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1404 | 1404.6038_arXiv.txt | The Double Helix Nebula (DHN), located 100 pc above Sgr A* in the Galactic center (GC), is a unique structure whose morphology suggests it is a magnetic feature \citep{mor2006}. Recent molecular observations toward the DHN by \citet{eno2013} revealed two candidate molecular counterparts of the DHN at radial velocities of $-35$ km s$^{-1}$ and 0 km s$^{-1}$ and discussed the model in which the DHN has its origin at the circumnuclear disk in the GC. In this paper, new CO observations toward the DHN using the CSO and Mopra telescopes are presented. The higher-resolution observations of $\sim$1 pc scale reveal the detailed distributions and kinematics of the two CO counterparts (the 0 km s$^{-1}$ and $-35$ km s$^{-1}$ features) and provide new information on their physical conditions. As a result, we find that the 0 km s$^{-1}$ feature with a mass of $3.3\times10^4$ M$_\odot$ coincides with the infrared emission of the DHN, indicating clear association with the DHN. The association of the $-35$ km s$^{-1}$ feature, with a mass of $0.8\times10^4$ M$_\odot$, is less clear compared with the 0 km s$^{-1}$ feature, but the complementary distribution between the molecular gas and the DHN and velocity variation along the DHN support its association with the DHN. The two molecular features are highly excited, as shown by the relatively high CO $J$=2--1/$J$=1--0 intensity ratios of $\sim$1.0, and have kinetic temperatures of $\sim$30 K, consistent with the typical molecular clouds in the GC. | The Galactic center (GC) has many outstanding structures that are not seen in the outer part of the Galaxy. In particular, several lines of evidence indicate that the magnetic field plays an important role in this region. A strong magnetic field of 50 $\mu$G has been suggested as an averaged figure within the central 400 pc region by an analysis of the non-thermal radio spectrum \citep{cro2010}, and many unique astrophysical structures related to the magnetic field have been discovered so far. Many linear, non-thermal radio filaments are present in the Radio Arc \citep{yus1984}, in which highly ordered magnetic field lines distributed vertically to the Galactic plane are traced by their radio synchrotron emission \citep[e.g.,][]{lan1999,lar2000,yus2004}. Their origin is still elusive, though numerous ideas have been advanced \citep{mor1996b}. On a larger scale, \citet{fuk2006} discovered two giant molecular loops $\sim$700 pc away from the center with a height of $\sim$200 pc, and they propose that they are a result of magnetic buoyancy driven by the Parker instability. Follow-up studies reveal that the footpoints of the loops have highly turbulent molecular clumps with velocity dispersions of $\sim$50 km s$^{-1}$, and magnetic reconnection has been discussed as the origin of these clumps \citep{tor2010a,tor2010b,kud2011}. The Double Helix Nebula (hereafter DHN) was discovered $\sim$100 pc above the Galactic center by \citet{mor2006} using infrared observations with Spitzer (Figure \ref{dhn}). It has an apparent helical morphology that can be seen in dust emission, implying that it is organized by a magnetic field. \citet{mor2006} suggest that the DHN was created by torsional Alfv\'en waves emitted from the circum-nuclear disk (CND) which surrounds the supermassive black hole, Sgr A*. On the other hand, \citet{tsu2010} use radio polarization measurements to hypothesize that the DHN is an extension of the polarized northern lobe of the magnetic Radio Arc. An interesting clue that supports the magnetic nature of the DHN is the presence of non-thermal radio emission distributed along the western rim of the DHN \citep{law2008}. Most recently, \citet{eno2013} present the observations of a $4^\circ \times 2^\circ$ area of the GC in the $^{12}$CO($J$=2--1) transition obtained using the NANTEN2 4m telescope with a beam size of 100$''$, finding that two molecular features at radial velocities of $\sim-$35 km s$^{-1}$ and 0 km s$^{-1}$ (hereafter the $-$35 km s$^{-1}$ and 0 km s$^{-1}$ features) coincide with the DHN. They also find that these features are located at the tops of molecular ridges elongated vertically to the Galactic plane, having lengths of $\sim$150 pc at the GC distance. Indeed, they estimate the distance of the ridges as 8$\pm$2 kpc, which is consistent with the distance to the GC, by carrying out an analysis of the $K$-band stellar extinction. It therefore seems quite likely that the DHN and its molecular counterparts have their origin at the GC. However, a spatial resolution of 100$''$, which corresponds to $\sim$4 pc at the GC, is much coarser than the typical size of the helical filaments of the DHN, $\sim$1--2 pc, and detailed comparisons of molecular emission with the 24 $\mu$m Spitzer image have not yet been possible. In this study, we present results of new molecular observations toward the DHN using the CSO and Mopra telescopes. The improved spatial resolutions of $\sim$33$''$ ($\sim$1.3 pc) enable a more detailed description of the $-35$ km s$^{-1}$ and 0 km s$^{-1}$ features and help clarify whether they are physically associated with the DHN. This paper is organized as follows; Section 2 summarizes the observations and Section 3 the results. The discussion is given in Section 4 and a summary in Section 5. In this study, we adopt a GC distance of 8.0 kpc. | Our detailed observations of the DHN with Mopra and the CSO indicate that both the $-35$ km s$^{1}$ and 0 km s$^{-1}$ features are associated with the DHN. The spatial distribution of the 0 km s$^{-1}$ feature shows remarkably good correspondence with the infrared emission of the DHN. The association of the $-35$ km s$^{-1}$ feature is less clear compared with the 0 km s$^{-1}$ feature, but the complementary distribution between the molecular gas and the DHN and velocity variation along the DHN support the association. The high excitation condition shown by the $^{12}$CO $J$=2--1/$J$=1--0 ratio (Figure \ref{ratio_all}) and estimated high temperature of about 30 K (Figure \ref{lvg}) also support the placement of the two molecular features within the CMZ. The two competing scenarios for the DHN are currently 1) a torsional Alfv\'en wave launched from the CND \citep{mor2006} and 2) an extension of the polarized northern lobe of the magnetic Radio Arc \citep{law2008,tsu2010}. \citet{eno2013} find that the $-35$ and 0 km s$^{-1}$ features are continuations to higher latitude of molecular ridges that extend down to the Galactic plane; they also find that they are located in the GC. The ridge at 0 km s$^{-1}$ appears to be pointing toward the CND rather than to the Radio Arc, although this does not provide an incontrovertible clue supporting the CND hypothesis. The results presented here for the detailed distribution of molecular emission toward the DHN indicate that the both the $-35$ and 0 km s$^{-1}$ features are associated with the DHN; this was not conclusive in \citet{eno2013}. These two molecular features cannot be easily understood with either of the two present scenarios, so further investigations including theoretical studies are required. The warm the warm temperature of the molecular counterparts of the DHN is a characteristic that helps associate these features with the clouds of the Central Molecular Zone. The energy injection rate required to keep the high temperature is estimated to be $1\times10^{36}$ erg s$^{-1}$ \citep{gol1978}. Here we assume a cylinder with a length of 30 pc for each feature to roughly estimate its volume, the diameters of which are estimated to be 10 pc and 5 pc for the $-35$ km s$^{-1}$ feature and 0 km s$^{-1}$ feature, respectively, and we also assume a uniform density of 10$^{3}$ cm$^{-3}$ and uniform temperature of the molecular gas, 30 K. It is reasonable to expect that the heating mechanism for the molecular gas is similar to that operating throughout the CMZ since 30~K is within a range of the typical temperatures of molecular gas in the CMZ, although the heating mechanisms in the CMZ are still under active discussion. One possibility is heating by UV radiation from the large population of massive stars in the CMZ. We estimate the total infrared luminosity toward the DHN ($l=0\fdg00$--$0\fdg08$, $b=0\fdg60$--$0\fdg85$) as $8.5\times10^5$ L$_\odot$ = $3.3\times10^{39}$ erg s$^{-1}$ using the integrated fluxes of the four IRAS bands and the equation given in the Table 1 of \citet{san1996}, 3.5 orders of magnitude larger than the cooling energy of the gas estimated above. In the 24 $\mu$m image in Figure \ref{dhn}, the diffuse emission distributed around the DHN accounts for roughly about 50~\% of the flux density of the DHN. Thus, if we consider the contribution of the diffuse emission, the total infrared luminosity is still much larger than the cooling energy. Stellar heating is therefore a possible explanation of the observed warm gas. Cosmic-rays are also a possible heating source for the molecular gas in the DHN. The non-thermal radio emission which is used to probe the distribution of the cosmic-ray electrons shows a distribution extending to high latitude \citep{yus2013}, including the northern part of the polarized lobe \citep{tsu2010}. Another way to heat molecular gas is dissipative heating of the kinetic energy of the turbulent gas via ion-neutral friction and/or magnetic reconnection. In the low latitude region of the CMZ close to the Galactic plane, highly turbulent molecular gas with a strong magnetic field possesses plenty of energy, but the velocity widths of the molecular features in the DHN are only about a few km s$^{-1}$, much smaller than the typical figures in the CMZ, making it less likely as the origin of the warm molecular gas in the DHN. | 14 | 4 | 1404.6038 |
1404 | 1404.5185.txt | Absolute cross sections for the {\it K}-shell photoionization of boron-like (B-like) O$^{3+}$ ions were measured by employing the ion-photon merged-beam technique at the SOLEIL synchrotron-radiation facility in Saint-Aubin, France. High-resolution spectroscopy with E/$\Delta$E $\approx$ 5000 ($\approx$ 110 meV, FWHM) was achieved with photon energy from 540 eV up to 600 eV. Several theoretical approaches, including R-Matrix, Multi-Configuration Dirac-Fock and Screening Constant by Unit Nuclear Charge were used to identify and characterize the strong 1s $\rightarrow$ 2p and the weaker 1s $\rightarrow$ 3p resonances observed in the {\it K}-shell spectra of this ion. The trend of the integrated oscillator strength and autoionisation width (natural line width) of the strong $\rm 1s \rightarrow 2p$ resonances along the first few ions of the B-like sequence is discussed. | Single and multiply ionisation stages of C, N, O, Ne and Fe have been observed in the ionized outflow in the planetary nebulae NGC 4051, measured with the satellite {\it XMM-Newton} \cite{Ogle2004} in the soft-x-ray region. Low ionized stages of C, N and O have also been used in the modelling of x-ray emission from OB super-giants \cite{Cassinelli1981}. Multiply ionization stages of O and Fe are also seen in the {\it XMM-Newton} spectra from the Seyfert galaxy NGC 3783, including UV imaging, x-ray and UV light curves, the 0.2 -- 10 keV x-ray continuum, the iron {\it K} - emission line, and high-resolution spectroscopy in the modelling of the soft x-ray warm absorber \cite{Blustin2002}. Detailed photoionization models of the brightest cluster of star formation in the blue compact dwarf galaxy Mrk 209 required abundances for ions of oxygen and nitrogen \cite{Diaz2007}. O [IV] {\it K}-lines are seen in the supernova remnant Cassiopeia (Cas A) in the infrared spectra taken by the Spitzer Space Telescope \cite{Smith2009}. In Seyfert galaxies based on photoionization models, O IV comes from higher ionization states and lower density regions and is an accurate indicator of the power of the active galactic nuclei (AGN) \cite{Melendez2008}. In the present study we focus our attention on obtaining detailed spectra on the triply ionized oxygen ion O$^{3+}$ (O IV) in the vicinity of its {\it K} - edge. Recent wavelength observations of {\it K}-transitions in atomic oxygen, neon and magnesium and their ions with x-ray absorption lines have been made with the High Energy Transmission Grating (HETG) on board the {\it CHANDRA} satellite \cite{Liao2013}. Strong absorption {\it K}-shell lines of atomic oxygen, in its various ionized forms, have been observed by the {\it XMM-Newton} satellite in the interstellar medium, through x-ray spectroscopy of low-mass x-ray binaries \cite{Pinto2013}. The {\it CHANDRA} and {\it XMM - Newton} satellite observations may be used for identifying the absorption features present in astrophysical sources, such as active galactic nuclei and x-ray binaries and for assistance in benchmarking theoretical calculations \cite{Gatuzz2013,Gorczyca2013}. Few experiments have been devoted to the study of {\it K}-shell photoionization on oxygen ions. Auger spectra of singly and doubly core-excited oxygen ions emitted in the collision of fast oxygen-ion beams with gas targets and foils were measured by Bruch and co-workers \cite{Bruch1979}. {\it K}-shell x-ray lines from inner-shell excited and ionized ions of oxygen, were observed using the Lawrence Livermore National Laboratory EBIT. With a multi-ion model they were able to identify the observed {\it K}-shell transitions of oxygen ions from O$^{2+}$ to O$^{5+}$. Up to now, {\it K}-shell photoionization cross-section results have been obtained only for O$^{+}$ ions by Kawatsura et al \cite{Kawatsura2002}. Measurements were made at Spring-8, using the merged-beam technique, on relative cross sections for double photoionization spectra in the energy range of the $\rm 1s \rightarrow 2p$ resonances, using a limited resolving power $\sim$ 310. {\it K}-shell single and double photoionization spectra of neutral oxygen have also been obtained \cite{Krause1994,Menzel1996,Stolte1997}, recently revisited with high resolution at the Advanced Light Source (ALS) and benchmarked against calculations using the R-matrix with pseudo-states method \cite{Stolte2013,Oxygen2013}. Theoretically, resonance energies and line widths for Auger transitions in B-like atomic ions have been calculated using a variety of methods, such as 1/Z perturbation theory \cite{safronova78,safronova96,safronova98,safronova99,Cornille1999}, multi-configuration Dirac Fock (MCDF) \cite{Chen1987,Chen1988}, the Saddle-Point-Method (SPM) with R-matrix, complex-coordinate rotation methods \cite{chung83,chung89,chung90,Lin2001,Lin2002}. Chen and Craseman \cite{Chen1987,Chen1988} calculated Auger and radiative decay of $1s$ vacancy states in the boron isoelectronic sequence using the Multi-configuration-Dirac-Fock approach (MCDF). Sun and co-workers \cite{Sun2011} used the saddle-point method with rotation to calculate energy levels and Auger decay widths for the $\rm1s2s^22p^2$ and $\rm 1s2s2p^3$ $^{2,4}L$ levels in B-like carbon and found suitable agreement with the re-calibrated spectrum of Bruch and co-workers \cite{Bruch1985} and the combined theoretical work and high resolution synchrotron measurements performed at the ALS \cite{Schlachter2004}. In the case of O$^{3+}$ ions, recent saddle-point with rotation calculations by Sun and co-workers \cite{Sun2013} for the energy levels and Auger and radiative decay rates for the $\rm 1s2s^22p^2$ and $\rm 1s2s2p^3$ $^{2,4}L$ levels were compared to the earlier beam-foil experimental measurements of Bruch and co-workers \cite{Bruch1979}, the MCDF work of Chen and Craseman \cite{Chen1987,Chen1988} and further extended to the higher lying $\rm 1s2p^4$ levels of other B-like ions \cite{Sun2013b}. State-of-the-art {\it ab initio} calculations for Auger inner-shell processes were first performed on this B-like system by Zeng and Yuan \cite{Zeng2002} and then by Pradhan and co-workers \cite{Pradhan2003} using the R-matrix method \cite{rmat}. This work followed a similar procedure to {\it K}-shell studies on Be-like B$^+$ ions by Petrini \cite{Petrini1981}. Garcia and co-workers \cite{Garcia2005}, further extended this work by using the R-matrix optical potential method within an intermediate-coupling scheme \cite{Burke2011}. Photoionization from the ground state, along the oxygen iso-nuclear sequence was investigated, in the photon energy region of the {\it K}-edge. In the present study we compare our results from the multi-configuration Dirac Fock (MCDF), R-matrix with pseudo-states (RMPS) approach, and the SCUNC semi-empirical methods \cite{Sakho2013a,Sakho2013b} with measurements made at SOLEIL, prior EBIT measurements \cite{Gu2005}, {\it XMM} and {\it CHANDRA} satellite observations \cite{Blustin2002,Kaastra2005, Kallman2012, Pinto2013,Liao2013} and other theoretical results \cite{ Chen1987,Chen1988,Zeng2002,Pradhan2003,Garcia2005,Gu2010}. In this paper we present detailed measurements of the absolute {\it K}-shell single photoionisation cross sections for B-like oxygen ions, in the 542--548 eV region and 594--599 eV photon energy range that were explored experimentally. Theoretical predictions are made from the Screening Constant by Nuclear Unit Charge (SCUNC), MCDF and R-matrix with pseudo-states methods to compare with the measurements. These calculations enable the identification and characterization of the very strong $\rm 1s \rightarrow 2p$ and the weaker $\rm 1s \rightarrow 3p$ resonance peaks observed in the B-like oxygen spectra. The present investigation provides absolute values (experimental and theoretical) for photoionization cross sections for the n=2 inner-shell resonance energies, natural line widths and resonance strengths, occurring for the interaction of a photon with the $\rm 1s^22s^22p~^2P^o$ ground state and $\rm 1s^22s2p^2~^4P$ metastable state of the O$^{3+}$ ion. Our work would appear to be the first time that experimental measurements have been performed on this prototype B-like system in the photon energy region of the {\it K}-edge, and complements our recent studies on {\it K}-shell photoionization of atomic nitrogen ions \cite{Soleil2011,Soleil2013,Soleil2014} and previous investigations on B-like carbon, C$^+$ \cite{Schlachter2004} at the ALS, in the vicinity of the {\it K}-edge. The layout of this paper is as follows. Section 2 briefly outlines the experimental procedure used. Section 3 presents the theoretical work. Section 4 presents a discussion of the results obtained from both experiment and theory. In section 5 we present a discussion of the variation of the integrated oscillator strengths and line widths for the first three ions of the B-like sequence with increasing charge state. Finally in section 6 conclusions are drawn from the present investigation. | \label{sec:Conclusions} {\it K}-shell photoionization cross sections for B-like oxygen ions, O$^{3+}$, have been determined using state-of-the-art experimental and theoretical methods. High-resolution spectroscopy was able to be achieved with E/$\Delta$E = 5000, covering the energy range 540--630 eV. Several strong resonance peaks are found in the cross sections in the energy region 542--548 eV and 593--599 eV. These resonance peaks are identified as the 1s $\rightarrow$ 2p and 1s $\rightarrow$ 3p transitions in the O$^{3+}$ {\it K}-shell spectrum and assigned spectroscopically with their resonance parameters tabulated in Tables \ref{reson}, \ref{reson2} and \ref{reson3}. For the observed resonance peaks, suitable agreement is found between the present theoretical and experimental results both on the photon-energy scale and on the absolute cross-section scale for this prototype B-like system. A comparison between theory and experiment for the integrated oscillator strengths $f$ and Auger autoionization widths $\Gamma$, for the strong $\rm 1s \rightarrow 2p$ resonances of the first few members of the B-like isoelectronic sequence highlight differences, particularly in the present experimental studies on the O$^{3+}$ ion for the Auger widths of the $\rm 1s2s^22p^2~^2P$ and $\rm 1s2s^22p^2~^2S$ core-excited states. These differences are as yet unexplained and would require further independent investigations. The strength of the present study is the high resolution of the spectra along with theoretical predictions made using the state-of-the-art MCDF, R-matrix with pseudo-states methods and predictions from a semi-empirical approach. Cross section results from earlier R-matrix investigations (Garcia and co-workers \cite{Garcia2005}, Pradhan and co-workers \cite{Pradhan2003}) were restricted to the ground-state of this ion. The present results have been compared with high resolution experimental measurements made at the SOLEIL synchrotron radiation facility and with other theoretical methods so would be suitable to be incorporated into astrophysical modelling codes like CLOUDY \cite{Ferland1998,Ferland2003}, XSTAR \cite{Kallman2001} and AtomDB \cite{Foster2012} used to numerically simulate the thermal and ionization structure of ionized astrophysical nebulae. \ack The experimental measurements were performed on the PLEIADES beam line, at the SOLEIL Synchrotron radiation facility in Saint-Aubin, France. The authors would like to thank the SOLEIL staff and, in particular C Miron the local contact of the PLEIADES beam line during the experiment for their helpful assistance. M F Gharaibeh acknowledges funding from the Scientific Research Support Fund, Jordan, for supporting a research visit to SOLEIL, under contract number Bas/2/02/2010. B M McLaughlin acknowledges support from the US National Science Foundation through a grant to ITAMP at the Harvard-Smithsonian Center for Astrophysics, the RTRA network {\it Triangle de la Physique} and a visiting research fellowship from Queen's University Belfast. We thank John C Raymond and Randall K Smith at the Harvard-Smithsonian Center for Astrophysics for discussions on the astrophysical applications. The computational work was carried out at the National Energy Research Scientific Computing Center in Oakland, CA, USA, the Kraken XT5 facility at the National Institute for Computational Science (NICS) in Knoxville, TN, USA and at the High Performance Computing Center Stuttgart (HLRS) of the University of Stuttgart, Stuttgart, Germany. Stefan Andersson from Cray Research is acknowledged for his advice and assistance with the implementation of the parallel R-matrix codes on the Cray-XE6 at HLRS. The Kraken XT5 facility is a resource of the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number OCI-1053575. This research also used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. %+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ % % Reference section now follows % % Delete or change fake bibitem. delete next three % lines and directly read in your .bbl file if you use bibtex. % %+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ % | 14 | 4 | 1404.5185 |
