus to examine the relative contribution of the AGN and star formation to the bolometric luminosity of galaxies over a wide range of redshift. Powerful radio galaxies are crucial objects in understanding the evolution of massive galaxies. They present all phenomenology undergoing both active star formation and rapidly accreting supermassive black holes. Powerful radio jets, strong and highly ionized optical and near-IR emission lines, and luminous mid-IR continuum, for example, betray the presence of an accreting supermassive black hole \citep[e.g][]{Carilli1997, Vernet2001, Nesvadba2008, DeBreuck2010, Drouart2012, Rawlings2013}. They also have luminous submm emission, which is directly related to their vigorous star formation. Moreover, they have elliptical light profiles \citep{Matthews1964, vanBreugel1998, Pentericci1999,Zirm2003}, are extremely massive \citep{Rocca2004, Seymour2007} and are often associated with high density environments \citep[e.g.][]{Venemans2007,Falder2010,Hatch2011a, Kuiper2011, Galametz2012, Wylezalek2013b}. In other words, they have many hallmarks of a massive (perhaps cluster) galaxy in formation \citep{Miley2008}. By their fortuitous edge-on orientation, the radio galaxies present a dusty torus occulting the light from the hot accretion disk (type 2 AGN), enabling the simultaneous study of the host galaxy and the AGN, more easily than in the case of quasars (i.e. type 1 AGN, for a recent review, see \citealp{Antonucci2011}). Therefore, observing and characterising the different constituents of high redshift radio galaxies appears as our best chance to gain insights on the connection of the galaxy and black hole growth at much earlier stage in their history, more especially during the peak of the cosmic AGN and star formation activity \citep{Hopkins2006a,Aird2010}. Since characterising the host galaxy/BH through dynamic properties at high redshift is observationally expensive \citep{Nesvadba2011}, and beyond the reach of most of the current facilities, one has to rely on energetic diagnostics (such as SED decomposition) and empirical relations \citep[e.g. M$_{\rm BH}$-$\sigma$, M$_{\rm BH}$-M$_{\rm bulge}$, M$_{\rm BH}$-M$_{K}$]{Ferrarese2000,Neumayer2004,Merloni2010} to investigate this (non-)relation during the first half of the history of the Universe in larger samples. In this paper, we analyse the characteristics of the IR SEDs of a sample of 70 powerful radio galaxies spanning the redshift range from 1 to 5.2. This large sample allows us to compare the properties of the IR SED with their other characteristics (e.g. radio luminosities and sizes). The paper is organised as follows: \S~2 outlines the \herschel\ and sub-mm observations and data reduction; \S~3 demonstrates how the photometry was calculated in cases of isolated and blended sources in the \herschel\ images; \S~4 discusses the IR luminosities and the SED fitting procedure which was used to estimate the bolometric, AGN and starburst luminosities; \S~5 compares the IR emission with other properties of the radio galaxies; \S~6 discusses the interpretation of these luminosities in terms of physical parameters allowing us to put new constraints on the evolution of radio galaxies. Throughout this paper, we adopt the concordance cosmological model ($H_0= 70$\,kms$^{-1}$\,Mpc$^{-1}$, $\Omega_{\Lambda}=0.7$, $\Omega_{M}=0.3$). | We present new \herschel\ and sub-mm observations for the HeRG\'E sample consisting on 70 powerful radio galaxies spanning 1$<$$z$$<$5.2. Complemented by other data sets, we now have continuous coverage of the IR spectral energy distribution over the range from 16-870\mum. All galaxies in our sample have integrated IR luminosities L$_{\rm IR}$ $>$ 10$^{12}$\,\lsun, classifying them as ULIRGs, while half of all the sources at $z$$>$2 have L$_{\rm IR}$$>$ 10$^{13}$ L$_{\sun}$ and are HyLIRGs. We use the DecompIR code to decompose the IR SEDs of galaxies in our sample in a robust and uniform way into an