1404 | 1404.0722_arXiv.txt | In this paper we study wave propagation and scattering near a black hole. In particular, we assume a coherent emission source near the black hole and investigate the wavefront distortion as seen by a distant observer. By ignoring the spin nature of the electromagnetic radiation we model it by a complex scalar field. Then, the propagating wave near the observer can be decomposed using the Laguerre-Gaussian mode basis and its wavefront distortion can be characterized by the decomposition coefficient. We find that this decomposition spectrum is symmetric with respect to the azimuthal quantum number in the case that the wave source is located near a non-rotating (Schwarzschild) black hole, whereas the spectrum is generically asymmetric if the host black hole is rotating (Kerr). The spectral asymmetry, or the net orbital angular momentum carried by the wave, is intimately related to the black hole spin and mass, the wave frequency and the locations of the source and the observer. We present semi-analytical expressions and numerical results for these parameter-dependences. If the emitted radiation is temporally coherent, our results show that the secondary images (arising from the orbiting of the wavefront around the black hole) of the source can be almost as bright as its primary image. Separately, in the case of temporally-incoherent radiation, we show that the non-fundamental spectrum components in the primary image could be resolved by spatially-separated telescopes, although that would be degenerate with the telescope direction. Finally, our results suggest that the black-hole-induced spectral asymmetry is generally too weak to be observed in radio astronomy, even if the observer were located near an optical caustic. | Photon orbital angular momentum (POAM), as compared to photon spin angular momentum, was less known in optics up until about two decades ago, mostly due to the technical difficulties in generating light with definite POAM states and in finding appropriate applications for such light. In 1990, Tamm and Weiss \cite{Tamm} first managed to produce Laguerre-Gaussian (LG) laser beams in the laboratory, which have helical phase front and quantized POAM\footnote{LG modes are spatial eigenmodes of a wave which is freely propagating under the paraxial approximation and which has integer orbital angular momentum. See Sec.~\ref{sec2} for further details.}. Their studies paved the way for later proposals on applications of LG modes, including applications on quantum information processing and quantum cryptography \cite{Mair, Leach, Terriza, Gibson}, or even on future generations of gravitational wave detectors \cite{Vinet}. In addition, Harwitt \cite{Harwitt} proposed several astrophysical sources or mechanisms that possibly introduce nonzero POAM to light. These sources and mechanisms include maser beams that pass through inhomogeneous interstellar medium, luminous pulsars or quasars, and waves passing through the vicinity of a rotating black hole. Recently, Tamburini {\it et al.} \cite{Tamburini} performed a numerical simulation of radio emissions from an accretion disk surrounding a rotating black hole, assuming that different radiative sources in the disk are spatially coherent. In the simulation, they observed nontrivial POAM generation and asymmetric spectra in terms of the LG-mode basis, depending on the spin of the host black hole and the observer's location in the sky. It remains physically important to understand the physical mechanism for the generation of light with POAM near black holes, and obtain estimates for the POAM magnitude, which apparently encodes information about the host black hole. In this study we analyze the scalar wave emission from a coherent point source near a Kerr or a Schwarzschild black hole. We note that although the case of the electromagnetic wave which is considered in the above studies is a spin-$1$ field, in this paper we consider instead a complex scalar field, which has zero spin. We use the scalar field as a model for the electromagnetic field when its spin character is neglected. We employ this scalar model since it is a technically simpler case to study than the electromagnetic case and yet it is sufficient in order to understand the generation of POAM spectra. By assuming the wavelength of the radiation (not greater than $mm$ scale) to be much smaller than the size of the black hole (not less than $km$ scale), we calculate the wave received by a distant observer on the celestial sphere and the corresponding POAM spectrum. We investigate both the cases that the emission is temporally coherent and incoherent, as the two cases produce different POAM spectra. For completeness, we also study the scenario that the observer is located near an optical caustic of the background space-time, in which case the POAM asymmetry could be amplified, in addition to the wave itself. Part of the wave emitted from the vicinity of the black hole immediately propagates outwards and reaches the far-away observer, thus yielding the so-called primary image. However, other parts of the wave will typically orbit around the black hole a number of times before leaving the vicinity of the black hole and propagating outwards to reach the far-away observer; these wave signals will correspond to secondary images. We obtain the propagation of the wave via the calculation of an approximation to the retarded Green function of the wave equation in Kerr space-time. For the primary image we approximate the Green function by using the so-called Hadamard form (see, e.g.,\cite{Poisson}) and a calculation of the so-called van Vleck determinant, a biscalar which measures the degree of focusing of neighboring null geodesics. As for the later images -- for which the Hadamard form is not valid -- we instead approximate the Green function by a calculation of the quasi-normal modes in Kerr space-time in the high-oscillation-frequency limit (see, e.g.,\cite{Yang2013}). We shall show that, although the emission from a single non-rotating star in flat space-time generally contains only the fundamental LG mode (which contains zero angular momentum) at far distances, the presence of a rotating black hole near the star will generate a non-trivial POAM spectrum. Such spectrum is symmetric with respect to the LG basis (i.e., with respect to the azimuthal quantum number) for non-rotating Schwarzschild black holes and generically asymmetric for rotating Kerr black holes. That is, the asymmetric part of the spectrum contains the spin information of rotating black holes. As we shall show in Sec.~\ref{sec:specdegen}, the symmetric part of a POAM spectrum may be affected by the direction of the observation plane of a telescope array. This further emphasizes the importance of measuring the asymmetric part of the spectrum. An important difference between the case we study in this paper and that in \cite{Tamburini} is that here, as opposed to \cite{Tamburini}, we have a pointlike emission source. Therefore, the interference between waves emitted from sources at different spatial locations that occurs in \cite{Tamburini} is absent here. In our case, the main effect comes only from gravitationally twisting/merging the light bundles from a single emission source and we therefore expect the spectral asymmetry to be much smaller than in \cite{Tamburini} (see Secs.~\ref{sec:wave} and \ref{sec4} for details). This paper is organized as follows. In Sec.~\ref{sec2} we review the decomposition of a paraxial wave with respect to the LG basis, the definition of a POAM spectrum and the related quantity for detection. In Sec.~\ref{sec:GF} we describe the methods used for the calculation of the Green function. In Sec.~\ref{sec:wave} we analyze the wave emitted by a source near a black hole, using the Green function approach, and present our POAM results. In Sec.~\ref{sec4} we investigate the setting where the observer is located near an optical caustic and we conclude in Sec.~\ref{sec5}. Throughout this paper, we use geometric units $G=c=1$, the black hole mass $M$ is also set to $1$, unless otherwise specified, and the metric signature is taken to be $(- + + +)$. | \label{sec5} In this work, we have studied a wave that is emitted near a rotating black hole and eventually reaches a distant observer. We demonstrated that measuring the distortion of the wavefront provides an independent channel for obtaining information about the source, in addition to light-bending or other spectroscopic measurements. In order to characterize the wavefront distortion, we have adopted the previously-established POAM decomposition and we have applied it to the wave, which we have computed using the retarded Green function in Kerr space-time. While the POAM spectra of waves scattered by Schwarzschild black holes are shown to be always symmetric, any rotation in the host black hole generically generates asymmetry in the POAM spectrum. Since the symmetric part of the spectrum is degenerate with the tilt angle of the observation plane, we conclude that it is more likely to extract information about the source from the asymmetric part. The resulting POAM spectrum strongly depends on the temporal coherence of the emission source and the sky-location of the receiver. On the one hand, we find that the main contribution to the symmetric spectrum weight comes from the phase-variation in the sky of the direct signal. For generic receiver's locations, the magnitude of the square root of the weight, $\sqrt{w_{\pm 1}}$, is of order of $\eta$, which is roughly the ratio between the size of the telescope and the Airy disk size of the image, and it could be as large as $0.6$ for millimeter-wavelength sources near Sagittarius A*. If the receiver is located near a cusp point on the sky, we have shown, using techniques developed in catastrophe optics, that $\sqrt{w_{\pm 1}} \sim \eta/(\omega M)^{1/4}$; if the receiver is near a fold line in the sky, we have shown that $\sqrt{w_{\pm 1}} \sim \eta$ instead. On the other hand, we have shown that the asymmetric part of the POAM spectrum could be generated by the beating between phase and amplitude variation of the primary signal, or by the beating between the phase variation of the primary and secondary signals. This beating reflects the physical origin of nonzero POAM, either by coherently combining rays mis-aligned optical-axis, or by the interference of adjacent light bundles. Nevertheless, we find that the spectral asymmetry is generally too weak to be measured. This is in part due to the large distances between Earth and astrophysical black holes, which serve as strong-gravity lenses or ``phase plates". The best candidate for detection might be an extended region in the accretion disk near Sagittarius A* such that Earth lies near a fold line of its radiation. In this case, the spectral asymmetry for the $|l|=1$ mode can be as large as $10^{-5}$. However, even with advanced techniques available to cancel the effects from atmosphere turbulence, e.g. adaptive optics methods, this signal is still far below the sensitivity of current radio telescopes, such as millimeter-wavelength Very Long Baseline Interferometry arrays. | 14 | 4 | 1404.0722 |
1404 | 1404.7334_arXiv.txt | Interactions inside the cosmological dark sector influence the cosmological dynamics. As a consequence, the future evolution of the Universe may be different from that predicted by the $\Lambda$CDM model. We review main features of several recently studied models with nongravitational couplings between dark matter and dark energy. | The observed accelerated expansion of the Universe is usually assumed to have its origin in the existence of a mysterious component with effectively negative pressure, called dark energy (DE). Together with another up to now exotic component, dark matter (DM), it dominates the dynamics of the currently observable Universe, at least if standard general relativity (GR) is assumed to be valid up to the largest cosmological scales. The homogeneous and isotropic cosmic background dynamics is governed by Friedmann's equation \begin{equation}\label{friedmann} 3 \frac{\dot{a}^{2}}{a^{2}} \equiv H^{2} = \frac{8 \pi G}{3} \rho_{m} - \frac{k}{a ^{2}} + \frac{\Lambda}{3} \end{equation} and by the acceleration equation \begin{equation}\label{dda} \frac{\ddot{a}}{a} = - 4 \pi G\left(\rho_{m} + 3 p_{m} \right) + \frac{\Lambda}{3}\ , \end{equation} where $H$ is the Hubble rate and $a$ is the scale factor of the Robertson-Walker metric. The quantities $\rho_{m}$ and $p_{m}$ denote the energy density of the cosmic matter and the corresponding pressure, respectively. Cold dark matter (CDM) is characterized by a dynamically negligible matter pressure, i.e., $p_{m} \ll \rho_{m}$. Neglecting $p_m$, the equations (\ref{friedmann}) and (\ref{dda}) constitute the basis of the preferred cosmological model, the $\Lambda$CDM model, which does well in fitting most observational data (see, e.g., the recent results from WMAP 9 \cite{wmap9} and Planck \cite{planck}). Current observations are consistent with a spatially flat universe with fractions of about 70\% DE, provided by the cosmological constant $\Lambda$, and about 30\% matter (including CDM and baryons). But not only because of the notorious cosmological constant and coincidence problems (see, e.g. \cite{problems}), there is an ongoing interest in alternative models within GR itself and beyond it. It is useful to test potential deviations from the ``standard" description in order to constrain additional parameter sets which quantify these deviations. Among these alternative approaches there are phenomenological fluid models of the dark sector. These are straightforward generalizations of the $\Lambda$CDM model as can be seen as follows. With the definitions $\Lambda \equiv 8\pi\,G\,\rho_{\Lambda}$ and $p_\Lambda \equiv - \rho_{\Lambda}$, the cosmological constant is formally equivalent to a perfect ``fluid" with negative pressure. Then \begin{equation}\label{lnegp} H^{2} = \frac{8 \pi G}{3}\rho - \frac{k}{a ^{2}} \,,\qquad \ \frac{\ddot{a}}{a} = - \frac{4 \pi G}{3}\left(\rho + 3 p\right)\,, \end{equation} where $\rho = \rho_{m } + \rho_{\Lambda}$ and $p = p_{\Lambda}$. This analogy has been the starting point for generalized fluid models in which either the equation of state $p_\Lambda \equiv - \rho_{\Lambda}$ or $\rho_{\Lambda} = $ constant or both are modified. In the following section we summarize basic relation for the dynamics of perfect fluids. | Although the $\Lambda$CDM model \textit{grosso modo} is consistent with most observational data, the study of alternative descriptions continues to be of interest. Any competitive dynamical DE model has to make predictions for the currently observed cosmic dynamics that are similar to those of the $\Lambda$CDM model. We have reviewed here recent studies on interacting DE models. Investigating models with interactions in the dark sector allows us to address the coincidence problem. The problem of interacting models is to identify observational features which can unambiguously be attributed to a certain coupling. Interactions may provide corrections to uncoupled dark-sector models. But there are also models for which the accelerated expansion is an interaction phenomenon. Moreover, scenarios with nongravitational couplings in the dark sector may result in a future evolution of the Universe which is different from that of the $\Lambda$CDM model. | 14 | 4 | 1404.7334 |
1404 | 1404.0387_arXiv.txt | We present ALMA 880\micron\ continuum observations of 20 K and M-type stars in the Upper Scorpius OB association that are surrounded by protoplanetary disks. These data are used to measure the dust content in disks around low mass stars (0.1-1.6\msun) at a stellar age of 5-11\,Myr. Thirteen sources were detected in the 880\micron\ dust continuum at $\ge3\sigma$ with inferred dust masses between 0.3 and 52\mearth. The dust masses tend to be higher around the more massive stars, but the significance is marginal in that the probability of no correlation is $p\approx0.03$. The evolution in the dust content in disks was assessed by comparing the Upper Sco observations with published continuum measurements of disks around \about 1-2\,Myr stars in the Class~II stage in the Taurus molecular cloud. While the dust masses in the Upper Sco disks are on average lower than in Taurus, any difference in the dust mass distributions is significant at less than $3\sigma$. For stellar masses between 0.49\msun\ and 1.6\msun, the mean dust mass in disks is lower in Upper Sco relative to Taurus by $\Delta\mathrm{log\, M_{dust}} = 0.44\pm0.26$. | The lifetime of optically thick, gas-rich disks surrounding young stars provides empirical constraints on the timescales to form planetary systems and the mechanisms responsible for disk dispersal. The disk dissipation timescale is typically measured by surveying clusters or association of stars of various ages and identifying the fraction of stars that exhibit infrared emission in excess of the stellar photosphere, which is attributed to a circumstellar disk that absorbs and re-radiates the stellar radiation. Infrared surveys have shown that \about 80\% of K- and M-type stars are surrounded by a disk at an age of \about 1\,Myr, and declines to \aboutless 20\% at an age of \about 5\,Myr \citep{Haisch01,Mamajek04,Hernandez08}. Disks around A and B-type stars (\about 2-3\msun) appear to evolve on even shorter timescales \citep{Hernandez05,Carpenter06,Dahm09}. Submillimeter continuum observations provide additional key diagnostics of disk evolution. Whereas infrared emission is generally optically thick and traces the disk surface layer within \about 1\,AU of the star, submillimeter continuum emission is optically thin over most of the disk and can also probe the cool, outer disk. The submillimeter continuum emission is a measure of the surface area of millimeter-sized particles in the disk \citep[e.g.,][]{Ricci10b}, and can be used to estimate the dust mass with assumptions on the dust opacity and temperature structure of the disk. Hundreds of $\sim$ 1-2\,Myr old stars in the Taurus and Ophiuchus clouds have been surveyed in the submillimeter continuum with single dish telescopes and interferometers \citep{Beckwith90, Andre94, Motte98, Andrews05, Andrews07b, Schaefer09, Andrews13}, and the continuum and/or spectral-line emission have been resolved in dozens of stars \citep{Dutrey96, Simon00, Kitamura02, Andrews07a, Isella09, Andrews09, Andrews10, Kwon11, Guilloteau11}. Collectively, these extensive observations have established the disk properties around low-mass stars at an age of \about 1-2\,Myr. Submillimeter observations of stars at other ages are more limited, but nonetheless have begun to reveal how the dust mass evolves. Submillimeter and millimeter observations of the \about 2-3\,Myr IC~348 \citep{Carpenter02,Lee11} and the \about 5-11\,Myr Upper Scorpius OB association \citep{Mathews12a} demonstrate that these regions lack the luminous disks found in Taurus and Ophiuchus. However, the stellar samples observed so far in IC~348 and Upper Sco are incomplete, and \citet{Andrews13} have suggested that the lack of bright disks may be due to a selection bias toward late type stars rather than to intrinsically different distribution of disk submillimeter luminosities. After considering the lower mean submillimeter flux density observed in disks around lower mass stars, \citet{Andrews13} showed that the millimeter-wavelength luminosity distribution of the IC 348 and Taurus samples are statistically indistinguishable, while the Upper Scorpius OB Association (hereafter Upper Sco) sample appears to have only marginally ($\sim 2.5\sigma$) lower luminosities on average. More recently, \citet{Williams13} presented a large submillimeter survey of disks in the \about 3\,Myr old $\sigma$ Orionis cluster. In this case they found that the submillimeter luminosities are lower in $\sigma$ Orionis than in Taurus, indicating a decline of the amount of material in disks as star-forming regions age from $\sim 1$ to $\sim 3$\,Myr. We report new submillimeter continuum observations of K and M-type stars in Upper Sco obtained with ALMA during Cycle 0 Early Science. These data achieve nearly an order of magnitude better sensitivity than previous submillimeter surveys of disks in Upper Sco. We use these data to investigate any dependence of the disk properties with stellar mass, and compare these observations with existing submillimeter continuum measurements of stars in the younger Taurus region to investigate the evolution of dust masses. | The results presented in Section~\ref{comparison} indicate that the distribution of dust masses between Taurus and Upper Sco are statistically indistinguishable given the present sample sizes. To place limits on the differences in the mean dust mass between Taurus and Upper Sco, we used the mean dust masses values from the Kaplan-Meier estimator presented in Section~\ref{comparison}. We consider only the higher mass stars (0.49-1.6\msun) given the preponderance of upper limits in Upper Sco and especially Taurus for the lower mass stars. The change in the mean dust mass from Taurus to Upper Sco for the 0.49-1.6\msun\ stars is $\Delta\mathrm{log\,M_{dust}} = 0.44\pm0.26$. Thus the mean dust mass has declined by a factor of $\approx 2.8\pm1.6$, but, consistent with the analysis presented in Section~\ref{comparison}, the uncertainties are such that no decline in the mean dust mass is consistent with the data. The 3$\sigma$ upper limit to the change in the mean $\mathrm{log} M_\mathrm{dust}$ is 1.22\,dex, and thus formally, these data cannot exclude an order of magnitude change in the mean dust mass. The reason why the constraints on the mean dust mass remain poor can be readily ascertained from Figure~\ref{fig:mdust_usco}. For the 0.49-1.6\msun\ stars, half have dust masses between \about 10 and 50\mearth\ and half have masses less than 1\mearth. The gap in the dust mass distribution within this stellar mass range implies that the median disk properties remain uncertain by an order of magnitude. While the lower mean flux densities in Upper Sco relative to Taurus have been interpreted as a decrease in the dust masses, systematic differences in the dust composition or the grain size distribution can also lead to a decrease in the submillimeter flux density for a constant mass in solids. As an example, we computed the dust opacity by adopting the three most abundant species in the \citet{Pollack94} dust composition and assuming that the size distribution of particles can be represented by a power law of $n(a) \propto a^{-3.5}$. Increasing the maximum particle radius to 1\,cm from 1\,mm, but keeping the total mass in solids constant, would decrease the observed submillimeter flux density by a factor 2.7, which is consistent with the observed decrease in the flux density in Upper Sco relative to Taurus. In this scenario, the slope of the dust opacity between wavelengths of 1\,mm and 3\,mm will decrease to $\beta=0.66$ from $\beta=0.91$. While a systematic change of $\beta$ with stellar age has not been observed \citep{Ricci10a,Ubach12}, the uncertainties on the measurements for individual disks are typically $\Delta\beta \approx 0.2-0.4$ (1$\sigma$). Thus we cannot exclude the possibility that the size distribution of particles is changing between Upper Sco and Taurus but the overall mass of solids has remained the same. Sensitive, long wavelength observations can help break the degeneracy between variations in grain growth and disk mass in accounting for the reduced submillimeter flux. The sample for these observations was drawn from the Spitzer survey presented in \citet{Carpenter06} for a subset of the known Upper Sco population. Since that time, not only has the census of Upper Sco members been refined, the all-sky WISE survey between 3.5 and 22\micron\ has been completed, which can be used to assess the presence of a disk in all association members. Such a census has already by completed \citep{Rizzuto12,Luhman12}, and there are over 200 stars and brown dwarfs over all spectral types in Upper Sco that have an infrared excess characteristics of a disk, including primordial and debris disks. Future observations of this large sample with ALMA will probe the tentative correlations identified in this paper. | 14 | 4 | 1404.0387 |
1404 | 1404.2382_arXiv.txt | Gravitational-wave astronomy seeks to extract information about astrophysical systems from the gravitational-wave signals they emit. For coalescing compact-binary sources this requires accurate model templates for the inspiral and, potentially, the subsequent merger and ringdown. Models with frequency-domain waveforms that terminate abruptly in the sensitive band of the detector are often used for parameter-estimation studies. We show that the abrupt waveform termination contains significant information that affects parameter-estimation accuracy. If the sharp cutoff is not physically motivated, this extra information can lead to misleadingly good accuracy claims. We also show that using waveforms with a cutoff as templates to recover complete signals can lead to biases in parameter estimates. We evaluate when the information content in the cutoff is likely to be important in both cases. We also point out that the standard Fisher matrix formalism, frequently employed for approximately predicting parameter-estimation accuracy, cannot properly incorporate an abrupt cutoff that is present in both signals and templates; this observation explains some previously unexpected results found in the literature. These effects emphasize the importance of using complete waveforms with accurate merger and ringdown phases for parameter estimation. | \GW astronomy endeavours to infer the properties of astrophysical systems from the gravitational radiation they emit. For ground-based detectors, such as the Laser Interferometer Gravitational-wave Observatory (LIGO) and Virgo \cite{LIGO,Virgo}, a principal \GW source are binaries consisting of neutron stars or stellar-mass black holes that inspiral and eventually coalesce as GWs carry away energy and angular momentum. Parameters of interest for these systems include the component masses and spins and the location and orientation of the binary. With the upcoming advanced generation of \GW detectors \cite{AdvLIGO,AdvVirgo}, which are expected to make the first detections of coalescing black-hole and neutron-star binaries \cite{scenarios,ratesdoc}, efforts to predict parameter-estimation accuracy have intensified. Over the past two decades, a variety of techniques have been used for predicting the accuracy with which parameters can be extracted from a detected \GW signal. The \FIM formalism has been particularly popular because of its low computational cost and ease of use \cite{Vallisneri:2008}. Dozens of studies have used the \FIM tool, including the classic work of \cite{Finn:1992wt,CutlerFlanagan:1994,PoissonWill:1995}, ranging in applications from tests of GR \cite{Rodriguez:2012,PaiArun:2013} to sky-localization predictions for multi-messenger astronomy \cite{Fairhurst:2009, Fairhurst:2011, Grover:2013}. More recently, alternatives to the \FIM formalism have been considered, e.g., \cite{Hannam:2013,Ohme:2013,Cho:2013}. Finally, as computational resources have expanded, more costly Bayesian techniques \cite{Jaynes} have been employed to compute the full posterior probability density functions of the signal parameters. These techniques, based on stochastically sampling the parameter space with methods such as Markov chain Monte Carlo and nested sampling, have been used to consider measurements of masses and spins for different classes of systems and the sky-localization ability of different network configurations, e.g., \cite{vanderSluys:2008a,VeitchVecchio:2009,Raymond:2010,Veitch:2012,Rodriguez:2013BNS}. Despite the differences in methodology, all of the studies referenced above, and many others, share one common feature: they use waveforms that terminate abruptly in the band of the detectors. We do not expect most real \GW signals to exhibit such a steep falloff, but instead that they evolve smoothly through inspiral, merger and ringdown phases. However, accurate waveforms that included all phases of the \GW signal were not available until recent advances in numerical relativity (see \cite{Sperhake:2011,Pfeiffer:2012} for recent reviews) allowed analytical waveform families to be constructed by calibrating against numerical results, e.g., \cite{Ohme:2012,Santamaria:2010,Ajith:2011b,Pan:2011,Taracchini:2012, Taracchini:2013,Damour:2013}. Meanwhile, inspiral-only waveforms based on the post-Newtonian expansion and terminating at the \ISCO have been known for many years \cite{Blanchet:2014} and are computationally inexpensive to calculate. Consequently, it was natural for the early studies to make use of these waveforms. Even now, there are cases where it is beneficial to use post-Newtonian waveforms with an abrupt termination. Frequency-domain waveforms based on the stationary-phase approximation \cite{Damour2001,Damour2002,PNwaveforms:2009} are particularly well suited to both analytical and numerical studies. Such a waveform, terminated at the \ISCO, can be written as \ba \tilde{h}(f) &=& A(f) \exp\left[i \Psi(f)\right] H(f\sub{ISCO}-f) \label{eq:waveformmodel} \\ &\equiv& \tilde{h}^0(f) H(f\sub{ISCO}-f), \label{eq:cutoff} \ea where $f\sub{ISCO}$ is the GW frequency at the \ISCO, and $H$ is the Heaviside step function. These have been generally used for both \FIM calculations and parameter-estimation studies (as discussed above), with a few notable exceptions including \cite{VitaleZanolin:2010,S6PE,NINJA2}, as well as for gravitational-wave searches \cite{S6lowmass, findchirppaper, ihope}. However, the impact of the step function, i.e., the sharp waveform cutoff, is typically ignored in these applications. In this paper, we investigate in detail the effect of using waveforms with a sharp cutoff in the frequency domain on parameter recovery. After briefly recalling the likelihood and \FIM formalism (Sec.~\ref{sec:FIM}), we begin by considering the case where both the true signal and the waveforms used to recover it terminate abruptly. We show that the abrupt termination significantly alters the information content of the signal. In particular, while the accuracy of measurement typically scales inversely with the \SNR, parameters associated with an abrupt cutoff can be measured with an uncertainty proportional to the square of the inverse \SNR (Sec.~\ref{sec:SNR-scaling}). We describe the regime in which the abrupt waveform termination significantly impacts parameter-estimation accuracy (Sec.~\ref{sec:abrupt-sig}) and derive the likelihood function for a data set given a model with a sharp waveform cutoff (Sec.~\ref{sec:analytic-approx}). Subsequently, we consider the impact of the abrupt waveform termination on the \FIM formalism, and explain the apparent violation of the Cram{\'e}r--Rao bound found by \cite{Rodriguez:2013}, whose Bayesian confidence intervals on mass parameters were a few times smaller than those predicted by their \FIM (Sec.~\ref{sec:new_FIM}). Then, in Sec.~\ref{sec:fullsignal}, we investigate the impact of using template waveforms with an abrupt cutoff in searching for, and estimating the parameters of, signals which extend smoothly through merger and ringdown. We show that, at leading order, the parameter accuracies given by the \FIM are correct if inspiral-only information is used, although the presence of a merger and ringdown can lead to a systematic offset in the recovered parameters and the use of full inspiral--merger--ringdown waveforms for the analysis could allow for more accurate parameter estimation. We evaluate this bias in recovered parameters and identify the regime where cutoff waveforms introduce significant bias into signal recovery. While we limit our discussion to the specific application to \GW signals, we hope it is of interest to other fields which employ similar parameter-estimation techniques. | } We have studied the influence of an abrupt waveform cutoff on parameter estimation. Abrupt cutoffs are often used in \GW astronomy because of the uncertainty in the merger and ringdown components of the waveform, or for ease of computation. However, terminating the waveform can have undesired consequences if this occurs in the band of the detectors, that is if there is significant noise-weighted power at the cutoff frequency. It is therefore desirable to use complete inspiral--merger--ringdown waveforms. If these are not used, there are a number of effects to be aware of. We have shown that there is potentially a significant amount of information encoded in the (in-band) abrupt termination of waveforms. They may appear to provide more information than is available in practice. Therefore, studies using abruptly terminated signals and templates may overstate the accuracy with which parameters can be recovered. In this paper, we evaluated the information contained in such a cutoff, determined when it was significant, and described how it could be approximately incorporated into an analytic calculation. Although this study was based on frequency-domain waveforms, we expect the abrupt termination of time-domain waveforms to yield analogous additional information in the cutoff; however, in practice, abruptly terminating time-domain waveforms are often tapered to avoid artifacts when transforming into the frequency domain, which ameliorates this effect. The naive \FIM calculation is blind to the information encoded in the abrupt cutoffs.\footnote{All our analysis has been performed within a linearized framework. Therefore, many of our formulae are only directly applicable when considering small changes in parameters, just as the inverse \FIM can only be used to estimate the covariance in the linear-signal approximation. Our colleagues \cite{ChoLee:2014} further developed the present work by demonstrating the impact of abruptly terminating templates within the effective Fisher Information Matrix formalism \cite{Cho:2013}.} This can create a difference between various approaches for measuring parameter-estimation accuracy when the same models are used, and can cause an apparent violation of the Cram{\'e}r--Rao bound. It also means that the naive, inspiral-only \FIM can give incorrect, overly pessimistic predictions if the physical model really does call for an abrupt cutoff. While full parameter estimation with abruptly terminated waveforms incorporates unphysical information from the waveform termination, which can artificially improve parameter estimation accuracy, and the naive \FIM calculation avoids this problem, both ignore the information contained beyond the cutoff frequency, in the merger and ringdown phases of the waveform. Thus, there is a potential trade-off between the artificial gain of information from the sharp cutoff and the real loss of information from neglecting the merger and ringdown phases. The above results were obtained assuming that both the true signal and waveform template include a cutoff. Using abruptly terminated waveform templates to analyse a complete, non-terminating signal leads to a bias in the estimated parameters. This is not surprising, since the templates do not match their target signals. We have shown how to estimate the size of the bias, provided that it is sufficiently small that the linearized framework remains valid. In addition, we have shown that at lowest order the \FIM prediction of parameter covariances remains unaffected by the template cutoff if the signal to be searched for actually extends to higher frequencies. This proves, in hindsight, that previous \FIM results in the literature are meaningful, even for heavier systems containing black holes, if interpreted in the way outlined here. However, if the merger and ringdown power is significant, parameters could be extracted more accurately with full inspiral--merger--ringdown analyses than predicted by the naive, inspiral-only \FIM, so these studies may be overly pessimistic for massive systems. An interesting application of this final result is to algorithms that build template banks for \GW searches based on inspiral-only \FIM predictions. Our analysis indicates that such banks still cover the waveform manifold as desired if the underlying abruptly terminating templates are used to search for complete signals. However, the loss in \SNR, as well as the above-mentioned bias, generally remain unaccounted for. It is important to take care of the unintended consequences of using unphysical models with sharp cutoffs. The best solution for obtaining accurate estimates for parameter uncertainties lies in the use of waveforms that faithfully capture the merger and ringdown phases, cf.\ \cite{PNwaveforms:2009,Ohme:2012,Sampson:2013,S6PE}. | 14 | 4 | 1404.2382 |
1404 | 1404.2985_arXiv.txt | We study the effects of a class of features of the inflaton potential, corresponding to discontinuties in its derivatives. We perform fully numerical calculations and derive analytical approximations for the curvature pertubations spectrum and the bispectrum which are in good agreement with the numerical results. The spectrum of primordial perturbations has oscillations around the scale $k_0$ which leaves the horizon at the time $\tau_0$ when the feature occurs, with the amplitude and phase of the oscillations determined by the size and the order of the discontinuity. The large scale bispectrum in the squeezed and equilateral limits have a very similar form and are linearly suppressed. Both in the squeezed and equilateral small scale limit the bispectrum has an oscillatory behavior whose phase depends on the parameters determining the discontinuity, and whose amplitude is inversely proportional to the scale. Given the generality of this class of features they could be used to model or classify phenomenologically different types of non Gaussian features encountered in observational data such as the cosmic microwave background radiation or large scale structure. | In the last few decades the outstanding advances in observational cosmology have allowed for the first time to test theoretical cosmological models \cite{et, wmapcpr, pxvi,inflation2014}. Among the most important sources of cosmological observational data we can mention the Sloan Digital Sky Survey (SDSS), the Wilkinson Microwave Anisotropy Probe (WMAP), and the Planck mission, and other ground-based and sub-orbital experiments \cite{gbe1,gbe2}. According to the standard cosmological model the cosmic microwave background (CMB) radiation consists of photons which decoupled from the primordial plasma at the time when protons and electrons combined to form neutral light atoms. Although this radiation is extremely isotropic there are small fluctuations in the temperature of the order of $\Delta T/T \sim 10^{-5}$. And since the CMB radiation was emitted at a redshift of about $1100$ it provides a unique window on the early universe \cite{wmapfmr, pxxii, xc}. Inflation theory \cite{anewtype} explains the anisotropies of the CMB temperature as the consequence of primordial curvature perturbations whose statistical properties can be described by the n-points correlation functions. If the perturbations followed a perfectly Gaussian distribution the two points correlation function would be enough, but even the most recent observations are compatible with some non Gaussianity corresponding to $f_{NL}^{local}=2.5\pm5.7$ and $f_{NL}^{equil}=-16\pm70$~\cite{pxxii, pxxiv}, motivating the theoretical study of the conditions which could have generated it. Some recent developments in the study of models which could generate non Gaussianity and on their detection can be found for example in \cite{Hazra:2012yn,Dorn:2014kga,bingo,numerical2013}. The theoretical study of the effects of features of the inflaton potential was started in the seminal works of Starobinsky \cite{starobinsky}, and once CMB observational data became available it was shown that features can be used to model the glitches of the power spectrum \cite{constraints1,constraints2}. Some other interesting studies and reviews in this area can be found for example in \cite{Starobinsky:1998mj,Joy:2007na,Joy:2008qd,Mortonson:2009qv}. In this paper we focus on the effects of features of the inflaton potential on the primordial curvature perturbations, considering a class corresponding to a discontinuity in the derivatives of the potential. Our model is a generalization of other features which have been studied earlier such as the Starobinsky model or the mass step \cite{aer}. These kinds of features could have arisen through different mechanisms such as for example particle production \cite{pp}, or phase transitions \cite{Adams2}, but in this paper we study their effects from a purely phenomenological point of view, without investigating their fundamental origin. There is also an important observational motivation for studying this kind of potentials: recent analyses of CMB observations based on cubic Hermite interpolating polynomials (PCHIP) for the primordial curvature perturbations spectrum \cite{Gariazzo:2014dla} have in fact shown some evidence for a feature around the wave number $k=0.002$ Mpc${}^{-1}$, which is in good qualitative agreement with the results of our calculations for some of the potentials we consider. The paper is organized as following: first we define the features, then we give both a numerical and analytical solution for the background, and finally provide both numerical and analytical calculations of the spectrum and the bispectrum, giving details of the squeeze and equilateral limit and show the effects of varying the different parameters defining the feature, i.e., its amplitude and the order $n$ of the discontinuous derivatives. | We have studied the effects of a general type of features produced by discontinuities of the derivatives of the potential. We found that each different type of feature has distinctive effects on the spectrum and bispectrum of curvature perturbations which depend both on the order $n$ and on the amplitude $\lambda$ of discontinuity. The spectrum of primordial curvature perturbations shows oscillations around the scale $k_0$ which leaves the horizon at the time $\tau_0$ when the feature occurs, with amplitude and phase determined by the parameters $n$ and $\lambda$. Both in the squeezed and equilateral small scale limit the bispectrum has an oscillatory behavior whose phase depends on the parameters determining the discontinuity, and whose amplitude is inversely proportional to the scale. The large scale bispectrum in the squeezed and equilateral limits have a very similar form and are linearly suppressed. The analytical approximation for the spectrum is in good agreement with the numerical results, and improves substantially the accuracy for large scales respect to previous studies. The analytical approximations for the bispectrum are in good agreement with numerical calculations at large scales in both the squeeze and equilateral limit. At small scales we found an analytical template which is in very good agreement with the numerical calculations both in the squeezed and equilateral limit, and is able to account for both the oscillations and the amplitude of the bispectrum. The type of feature we have studied generalize previous models such as the Starobinsky model or the mass step \cite{aer}, providing a general framework to classify and model phenomenologically non Gaussian features in CMB observations or in large scale structure survey data. In the future it would be interesting to find the parameters which better fit different non Gaussian features in observational data and to investigate what more fundamental physical mechanism, such as phase transitions for example, could actually produce these features. | 14 | 4 | 1404.2985 |
1404 | 1404.6873_arXiv.txt | We present CN and CH indices and \caii\ triplet metallicities for 34 giant stars and chemical abundances for 33 elements in 14 giants in the globular cluster M2. Assuming the program stars are cluster members, our analysis reveals ($i$) an extreme variation in CN and CH line strengths, ($ii$) a metallicity dispersion with a dominant peak at [Fe/H] $\approx$ $-$1.7 and smaller peaks at $-$1.5 and $-$1.0, ($iii$) star-to-star abundance variations and correlations for the light elements O, Na, Al and Si and ($iv$) a large (and possibly bimodal) distribution in the abundances of all elements produced mainly via the $s$-process in solar system material. Following \citet{roederer11}, we define two groups of stars, ``$r+s$'' and ``$r$-only'', and subtract the average abundances of the latter from the former group to obtain a ``$s$-process residual''. This $s$-process residual is remarkably similar to that found in M22 and in M4 despite the range in metallicity covered by these three systems. With recent studies identifying a double subgiant branch in M2 and a dispersion in Sr and Ba abundances, our spectroscopic analysis confirms that this globular cluster has experienced a complex formation history with similarities to M22, NGC 1851 and $\omega$ Centauri. | Photometric studies have revealed complex structure in the colour-magnitude diagrams (CMD) of Galactic globular clusters (e.g., see review by \citealt{piotto09}). The subgiant branch region is of particular interest because differences in the luminosity of stars at this evolutionary stage require distinct ages and/or chemical compositions. Any globular cluster that exhibits a broadened or split subgiant branch must therefore have experienced a complex, and likely prolonged, chemical enrichment history when compared to globular clusters with a single subgiant branch population. $\omega$ Centauri and M22 (NGC 6656) are two Galactic globular clusters with multiple subgiant branches (e.g., \citealt{bedin04}; \citealt{marino09}). These two clusters are also notable for exhibiting a large star-to-star dispersion in the abundance of Fe-peak and neutron-capture elements (e.g., \citealt{norris95,smith00,marino09,marino11,johnson10,roederer11}). NGC 1851 is another globular cluster with multiple subgiant branches \citep{milone08}. Although the difference in metallicity between the two populations, $\Delta$[Fe/H]~$\approx$~0.07~dex \citep{carretta101851}, is less pronounced in NGC 1851 compared to $\omega$ Cen and M22, a large star-to-star dispersion in the neutron-capture element abundances is also present (e.g., \citealt{yong081851,villanova09,carretta11}). While theoretical studies indicate that multiple population globular clusters could be formed through mergers or that some may be the remnants of dwarf galaxies (e.g., \citealt{bekki03,carretta10,bekki11,bekki12}), understanding the sequence of events that produce multiple population globular clusters remains a major challenge (e.g., \citealt{marcolini07,dercole08,dantona10,conroy11,herwig12,vesperini13}). An important step in advancing our knowledge of the formation of multiple population globular clusters is to understand the full range of phenomena and relative frequency present in the Galactic globular cluster system. \citet{piotto12} identified five new Galactic globular clusters with broadened or split subgiant branches based on \hst\ photometry. Their sample included M2 (NGC 7089), a little-studied cluster. \citet{smith90} measured the strengths of the CN and CH molecular features in a sample of 19 M2 red giants. In addition to the usual bimodal distribution of CN band strengths \citep{smith87}, they noted that two objects are CH stars. CH stars are rare in globular clusters, and at the time of that paper, the only other clusters known to contain CH stars included the apparently normal cluster M55 as well as the peculiar systems M22 and $\omega$ Cen. \citet{smolinski11} studied the CN and CH bands from Sloan Digital Sky Survey spectroscopy in a number of globular clusters including M2. They did not identify any stars with unusually strong CN or CH in this cluster, and all of their program stars lie on the canonical red giant branch (RGB). \citet{lardo12} studied the CN and CH band strengths as well as the C and N abundances in a sample of 35 M2 red giants. They also noted the presence of an additional RGB in the $V$ versus $U-V$ CMD. Both CH stars identified by \citet{smith90} are located on the anomalous RGB (see Figure 14 in \citealt{lardo12}). Examination of the \citet{grundahl99} \strom\ photometry also confirms the peculiar nature of the RGB. While \citet{lardo12} did not observe any stars on the anomalous RGB, in a subsequent study they obtained spectra for such stars \citep{lardo13}. Stars belonging to the two RGBs had distinct C, N, Sr and Ba abundances and \citet{lardo13} argued that M2 has experienced a complex star formation history with similarities to $\omega$ Cen, M22 and NGC 1851. High-resolution spectroscopy and chemical abundance measurements for a larger suite of elements for stars on the canonical and anomalous RGBs of M2 are essential to reveal the true nature of this multiple population globular cluster. The purpose of this paper is to measure CN and CH indices and chemical abundances for a sample of stars in M2 belonging to the canonical and anomalous RGBs. The sample selection and observations are described in Section 2. Section 3 contains the analysis. The results are presented in Section 4. Section 5 includes a discussion on the nature of this cluster. | In this paper we present a spectroscopic analysis of giant stars in the multiple population globular cluster M2. Our principal and novel results include the following. First, we identify a star-to-star dispersion in iron abundance with the anomalous RGB stars (i.e., stars lying redward of the dominant RGB) being more metal-rich than the canonical RGB objects. The iron abundance distribution has a dominant peak at [Fe/H] $\approx$ $-$1.7 and smaller peaks at $-$1.5 and $-$1.0, although membership for the latter group remains to be established. Secondly, the neutron-capture element abundances exhibit a star-to-star dispersion with a possible bimodal distribution. In this regard, M2 is chemically similar to the globular clusters M22, NGC 1851 and $\omega$ Cen, whose subgiant branches exhibit multiple sequences. It is likely that M2 has therefore experienced a similarly complex formation history. Thirdly, when subtracting the average abundances in the $r$-only group from those of the $r+s$ group, the abundance residual exhibits a striking correlation with the fraction of each element attributed to the $s$-process in solar system material. This residual is remarkably similar to that found in M22 and in M4 $-$ M5. Such a similarity would indicate that M2, M22, and M4 were enriched by $s$-process material of identical composition and potentially offers important observational constraints on the nature of the $s$-process in low metallicity environments. A comparison with theoretical predictions reveals that AGB stars with masses less than 3 \msun\ are unlikely to have played a major role in the chemical enrichment of M2. In addition to the AGB star contribution, some source(s) is needed to increase the abundances of the elements from Si to Zn in the $r+s$ group relative to the $r$-only group. Additional studies are essential to understand the formation and evolution of this complex cluster. | 14 | 4 | 1404.6873 |