AGN and SB components. To make these fits, we assume a single AGN template and a variety of starburst templates. Our results for the AGN contribution are conservative in that we assumed a single template and it is possible that this template could lead to an underestimate of its contribution to the IR SED. The estimated \liragn\ and \lirsb\ from our decomposition imply both high black hole mass accretion rates (1\msunyr$<$\mdotbh$<$100\msunyr) and vigorous on-going star formation (100\msunyr$<$SFR$<$5000\msunyr). Although no strong correlation is detected between these rates, this result implies that both the black hole and its host galaxy are experiencing rapid growth, with the relative growth of the black hole exceeding that of the host galaxy. Assuming empirical relations and basic physical assumptions, we estimate \mbh\ from the stellar masses and infrared AGN luminosities. The black holes appear overly massive compared to their hosts and are likely accreting close to the Eddington limit ($\lambda$$\sim$1), similar to estimates for radio quiet quasars. Alternatively, for lower Eddington rates, the black holes are more massive than predicted by the local M$_{BH}$-M$_{buldge}$ relationship. We derive the specific growth properties, both the specific star formation rate, sSFR, and the specific black hole mass accretion rate, \smdot. Compared to galaxies that lie along the sSFR-stellar mass relation at $z$$\ga$2.5 radio galaxies appear to have higher sSFR. At $z$$\la$2.5, radio galaxies appear have the same or perhaps lower sSFR generally. We explore different scenarios for the future growth of radio galaxies. These scenarios are that high redshift powerful radio galaxies (i) will never land on the \mbhbulge\ relation; (ii) will land on the local \mbhbulge\ relation, but at low redshift; (iii) will land on the \mbhbulge\ on a longer timescale than our estimated $R_{lag}$; or (iv) are indeed experiencing a symbiotic growth. However, observational evidence favours the scenario in which radio galaxies will land again on the \mbhbulge\ relation, but on a long timescale (most probably $>>$100 Myr). | 14 | 4 | 1404.1080 |
1404 | 1404.1613_arXiv.txt | The non-thermal nature of the X-ray emission from the shell-type supernova remnants (SNRs) \gone\ and \gthree\ is an indication of intense particle acceleration in the shock fronts of both objects. This suggests that the SNRs are prime candidates for very-high-energy (VHE; $E > 0.1$\,TeV) \gammaray\ observations. \gone, recently established as the youngest known SNR in the Galaxy, also offers a unique opportunity to study the earliest stages of SNR evolution in the VHE domain. The purpose of this work is to probe the level of VHE \gammaray\ emission from both SNRs and use this to constrain their physical properties. Observations were conducted with the \hess\ (High Energy Stereoscopic System) Cherenkov telescope array over a more than six-year period spanning 2004--2010. The obtained data have effective livetimes of 67\,h for \gone\ and 16\,h for \gthree. The data are analyzed in the context of the multi-wavelength observations currently available and in the framework of both leptonic and hadronic particle acceleration scenarios. No significant \gammaray\ signal from \gone\ or \gthree\ was detected. Upper limits (99\% confidence level) to the TeV flux from \gone\ and \gthree\ for the assumed spectral index $\Gamma = 2.5$ were set at $5.6\times10^{-13}$\,cm$^{-2}$\,s$^{-1}$ above 0.26\,TeV and $3.2\times10^{-12}$\,cm$^{-2}$\,s$^{-1}$ above 0.38\,TeV, respectively. In a one-zone leptonic scenario, these upper limits imply lower limits on the interior magnetic field to $B_{\rm{G1.9}} \gtrsim 11$\,$\mu$G for \gone\ and to $B_{\rm{G330}} \gtrsim 8$\,$\mu$G for \gthree. In a hadronic scenario, the low ambient densities and the large distances to the SNRs result in very low predicted fluxes, for which the \hess\ upper limits are not constraining. | Supernova remnants (SNRs) are