1404 | 1404.1687.txt | The lithium abundances for 378 G/K giants are derived with non-LTE correction considered. Among these, there are 23 stars that host planetary systems. The lithium abundance is investigated, as a function of metallicity, effective temperature, and rotational velocity, as well as the impact of a giant planet on G/K giants. The results show that the lithium abundance is a function of metallicity and effective temperature. The lithium abundance has no correlation with rotational velocity at vsini $<$ 10 km s$^{-1}$. Giants with planets present lower lithium abundance and slow rotational velocity (vsini $<$ 4 km s$^{-1}$). Our sample includes three Li-rich G/K giants, 36 Li-normal stars and 339 Li-depleted stars. The fraction of Li-rich stars in this sample agrees with the general rate of less than 1$\%$ in literature, and the stars that show normal amounts of Li are supposed to possess the same abundance at the current interstellar medium. For the Li-depleted giants, Li deficiency may have already taken place at the main sequence stage for many intermediate-mass (1.5-5 M$_{\odot}$) G/K giants. Finally, we present the lithium abundance and kinematic parameters for an enlarged sample of 565 giants using a compilation of literature, and confirm that the lithium abundance is a function of metallicity and effective temperature. With the enlarged sample, we investigate the differences between the lithium abundance in thin-/thick-disk giants, which indicate that the lithium abundance in thick-disk giants is more depleted than that in thin-disk giants. | Lithium is an important element in the understanding of chemical evolution history of the Galaxy, as well as in the study of the mixing process in stellar interiors. As is known, the lithium abundance is believed to be a function of metallicity, effective temperature, stellar mass, age, stellar rotation and chromospheric activity. The behavior of lithium as a function of effective temperature has been well studied both for subgiants (De Medeiros et al. 1997; L$\grave{e}$bre et al. 1999; Randich et al. 2000; Mallik et al. 2003) and giants (Brown et al. 1989; Wallerstein et al. 1994; De Medeiros et al. 2000; de Laverny et al. 2003, L$\grave{e}$bre et al. 2006). Based on these literatures, we can conclude that the abundance of lithium becomes depleted with decreasing effective temperature among stars with spectral types of G to K, while also showing a wide dispersion for stars with spectral types of F8 to G0. Such behavior demonstrates that convective mixing is more severe for G and K type stars. Therefore, giants with spectral types of G and K are expected to show lower lithium abundances. The lithium behavior as a function of stellar rotation (e.g. De Medeiros et al. 2000, de Laverny et al. 2003, L$\grave{e}$bre et al. 2006) and chromospheric activity (Ghezzi et al. 2010, Takeda et al. 2010) have also been studied by many investigations. It is suggested that fast rotation and active chromospheric activity lead to high A$_{\rm{Li}}$, where A$_{\rm{Li}}$ = log$\varepsilon$(Li). However, the effect of age is related to the effect of rotation and chromospheric activity, since young stars rotate faster and exhibit more violent chromospheric activities than old stars. The lithium behavior in dwarfs with and without planets has been well studied, but there are conflicting conclusions. Some studies (e.g. Israelian et al. 2004, Takeda \& Kawanamoto 2005, Chen et al. 2006, Israelian et al. 2009) have found that lithium abundance dilution is slightly higher in stars with planets compared to those without them. Also, other studies (e.g. Luck \& Heiter 2006, Baumann et al. 2010) found that there is no difference in lithium abundance between stars with and without planets. However, such kind of researches have not been carried out on a large sample of giants. A study of lithium abundances derived from a large homogeneous sample is desired, which allows a better understanding of lithium depletion. With more and more planets (23 planets up until now) released from the Okayama Planet Search program (Sato et al. 2003) and the Xinglong Planet Search program (Liu et al. 2008), this gives us a chance to systematically study the effect of planets on the lithium abundance for G/K giants. %lithium abundance is expected to be different in thin/thick-disk stars. As is known, chemical composition is different in thin and thick disk stars in the solar neighborhood, particularly for the $\alpha$-elements and oxygen (e.g. Bensby 2005; Reddy et al. 2006). But whether the lithium abundance is different in thin/thick-disk stars was not known before Ram\'{\i}rez et al. (2012), who investigated the behavior of lithium abundance in thin-/thick-disk stars among dwarfs and subgiants. They observed a difference in lithium abundance between thin- and thick-disk stars, reflecting different degrees of lithium depletion rather than differences in lithium enrichment of the interstellar medium. With a catalog supplemented from the literature (Luck $\&$Heiter 2007, hereby Luck07), our sample has been enlarged to 565 giants, which can be used to explore the different properties of thin-/thick-disk giants. In this paper, we analyze the lithium abundance for 378 G/K giants. The purpose of this work is to investigate the behavior of the lithium abundance as a function of metallicity, effective temperature, and stellar rotation, as well as to explore if there is any difference between giants with and without planets. The paper is organized as following: section 2 gives the sample selection and observational data; section 3 describes the method of analysis; section 4 presents our discussion; section 5 confirms the lithium abundance as a function of metallicity and effective temperature and the effect of thin-/thick-disk star in a sample of literature compilation 565 giants; finally the results are summarized in the last section. | The lithium abundance is supposed to depend on metallicity, effective temperature, stellar mass, age, stellar rotation and chromospheric activity for giants. However, the effect varies from different samples and different studies. In this work, we study the behavior of lithium abundance as a function of [Fe/H], T$_{\rm{eff}}$, and stellar rotation, as well as whether stars that host planets can affect their lithium abundances. We know that there are large uncertainties in stellar mass and age for red giants and red clump giants from the evolutionary tracks, hence we do not investigate the relations of lithium abundance against stellar mass and age in this study. \subsection{Lithium abundance versus [Fe/H]} The lithium abundance versus metallicity for our sample is plotted in Figure 5. The open dots, open squares, open triangles and stars respectively represent the sub-sample with clear Li detections, with undistinguished Li detections, with upper limits of lithium abundance, and with planets. The metallicity of our sample ranges from -0.8 to 0.2, but in the lower-metallicity region with [Fe/H] $<$ -0.4, only a few stars show Li detections. However, for those with [Fe/H] $>$ -0.4, about half of them have Li detections. According to theoretical models, the surface lithium is diluted by a factor of 28 to 61 for Red Giant Branch (RGB) stars with a mass of 1-5 M$_{\odot}$ (Iben 1965, 1966, 1967a,b). These depletions correspond to a decrease in lithium abundance of 1.8-1.4 dex relative to the assumed initial value from the main sequence. However, some works based on observation found that the depletion is more severe than the theoretical prediction. For instance, Brown et al. (1989) derived an average lithium abundance lower than 0.0 dex for 891 late-G to K giants, which is at least 1.5 dex below the predicted value; Luck $\&$ Wepfer (1995) found that lithium is depleted by a factor of 100 to 1000 for bright giants; and de Laverny et al. (2003) found a dilution by a factor of at least 600 for G0III type giants with a mass of 2 to 3 M$_{\odot}$. In our sample, Li depletion reached a factor of 770 for objects with Li detections compared with the current interstellar medium value of A$_{\rm{Li}}$ $\approx$ 3.3, which is far more diluted than the theoretical prediction. The over depletion was also found by other studies focusing on giants (eg. Brown et al. 1989, De Medeiros et al. 2000, de Laverny et al. 2003). If the over depletion is due to an extra-mixing mechanism existed in red giants/red clump giants, the [C/Fe] ratio, which indicates the degree of evolution-induced envelope mixing, would also reflect this difference; therefore, a correlation may be expected between A$_{\rm{Li}}$ and [C/Fe], which is not shown in Figure 6. From literatures we know that early-F type stars($\sim$ 1.5 M$_{\odot}$) show a considerable diversity in A$_{\rm{Li}}$ (e.g. Boesgaard \& Tripicco 1986). For A type stars($\sim$ 2 M$_{\odot}$), A$_{\rm{Li}}$ is ranging from normal to undetected value (e.g. Takeda et al. 2012). For rapidly rotating A-B type stars (2-4 M$_{\odot}$), it is very hard to detect the surface Li value. This is probably because in early type stars, surface Li is depleted because of the envelope mixing due to meridional circulation. It is more convincing that Li deficiency may have already existed in the main sequence phase for many 1.5-5 M$_{\odot}$ stars and was carried over to the evolved G/K giants. Except for three Li-rich stars with A$_{\rm{Li}}$ $>$ 1.7, the lithium abundance is increasing towards a higher metallicity in Figure 5. The dispersion of Li abundance at higher metallicities is very large (with a maximum of about 2.0 dex). %------------------------------------------------------------ fig5 \begin{figure} \plotone{f5.eps} \epsscale{.70} \caption{Lithium abundance versus metallicity. The symbols are the same as in Figure2. Two dash lines divide the regions corresponding to Li-rich, Li-normal and Li-depletion.} \label{Fig. 5} \end{figure} %------------------------------------------------------------ fig6 \begin{figure} \plotone{f6.eps} \epsscale{.60} \caption{Lithium abundance versus [C/Fe]. The symbols are the same as in Figure2.} \label{Fig. 6} \end{figure} \subsection{Li-rich stars and Li-normal stars} As predicted by theoretical models, typical RGB stars, with solar metallicity and stellar mass between 1.0 to 5.0 M$_{\odot}$ and which have undergone the first dredge up stage, are expected to show A$_{\rm{Li}}$ $<$ 1.8-1.4 dex. We have chosen the value of A$_{\rm{Li}}$ $>$ 1.7 dex, and 1.3-1.7 dex as the standard to define a star as being abnormally Li-rich or Li-normal, as suggested by some investigations (e.g. Brown et al. 1989, Gonzalez et al. 2009). Among all samples, the three stars HD65228, HD212430 and HD102845 show A$_{\rm{Li}}$ $>$ 1.7, and are thus classified as Li-rich giants. There are 36 stars that exhibit the expected lithium abundances (1.3 $\leq$ A$_{\rm{Li}}$ $\leq$ 1.7), i.e. Li-normal stars, and the remaining Li-depletion stars show an abundance of A$_{\rm{Li}}$ $<$ 1.3. Some researches (e.g. Brown et al. 1989, Charbonnel $\&$ Balachandran 2000, Ram\'{\i}rez et al. 2012) show that the previous results indicate the fraction of Li-rich giants is less than 1$\%$, which agrees well with our results. To check the mass and evolutionary status of the Li-rich and Li-normal giants, we plot their positions in H-R diagram in Figure 7, by adopting the stellar evolutionary tracks of YY (Yi et al. 2003) with the mean metallicity Z = 0.008 ([Fe/H] = -0.4, blue line) and solar metallicity Z = 0.02 ([Fe/H] = 0, green line). The chosen mass range is 1.0 to 5 M$_{\odot}$, but most of them lie within 2-4 M$_{\odot}$. Three sizes of the symbols correspond to Li-rich, Li-normal and Li-depletion giants. Li-rich giants with A$_{\rm{Li}}$ $>$ 1.7 are represented by the largest, filled symbol, and 36 Li-normal giants with 1.3 $\leq$ A$_{\rm{Li}}$ $\leq$ 1.7 by mid-size symbol. As a result of selection strategy in our sample, i.e., only late G and K giants are selected for planet search program, the majority of stars which are classified as RGBs are located in the same region of the H-R diagram. According to the statement of Charbonnel \& Balachandran(2000), the Li production phase is very short, which supports the result of observations that less than 1$\%$ giants are Li-rich, as confirmed both in previous studies and our work. HD65228, possessing the highest lithium abundance in our sample, is located on the blue side of the Hertzsprung gap. This star just began to develop a convective envelope, and a high lithium abundance is expected by the standard theory prediction. For HD212430 and HD102845, they are located in the clump region of the H-R diagram, hence there are two possible scenarios to explain such high Li abundances (Brown et al. 1989). One is that these two stars might be the first ascent giants, which are partly evolved, and assumed to have left the main sequence with their initial surface Li (A$_{\rm{Li}}$ $\approx$ 3.3). The other explanation is that they have a special circumstance that show high surface Li abundances, which is called the Cameron-Fowler mechanism (Cameron \& Fowler 1971), and predicts that carbon isotopic ratios will decrease. Li production precedes the extra-mixing phase which connects the convective envelope with the CN-burning region to produce the low $^{12}$C/$^{13}$C ratio. The mixing result in the production of $^{7}$Li, which is then convected to the surface. We know that 96\% of the evolved stars show a low $^{12}$C/$^{13}$C ratio (Charbonnel \& Do Nascimento 1998), which is in disagreement with standard predictions. Thus the most reasonable explanation is that they have undergone a period of Li-production. The 36 giants that have normal amounts of Li, which contain about 10 \% of our sample, are supposed to show the present interstellar medium abundance of A$_{\rm{Li}}$ $\approx$ 3.3, and have experienced the expected dilution phase during the first dredge-up phase. The surface lithium abundance decreases with respect to its value at the end of the main sequence by a factor of 30 to 60, depending on the stellar mass and metallicity. %------------------------------------------------------------ fig7 \begin{figure} \epsscale{.60} \plotone{f7.eps} \caption{Lithium abundance in H-R diagram. The symbols are the same as in Figure2. Three sizes of the symbols correspond to Li-rich, Li-normal and Li-depletion giants.\label{Fig. 7}} \end{figure} \subsection{Lithium abundance versus effective temperature} Figure 8 shows that the lithium abundance is a function of temperature£¬ with the detection limit increasing when the effective temperature increases. Generally, from our sample, the lithium abundance increases towards a higher metallicity for our sample, but in the narrow range of 4800-5100 K, there is no clear correlation between lithium abundance and effective temperature. Previous studies (Wallerstein et al. 1994, De Medeiros et al. 2000, de Laverny et al. 2003) have demonstrated that the lithium abundance is a function of effective temperature. However, we also notice that, within the color index range of 0.8 $<$ B-V $<$ 1.0, the well established gradual decline of lithium abundances as a function of effective temperature is not clear in many studies (Wallerstein et al. 1994, De Medeiros et al. 2000). The lithium abundances span two orders at a given effective temperature for our sample, suggesting that the stellar evolution stage and mass vary with dilution (De Medeiros et al. 2000). %------------------------------------------------------------ fig8 \begin{figure} \epsscale{.60} \plotone{f8.eps} \caption{Lithium abundance versus effective temperature. The symbols are the same as in Figure2.} \label{Fig. 8} \end{figure} To get rid of the effect of population, we divide our sample into 3 groups by metallicity: -0.8 $<$ [Fe/H] $\leq$ -0.4, -0.4 $<$ [Fe/H] $\leq$ -0.1, and -0.1 $<$ [Fe/H] $\leq$ 0.2; we then plot the lithium abundance versus effective temperature in Figure 9. To get the general behavior of lithium in red giants, the three Li-rich stars (A$_{\rm{Li}}$ $>$ 1.7) HD65228, HD212430 and HD102845 are not plotted in these figures. It is clear that there is no correlation between the lithium abundance and effective temperature in the metallicity range of -0.1 $<$ [Fe/H] $\leq$ 0.2, but with weak correlation in the metallicity range of -0.4 $<$ [Fe/H] $\leq$ -0.1. Although there are only four stars with clear Li detections in the metallicity range of -0.8 $<$ [Fe/H] $\leq$ -0.4, the lithium abundance as a function of effective temperature is quite clear. %------------------------------------------------------------ fig9 \begin{figure} \epsscale{.50} \plotone{f9a.eps} \plotone{f9b.eps} \plotone{f9c.eps} \caption{Lithium abundance against effective temperature in three different metallicity coverage. (a). -0.8 $<$ [Fe/H] $\leq$ -0.4, (b)-0.4 $<$ [Fe/H] $\leq$ -0.1, (c) -0.1 $<$ [Fe/H] $\leq$ 0.2. The symbols are the same as in Figure2.}\label{Fig. 9} \end{figure} \subsection{Lithium abundance versus rotational velocity} The rotational velocities in this analysis for 321 giants are taken from Takeda et al. (2008), but the rotational velocity are not available for the other 57 giants in Liu et al. (2010). For these 57 giants, the total macrobroadening function is a convolution of instrumental broadening, rotation and macroturbulence, and can be derived from the process of deriving the lithium abundance, with a maximum value of 8 km s$^{-1}$. Therefore, the rotational velocity should be no faster than 8 km s$^{-1}$. Considering that there is no systematic difference between a sample of 321 and 378, we only compare the lithium abundance versus rotational velocity for the 321 sample giants in Figure 10. Since our sample is taken from the planet search program, which select stars with slow rotational velocity to ensure the spectral line will not be broadened too much, the rotational velocity for most of our sample is slower than 6 km s$^{-1}$, and there are only a few between 6-11 km s$^{-1}$. Therefore, it is not surprising that the lithium abundance shows no correlation with rotational velocity when it is smaller than 10 km s$^{-1}$. The spread in lithium abundance is large in the values of vsini $<$ 10 km s$^{-1}$, and only two stars show 10 km s$^{-1}$ $<$ vsini $<$ 11 km s$^{-1}$ in this sample. One of the latter presents the highest lithium abundance and the other has only been assigned with an upper limit. HD65228, the most Li-rich object, shows the highest rotational velocity of 10.28 km s$^{-1}$, and it also shows the highest temperature in our sample. Previous studies (De Medeiros et al. 2000, de Laverny et al. 2003, L$\grave{e}$bre et al. 2006) found that the stars with higher or moderate rotational velocity (vsini $>$ 10 km s$^{-1}$) tend to show higher lithium abundances. Our results are consistent with the results from de Laverny et al. (2003), in which lithium abundance shows a wide spread at vsini $<$ 4 km s$^{-1}$. %------------------------------------------------------------ fig10 \begin{figure} \epsscale{.70} \plotone{f10.eps} \caption{Lithium abundance versus rotational velocity. The symbols are the same as in Figure2.} \label{Fig. 10} \end{figure} Considering that many stars in our sample have an effective temperature ranging from 4800-5100 K, we plot the lithium abundance for stars with the temperature of 4800-5100 K against metallicity and rotational velocity in Figure 11, for the purpose of taking off the effect of effective temperature. We omit the three lithium rich giants (A$_{\rm{Li}}$ $>$ 1.7) in Figure 11 to show the general behavior of lithium in red giants. It becomes more clear that the lithium abundance is not correlated with metallicity, or rotational velocity in the temperature range of 4800-5100 K. %------------------------------------------------------------ fig11 \begin{figure} \epsscale{.50} \plotone{f11a.eps} \plotone{f11b.eps} \caption{Lithium abundance against metallicity, and rotational velocity when 4800 $\leq$T$_{\rm{eff}}$ $\leq$ 5100 K. The symbols are the same as in Figure2.}\label{Fig. 11} \end{figure} \subsection{Lithium in planet-hosting giants and giants with not known giant planets} Lithium abundances are believed to be important for potentially providing a better understanding of processes involved in the formation and evolution of planetary systems. There are extensive studies on lithium in dwarfs that host planets and those without giant planets; however, there are conflicting results. It has been found in many studies (Israelian et al. 2004, Takeda \& Kawanomoto 2005, Chen et al. 2006, Israelian et al. 2009) that dwarfs that host planets, with effective temperature ranging from 5600 to 5850 K, exhibit severely depleted Li. A large fraction of the comparison sample only shows partially inhibited depletion. However, some studies (e.g. Luck \& Heiter 2006, Baumann et al. 2010) have found that there is no difference in lithium abundance between stars with and without planets, and they also claimed that the previously found differences were attributed to different stellar age and metallicity between stars that host planets and comparison samples. Thus it is important to perform a comparison between stars with and without planets with similar parameters (metallicity and age), and in a consistent way. Although many studies focus on whether lithium is more depleted, or not, in dwarfs that host planets, such kind of investigations have not been taken among giants. With more and more giants with planets released by the Okayama and Xinglong planet search program, it is now possible for us to explore the lithium behavior in giants with and without planets in more detail. From Figure 5, which describes the lithium behavior against effective temperature, a remarkable feature appears: among 23 planet-hosting giants, only 8 stars have Li being detected, with a maximin of A$_{\rm{Li}}$ = 1.01. However, among the 355 stars which are not known to have planets, 271 stars show Li detections. It can also be concluded from Figure 10(b-c) that differences in metallicity from the stars with and without giant planets cannot explain the diverse behavior of lithium abundances. In addition, from the H-R diagram (Figure 7), the stars with and without planets are located in the same regions, suggesting that there is no difference in terms of stellar evolution for the two sets of samples. The reason is probably due to the fact that lithium is easy to deplete in stars with planets. This effect is also unveiled among dwarfs with planets (e.g. Israelian et al. 2004, Chen et al. 2006); however, this is the first time that this aspect has been noticed for giants. Some studies(e.g. Siess \& Livio 1999, Adam$\acute{o}$w et al. 2012) found that Li-enrichment may be caused by planet accretion; however, there are no Li-rich giants in our 23 planet-hosting giants, which may suggest that such situation where the accretion of a planet leads to the formation of a Li-rich giant may be very rare. Since the number of giants with planets is limited in this sample, more targets with planets are necessary for a more detailed study. All planet-hosting giants have vsini $<$ 4 km s$^{-1}$, which is due to the fact that giants with lower rotational velocity are more suitable for detection of planets with the radial velocity method, since stars with rapid rotation normally show strong stellar activity, thus there are severe variations in intrinsic RV. We present the lithium abundances for 378 intermediate-mass late G/K giants by the spectrum synthesis method, among which 321 stars come from the Okayama planet search program and 57 stars from the Xinglong planet search program. The non-LTE correction is performed, resulting in a correction of 0.05-0.28 dex, with the majority around 0.18 dex. The lithium abundance as a function of metallicity, effective temperature and rotational velocity are discussed. The main results are summarized as follows: \\ 1. Our sample includes three Li-rich giants, 36 Li-normal stars and 339 Li-depleted stars. The fraction of Li-rich stars in this sample agrees with previous works, which predict that less than 1$\%$ giants are Li-rich. Stars with normal amounts of Li are supposed to present the abundance of current interstellar medium and have experienced the expected dilution phase during the first dredge-up phase. For the 339 Li-depleted stars, the abundance of Li is depleted far more than the theoretical prediction, suggesting that the Li deficiency may have already taken place in the main sequence stage for many 1.5-5 M$_{\odot}$ stars which has been carried over to the evolved G/K giants.\\ 2. The lithium abundance is a function of effective temperature and metallicity, but for stars within the temperature range of 4800-5100 K, there is no clear correction between lithium abundance and effective temperature.\\ 3. The lithium abundance is not correlated with rotational velocity when it is smaller than 10 km s$^{-1}$, which is consistent with the results of previous studies. \\ 4. For giants with planets, the lithium abundance is easy to deplete. Stars with and without planets are located in the same region on the H-R diagram, suggesting that there is no difference \textbf{on} the stage of stellar evolution for stars with planets and those without planets. All giants harboring planets have vsini $<$ 4 km s$^{-1}$. The reason that planet-hosting giants show smaller rotational velocity is due to the fact that lower rotational velocity shows a suitable pattern to detect planets using the radial velocity method. In Section 5, we provide a catalog of stellar parameters, lithium abundances for 565 giants, with supplementary of 187 stars from Luck07. These data are used to investigate the lithium behavior as a function of metallicity and effective temperature, and the differences in lithium behavior for thin-/thick-disk stars. The lithium abundances slightly increase with metallicity and effective temperature in this enlarged sample of G/K giants, and thick-disk stars present lower lithium abundance than thin-disk stars, reflecting different degrees of lithium depletion in these two populations. | 14 | 4 | 1404.1687 |
1404 | 1404.6332_arXiv.txt | One of the key parameters that characterize spiral arms in disk galaxies is a pitch angle that measures the inclination of a spiral arm to the direction of galactic rotation. The pitch angle differs from galaxy to galaxy, which suggests that the rotation law of galactic disks determines it. In order to investigate the relation between the pitch angle of spiral arms and the shear rate of galactic differential rotation, we perform local $N$-body simulations of pure stellar disks. We find that the pitch angle increases with the epicycle frequency and decreases with the shear rate and obtain the fitting formula. This dependence is explained by the swing amplification mechanism. | } Spiral structures are ubiquitous in various astrophysical disks. In spiral galaxies, there are distinct spiral arm structures. Grand-design spiral galaxies have long continuous symmetric arms, while flocculent spiral galaxies have patchy irregular spiral arms. In a protoplanetary gas disk, gravitational instability can occur during some phase of its evolution, which can produce spiral arms \citep{Gammie2001}. Also in Saturn's rings, the spiral structures in a broad sense exist. The azimuthal brightness asymmetry is observed in the rings \citep[e.g.,][]{French2007}, which indicates the existence of the small scale spiral structures called as self-gravity wakes observed in $N$-body simulations \citep{Salo1992a, Salo1995}. The wakes are caused by the gravitational instability of the ring. Our understanding of the origin of spiral arms in galaxies is still incomplete. One of the theories to explain spiral arms in galaxies is the density wave theory \citep{Lin1964, Lin1966}. Spiral structures are considered as a quasi-stationary standing wave pattern that rotates around the galactic center with a constant pattern speed. The spiral arms may be excited by tidal interactions with companion galaxies \citep[e.g.,][]{Oh2008} or the central bars \citep[e.g.,][]{Buta2005, Salo2010}. In a differentially rotating disk, a leading density pattern rotates to a trailing one due to the shear. If Toomre's $Q$ value is larger than unity but not too much, the amplitude of the pattern can be enhanced during the rotation. This mechanism is called swing amplification \citep{Goldreich1965, Julian1966, Toomre1981}. If a perturber such as the corotating over-dense region exists, trailing patterns form \citep{Julian1966}. In $N$-body simulations, since a disk consists of a finite number of stars, small density noise always exists. Thus, even if there is not a perturber, the small leading wave always exists, and the trailing wave can grow spontaneously due to the swing amplification mechanism \citep{Toomre1991}. The spirals generated by the swing amplification are not stationary but transient and recurrent, which appear and disappear continuously. This transient and recurrent picture is supported by $N$-body simulations for multi-arm spirals \citep{Sellwood1984, Baba2009, Sellwood2000, Sellwood2010, Fujii2011}. The linear theory of the swing amplification gives the amplification factor and the most unstable wavelength, but it cannot explain the overall evolution of spiral arms. \cite{Baba2013} studied the dynamics of stars in spiral arms and found that the nonlinear particle wave interaction is important to understand the damping and growing phase of spiral arms. \cite{DOnghia2013} performed high-resolution $N$-body simulations including initial density inhomogeneities that induce the spiral patterns due to the swing amplification. Once spiral arms form, the spiral arms remain. This results from the nonlinear effect. The local underdense and overdense regions act as perturbers, which maintain the spiral structure. One of the key parameters to characterize the morphology of spiral galaxies is the pitch angle. The pitch angle is the angle between the tangents to a spiral arm and a perfect circle, which measures how tightly the spiral arms are wound. \cite{Julian1966} investigated the response of the particle density to an imposed perturbation using the collisionless Boltzmann equation. They found the trend that the pitch angle decreases with the shear rate. The correlation between the shear rate and the pitch angle enables us to determine a rotation curve from the spiral structure. The epicycle frequency $\kappa$ is related to the shear rate $\Gamma$: \begin{equation} \Gamma = \frac{2 A}{\Omega} = - \frac{\mathrm{d}\log\Omega}{\mathrm{d}\log R} = 2 - \frac{\kappa^2}{2 \Omega^2}, \label{eq:sheartate} \end{equation} where $A$ is the first Oort constant, and $\Omega$ is the circular frequency. The observational study shows the relation that the pitch angle decreases with the shear rate, and the fitting formula is given as \citep{Seigar2005, Seigar2006}: \begin{equation} \theta = (64.25 \pm 2.87)^\circ - \Gamma (36.62 \pm 2.77) ^\circ . \label{eq:seigar} \end{equation} \cite{Grand2013} performed global $N$-body simulations and investigated the spiral patterns using Fourier analysis. From the spiral phase variation they calculated the pitch angle of the spiral arm. They found that galaxies of the higher shear rate have the smaller pitch angle. They did not study the dependence of the pitch angle on Toomre's $Q$ value since $Q$ evolves over time. It is expected that the pitch angle barely depends on $Q$ from \cite{Julian1966}. In order to understand the dynamics of spiral arms, we investigate the pitch angle dependence on the shear rate by local $N$-body simulations of pure stellar disks. Section \ref{sec:simulation} summarizes the calculation method. In Section \ref{sec:result}, we present the simulation results. In Section \ref{sec:discussion}, we discuss the relation between the pitch angle and the shear rate by using the linear theory. Section \ref{sec:summary} gives a summary. | } We performed the local $N$-body simulations of stellar disks and calculated the pitch angle $\theta$ of the spiral arms as a function of the shear rate $\Gamma$. We found that $\theta$ is well fitted by Equation (\ref{eq:esti}), which agrees well with the observational results \citep{Seigar2006}. The pitch angle $\theta$ decreases with $\Gamma$. For large $\Gamma$ or small $\kappa$, the winding due to the shear is so effective that $\theta$ is small. We also calculated the time evolution of the wavelet amplitude using the liner theory \citep{Julian1966}. The leading wavelet rotates and is amplified owing to the swing amplification mechanism \citep{Toomre1981, Toomre1991}. The spiral arm can be interpreted as the wavelet amplified by this mechanism. We calculated the time when the density amplitude is maximum and $\theta$ at that time. If Toomre's $Q$ value is larger than $1.5$, $\theta$ is approximately given by Equation (\ref{eq:est2}). Although the initial $Q$ is small, $Q$ increases rapidly due to heating by the spiral arms and exceeds $1.5$ finally. Thus, $\theta$ calculated by the numerical simulations agrees with Equation (\ref{eq:est2}). All these results suggest that the spiral arms in this simulation are formed by the swing amplification from the leading wavelet in the density fluctuation. The present simulation and linear theory employed the local approximation. We may directly apply these results to flocculent spiral galaxies. Strictly speaking, we should not apply these results to grand-design spiral galaxies. However, we expect that these results are useful for understanding the basic physics of spiral arms in general. In recent years, it was found that the nonlinear effect is significant to understand the overall activity of the spiral arms \cite[e.g.,][]{Baba2013, DOnghia2013} We found that the linear theory can predict the correct pitch angle that is consistent with the numerical simulation. This indicates that the linear theory is still useful to explain the shape of the spiral arms. We will investigate the non-linear process of spiral arm formation by gravitational instability in more detail in the future work. | 14 | 4 | 1404.6332 |
1404 | 1404.3735_arXiv.txt | The isotropy of the universal Hubble expansion is a fundamental tenet of physical cosmology, but it has not been precisely tested during the current epoch, when dark energy is dominant. Anisotropic expansion will produce a shearing velocity field, causing objects to stream toward directions of faster expansion and away from directions of slower expansion. This work tests the basic cosmological assumption of isotropic expansion and thus the isotropy of dark energy. The simplest anisotropy will manifest as a quadrupolar curl-free proper motion vector field. We derive this theoretical signature using a tri-axial expanding metric with a flat geometry (Bianchi \rm{I} model), generalizing and correcting previous work. We then employ the best current data, the Titov \& Lambert (2013) proper motion catalog of 429 objects, to measure the isotropy of universal expansion. We demonstrate that the Hubble expansion is isotropic to 7\% ($1\,\sigma$), corresponding to streaming motions of 1 microarcsecond yr$^{-1}$, in the best-constrained directions ($-$19\% and +17\% in the least-constrained directions) and does not significantly deviate from isotropy in any direction. The Gaia mission, which is expected to obtain proper motions for 500,000 quasars, will likely constrain the anisotropy below 1\%. | The isotropy of the cosmic expansion is well-constrained for the early universe, particularly by Cosmic Microwave Background observations, and is a basic tenet of physical cosmology. The change from a matter-dominated to a dark energy-dominated universe in recent times, however, raises the possibility of a dark energy-driven anisotropic expansion if dark energy is itself anisotropic. There is no obvious reason for such symmetry breaking, but observational tests of something as fundamental as the isotropy of the Hubble expansion should be made for late times (the current epoch). One such test is possible via extragalactic proper motions: if the expansion is anisotropic, then quasars and galaxies will stream toward directions of faster expansion and away from directions of slower expansion. The signature of anisotropic expansion in a homogeneous universe is thus a curl-free proper motion vector field \citep[to first order;][]{quercellini09,fontanini09,titov09}. The term ``cosmic parallax'' has been used by some to indicate a general relative angular motion of objects in the universe \citep[e.g.,][]{quercellini09,fontanini09} and used by others in a more canonical sense to indicate apparent angular motion induced by the motion of the observer \citep[e.g.,][]{ding09}. We favor the latter usage; this paper therefore treats the apparent proper motion induced by anisotropic cosmic expansion \citep{amendola13}, referenced to the International Celestial Reference Frame (ICRF) in the current epoch. The observed proper motions are therefore relative, but are not necessarily induced by the observer's motion. In this paper, we present a simple model of anisotropic expansion and fit the model to the \citet{titov13} proper motion catalog to place a new constraint on the isotropy of the Hubble expansion and thus on the isotropy of dark energy. We assume $H_\circ=72$~km~s$^{-1}$~Mpc$^{-1}$ and a flat cosmology (this treatment is independent of specific assumptions about $\Omega_\Lambda$ and $\Omega_M$, provided $\Omega_\Lambda + \Omega_M = 1$). | We have demonstrated how anisotropic Hubble expansion can be measured or constrained using extragalactic proper motions, and we applied this technique to the best current proper motion catalog \citep{titov13} to place a new constraint on the isotropy of the Hubble expansion and thus on the isotropy of dark energy. No significant anisotropy was detected; the Hubble expansion is isotropic to 7\% ($1\,\sigma$), corresponding to streaming motions of 1~$\mu$as~yr$^{-1}$, in the best-constrained directions ($-$19\% and +17\% in the least-constrained directions) and does not significantly deviate from isotropy in any direction. The Gaia mission, which is expected to obtain proper motions for 500,000 quasars, will likely constrain the anisotropy below 1\%. | 14 | 4 | 1404.3735 |
1404 | 1404.6705.txt | {In this work we show that the general singlet extension of the MSSM can naturally provide a self-interacting singlino dark matter to solve the small cosmological scale anomalies (a large Sommerfeld enhancement factor can also be obtained). However, we find that the NMSSM (the singlet extension of the MSSM with $Z_3$ symmetry) cannot achieve this due to the restricted parameter space. In our analysis we introduce the concept of symmetric and antisymmetric viscosity cross sections to deal with the non-relativistic Majorana-fermion dark matter scattering.} \begin{document} | As the standard model of the Big Bang cosmology, the $\Lambda$CDM model can account for most observations of the Universe. A crucial ingredient of this model is the existence of cold dark matter (CDM), which, with a proper cosmological constant, can successfully predict the large scale structure of the Universe. However, the predictions on small scale structures seem not so successful and some anomalies exist:~\cite{Bringmann:2013vra} 1) \textit{missing satellites} -- There should be many more dwarf-sized subhalos (satellites) than observed in the DM halo of the Milky Way (MW). And the observed galaxy luminosity and H{\sc i}-mass functions beyond the MW show shallower faint-end slopes than predicted. \cite{Klypin:1999uc} 2) \textit{cusp vs ~core} -- It seems to have cored inner density profiles in the low surface brightness and dwarf galaxies, this is at odds with CDM cusps predicted by simulations~\cite{deNaray:2011hy}. 3) \textit{too big to fail} -- In comparison with the densest and most massive satellites found in simulations, the observed brightest satellites of the MW attain their maximum circular velocity at a too large radii.~\cite{BoylanKolchin:2011de}. There are various ways to solve these small scale problems, such as the nonthermal production of warm dark matter \cite{Lin:2000qq} or the baryon feedback in the galaxies to make small halos dark \cite{Bullock:2010uy}. Also, recently the author of \cite{Tulin:2012wi,Ko:2014nha} proposed another self-interacting Dirac-fermion DM scenario with a light mediator ($\lsim$ 100 MeV) to solve these small scale anomalies. With a light force carrier, the dark matter scattering cross section could have a non-trivial velocity dependence. All of the small scales (the dwarf size, the Milky Way size as well as the galaxy cluster size) can have appropriate cross sections, thus leaving enough parameter space for the mass of DM, the force carrier and the coupling strength. Besides, the authors also showed that the DM self-interactions can be correlated with the effect of Sommerfeld enhancement in DM annihilation which is being probed through indirect detection experiments. This self-interacting DM scenario perfectly explain the anomalies in the simulations of small scale structures. Therefore, it is necessary to check if such a scenario can be realized in popular new physics theories like low energy supersymmetry (SUSY). In SUSY the better known DM candidate is the Majorana-type neutralino, which is composed of bino, wino and higgsinos. Apparently, if the neutralino can have self-interactions through a light force carrier, such a carrier can not have sizable standard model (SM) interaction due to the stringent constraints from both collider and DM detection experiments. Thus, this light force carrier should be composed mainly of a singlet with respect to the SM gauge groups, which cannot be found in the minimal supersymmetric standard model (MSSM). Fortunately, there are various singlet extensions of the MSSM, among which the next-to-minimal supersymmetric standard model (NMSSM) seems most attractive \cite{fayet,NMSSM}. In the NMSSM, all the parameters in the superpotential are dimensionless and electroweak symmetry breaking is triggered by the TeV-scale soft SUSY breaking terms. The SUSY preserving $\mu$ term in the superpotential of the MSSM is generated by the vacuum expectation values (VEV) of a singlet superfield $S$. It is shown that in the NMSSM a light singlet scalar at several GeV can survive the DM detection limits and the collider constraints \cite{NMSSM2}. On the other hand, if we do not impose any discrete symmetry (in the NMSSM it is $Z_3$) and allow for all possible interactions of the singlet field, then we have the general singlet extension of the MSSM (GMSSM), (more detail can be seen in \cite{Kaminska:2014wia}) which was used to explain the PAMELA anomaly \cite{Hooper:2009gm,Wang:2009rj}. Compared with the NMSSM, the GMSSM has a larger parameter space. In the GMSSM, the singlet can form a dark sector in case of a very small $\lambda$. The singlino-like dark matter can annihilate into the light singlet-like scalar, which can give the correct DM relic density and a proper Sommerfeld enhancement factor. In this model, the singlet scalar can be even lighter than in the NMSSM due to a larger parameter space. So it is intriguing to check if such a singlet scalar in the NMSSM or GMSSM can serve as the light force carrier mediated in the DM self-interactions, which is the aim of this work. In this work we focus on the NMSSM and GMSSM to check if the self-interacting DM scenario can be realized. In our study we will take into account the constraints from DM relic density, the DM direct detection experiments as well as the proper non-relativistic scattering cross sections between DM. We organize the content as follows. In Sec. \ref{sec2}, we will discuss the general DM interactions. In Sec. \ref{sec3} and Sec. \ref{sec4}, we will respectively check the NMSSM and GMSSM to figure out the possibility of realizing the self-interacting DM scenario to solve the small cosmological scale anomalies. Sec. \ref{sec5} contains our conclusions. | \label{sec5} In this paper we studed the possibility of the DM self-interaction to solve the small cosmological scale anomalies in the singlet extensions of the MSSM. We first checked the NMSSM and found that the correlation between the DM annihilation rate and DM-nucleon SI cross section strongly constrains this model so that it cannot realize the DM self-interacting scenario. For the GMSSM, the parameter space was found to be large enough to realize the DM self-interacting scenario and at the same time can give a large Sommerfeld enhancement factor. Also, we found that for Majorana-fermion DM, we must use viscosity cross sections ($\sigma_{VS}$ and $\sigma_{VA}$) in DM simulations. | 14 | 4 | 1404.6705 |