believed to be sites of efficient particle acceleration and are expected to produce very-high-energy (VHE; $E > 0.1$\,TeV) \gammarays\ through the interaction of accelerated, high-energy particles with ambient medium and fields. TeV \gammaray\ emission is currently detected from a number of SNRs. Of particular interest are those SNRs whose X-ray spectra are dominated by non-thermal emission such as RX\,J1713$-$3946 \citep{J1713Nature,Aharonian06RXJ1713,Aharonian07RXJ1713}, RX\,J0852.0$-$4622 (Vela Jr.) \citep{Aharonian05VelaJr,Aharonian07VelaJr}, and SN\,1006 \citep{sn1006}. Synchrotron emission from these SNRs reveals the existence of high-energy electrons which implies that intensive particle acceleration is occurring at their shock fronts. It makes these sources particularly interesting for \gammaray\ astronomy since high-energy particles accelerated at shock fronts can produce VHE \gammarays\ through the inverse Compton (IC) scattering of relativistic electrons on ambient photon fields, through Bremsstrahlung radiation of relativistic electrons, and through proton-nucleus interactions, and subsequent $\pi^0$ decay. In this paper, the results of \hess\ observations of two other SNRs with dominant non-thermal X-ray emission, \gone\ \citep{reynolds08} and \gthree\ \citep{torii06}, are presented. The paper is organized as follows: In \textsection 2, the general properties of \gone\ and \gthree, based on radio and X-ray observations, are presented. The \hess\ data analyses and results are described in \textsection 3. In \textsection 4, the non-detection of the SNRs is discussed in the context of leptonic and hadronic particle acceleration scenarios. Finally, the conclusions are summarized in \textsection 5. \begin{table*} \centering \caption{\hess\ observations of SNRs \gone\ and \gthree.} \label{data} \begin{tabular}{c c c c c c} \hline \hline \\ SNR & Observation period & Livetime & Median offset angle & Median zenith angle & Threshold energy \\ \hline \\ \gone\ & March 2004 -- July 2010 & 67\,h & $1.3\deg$ & $16\deg$ & 0.26\,TeV \\ \gthree\ & June 2005 -- May 2009 & 16\,h & $1.6\deg$ & $30\deg$ & 0.38\,TeV \\ \hline \end{tabular} \end{table*} | The synchrotron nature of the X-ray emission indicates that electrons in both SNRs are accelerated to very high (TeV) energies. For such high energies, the acceleration process should run very similarly for electrons and hadrons. Some important differences arise from the cut-off in the electron spectrum (due to electron radiation losses; see e.g. \citet{Reynolds_Keohane_99}) and in the number of accelerated particles in each distribution. Nonetheless, the existence of high-energy electrons directly shows that there should also exist hadrons accelerated to energies at least as high. This leads to the expectation of \gammaray\ emission from inverse Compton (IC) scattering of relativistic electrons on photon fields and/or from hadronic (e.g. proton-nucleus) interactions. The non-detection of this emission allows constraints to be placed on parameters such as the magnetic field strength, the ISM density, the distance and the cosmic-ray (CR) efficiency, the latter defined as the fraction of SN explosion energy that is transferred to the particle acceleration. \begin{table} \centering \caption{SED model fitting parameters.} \label{param} \begin{tabular}{ccccc} \\ \hline\hline && \\ SNR & $\Gamma_{\mathrm{e}}$ & $B$ & $E_\mathrm{cut}$ & $W_\mathrm{tot}$ \\ & & [$\mu$G] & [TeV] & [erg] \\ \hline \multicolumn{5}{c}{Uncooled electron spectrum}\\ \hline && \\ \gone & 2.2 & $>12.1$ & $<44$ & $<4.2\times10^{48}$ \\ \gthree & 2.2 & $>8.0$ & $<21$ & $<13.2\times10^{48}$ \\ \hline \multicolumn{5}{c}{Dominating synchrotron losses}\\ \hline && \\ \gone & 2.0 & $>8.6$ & $<80$ & -- \\ \gthree & 2.0 & $>4.3$ & $<56$ & -- \\ \hline \end{tabular} \end{table} \subsection{Leptonic scenario} \label{lept_scen} Although the comparison of the X-ray and radio data reveals general anti-correlation