1404 | 1404.4924_arXiv.txt | The X-ray synchrotron emission of each of the young supernova-remnants (SNRs) SN1006, Kepler, Tycho, RCW86 and Cas A, is roughly given by $\nu L_{\nu}\sim 10^{45}\erg/t$, where $t$ is the remnant's age. The electrons emitting the X-ray emission cool fast, implying that the X-ray emission is calorimetric and equal to half of the cosmic ray (CR) electron acceleration efficiency (per logarithmic interval of particle energies, at multi TeV energies). Assuming Sedov-Taylor expansion, the resulting CR electron yield per SNR is estimated to be $E^2dN_e/dE\approx 6\nu L_{\nu}t \sim 10^{46}\rm erg$. This is about two orders of magnitudes below the required amount for explaining the observed electron CRs at $E\sim 10\rm GeV$. Possible resolutions are 1. a soft acceleration spectrum allowing much more energy at $E\sim 10\rm GeV$ compared to $E\sim 10\rm TeV$, 2. an increased acceleration efficiency at later phases of the SNR evolution (unlikely), or 3. SNRs are not the source of CR electrons. | \rm erg$}\label{sec:X-rays} One of the most exciting developments in the high energy study of supernovae remnants (SNRs) is the identification of non-thermal X-rays which are likely due to synchrotron emission of multi-TeV accelerated electrons \citep[e.g.][]{Koyama95,Fink94,Allen97}. An interesting aspect of this emission is that the non-thermal flux of the nearby young SNRs , Cas A, Kepler, Tycho, RCW86 and SN1006 is found to be of similar magnitude, $\nu f_{\nu, X}\sim 10^{-10} \rm ergs~cm^{-2} ~s^{-1}$ (see table \ref{table:SNRs}). This is in striking contrast with the non-thermal radio flux of these remnants. The radio flux of Cas A is $\sim 100$ times larger than that of other nearby remnants. \begin{table}[ht] \centering % \caption{Nearby young, shell supernova remnants} % \begin{tabular}{c c c c c c} % \hline\hline % SNR & d\footnote{Adopted from \citet{Green09} based on expansion and shock velocity estimates from proper motions or $H\alpha$ line widths.} & $t^{\rm a}$& $f_{\nu}(1\rm{GHz})^a$& $\nu f_{\nu,X}$\footnote{Non thermal emmision, estimated from \citep[][]{Berezhko06,Araya10,Giordano12,Lemoine-Goumard12,Acero10}} & $\mathbf{\nu L_{\nu,X}\cdot t}$\\ & [kpc] & [yr] & [Jy] &$[\rm erg~ cm^{-2} s^{-1}]$& [$\mathbf{10^{45}} \rm \textbf{erg}$] \\[1 ex] \hline % Cas A & 3.4 & $\sim 300$ & 2700 & $\sim 3\times10^{-10}$ & $\sim \mathbf{4}$ \\ [1ex] % Kepler& 2.9 & $400$ & 20 & $\sim 3\times10^{-11}$ & $\sim \mathbf{0.4}$\\ Tycho& 2.4 & $400$ & 60 & $\sim 10^{-10}$ & $\sim \mathbf{1}$\\ RCW86&2.3& $\sim 2000 \footnote{Assuming this is the remnant of the SN at 186AD \citep[e.g.][]{Stephenson02}}$& 50 & $\sim 10^{-10}$ & $\sim \mathbf{4}$\\ SN1006&2.2& $ 1000$ & 20 & $\sim 10^{-10}$ & $\sim \mathbf{2}$\\ \hline % \end{tabular} \label{table:SNRs} % \end{table} The likely explanation for the significant difference between the radio and X-ray properties (both emitted by accelerated electrons which interact with the magnetic field in the remnant) is that the high energy electrons that emit the X-rays are efficiently cooled by this emission \citep[e.g.][]{Vink03}. While the radio emission strongly depends on the magnetic field value $B$, $L(\rm 1GHz)\propto B^{3/2}$, the X-ray is calorimetric and independent of $B$, being proportional to the acceleration rate. The difference in radio flux thus likely results from a large difference in magnetic field value. The condition for fast cooling can be verified directly by comparing the cooling time and the age of the remnants. The cooling time, $t_{\rm cool}=\vep/\abs{\dot\vep}$, of an isotropic distribution of electrons with energies $\vep=\gamma m_e c^2$, moving through a magnetic field $B$ and therefore emitting synchrotron with a luminosity $-\dot \vep=(4/3)\gamma^2\sig_T(B^2)/(8\pi)c$ at a typical frequency $\nu\approx \gamma^2 eB/(10 m_e c^2)$ is approximately: \begin{align}\label{eq:tcool} t_{\rm cool}\approx& 60\rm{yr}\left(\frac{\vep}{20 \rm TeV}\right)^{-1}\left(\frac{B}{100\mu \rm G}\right)^{-2}\cr \approx& 60\rm{yr} \left(\frac{h\nu}{\rm keV}\right)^{-1/2}\left(\frac{B}{100\mu \rm G}\right)^{-3/2}. \end{align} The magnetic fields in these remnants have to be large given that the X-ray emission is $\gtrsim 100$ brighter than the TeV emission \citep{Albert07,Aharonian08,Aharonian09,Acero10,Acciari11}. A minimal magnetic field \begin{equation} B\gtrsim30\mu\rm{G} \left(\frac{\nu L_{\nu,\rm TeV}}{0.01\nu L_{\nu,\rm X}}\right)^{-1/2} \end{equation} is required so that the X-ray emission is sufficiently brighter than the Inverse Compton emission from the same electrons as they interact with the CMB photons. The large magnetic fields imply cooling times of multi-keV emitting electrons which are shorter than the age of the remnants, supporting the fast-cooling interpretation. Given that the X-rays are calorimetric, they directly probe the acceleration efficiency of electrons, \begin{equation} \nu L_{\nu,\rm syn}=\frac12\vep^2\frac{d\dot N_{e,SNR}}{d\vep}, \end{equation} where ${d\dot N_{e,SNR}}/{d\vep}$ is the generation rate of accelerated electrons at the shock and the factor of $0.5$ is due to the fact that the synchrotron frequency is proportional to the square of the electron energy so $d\log\vep=0.5d\log\nu$. We next relate this luminosity to the total yield of electrons. Like other cosmic rays, the electrons are trapped within the SNR and eventually lose their energy due to adiabatic expansion. Once the SNR becomes radiative, the CRs can escape. We conservatively assume that the CRs in the remnant at the latest phases escape the SNR without further losses. Assuming a constant fraction of the thermal energy behind the shock is converted to CRs, the electron CR energy is constant during the Sedov-Taylor phase \citep[e.g.][]{Chevalier83}. This CR electron energy, $\vep^2dN_{e,SNR}/d\vep$ (assumed to be independent of $\vep$), is given by \begin{equation} \vep^2\frac{dN_{e,SNR}}{d\vep}=A_{r}\vep^2\frac{d\dot N_{e,SNR}}{d\vep}t\approx 6 \nu L_{\nu,\rm syn} t \end{equation} where $A_{r}\approx 3$ is a dimensionless coefficient which is approximately equal to $3$ and is calculated in \sref{sec:ST} based on the results of \cite{Chevalier83}. Given the non-thermal X-rays of these SNRs, $ \nu L_{\nu,\rm syn} t\sim 1\times 10^{45}\rm erg$, the implied CR electron yield is of order $\sim 10^{46}\rm erg$, which is a tiny fraction of the supernova energy, $E_{\rm SNR}\sim 10^{51}\rm erg$. In fact, as we next argue, this is about two orders of magnitudes smaller than the required yield in order to account for the observed CR electrons. | 14 | 4 | 1404.4924 |
|
1404 | 1404.1676_arXiv.txt | We analyze the three dimensional anisotropy of the galactic cosmic ray (GCR) intensities observed independently with a muon detector (MD) at Nagoya in Japan and neutron monitors over four solar activity cycles. We clearly see the phase of the free-space diurnal anisotropy shifting toward earlier hours around solar activity minima in $A>0$ epochs, due to the reduced anisotropy component parallel to the mean magnetic field. This component is consistent with a rigidity independent spectrum, while the perpendicular anisotropy component increases with GCR rigidity. We suggest that this harder spectrum of the perpendicular component is due to contribution from the drift streaming. We find that the bidirectional latitudinal density gradient is positive in $A>0$ epoch, while it is negative in $A<0$ epoch, in accord with the drift model prediction. The radial density gradient of GCRs, on the other hand, varies with $\sim$11-year cycle with maxima (minima) in solar maximum (minimum) periods, but we find no significant difference between the radial gradients in $A>0$ and $A<0$ epochs. The corresponding parallel mean free path is larger in $A<0$ than in $A>0$. We also find, however, that parallel mean free path (radial gradient) appears to persistently increase (decreasing) in the last three cycles of weakening solar activity. We suggest that simple differences between these parameters in $A>0$ and $A<0$ epochs are seriously biased by these long-term trends. | The solar wind is a supersonic plasma blowing radially outward from the sun toward a vast space filled by cold and thin interstellar plasma. The global structure of the region called the ``heliosphere'', which is a region dominated by the solar wind plasma and the solar magnetic field, is of great interest for both solar- and astrophysicists. The Interplanetary Magnetic Field (IMF) is the term representing the solar magnetic field carried outward by the solar wind into the heliosphere as magnetic field lines from the Sun are dragged along by the highly conductive solar wind plasma \citep{Par58}. Because of the dominant dipole component of the solar magnetic field, the IMF is divided into two magnetic sectors in the northern and southern hemisphere separated by the Heliospheric Current Sheet (HCS) which develops into a ``wavy'' three dimensional structure. The inclination of the magnetic dipole from the rotation axis increases with increasing the solar activity and reverses during the solar activity maximum epoch when the inclination becomes maximum. The Sun has a strong and complex magnetic field, and the physical properties of the heliosphere is directly connected to the properties of the magnetic field varying with a period of about 11 years.\par Temporal variations in the inner heliosphere can be deduced from the ground-based observations of the high-energy Galactic Cosmic Rays (GCRs). GCRs are high-energy nuclei (mostly protons) accelerated in our galaxy and continuously arriving at the earth after traveling through the heliosphere. After entering the heliosphere, GCRs interact with the IMF being carried outward by the solar wind. The interaction with the large-scale ordered field causes the gradient- and curvature-drift motions of GCRs in the heliosphere, while the interaction with the irregular (or disordered) field component results in the pitch angle scattering of GCRs. The scattering by the magnetic irregularities embedded in the expanding solar wind causes the deceleration (called the adiabatic cooling) and also causes an outward convection which leads to lower GCR intensities closer to the Sun. The resulting positive radial gradient of GCRs produces an inward diffusion, flowing preferentially along the ordered IMF lines. A steady state distribution is realized when the inward diffusion is balanced with the outward convection. The GCR intensity measured at the Earth changes with various time scales. The solar cycle variation of the solar wind parameters, such as the solar wind velocity, the magnitude and orientation of the IMF, the tilt angle of the HCS and the mean free path of the pitch angle scattering of GCRs in the turbulent magnetic field, alters the spatial distribution of GCR density in the heliosphere. The drift model of GCR transport predicts a bi-directional latitudinal gradient pointing in opposite directions on the opposite sides of the HCS if the HCS is flat \citep{Jok79}. The predicted spatial distribution of the GCR density has a minimum along the HCS in the ``positive'' polarity period of the solar polar magnetic field (also referred as $A>0$ epoch), when the IMF directs away from (toward) the Sun in the northern (southern) hemisphere, while the distribution has the local maximum on the HCS in the ``negative'' period ($A<0$ epoch) with the opposite field orientation in each hemisphere. The field orientation reverses every 11 years around the maximum period of the solar activity. A tilted current sheet introduces modifications around the wavy HCS. For example the intensity minimum (for $A>0$) will not be right at the HCS, but the general tendencies in the sense of the latitudinal gradient remain the same as outlined above \citep{Jok82}.\par The variation of the spatial distribution of GCR density causes the variation of the directional anisotropy of the GCR intensity measured at the Earth. One such variation is the 22-year variation of the solar diurnal anisotropy in which the phase (or the local solar time of maximum intensity) of the anisotropy shifts towards earlier hours around every $A>0$ solar minima \citep[][and references therein]{Tha53, For67, Ahl88, Bie91}. By analyzing the anisotropy observed with neutron monitors (NMs) in 1968-1988, \citet{Che93} (hereafter referred as Paper I) revealed that the observed phase-shift of the diurnal anisotropy is due to the decrease of the diffusion streaming parallel to the IMF in $A>0$ solar minima. The parallel diffusion streaming is proportional to the radial gradient ($G_r$) of GCR density multiplied by the parallel mean free path ($\lambda_{\|}$) of the pitch angle scattering. The simple drift model predicts smaller $G_r$ in $A>0$ epoch than in $A<0$ epoch, if the diffusion coefficients are same in both epochs \citep{Kot83}. Finding a significant 11-year solar cycle variation but no clear 22-year variation in the observed $G_r$, however, Paper I suggested that the smaller parallel streaming in the $A>0$ solar minimum period was caused by the smaller $\lambda_{\|}$, possibly due to the magnetic helicity effect in the turbulent magnetic field \citep[Paper I;][]{Bie86, Bie87}.\par The GCR anisotropy (or the streaming) vector in three dimensions (3D) consists of three components, two lying in the ecliptic plane and the other pointing normal to the ecliptic plane. The two ecliptic components, parallel and perpendicular to the IMF, are derived from the amplitude and phase of the solar diurnal anisotropy corrected for the contribution from the radial solar wind convection. Paper I analyzed the diurnal anisotropy in free space, corrected for the geomagnetic deflection of GCR orbits, by assuming a power law type ($\propto p^\gamma$) dependence of the anisotropy amplitude on the GCR rigidity ($p$) with the spectral index ($\gamma$) and the upper limiting rigidity ($P_u$) fixed at 0 and 100 GV, respectively. The zero spectral index of the diurnal anisotropy has been assumed in many analyses based on the original convection-diffusion picture of the GCR transport in which the stationary GCR distribution in the heliosphere results from the inward diffusion balancing with the outward convection by the solar wind which is independent of the rigidity \citep{Par65, Gle67, Gle69}. The upper limiting rigidity ($P_u$) set at 100 GV was also a reasonable assumption for the analysis of NM data alone, because $P_u$ representing the break-down rigidity of the diffusion picture is expected to be much higher than the median primary rigidity to which the NMs used in Paper I respond. \citet{Mun97} assumed $\gamma=0$ but treated $P_u$ as a free parameter in their analyses of the diurnal anisotropy observed with multi-directional muon detectors (MDs) which have median responses to GCRs with higher rigidity than NMs. They found $P_u$ changing between 100 and 300 GV in a clear correlation with the solar activity \citep{Mun02}. \citet{Hal97} treated both $\gamma$ and $P_u$ as free parameters in their analyses of the NM and MD data and reported the temporal variation of each parameter in solar activity and solar magnetic cycles.\par All these works take account of the rigidity dependence of the amplitude varying as a function of time, but they still assume that the phase is independent of rigidity. In other words, they assumed a common rigidity spectrum for two ecliptic components, parallel and perpendicular to the IMF. \citet{Bie91} (hereafter referred as Paper II), on the other hand, also reported that the magnitude of the observed phase variation in $A>0$ solar minimum increases with GCR rigidity \citep{Agr83}. This rigidity dependent feature of the observed phase variation cannot be reproduced properly, as long as the rigidity spectrum common for two ecliptic components is assumed. This observed feature has been confirmed by other papers \citep[e.g.][]{Oh10}, but its physical origin is still left unknown.\par The third component of the anisotropy, that is, the north-south (NS) anisotropy normal to the ecliptic plane has been derived also from NM and MD data in a couple of different ways. \citet{Bie86} and Paper I derived this anisotropy from the difference between count rates in a pair of NMs which are located near the north and south geomagnetic poles and observing intensities of GCRs arriving from the north and south pole orientations, respectively. They found a $\sim$10-year cycle variation in this component anisotropy which implied the radial gradient ($G_r$) of GCR density changing in correlation with the solar activity, while they found no significant difference of $G_r$ in $A>0$ and $A<0$ epochs in a contradiction with the simple drift model prediction. Due to 23.4$\degr$ inclination of Earth's rotation axis from the ecliptic normal, the NS anisotropy normal to the ecliptic plane can be also observed as a diurnal variation of count rate in the sidereal time with the maximum phase at $\sim$18:00 local sidereal time \citep{Swi69}. \citet{Yas80} analyzed this sidereal diurnal variation observed by NMs and MDs during 5 years between 1969 and 1973 and found that observations were reproduced best by the average rigidity spectrum with $\gamma=0.3$ and $P_u=200$ GV. This was the first experimental indication that the rigidity spectrum of the anisotropy has a positive spectral index. \citet{Hal94} also applied the same method to NM and MD data observed between 1957 and 1985 and found the average spectrum with $\gamma=0.5$ and $P_u=400$ GV, again with a positive $\gamma$. This suggested that each of two ecliptic components may also have a spectrum with non-zero $\gamma$.\par A possible drawback of deriving the NS anisotropy from the sidereal diurnal variation is that the expected amplitude of the sidereal diurnal variation ($\sim$0.03 \%) is approximately an order of magnitude smaller than the solar diurnal variation ($\sim$0.3 \%). The small signal in the sidereal time can be easily influenced by the solar diurnal anisotropy changing in a year. Another difficulty is that one can obtain only the yearly mean anisotropy. This is because of the fact that the influence from the solar diurnal variation, even if it is stationary through a year, can be eliminated in the sidereal time only when the diurnal variation is averaged over integral year(s). This makes it difficult to deduce reliable error of the yearly mean anisotropy. \citet{Mor79} proposed another way to derive the NS anisotropy from the ``GG-component'' of a multi-directional MD at Nagoya in Japan. The GG-component is a difference combination between intensities recorded in the north- and south-viewing directional channels designed to measure the NS anisotropy free from the atmospheric temperature effect \citep{Nag72}. \citet{Lau03} showed that GG-component can be used for deriving reliable sector polarity of the IMF. By using a global network of four multi-directional MDs which are capable of observing the NS anisotropy on hourly basis, \citet{Oka08} confirmed that the north-south anisotropy deduced from the GG-component is consistent with the anisotropy observed with the global network.\par In the present paper, we extend the analysis by Paper I to the most recent period and derive the long-term variation of the modulation parameters from the 3D anisotropy observed during 44 years by the Nagoya multi-directional MD which has a median rigidity of 60 GV for primary GCRs. We also analyze the anisotropy observed during the same period by NMs which have the median response to 17 GV primary GCRs. We derive the NS anisotropy from the GG-component of the Nagoya MD. We particularly examine the rigidity dependences of each component of the anisotropy and each modulation parameter by comparing them derived from MD and NM data at 60 GV and 17 GV, respectively. We do not intend to determine each rigidity spectrum quantitatively by, for instance, calculating both $\gamma$ and $P_u$ as free parameters in best-fit calculation as a function of time. In such best-fit calculations, we often see a significant anti-correlation between the best-fit $\gamma$ and $P_u$ \citep{Hal94, Hal97}. A large $P_u$ with a small (or negative) $\gamma$ often returns similar $\chi^2$-value as a small $P_u$ with large (or positive) $\gamma$ does, increasing the systematic error of each best-fit value. We instead examine the rigidity spectrum qualitatively based on the ratio between parameters derived from NM and MD data with a common assumption of the spectrum with fixed values of $\gamma =0$ and $P_u=100$ GV, respectively, as done in Paper I. If the ratio is close to one, the spectrum is consistent with the assumption. If the ratio is significantly larger (smaller) than one, on the other hand, we can conclude that the spectrum is harder (softer) than the assumed one. In this way, we can make a qualitative but reliable examination of the rigidity dependence of each parameter. We will present quantitative analyses of the rigidity dependence elsewhere. It will be shown in the present paper that three components of the anisotropy have different rigidity dependence. This naturally explains the rigidity dependent feature of the observed phase variation mentioned above. We will also suggest that the different rigidity dependence for three anisotropy components are possibly due to the relative contribution from the drift (diamagnetic drift) which is different in each component.\par The outline of this paper is as follows. In section 2, we describe the data analysis and results in detail. The conclusions and discussions are given in section 3. For readers' references, we also present our results in a numerical data table in Appendix A. In Appendix B, we show how the obtained results depend on the assumed value of $P_u$. | We examined the energy dependence of the long-term variations of the 3D anisotropy of GCR intensity by analyzing the data recorded in 1970-2013 by NMs (Swarthmore/Newark, Alert/Thule and McMurdo) which have median responses to $\sim$17 GV primary GCRs and the Nagoya MD which has the median response to $\sim$60 GV GCRs. The derived free-space harmonic vector of the diurnal anisotropy changes its phase to earlier hours in $A>0$ solar minima from the $\sim$18:00 local time known as the phase of the ``corotation'' anisotropy, while the amplitude changes in 11-year cycle decreasing to a small value in years around every solar minimum. We note that the magnitude of the phase change is significantly larger in MD data than in NM data indicating a marked rigidity dependence of the phase change. A clear 22-year variation is seen in the parallel component ($\xi_{\|}$) of the anisotropy confirming the conclusion of Paper II that $\xi_{\|}$ is primarily responsible for the phase change. The north-south anisotropy ($\xi_z$) derived from the GG-component of Nagoya MD also shows an 11-year cycle with minima in years around every solar minimum.\par The ecliptic anisotropy components ($\xi_{\|}$ and $\xi_{\bot}$) derived from NM and MD data vary in a close correlation with each other, while no such correlation is seen in the variation of $\xi_z$. The mean ratio between $\xi_{\|}$s in MD and that in NM data is roughly consistent with a rigidity independent spectrum, while the rigidity spectrum of $\xi_{\|}$ is systematically softer in $A>0$ than in $A<0$. % On the other hand, $\xi_{\bot}$ and $\xi_z$ derived from MD data are significantly larger than those from NM data, indicating that these components increase with $P_m$. According to equations (\ref{xparG})-(\ref{xzG}), $\xi_{\bot}$ and $\xi_z$ include contributions from the gyration of particles (connected to diamagnetic drift) added to perpendicular diffusion, while $\xi_{\|}$ is caused by the parallel diffusion alone. It is reasonable, therefore, to expect that the observed harder rigidity spectra of $\xi_{\bot}$ and $\xi_z$ are due to effects from drift. Based on numerical simulations of particle propagation in turbulent magnetic field, \citet{Min07} has shown that drifts are suppressed by magnetic turbulence, but the suppression sets in at lower turbulence amplitudes for low-energy than for high-energy cosmic rays. This may give a possible explanation for why the contribution of drift streaming results in a harder rigidity spectrum. If this is the case, we may well need two different spectra, representing diffusion and drift, combined in $\xi_{\bot}$ and $\xi_z$, to reproduce the correct rigidity dependence of the diurnal anisotropy in space. We will present such analyses elsewhere.\par Equations (\ref{xparG})-(\ref{xzG}) also imply that the drift contribution to $\xi_{\bot}$ is proportional to $G_{|z|}$, while the drift contribution to $\xi_z$ is proportional to $G_r$. By comparing $G_r$ and $G_{|z|}$ derived from NM and MD data, we find that the rigidity dependences of $G_r$ and $\xi_z$ are harder than those of $G_{|z|}$ and $\xi_{\bot}$. \citet{Yas80} and \citet{Hal94} analyzed the north-south anisotropy observed with NMs and MDs monitoring a wide range of $P_m$ and found $\xi_z$ increasing with the rigidity up to several hundred GV. This is in a qualitative agreement with the present paper.\par We finally discuss the long-term variations of the modulation parameters. Figure \ref{fig:LG} shows the temporal variation of $\lambda_{\|} G_r = \xi_{\|} / \cos \psi$ (see equation (\ref{xparG})). Clearly seen is that the mean magnitude of $\lambda_{\|} G_r$ is significantly smaller in $A>0$ (solid circles) than in $A<0$ periods (open circles). The mean magnitude of $\lambda_{\|} G_r$ derived from MD data and that from NM data in $A<0$ epoch are 1.07$\pm$0.03 and 1.14$\pm$0.02, respectively, which are fairly consistent with each other. The mean magnitudes in $A>0$ periods are 0.68$\pm$0.04 \% and 0.89$\pm$0.05 \%, respectively. Combined with the solar wind convection, this reduction of $\lambda_{\|} G_r$ results in the observed phase shift of the diurnal anisotropy to earlier hours in $A>0$ as suggested by Paper I. We also note that the ratio of $\lambda_{\|} G_r$ for MD to that for NM data is smaller in $A>0$ than in $A<0$ periods, indicating the softer rigidity spectrum of this component for $A>0$ than for $A<0$ (see discussion of figure \ref{fig:IMFcomp} in the preceding section). This larger decrease of $\lambda_{\|} G_r$ in $A>0$ epoch in MD data than in NM data is responsible to the larger phase shift of the diurnal anisotropy in $A>0$ solar minimum epoch in MD data. The harder rigidity spectrum of $\xi_{\bot}$ than that of $\xi_{\|}$ mentioned above is also partly responsible to the larger phase shift in MD data in $A>0$ minimum epochs. \citet{Hal97} used the NM and MD data for analyzing the rigidity spectrum of the diurnal anisotropy and obtained the average $G(p)$ proportional to $p^{-0.1\pm0.2}$ with $P_u = 100\pm25$ GV. Although their spectrum seems to be consistent with $G(p)$ assumed in this paper, such a common spectrum for $\xi_{\|}$ and $\xi_{\bot}$ cannot reproduce the observed feature that the phase shift observed by MD in $A>0$ solar minimum epoch is significantly larger than that by NM.\par The 11- and 22-year variations are also apparent in the modulation parameters shown in figure \ref{fig:ModParam}. The bidirectional latitudinal density gradient ($G_{|z|}$) in the top panel is positive (negative) in $A>0$ ($A<0$) epoch in accord with the drift model prediction of the local minimum (maximum) of GCR density around the HCS. This 22-year variation looks more significant in MD data than in NM data, with a smaller error of each data point. The mean magnitude of $G_{|z|}$ is larger in $A<0$ than in $A>0$ in both MD and NM data. The 11-year variation is evident in the radial density gradient ($G_r$) in the middle panel of figure \ref{fig:ModParam}, while we cannot identify a clear 22-year variation as reported by \citet{Bie86}. The mean $G_r$ deduced from MD (NM) data is 0.89$\pm$0.11 (1.04$\pm$0.08) \%/AU in $A>0$ epoch, while it is 0.99$\pm$0.12 (1.13$\pm$0.10) \%/AU in $A<0$ epoch. It is noted that we find a poor correlation between temporal variations of $G_{|z|}$ and $G_r$ in both NM and muon data.\par The mean parallel mean free path ($\lambda_{\|}$), on the other hand, turns out to be significantly larger in the $A<0$ than in the $A>0$ epochs, in the both MD and NM data. We find that the mean $\lambda_{\|}$ deduced from MD (NM) data is 0.90$\pm$0.10 (0.89$\pm$0.06) AU in $A>0$, while it is 1.32$\pm$0.13 (1.14$\pm$0.10) AU in $A<0$. Paper I suggested that the 22-year variation of $\lambda_{\|}$ is responsible for the reduction of $\lambda_{\|} G_r$ in $A>0$ and for the 22-year variation of the diurnal anisotropy. The two bottom panels of figure \ref{fig:LG} show the correlation between $G_r$ and $\lambda_{\|}$ (both in logarithmic scale) on the vertical ($y$) and horizontal ($x$) axes, respectively. Since $\lambda_{\|}$ on the $x$-axis is deduced from $\lambda_{\|} G_r$ divided by $G_r$ on the $y$-axis, data points in this scatter plot align on a straight line when $\lambda_{\|} G_r$ is constant during the analysis period. Solid and dashed straight lines in each panel display functions of $y = c/x$ best-fitting to data in $A>0$ and $A<0$ epochs, respectively, each with the intercept $c$ as a best-fit parameter. It is seen that, for the MD data (left panel) the best-fit $c$ for $A>0$ data (solid circles) is about 64 \% of that for the $A<0$ data (open circles). This is consistent with the lower $\lambda_{\|}$ value derived from MD data for $A>0$ epochs which is 68 \% (=0.90/1.32) of that in $A<0$ epoch, indicating that the 22-year variation of $\lambda_{\|} G_r$ in the left panel is due to the 22-year variation of $\lambda_{\|}$ on the horizontal axis.\par However, as mentioned in connection with figure \ref{fig:ModParam} in the preceding section, we also find that $\lambda_{\|}$s ($G_r$s) from NM and MD data appear to persistently increase (decrease) during the last three solar activity cycles reaching maximum (minimum) in 2008-2009. Figure \ref{fig:CycleAve} displays the mean $G_r$ and $\lambda_{\|}$ in $A>0$ and $A<0$ epochs, each as a functions of time. It is clear particularly in the MD data (left panels) that there is a long-term trends indicated by a best-fit solid line in each panel. This trend enhances the difference between $A>0$ and $A<0$ means of $\lambda_{\|}$, while it reduces the difference between means of $G_r$. The simple means of $G_r$ or $\lambda_{\|}$ in all $A>0$ and $A<0$ epochs are, therefore, seriously biased by these long term trends. If we look at the deviation of each data point from the solid line in the MD data, on the other hand, we find that $G_r$ and $\lambda_{\|}$ are both larger (smaller) in $A<0$ ($A>0$) epoch, although only at one sigma level.\par The phase-shift of the diurnal anisotropy toward earlier hours in the $A>0$ epochs is a robust consequence of particle drifts in the inhomogeneous large-scale HMF (heliospheric magnetic fields). The observed phase shift in $A>0$ epoch arises naturally in various drift models employing different approaches \citep{Lev76, Erd80, Pot85}. The reproduction of the north-south anisotropy, which is formed by the interplay of drift and perpendicular diffusion, is more challenging for theoretical models. This is particularly true for the $A>0$ epoch, when latitudinal gradients tend to point away from the current sheet, but the intensity minimum of GCRs is not precisely on the HCS. Hence one cannot expect a one-to-one correlation between the field polarity and the NS anisotropy \citep{Oka08}. \citet{Kot01} modeled the 3D anisotropy in a simulation including a wavy HCS with possible variations in the solar wind speed leading to the formation of corotating interaction regions. Their results are in qualitative agreement with the observed phase-shift and reduction of radial gradient in the $A>0$ epochs as well as with the opposite sense of latitudinal gradient around the HCS around solar minima of $A>0$ and $A<0$ epochs. The simulation results for the variation of the NS anisotropy remained inconclusive.\par It is important to keep in mind that solar cycles are not identical and, as mentioned in the previous section, long-term changes do occur. A particularly interesting recent example is the long and unusual last solar cycle, when the GCR intensity at the Earth reached record-high level \citep{Mew10}. The most plausible explanation is that the magnetic field was weakest ever recorded \citep{McC08} and the weaker field allowed faster diffusion of GCRs into the inner part of the heliosphere. Another remarkable feature of the last solar cycle was that the HCS remained tilted for a long time and did not flatten the same way as in other cycles. Figure \ref{fig:IMFcomp} shows that $\xi _z$ turned out to be larger in the last solar minimum than during previous solar minima. This most likely shows the effect of the tilted HCS. The streaming component normal to the HCS cannot abruptly change, but has to change continuously at the HCS. Hence $\xi _z$ has to go to a small value when the HCS flattens, while it can be larger if the HCS is tilted. This feature is more apparent for MD data than for NM data.\par The dynamic range of $\lambda_{\|}$ (or $G_r$) due to the 11-year variation in the lower panels of figure \ref{fig:LG} is close to an order of magnitude and much larger than the 22-year variation. Small signature of its 22-year variation can be easily masked by the 11-year variation with much larger amplitude. In order to analyze the 22-year variation of each modulation parameter, therefore, it is necessary to minimize the influence of the 11-year variation as much as possible. Also simple means of $\lambda_{\|}$ and $G_r$ in each of $A>0$ and $A<0$ epochs may be seriously biased by their long term trends as seen above. For identifying the physical origin of the 22-year variation correctly, it is also necessary to analyze its rigidity dependence. The long-term observation with the Nagoya MD, as well as the observations with NMs, makes such analyses possible. | 14 | 4 | 1404.1676 |
1404 | 1404.4053_arXiv.txt | Using the suite of high-resolution zoom re-simulations of individual haloes by Martig et al., and the large-scale simulation \emph{MassiveBlack-II}, we examine the differences in measured galaxy properties from techniques with various aperture definitions of where galaxies end. We perform techniques popular in the literature and present a new technique of our own, where the aperture radius is based on the baryonic mass profiles of simulated (sub)haloes. For the average Milky-Way-mass system, we find the two most popular techniques in the literature return differences of order 30 per cent for stellar mass, a factor of 3 for gas mass, 40 per cent for star formation rate, and factors of several for gas accretion and ejection rates. Individual cases can show variations greater than this, with the severity dependent on the concentration of a given system. The average difference in integrated properties for a more general galaxy population are not as striking, but are still significant for stellar and gas mass, especially for optical-limit apertures. The large differences that can occur are problematic for comparing results from various publications. We stress the importance of both defining and justifying a technique choice and discourage using popular apertures that use an exact fraction of the virial radius, due to the unignorable variation in galaxy-to-(sub)halo size. Finally, we note that technique choice does not greatly affect simulated galaxies from lying within the scatter of observed scaling relations, but it can alter the derived best-fit slope for the Kennicutt-Schmidt relation. | 14 | 4 | 1404.4053 |
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1404 | 1404.2958_arXiv.txt | {} { We propose to infer the output of the ionising continuum-leaking properties of galaxies based upon their \lya\ line profiles. } {We carried out \lya\ radiation transfer calculations in two models of \hii\ regions. These models are porous to ionising continuum escape: 1) we define Lyman-continuum (LyC) optically thin star clusters, in which massive stars produce enough ionising photons to keep the surrounding interstellar medium transparent to the ionising continuum, in other words, almost totally ionised, and 2) we define riddled ionisation-bounded media that are surrounded by neutral interstellar medium, but have holes, which results in a covering fraction lower than unity. } {The \lya\ spectra that emerge from these configurations have distinctive features: 1) a classical asymmetric redshifted profile in the first case, but with a small shift of the profile maximum compared to the systemic redshift (\vpeak\ $\leq 150$\,\kms); 2) a main peak at the systemic redshift in the second case (\vpeak\,$= 0$), with a non-zero \lya\ flux bluewards of the systemic redshift as a consequence. If in a galaxy that leaks ionising photons the \lya\ component that emerges from the leaking star cluster(s) is assumed to dominate the total \lya\ spectrum, the \lya\ shape may be used as a pre-selection tool for detecting LyC-leaking galaxies in objects with high spectral resolution \lya\ spectra (R $\geq 4000$). Our predictions are corroborated by examination of a sample of ten local starbursts with high-resolution HST/COS \lya\ spectra that are known in the literature as LyC leakers or leaking candidates. } {Observations of \lya\ profiles at high resolution are expected to show definite signatures revealing the escape of Lyman-continuum photons from star-forming galaxies.} | \label{s_intro} Determining the population of objects that reionised the Universe and maintained the subsequent thermal history of the intergalactic medium (IGM) remains an outstanding and urgent question in observational cosmology. Observations show that some active galactic nuclei were in place almost at the reionisation epoch, but their numbers were grossly insufficient to reproduce the necessary background of Lyman-continuum (LyC; $<912$\AA) radiation \citep[e.g.][]{Cowie09, Fontanot12}. This leaves star-forming galaxies to reionise the Universe, and, while they undoubtedly are in place at the relevant epoch, with hints for a steep luminosity function (LF) at the faint end \citep{Alavi14}, it still appears that the current populations are insufficient to have completed reionisation by $z\approx 6$ \citep[e.g.][and references therein]{Robertson13}. Moreover, simply knowing that galaxies are in place is not sufficient: they must also emit enough LyC radiation. In the very nearby Universe this is manifestly not the case, where space-borne UV telescopes such as the HUT (Hopkins Ultraviolet Telescope) and FUSE (Far Ultraviolet Spectroscopic Explorer) have reported a large number of upper limits \citep[e.g.][]{Leitherer95, Heckman01, Deharveng01, Grimes09} and only a small number of weak detections with escape fractions of only a few percent \citep[e.g.][]{Leitet11,Leitet13, Borthakur14}. Despite the much larger samples of galaxies that have been studied in LyC at $z\sim 1$ with the Galaxy Evolution Explorer (GALEX) and the Hubble Space Telescope (HST), the situation still does not change much, and still no individual LyC-leaking galaxies are reported \citep{Malkan03, Siana07, Cowie09, Siana10}. The beginnings of the necessary evolution seem to set in at higher redshifts of $z\sim 3$. LyC emission has been reported in large samples of Lyman break galaxies (LBGs) and \lya-emitters (LAEs), using both spectroscopic \citep{Steidel01, Shapley06} techniques and narrowband imaging bluewards of the restframe Lyman limit \citep{Iwata09, Nestor11, Nestor13, Mostardi13}. Curiously, most narrowband images of the emitted LyC show spatial offsets from the non-ionising UV continuum, which may indeed be consistent with models of LyC leakage being facilitated by supernova winds (Clarke \& Oey 2002) or unresolved galaxy mergers (Gnedin et al. 2008). Alternatively, the spatial offsets may also be explained by projected galaxies at lower redshift that contaminate the observed LyC \citep{Vanzella10, Vanzella12}, although simulations performed by \citet{Nestor13} suggest that this probably does not account for all detections. Another particularly relevant result from $z\sim 3$ is that LyC leakage seems to be stronger from LAEs than from LBGs. Theorists have repeatedly shown that LyC leakage generally increases at lower galaxy masses \citep[e.g.][]{Ferrara13, Yajima11, Wise09}, which superficially seems to be consitent with the stronger LyC leakage found from $z\sim 3$ LAEs, which tend to occupy lower mass haloes \citep{Ouchi05, Gawiser06, Guaita11}. Because the UV LFs found in the high-$z$ Universe are particularly steep \citep{Alavi14, Dressler14} and LyC escape fractions increase moving downwards across the galaxy LF, the case may indeed be that faint \lya-emitting galaxies were the main contributors to reionisation. The evolution of the number of \lya\ emitting galaxies among the population of LBGs with a sudden drop at $z > 6$ \citep{Stark10, Ono12, Schenker14} is usually interpreted as due to an increase of the neutral fraction of the IGM. But if \lya-emitting galaxies have a non-negligible LyC escape fraction ($\geq 15\%$) at z>6 and if this increases again towards higher z, then these galaxies become fainter in \lya\ at levels that could (partially) mimic a reionisation signature \citep{Hayes11, Dijkstra14}. This reasoning can be generalised to all nebular lines: along the same idea, \citet{Zackrisson13} proposed to search for weak nebular lines in the spectra of galaxies of the reionisation epoch as a probe for LyC leakage. In the local Universe, \citet{Lee09} observed a systematic underestimate of the star formation rate derived from H$\alpha$ luminosity, SFR(H$\alpha$), compared to SFR(UV), the star formation rate derived from ultraviolet luminosity, in dwarf galaxies among their sample of nearby galaxies, which can be interpreted as the result of a higher escape of ionising photons in smaller galaxies. To explain the low success rate of LyC-leaking detections, the commonly invoked explanation is that the galaxies responsible for reionisation are the faintest ones, which are below our current continuum detection threshold \citep[e.g.][]{Ouchi08}. On the other hand, a huge amount of spectroscopic data are available in \lya, up to the reionisation redshift \citep[e.g.][]{Shapley03,Hu10,Stark10,Guaita10,Guaita11,Dressler11,Bielby11, Pentericci10,Pentericci11, Kulas12,Jiang13a, Jiang13b, Ellis13, Schenker13}. Could we tell from the \lya\ line shape if a galaxy is a good candidate for continuum leaking? This is the starting point of our study. Based on \lya\ radiation transfer modelling, we first present the theoretically expected \lya\ spectral characteristics of continuum-leaking galaxies. We then compare our diagnostics with two other indirect diagnostics of continuum leaking that have been proposed in the literature, which are (a) a low covering fraction of the interstellar absorption lines that are in a low-ionisation state (LIS)\citep[e.g.][]{Heckman11, Jones13}, and (b) a high ratio of \oiiil/\oiill\ as a proxy for density-bounded \hii\ regions \citep{Nakajima14,Jaskot13, Kewley13}. Finally we compare the different indicators for a sample of low-redshift galaxies. Our paper is structured as follows. The link between Lyman-continuum leakage and the \lya\ line profile is discussed in Sect.\ \ref{s_LyaLyC}. In Sect.\ \ref{s_compare} we compare the different leaking indicators for a sample of low-redshift galaxies. Our main results are discussed in Sect.~\ref{s_discuss} and are summarised in Sect.\ \ref{s_conclude}. | \label{s_conclude} We have carried out \lya\ radiation transfer simulations in two idealised configurations of LyC-leaking star-forming galaxies: \begin{enumerate} \item Homogeneous spherically expanding ISM shells with a central \lya\ source, but with extremely low column densities ($N_{\rm HI} \leq 10^{18}$ cm$^{-2}$), \item clumpy spherical shells with a non-unity covering fraction, called riddled ionisation-bounded \hii\ regions. \end{enumerate} In both cases, we find that the emerging \lya\ spectrum has remarkable features that may be possible to identify in observed \lya\ spectra, assuming that the \lya\ spectrum from a galaxy may be dominated by the \lya\ component emerging from LyC-leaking star clusters. According to the first scenario, the \lya\ spectrum will have a classical asymmetric redshifted profile, but with a small shift (\vpeak\ $\leq 150$\,\kms). According to the second scenario, the main feature is a peak at the systemic redshift of the star cluster, with, as a consequence, a non-zero flux bluewards of the \lya\ line centre. These two signatures may be used to distinguish or select leaking candidates at all redshifts for objects with high spectral resolution and well-determined systemic redshift. We have examined how these diagnostics compare with observed \lya\ spectra from the local Universe where either the LyC escape fraction has been directly measured \citep{Bergvall06, Leitet13} or has been derived from LIS absorption lines studies \citep{Heckman11}. We also tested our predictions against a sample of non -leaking galaxies of the same team. Although the number of objects is very small to derive statistically robust conclusions, the expected trends seem to be at work (\vpeak\ and $S_{\rm peak}$ smaller for leakers than non-leakers). We proposed two additional galaxies as good candidates for LyC leaking: GP\,1219+1526, based on the small separation of the peaks in its \lya\ profile, and a high \oiii/\oii\ ratio, could be leaking according to our first scenario of a density-bounded region; Tol\,1214--277, described in \citet{Thuan97}, based on its very peculiar \lya\ spectral shape (symmetrical triple peak with the main peak at \vpeak\ = 0), and indications of non-total coverage of LIS absorption lines, could be leaking from a riddled ISM. There are well-known objects in the local Universe from which a strong LyC flux is detected, belonging to the family of AGNs. As another validation of our diagnostics, we verified in the literature that \lya\ spectra from these known LyC leakers are in emission, and peak at the line centre. Our predictions need to be tested on larger samples with well-determined systemic redshifts and high spectral resolution \lya\ profiles. But apparently a small shift of the maximum of the \lya\ profile with respect to the systemic redshift (\vpeak\ $\leq 150$\,\kms) may be a good proxy for a non-zero escape fraction of ionising radiation from galaxies. | 14 | 4 | 1404.2958 |