for both SNRs indicating that radio and X-ray emitting electrons may not come from the same population, the one-zone leptonic model is used to obtain constraints on physical parameters of the remnants and ambient media. Assuming that the radio and X-ray emission are produced by the same electron population via synchrotron radiation, one can predict the $\gamma$-ray emission expected from the IC scattering of the same electrons on the cosmic microwave background (CMB) photons and other ambient photon fields. Although in the vicinity of the GC, the contribution of the infrared (IR) and optical photon fields to the resulting IC emission can be comparable to or even exceed the contribution from the CMB photons alone \citep{porter06}, it is very difficult to determine the interstellar radiation field at the location of a specific object. Therefore, in this paper, we first consider CMB photons alone, since it is possible that there is no significant source of target photons in the proximity of \gone\ and \gthree, but then also discuss a potential contribution of the IR and optical photon fields to the overall IC emission and its impact on the resulting constraints on magnetic field and electron population parameters. \begin{table} \centering \caption{Parameters of optical and IR photon fields.} \label{photons} \begin{tabular}{c c c c c} \hline \hline && \\ SNR& \multicolumn{2}{c}{Optical photons} & \multicolumn{2}{c}{IR photons}\\ &&\\ & $T_{\rm{opt}}$ & energy density & $T_{\rm{IR}}$ & energy density\\ & [K] &[eV\,cm$^{-3}$] & [K] & [eV\,cm$^{-3}$]\\ \hline &&\\ \gone\ & 4300 & 14.6 & 48 & 1.5\\ \gthree\ & 3500 & 2.4 & 39 & 1.4\\ \hline \end{tabular} \end{table} The spectral energy distribution (SED) for \gone\ and \gthree\ is calculated assuming the stationary case and the exponentially cut-off power-law distribution of the electron density with energies, \begin{equation} {N_{\mathrm{e}}\left(\gamma\right) = K_{\mathrm{e}}\,\gamma^{-\Gamma_{\mathrm{e}}}\,e^{-\frac{\gamma}{\gamma_{\mathrm{cut}}}}, } \end{equation} where $\gamma$ is the electron Lorentz factor, $K_{\mathrm{e}}$ is the normalization, $\Gamma_{\mathrm{e}}$ is the spectral index, and $\gamma_{\mathrm{cut}} = E_{\mathrm{cut}} / \mathrm{m}_{\mathrm{e}}c^2$ is the cut-off Lorentz factor with the cut-off energy $E_\mathrm{cut}$ and the electron mass $\mathrm{m}_{\mathrm{e}}$. The synchrotron emission is calculated according to \citet{rybicki&lightman79} assuming the isotropic magnetic field and the isotropical distribution of the electron velocities. The correct integration over angle $\alpha$ between the electron velocity and the magnetic field is established using the function $G(x)$ introduced by \citet{AKP2010}. The IC emission is estimated according to \citet{blumenthal&gould} using the Klein-Nishina cross section. In Fig.~\ref{sed_G1.9_and_G330}, SED models for \gone\ and \gthree\ are presented. The IC contribution to the SED is presented for two different assumed values of the magnetic field $B$. The synchrotron contribution to the SED (black solid lines) is modeled with the electron spectral index $\Gamma_{\mathrm{e}} = 2.2$ on both cases, which represents the multi-wavelength (MWL) observational data quite well. This electron spectral index corresponds to the radio spectral index of $\alpha = 0.6$. For \gthree, this value is very different from the observed spectral index of 0.3 reported by \citet{clark75} based on two observed points: at 408 MHz (Molongo Cross Telescope) and 5000 MHz (Parkes 64m radio telescope). However, subsequent observations at 843 MHz with the Molongo Observatory Synthesis Telescope \citep{whiteoak&green96} revealed a flux density which does not agree with such a low spectral index. The choice of $\alpha=0.6$ in this work is motivated by the necessity of fitting the X-ray data, which cannot be explained for $\alpha=0.3$ within this model. Comparing the \hess\ integral flux ULs on the TeV $\gamma$-ray emission above the safe energy threshold (see Table~\ref{UL}; for assumed $\Gamma = 2.5$) to the predicted \gammaray\ flux above the same energy, within the context of the leptonic model presented above, one can calculate lower limits on the interior magnetic field strength $B$. The lower limits are found to be 12.1\,$\mu$G for \gone\ and 8.0\,$\mu$G for \gthree. Lower limits on $B$ in turn allow ULs on the electron cut-off energy, $E_\mathrm{cut}$, and the total energy in electrons, $W_\mathrm{tot}$, to be determined (see Table~\ref{param}). Physical assumptions made in the model above are the same as in the \texttt{srcut} model for the synchrotron emission used to fit the X-ray data. Therefore, it might be useful to compare roll-off frequencies of the synchrotron spectrum of \gone\ and \gthree\ implied from this work with those obtained in the \texttt{srcut} fits in earlier studies. It should be noted though, that the srcut model is an approximation and is exact only for the radio spectral index $\alpha = 0.55$ (corresponding to the electron index $\Gamma_\mathrm{e} = 2.1$). The estimate of the $\nu_{\mathrm{roll}}$ can differ from the real value by 20\% depending on the spectral index, and will be lower (resp. higher) for $\alpha<$ (resp. $>$) 0.55. The roll-off frequency $\nu_{\mathrm{roll}}$ is the the characteristic frequency of the photon emitted by the electron with the energy $E_\mathrm{cut}$ and it is given by \citep[with an error corrected]{Reynolds_Keohane_99} \begin{equation} \nu_{\mathrm{roll}} = 1.6\times10^{16}\left(\frac{E_{\mathrm{cut}}}{10\hbox{ TeV}}\right)^{2}\left(\frac{B}{10\hbox{ $\mu$G}}\right) [\hbox{Hz}]. \end{equation} For \gone, the roll-off frequency obtained in this work, $\nu_{\mathrm{roll,\,G1.9}} = 3.7\times10^{17}$\,Hz, is consistent with the one obtained in \citet{reynolds09}. In the case of \gthree, $\nu_{\mathrm{roll,\,G1.9}} = 5.6\times10^{16}$\,Hz is an order of magnitude higher than the one derived by \citet{torii06}, which can be naturally explained by the different assumed spectral index: in \citet{torii06} the value of the radio spectral index was fixed to $\alpha = 0.3$, while in this work the synchrotron emission from \gthree\ is modeled for $\alpha=0.6$. The electron spectrum of the form of the power law with the exponential cut-off is valid only if the energy losses due to the synchrotron emission can be neglected. This regime is plausible for both \gthree\ and especially \gone\ due to their young age. The "break" energy above which synchrotron cooling starts to play an important role is given by the expression \citep{blumenthal&gould} \begin{equation} E_{\mathrm{syn}} = 1.3 \times 10^{3} \left(\frac{t_{\mathrm{age}}}{100\,\mathrm{y}}\right)^{-1} \left(\frac{B}{10\,\mu\mathrm{G}}\right)^{-2}\,\mathrm{TeV}. \end{equation} For the estimated ages of the SNRs and derived lower limits of the magnetic field upper limits on the break energy can be calculated resulting in $\sim900$ TeV for \gone\ and $\sim200$ TeV for \gthree. However, the higher magnetic field would significantly decrease the estimate of the break energy, i.e. a synchrotron cooling can occur. Significant synchrotron cooling modifies the shape of the initial electron spectrum obtained from the acceleration process. The modified electron spectrum is steepened by one and features a super-exponential cut-off \citep{ZA2007}: \begin{equation} N_{\mathrm{e}}(\gamma) \propto \gamma^{-(\Gamma_{\mathrm{e}}+1)} e^{-\left(\frac{\gamma}{\gamma_{\mathrm{cut}}}\right)^2}. \end{equation} Following a similar procedure as presented above for the case of the uncooled electron spectrum, the lower limit on the magnetic field and the upper limit on the cut-off energy can be estimated. The spectral index obtained in the particle acceleration is assumed to be $\Gamma_{\mathrm{e}} = 2$ and the radio data is not taken into account. In this scenario, the lower limits on magnetic field are $8.6\,\mu$G (29\% difference) for \gone\ and $4.3\,\mu$G (46\% difference) for \gthree. Upper limits on cut-off energies are 80 TeV (81\% difference) and 56 TeV (167\% difference) correspondingly. \begin{figure} \centering \resizebox{\hsize}{!}{\includegraphics{G1.9_and_G330_SED_plot_hap_11_02_20points_synchlos.eps}} \caption{Spectral energy distributions of \gone\ (\emph{top}) and \gthree\ (\emph{bottom}) in a leptonic scenario. The \hess\ upper limits on the differential flux are shown assuming two different spectral indices, 2.0 (lower curve) and 3.0 (upper curve). The multi-frequency radio data shown for \gone\ was compiled by \citet{green08}; additional upper limits in the IR domain \citep{Arendt89} are not shown because they lie outside of the plotted range and are not constraining. The solid and dot-dashed lines represent the modeled synchrotron and IC emission spectra from uncooled and cooled (due to synchrotron losses) electron spectrum, respectively. For the IC emission, dotted (resp. dashed) lines correspond to the contribution due to IC scattering on CMB (resp. IR) photons, in the case of the uncooled electron spectrum. The IC emission is calculated for two assumptions on $B$. Note that the lower limit on the magnetic field is calculated comparing the integral upper limit on the \gammaray\ flux above the safe energy threshold to the model prediction of the flux above the same energy. See Section \ref{lept_scen} for details.} \label{sed_G1.9_and_G330} \end{figure} To calculate the contribution of optical and IR photon fields (see Table~\ref{photons}), the interstellar radiation field (ISRF) model of \citet{porter06} was used. To simplify calculations ISRF models were fit with Planck distributions for optical, IR and CMB photons. For \gone, the adopted ISRF at $R = 0$\,kpc and $z = 0$\,kpc was used, where $R$ is the distance from the GC and $z$ is the height above the Galactic plane. For \gthree, the ISRF at $R = 4$\,kpc and $z = 0$\,kpc was adopted. The ISRF at $R = 0$\,kpc and $z = 0$\,kpc can be described with an optical radiation at a temperature $T_{\rm{opt}} = 4300$\,K with an energy density of $14.6$\,eV\,cm$^{-3}$ and a contribution from IR radiation at a temperature $T_{\rm{IR}} = 48$\,K with an energy density of $1.5$\,eV\,cm$^{-3}$. Similarly, the ISRF at $R = 4$\,kpc and $z = 0$\,kpc can be fit with the contribution from optical radiation at a temperature $T_{\rm{opt}} = 3500$\,K with an energy density of $2.4$\,eV\,cm$^{-3}$ and a contribution from IR radiation at a temperature $T_{\rm{IR}} = 39$\,K with an energy density of $1.4$\,eV\,cm$^{-3}$. The contribution of the optical photons to the IC emission appears to be less than 1\% even in the relative vicinity of the GC and does not affect the derived constraints on the physical parameters presented in Table \ref{param}. In contrast, the inclusion of the IR photons in the modeling provide a significant effect on the results\footnote{An uncooled electron spectrum is assumed}. In this case the lower limits on the magnetic field are estimated to be 15.1\,$\mu$G (25\% difference) and 10.5\,$\mu$G (31\% difference) for \gone\ and \gthree\ respectively. The higher the limits are on the magnetic field, the stronger the constraints are on the cut-off energy and the total energy in electrons. For \gone, $E_\mathrm{cut}<40$\,TeV (10\% difference) and $W_\mathrm{tot}<3.0\times10^{48}$ erg (30 \% difference) and for \gthree, $E_\mathrm{cut}<18$\,TeV (14\% difference) and $W_\mathrm{tot}<8.5\times10^{48}$\,erg (36\% difference). In Fig. \ref{sed_G1.9_and_G330}, the contribution of the IR photons to the overall IC emission SED is shown with dashed lines. The leptonic model of the broadband emission from \gone\ presented in this paper is similar to the purely leptonic model (in the test particle limit) considered by \citet{ksenofontov10}. The main difference is that \citet{ksenofontov10} assume a radio spectral index $\alpha = 0.5$, i.e. electron spectral index $\Gamma_{\mathrm{e}} = 2.0$, whereas in this paper the radio spectral index $\alpha = 0.6$ ($\Gamma_{\mathrm{e}}=2.2$) was adopted based on radio observations. Taking into account this difference, the results obtained by the two models are compatible. Nevertheless, given the low value obtained for the lower limit on $B$, the purely leptonic scenario, with an unmodified shock and without magnetic field amplification, cannot be ruled out, in contrast to what was suggested by \citet{ksenofontov10}. \subsection{Hadronic scenario} The \hess\ ULs on the \gammaray\ flux from \gone\ and \gthree\ can also be compared to predictions based on a hadronic scenario, where $\pi^0$ mesons would be created when CR ions accelerated in the supernova blast wave collide with the ambient thermal gas, producing \gammarays\ via $\pi^0$ decay. Since both SNRs exhibit synchrotron X-ray emission which reveals the existence of electrons with energies $\gtrsim 20$\,TeV, the maximum energy of accelerated hadrons should be at least 20 TeV. This suggests that the spectrum of $\gamma$-rays produced in proton-nucleus interactions extends up to at least a few TeV. The expected VHE flux from an SNR in a hadronic scenario can be then described, according to \citet{drury94}, as \begin{eqnarray}\nonumber \label{hadronic} F(> E) \approx && 8.84 \times 10^{6} q_{\gamma}(\geq \hbox{1\,TeV}) \left( \frac{E}{\hbox{1\,TeV}}\right)^{1-\Gamma_{\mathrm{p}}} \\ && \theta \left(\frac{E_{\rm{SN}}}{10^{51}\hbox{\,erg}}\right)\left(\frac{d}{1 \hbox{\,kpc}}\right)^{-2}\left(\frac{n}{1\hbox{\,cm}^{-3}}\right) \hbox{\,cm}^{-2} \hbox{\,s}^{-1} \end{eqnarray} where $q_{\gamma}$ is the $\gamma$-ray emissivity normalized to the CR energy density, $\Gamma_{\rm{p}}$ is the spectral index of the relativistic protons distribution, $\theta$ is the CR acceleration efficiency, and $E_{\rm{SN}}$ is the SN explosion energy, $d$ is the distance to the SNR and $n$ is the ISM density. The emissivity $q_{\gamma}(\geq\hbox{1\,TeV})$ also depends on $\Gamma_{\rm{p}}$ (inversely proportional), and \citet{drury94} have calculated $q_{\gamma}$ for spectral indices 2.1--2.7 \citep[see Table~1 in][]{drury94}, taking into account the contribution of nuclei other than H by multiplying the pure proton contribution by a factor of 1.5. The values $\Gamma_{\rm{p}} = 2.1$ and $q_{\gamma} = 1.02 \times 10^{-17}$ are adopted to predict the highest possible flux. Furthermore, in this scenario, only emission from neutral pion decay is taken into account; charged pion decay will contribute IC and Bremsstrahlung emission but with a much smaller contribution to the energetics. After fixing the spectral index and the CR production rate, four parameters remain free: $\theta$, $E_{\rm{SN}}$, $d$ and $n$. Assuming the explosion energy released is $10^{51}$\,erg and taking into account the estimated distance to the SNR, one can constrain the product of the CR efficiency and the ISM density using the \hess\ UL. The resulting \gammaray\ spectrum should roughly follow the energy spectrum of protons. Since $\Gamma_{\mathrm{p}} = 2.1$ is assumed, the \hess\ UL with the assumed index of 2.0 should be used for placing constraints as the closest to the modeled \gammaray\ spectrum. The expected flux above 0.26 TeV from \gone\ assuming $d = 8.5$\,kpc is then \begin{equation} \label{hadronicG1.9} F_{\rm{G1.9}}(>\hbox{ 0.26 TeV}) \approx 5.5\times10^{-12} \theta_{\rm{G1.9}} \left(\frac{n_{\rm{G1.9}}}{1\hbox{ cm}^{-3}}\right) \hbox{ cm}^{-2} \hbox{ s}^{-1}. \end{equation} The \hess\ UL on the flux above the same energy, $4.9 \times 10^{-13}\hbox{ cm}^{-2} \hbox{ s}^{-1}$, can be used to provide an UL on the product of the density and efficiency, \begin{equation} \theta_{\rm{G1.9}} \left(\frac{n_{\rm{G1.9}}}{1\hbox{ cm}^{-3}}\right) < 0.09. \end{equation} During the free expansion stage of the SNR's evolution, which \gone\ is assumed to be in, the CR efficiency $\theta$ is expected to be very low, $\theta \ll 1$ \citep{drury94}. \citet{ksenofontov10} show that at the age of 100\,y, the CR efficiency for \gone\ should be about $3\times10^{-3}$. The typical value of the CR efficiency during the adiabatic stage of SNR evolution $\theta = 0.1$ can serve as ULs for the case of \gone. Here, the range of values $3\times10^{-3}\leq\theta_{\mathrm{G1.9}} \leq 0.1$ is considered. This leads to an UL on the ISM density $n_{\rm{G1.9}} < (1 - 30)$\,cm$^{-3}$ depending on the assumed $\theta_\mathrm{G1.9}$. This UL is 2--3 orders of magnitude higher than the estimate based on the Type Ia SN model of \citet{dwarkadas&chevalier} and the \hess\ flux UL is therefore not constraining. On the other hand, assuming the density $n_{\rm{G1.9}} \approx 0.04$\,cm$^{-3}$ \citep{reynolds08}, an UL on the CR efficiency can be obtained, $\theta_{\rm{G1.9}} < 2.3$. Since $\theta$ is defined only in the range 0--1, this limit is also not constraining. For SNR \gthree, the expected flux above 0.38\,TeV at the distance of 5\,kpc is \begin{equation} \label{hadronicG330} F_{\rm{G330}}(>\hbox{ 0.38 TeV}) \approx 10^{-11} \theta_{\rm{G330}} \left(\frac{n_{\rm{G330}}}{1\hbox{ cm}^{-3}}\right) \hbox{ cm}^{-2} \hbox{ s}^{-1}. \end{equation} The \hess\ UL on the flux above this energy $2.5\times10^{-12}\hbox{ cm}^{-2} \hbox{ s}^{-1}$ constrains the product of the CR efficiency and the density \begin{equation} \theta_{\rm{G330}} \left(\frac{n_{\rm{G330}}}{1\hbox{ cm}^{-3}}\right) < 0.25. \end{equation} It corresponds to an UL on the ISM density $n_{\rm{G330}}<2.5$ cm$^{-3}$, assuming the typical value of the CR efficiency during the adiabatic stage of SNR evolution, $\theta_{\rm{G330}} = 0.1$, and to an UL on the CR efficiency $\theta_{\rm{G330}}<2.5$ assuming the \citet{park06} estimate on the ISM density $n_{\rm{G330}} \approx 0.1$\,cm$^{-3}$. In the case of \gthree, ULs estimated within the hadronic scenario are also not strongly constraining. Estimates of the ULs on the product of the CR efficiency and the density of both \gone\ and \gthree\ are within the range of estimates for a subset of 20 other SNRs recently studied by \citet{bochow}. Alternatively, with existing estimates of the ISM densities and assumptions on CR efficiencies, one can predict the expected fluxes from \gone\ and \gthree. For example, assuming $n_{\rm{G1.9}} = 0.04\,$cm$^{-3}$ and $\theta_{\rm{G1.9}} = (0.003 - 0.1)$, the expected VHE \gammaray\ flux from \gone\ above 0.26\,TeV according to Eq.~\ref{hadronicG1.9} is in the range of $(0.07 - 2.2)\times10^{-14}\hbox{ cm}^{-2} \hbox{ s}^{-1}$, 1--3 orders of magnitude lower than the \hess\ UL. For \gthree, assuming $n_{\rm{G330}} = 0.1\,$cm$^{-3}$ and $\theta_{\rm{G330}} = 0.1$ according to Eq. \ref{hadronicG330} one can calculate the expected flux above 0.38 TeV of $1\times10^{-13}\hbox{ cm}^{-2} \hbox{ s}^{-1}$, 25 times lower than the UL. Although the \hess\ ULs for both SNRs do not constrain the predictions of this scenario, it should be noted that there exist non-negligible uncertainties in many of the model parameters. In particular, the expected $\gamma$-ray flux is very sensitive to the estimate of the distance to the source. According to \citet{ksenofontov10}, the dependence of the $\gamma$-ray flux on the distance for \gone, taking into account the relations between the distance and the ISM density, SNR radius and shock velocity, is $F_{\gamma} \propto d^{-11}$. Therefore, even a small decrease in the distance estimate would significantly increase the expected flux and consequently improve the constraints on the ISM density and the CR efficiency. Specifically, a reduction of the distance to \gone\ by $46\%$ to 4.6\,kpc would increase the expected flux, calculated for the lowest assumed CR efficiency of $0.003$, to the level of the \hess\ UL. For \gthree, the expected flux scales simply as $d^{-2}$ and would be compatible with the \hess\ UL if the distance to the source were reduced by $25\%$, to 3.8\,kpc. | 14 | 4 | 1404.1613 |
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