1404 | 1404.0670_arXiv.txt | % Global extreme ultraviolet (EUV) waves are spectacular traveling disturbances in the solar corona associated with energetic eruptions such as coronal mass ejections (CMEs) and flares. \editor{Over the past 15 years, observations from three generations of space-borne EUV telescopes} have shaped our understanding of this phenomenon and at the same time led to controversy about its physical nature. Since its launch in 2010, the {\it Atmospheric Imaging Assembly} (AIA) onboard the {\it Solar Dynamics Observatory} (SDO) has observed more than 210 global EUV waves in exquisite detail, thanks to its high spatio--temporal resolution and full-disk, wide-temperature coverage. A combination of statistical analysis of this large sample, more than 30 detailed case studies, and data-driven MHD modeling, has been leading their physical interpretations to a convergence, % favoring a bimodal composition of an outer, fast-mode magnetosonic wave component and an inner, non-wave CME component. Adding to this multifaceted picture, AIA has also discovered new EUV wave and wave-like phenomena associated with various eruptions, including quasi-periodic fast propagating (QFP) wave trains, magnetic Kelvin--Helmholtz instabilities (KHI) in the corona and associated nonlinear waves, and a variety of mini-EUV waves. Seismological applications using such waves are now being actively pursued, especially for the global corona. We review such advances in EUV wave research focusing on recent SDO/AIA observations, their seismological applications, related data-analysis techniques, and numerical and analytical models. | \label{sect_intro} The dynamic, magnetized solar corona hosts a variety of waves and wave-like phenomena that are believed to play important roles in many fundamental, yet enigmatic processes, such as % corona heating ({\it e.g.} \opencite{IonsonJ.Alfven.wave.heat.corona.1978ApJ...226..650I}, \opencite{HeyvaertsPriest.Alfven-wave-heat-corona.1983A&A...117..220H}) and solar-wind acceleration (see reviews by \opencite{Ofman.solarwind-review.2010LRSP....7....4O} and \opencite{CranmerS.solar.wind.model.review.2012SSRv..172..145C}). Such waves also carry critical information that can be used to decipher otherwise elusive % physical parameters of the corona, such as the magnetic-field strength, via a technique called {\it coronal seismology} \cite{Uchida.coronal-seismology.1970PASJ...22..341U,Roberts.coronal-seismology.1984ApJ...279..857R,% Nakariakov.TRACE-loop-oscil.1999Sci...285..862N,NakariakovOfman.B-from-oscil.2001A&A...372L..53N,% Nakariakov.wave-review.2005LRSP....2....3N}. Space-borne extreme ultraviolet (EUV) imagers have been the prime instruments observing traveling coronal disturbances for decades, thanks to a wide range of EUV emission produced by ions at various coronal temperatures. % The most spectacular examples are EUV disturbances expanding across a fraction of the solar disk, often in annular shapes and commonly associated with coronal mass ejections (CMEs) and flares. They were discovered by the {\it Extreme-ultraviolet Imaging Telescope} (EIT: \opencite{SOHO.EIT.1995SoPh..162..291D}) onboard the {\it Solar and Heliospheric Observatory} (SOHO) and rekindled broad interest in large-scale coronal (shock) waves \cite{Moses.EIT-wave.1997SoPh..175..571M,DereK.EIT.1st-result.1997SoPh..175..601D,% ThompsonB.EIT-wave-discover.1998GeoRL..25.2465T}. They are thus often called ``EIT waves", as well as ``(global) EUV waves" \cite{Patsourakos.Vourlidas.EIT-wave-review.2012SoPh..281..187P}, ``coronal bright fronts" \cite{GallagherP.LongD.EIT.wave.review.2011SSRv..158..365G}, or ``large-scale coronal propagating fronts" \cite{NittaN.AIA.wave.stat.2013ApJ...776...58N}. Here we adopt the most commonly used term ``EIT waves", while we reserve ``EUV waves" for propagating EUV disturbances in general -- the subject of the present review. Over the past decade and a half, three generations of EUV telescopes, notably SOHO/EIT, the {\it Extreme UltraViolet Imager} (EUVI: \opencite{WuelserJ.STEREO-EUVI.2004SPIE.5171..111W}) onboard the {\it Solar TErrestrial RElations Observatory} (STEREO: \opencite{Kaiser.STEREO-mission.2008SSRv..136....5K}), and the {\it Atmospheric Imaging Assembly} (AIA: \opencite{LemenJ.AIA.instrum.2012SoPh..275...17L}) onboard the {\it Solar Dynamics Observatory} (SDO: \opencite{PesnellD.SDO.mission.2012SoPh..275....3P}), have each contributed to shaping our evolving understanding of EIT waves in specific and EUV waves in general. SDO/AIA in particular, as the most advanced solar EUV imager to date, has led to breakthroughs in coronal-wave research. During its 3.5 years of operation, AIA has not only been bringing the long-standing debate on the nature of EIT waves to a closure by establishing a bimodal composition with both wave and non-wave components \cite{Patsourakos.Vourlidas.EIT-wave-review.2012SoPh..281..187P}, but also discovered new types of EUV waves, especially quasi-periodic fast propagating (QFP) wave trains \cite{LiuW.FastWave.2011ApJ...736L..13L} and nonlinear waves associated with magnetic Kelvin--Helmholtz instabilities (\opencite{Ofman.Thompson.AIA.KH.instab.2010AGUFMSH14A..02O}, \citeyear{Ofman.Thompson.AIA.KH.instab.2011ApJ...734L..11O}; \opencite{Foullon.AIA.KH.instab.2011ApJ...729L...8F}), adding to the multitude of aspects of this complex phenomenon. Global coronal seismology utilizing these large-scale EUV waves is becoming a reality. As an active research subject, observations and models of EUV waves have been reviewed extensively in the past, each with a somewhat different focus. Interested readers are referred to \inlinecite{WarmuthA.EIT-wave-review.2007LNP...725..107W} for a review based mainly on SOHO and multiwavelength observations, to \inlinecite{Wills-Davey.EIT-wave-review.2009SSRv..149..325W}, \inlinecite{GallagherP.LongD.EIT.wave.review.2011SSRv..158..365G}, and \inlinecite{ZhukovA.EIT.wave.review.STEREO.2011JASTP..73.1096Z} for updates with early STEREO observations, to \inlinecite{Patsourakos.Vourlidas.EIT-wave-review.2012SoPh..281..187P} for a synthesized view from SOHO, STEREO, {\it Hinode}, and SDO in its first year of operation, and to \inlinecite{VrsnakCliver.corona-shock-review.2008SoPh..253..215V} and \inlinecite{ChenPF.CME.review.2011LRSP....8....1C} for related subjects of coronal shocks and CMEs, respectively. The aim of this review is to summarize the current knowledge of EUV waves, focusing on the unique and revolutionary contributions made by SDO/AIA to observations of three types of waves generally associated with eruptions, {\it i.e.} EIT waves, QFP wave trains, and small-scale waves including mini-EUV waves and magnetic Kelvin--Helmholtz instability nonlinear waves. We strive to make our review complementary to the existing literature with different perspectives and minimal overlap yet without sacrificing completeness. \editor{We review here mainly published material, together with some new results such as structural oscillations of wide-ranging periods triggered by EIT waves, long periodicities of EIT waves themselves, and new clues to the relationship between quasi-periodic wave trains inside and outside CME bubbles (see \figs{908_oscil-fits.eps}, \ref{0908_long-fft.eps}, and \ref{QFP-2trains.eps}). } % Other types of waves that can be seen in EUV and are generally associated with traditional local coronal seismology are not covered in this review. This is partly because these waves have been extensively studied in the last decade and a half, especially with SOHO and TRACE, while SDO/AIA has not yet made significant advances in their observations. Such waves include standing (oscillations) or propagating magnetosonic waves of slow modes \cite{Ofman.UVCS-polar-hole-wave.1997ApJ...491L.111O,DeMoortel.TRACE-slow-mode-discover.2000A&A...355L..23D}, fast kink modes \cite{Aschwanden.1st-TRACE-wave.1999ApJ...520..880A,Nakariakov.TRACE-loop-oscil.1999Sci...285..862N,% NakariakovOfman.B-from-oscil.2001A&A...372L..53N}, % and fast sausage modes \cite{Nakariakov.sausage-mode-Nobeyama.2003A&A...412L...7N}, as well as \Alfven waves \cite{Tomczyk.Alfven-wave.2007Sci...317.1192T,Jess.Alfven-wave.2009Sci...323.1582J}. Interested readers are referred to relevant reviews \cite{AschwandenM2004psci.book.....A,Nakariakov.wave-review.2005LRSP....2....3N,% Banerjee.Magnetoseismology-review.2007SoPh..246....3B,RobertsB.coronal.seismology.progress.2008IAUS..247....3R,% Ofman.oscil.model-review.2009SSRv..149..153O} and recent AIA observations ({\it e.g.} \opencite{Aschwanden.Schrijver.AIA.loop.oscil.2011ApJ...736..102A}; \opencite{McIntoshS.Alfven.wave.heat.corona.solar.wind.2011Natur.475..477M}; \opencite{WangTJ.AIA.transverse.oscil.2012ApJ...751L..27W}; \opencite{GosainS.FoullonC.2010-09-08_EUV.wave.flmt.oscil.2012ApJ...761..103G}; \opencite{WhiteRS.Verwichte.AIA.loop.oscil.2012A&A...537A..49W}; \opencite{SrivastavaAK.kink.oscil.2011Aug9.X69.flare.2013ApJ...777...17S}; \opencite{ThrelfallJ.cmpr.wave.CoMP.AIA.2013A&A...556A.124T}). We organize this article as follows: After a brief description of relevant EUV telescopes in Section~\ref{sect_instr}, we review in Sections~\ref{sect_EIT}\,--\,\ref{sect_mini-wave} observations of the three types of EUV waves mentioned above. We then review their coronal seismological applications in Section~\ref{sect_seism} and related data-analysis techniques and numerical and analytical models in Section~\ref{sect_method}, followed by conclusions and future prospects in Section~\ref{sect_conclude}. | \label{sect_conclude} We have presented a review of recent advances in EUV wave research focusing on new observations since the launch of SDO and related data-analysis techniques and models. Thanks to its advanced capabilities, SDO/AIA not only played a critical role in ending the 15-year-long debate on the nature of EIT waves, allowing them to be used for coronal seismology, but also opened new research areas for newly discovered coronal phenomena, such as QFP wave trains and magnetic KH instabilities with associated nonlinear waves. We summarize below the current status and future prospects of these topics. % Backed up with strong observational and numerical evidence, the {\it hybrid or bimodal nature of EIT waves} has been established. In this general picture, an outer EUV front of a true fast-mode (shock) wave travels ahead of an inner non-wave component of CME-driven compression. Heating due to electric current dissipation or magnetic reconnection may contribute to the EUV emission at the inner, CME front, but not the outer, true wave front. AIA revealed an average EIT wave speed $>\,$$600 \kmps$ that is well expected for coronal fast-mode waves but much higher than the typical speeds of 200\,--\,$400 \kmps$ from previous SOHO/EIT measurements. A wide range of behaviors intrinsic to fast-mode waves are now commonly observed, including quasi-periodic wave trains, reflections and transmissions, coherent periodicities, sequential structural oscillations, and heating-cooling cycles. The impulsive lateral and downward expansions of a CME are believed to be key in generating EIT waves (see \sect{sect_EIT}). Outstanding questions regarding EIT waves include: \begin{enumerate} \item quantitative relation between their generation and CME (lateral) expansion; \item their roles in transporting energy and triggering sympathetic eruptions; \item their physical relation with Type-II bursts, Moreton waves, and SEPs. \end{enumerate} As one of AIA's discoveries, QFP wave trains with typical speeds of 500\,--\,$2200 \kmps$ are evidence of fast-mode magnetosonic waves in funnel-shaped waveguides from active regions. They are commonly associated with quasi-periodic flare pulsations (\sect{sect_QFP}). Open questions on QFPs include: \begin{enumerate} \item the origin of periodicities, especially those not identified in flare pulsations with possible connections to three-minute sunspot and other (sub)surface oscillations; % \item their roles in energy transport and coronal heating; \item the relation between QFPs within funnels and quasi-periodic wave trains within EIT waves ahead of CME flanks. \end{enumerate} Small-scale EUV waves including mini-EUV waves and KHI waves are relatively new and require further investigation to fully uncover the statistical distributions of their physical parameters. Mini-EUV waves are less energetic but more numerous than their large-scale counterparts (\sect{sect_mini-wave}). Thus their total energy budget could be significant for the quiet Sun. As for nano- or micro-flares in the flare size distribution, mini-EUV waves may play an important role in the full spectrum of EUV waves of hierarchic sizes. Such possibilities could be topics of future research. Seismological practice using EIT waves and QFPs to probe the coronal magnetic fields and thermal states and wave-energy fluxes is being actively pursued. % The currently inferred quiet-Sun magnetic fields are in the range of 1\,--\,10~G with uncertainties of about the same order (\sect{sect_seism}). Improving this accuracy, {\it e.g.} with refined density and temperature estimates, will be a critical future task. There are other potential diagnostic techniques to be explored, {\it e.g.} by including mini-EUV waves and using wave reflections and transmissions to probe topological interfaces. A whole suite of data-analysis techniques is becoming mature and has started to produce fruitful results (\sect{subsect_analysis}). However, automatic detection and tracking of EUV waves have not been widely tested or used. Their performance in data-processing pipelines % remains to be seen and will be critical to fully explore rich observations offered by AIA and other instruments. We emphasize that detailed analysis of individual well-observed events and statistical analysis of large samples are equally important. Numerical models are crucial in lending credence to data interpretation and in understanding % the underlying physics. Particularly useful are those 3D MHD models with realistic initial and boundary conditions % that can produce synthesized observables to be directly compared with observations (\sect{subsect_model}). In the years to come, the diagnostic power enabled by AIA's spatio--temporal and thermal coverage remains to be fully exploited to answer the above open questions about coronal EUV waves. The future EUV imager and spectrometer onboard the {\it Solar Orbiter} mission, scheduled for launch in 2017, and the EIS counterpart onboard the currently planned {\it Solar-C} mission will likely make further contributions. Additional constraints can be obtained from complementary observations of the solar atmosphere beyond the corona or at wavelengths outside the EUV regime. % The {\it Interface Region Imaging Spectrograph} (IRIS: \opencite{DePontieuB.IRIS.mission.2014SoPh..tmp...25D}), launched in June 2013, can detect potential UV signatures of coronal waves and Moreton waves in the transition region and chromosphere, such as Doppler, density, and temperature perturbations, and help identify the origin of QFP wave periodicities in regard to flares and chromospheric oscillations. The ground-based {\it Daniel K.~Inouye Solar Telescope} (DKIST), previously known as the {\it Advanced Technology Solar Telescope} (ATST), with first light expected in 2019, % will provide imaging and spectroscopic observations of the solar atmosphere from the photosphere to the corona in visible and near-infrared regimes and offer critical plasma and magnetic field diagnostics simultaneously. \begin{acks} This work is supported by the NASA Living With a Star (LWS) Program (grant NNX11AO68G). Additional support to LO was provided by NASA grant % NNX12AB34G. % \editor{ % Special thanks go to Barbara Thompson for inviting both authors to % the 2013 LWS SDO Science Workshop that led to this topical issue and this review. We are grateful to the anonymous referee for constructive comments and suggestions that helped improve this article. WL~thanks Nariaki Nitta, Cooper Downs, Barbara Thompson, Angelos Vourlidas, Peng-Fei Chen, Spiros Patsourakos, and Kyoung-Sun Lee for critical comments on the manuscript and/or fruitful discussions. We thank Suli Ma, Alexander Warmuth, Nariaki Nitta, Ding Yuan, Ute M\"{o}stl (now Ute Amerstorfer), Nat Gopalswamy, Jason Byrne, and David Pascoe for providing the original figures, % and especially Cooper Downs, Liheng Yang, Ting Li, Eoin Carley, and Ryun-Young Kwon for customizing their figures to fit the layout of this article. \figs{3mission.eps}c and \ref{3mission.eps}d, \ref{bimod_MaSL.eps}, \ref{0908_global-train.eps}, \ref{Nitta_stat_v-a.eps}~(right), \ref{reflect.eps}, \ref{908_oscil-fits.eps}a, \ref{908_oscil-fits.eps}c, and \ref{908_oscil-fits.eps}i, \ref{thermal.eps}, \ref{Nitta_stat_hist.eps}, \ref{QFP-overview.eps}~(middle and right), \ref{QFP-2trains.eps}a, \ref{mini_wave.eps}, \ref{seism.eps}, \ref{data-tech.eps}a\,--\,\ref{data-tech.eps}c, and \ref{MHD-models.eps}~(left and middle) are reproduced by permission of the AAS. \figs{Nitta_stat_v-a.eps}~(left), \ref{QFP-overview.eps}~(left), \ref{data-tech.eps}~(right), and \ref{MHD-models.eps}~(right) are reproduced with permission from Astronomy \& Astrophysics, \copyright~ESO. } % \end{acks} | 14 | 4 | 1404.0670 |
1404 | 1404.5922_arXiv.txt | \noindent The onset of a solar eruption is formulated here as either a magnetic catastrophe or as an instability. Both start with the same equation of force balance governing the underlying equilibria. Using a toroidal flux rope in an external bipolar or quadrupolar field as a model for the current-carrying flux, we demonstrate the occurrence of a fold catastrophe by loss of equilibrium for several representative evolutionary sequences in the stable domain of parameter space. We verify that this catastrophe and the torus instability occur at the same point; they are thus equivalent descriptions for the onset condition of solar eruptions. | \label{s:introduction} The force-free equilibrium of a coronal magnetic flux rope that carries a net current requires the presence of an external poloidal field perpendicular to the current \citep{Shafranov1966, vanTend&Kuperus1978}. Magnetic flux associated with the current is squeezed between the current and the photospheric boundary. This can be described as an induced current in the boundary or, equivalently, as an oppositely directed image current, implying an upward Lorentz force on the coronal flux \citep{Kuperus&Raadu1974}. The force is balanced by a Lorentz force from the external poloidal field. As the photospheric flux distribution and the corresponding external field gradually change, the configuration evolves quasi-statically along a sequence of stable equilibria for most of the time. However, it may encounter an end point of such a sequence, where continuing photospheric changes trigger a dynamic evolution. The transition of an equilibrium flux rope to a state of non-equilibrium has become a standard model for the onset of eruptive phenomena, including the eruption of prominences, coronal mass ejections, and flares. It has been formulated as a catastrophe or as an instability in the framework of ideal magnetohydrodynamics (MHD). The formulation as \emph{catastrophe} involves a sequence of equilibria, i.e., the equilibrium manifold in parameter space, and an ``evolutionary scenario'' for the motion of the system point on the manifold as a control parameter evolves continuously (representing gradual changes at the boundary). Thus, it includes a model for the pre-eruptive evolution. A catastrophe occurs if the system point encounters a critical point on the equilibrium manifold. Most relevant for solar eruptive phenomena is the case that the critical point is an end point, or nose point, of the equilibrium manifold in the direction of the changing parameter. The catastrophe then occurs by a \emph{loss of equilibrium}, sometimes also referred to as \emph{``non-equilibrium''}. The formulation as \emph{instability} considers the evolution of a small perturbation acting on an equilibrium at any point on the equilibrium manifold. A full description of instability includes the temporal evolution of the perturbation, but in order to find a criterion for onset of eruption, only the point(s) of marginal stability must be located in parameter space. As a parameter changes, the system point moves from the stable part of the equilibrium manifold across a point of marginal stability to the unstable part, i.e., in this formulation the equilibrium is not lost but turns to an unstable equilibrium. A model for the pre-eruptive evolution does not enter here; the points of marginal stability are independent of the pre-eruptive evolution. The modeling of solar eruptions has so far mostly used either a catastrophe formulation or an instability formulation, although they are related to each other. An analysis of this relationship should be helpful for unifying some of the independent developments in the modeling, which we summarize next. A model of eruption onset from the force-free equilibrium of a flux rope was established by \citet{vanTend&Kuperus1978} who focused on instability, but also related the instability to the fact that the equilibrium may be lost \cite[see also][]{Molodenskii&Filippov1987}. They considered a translationally invariant coronal current in the center of a magnetic flux rope above a plane photospheric surface. The current was approximated as a line current immersed in an external poloidal field $B_\mathrm{e}$, and only its external, large-scale equilibrium was analyzed. It was found that the height dependence $B_\mathrm{e}(h)$ determines whether the configuration is stable or unstable. The current is unstable to an upward displacement if $B_\mathrm{e}$ decreases sufficiently rapidly with height $h$ above the boundary surface. In the two-dimensional (2D) translationally invariant geometry, the ``decay index'' $n=-d\ln B_\mathrm{e}/d\ln h$ must exceed $n_\mathrm{cr}=1$ for instability. This critical value was derived under the assumption that any change of current produced by the perturbation can be neglected, which is consistent with conservation of magnetic flux between the current channel and the boundary surface in the limit of vanishing current channel radius $a$ \citep{Forbes1990}. A slightly higher value results if the constraint of flux conservation is imposed for $a>0$; then $n_\mathrm{cr}=1+1/(2c)$, where $c=\ln(2h/a)+1$ \citep{Demoulin&Aulanier2010}. An MHD description of the configuration, including internal force-free equilibrium of the current channel, was developed by \citet{Priest&Forbes1990} and \citet{Forbes&Isenberg1991} and further elaborated in a series of papers by \citet{Isenberg&al1993}, \citet{Forbes&Priest1995}, \citet{Lin&Forbes2000}, and \citet{Lin&vanBallegooijen2002}. All of these investigations described the onset of eruption as the occurrence of a catastrophe. The condition of flux conservation between the current channel and the photosphere was adopted in some cases, but other assumptions were considered as well, in order to model the changes in photospheric flux budget (flux cancellation or emergence) which are often observed in the pre-eruption phase \citep{Martin&al1985, Feynman&Martin1995}. Various evolutionary scenarios and external field models were analyzed. Accordingly, various locations of the critical point in parameter space were obtained. More recently, \citet{Longcope&Forbes2014} have found that a flux rope in quadrupolar external field can reach a catastrophe along various evolutionary paths, depending on the detailed form of the initial equilibrium. Some equilibria can be driven to a catastrophe and instability through reconnection at a lower, vertical current sheet, a process often referred to as ``tether cutting'' \citep{Moore&al2001}. While other equilibria can be driven to a catastrophe and instability through reconnection at an upper, horizontal current sheet, a process referred to as ``breakout'' \citep{Antiochos&al1999}. Some equilibria can be destabilized by both processes, but others only by one and not the other. Still other equilibria undergo no catastrophe and instability, but evolve at an increasingly rapid rate in response to slow steady driving. The occurrence of a catastrophe has also been demonstrated for toroidal current channels. \citet{Lin&al1998} considered a toroidal flux rope encircling the Sun in the equatorial plane with an induced current in the solar surface, or equivalently, an image inside the Sun of the current channel. \citet{Lin&al2002} studied a toroidal current channel one half of which is submerged below the (plane) photosphere. In this geometry, the submerged half of the channel represents the image current, but the evolution of the channel's major radius implies that the footpoints move across the solar surface. The latter unsatisfactory feature was remedied by \citet{Isenberg&Forbes2007}; however, the resulting complex expressions for line-tied equilibrium of a partial torus have not yet allowed a determination of the location of catastrophe or the onset of instability in general form. The freely expanding toroidal current channel investigated in \citet{Lin&al2002} is essentially a tokamak equilibrium \cite[or Shafranov equilibrium,][]{Shafranov1966} whose external poloidal field is due to a pair of point sources. This equilibrium was first explicitly given in \citet{Titov&Demoulin1999}. The expansion instability of the Shafranov equilibrium is referred to in fusion research as one of the axisymmetric tokamak modes (the other one being a rigid displacement along the axis of symmetry). Its first consideration \citep{Osovets1959} gave the threshold for instability as $n=-d\ln B_\mathrm{e}/d\ln R>n_\mathrm{cr}=3/2-(c-1)/[2c(c+1)]$, where $c=\mathcal{L}/(\mu_0R)=\ln(8R/a)-2$, and $\mathcal{L}$, $R$, and $a$ are the inductance and the major and minor radii of the torus, respectively. The derivation used the large aspect ratio approximation $R\gg a$ for the inductance $\mathcal{L}$, neglected the internal inductance of the current channel, and assumed that the minor radius does not change as the torus expands in a vacuum field. The term $(c-1)/[2c(c+1)]<0.1$ for all $c>1$, so the threshold of instability lies close to $3/2$. The instability was also considered by \citet{Titov&Demoulin1999}, who estimated $n_\mathrm{cr}\sim2$, and by \citet{Kliem&Torok2006}, who obtained $n_\mathrm{cr}=3/2-1/(4c)$, assuming that the minor radius expands proportionally to the major radius, and they called the instability a ``torus instability''; both investigations were performed without awareness of the original work by \citeauthor{Osovets1959}. An instability of this type was also realized (without quantifying it) as a possible cause of eruptions by \citet{Krall&al2000}. \citet{Olmedo&Zhang2010} proposed an analytical model for the instability of a line-tied partial torus, and found $n_\mathrm{cr}\to2$ in the limit of a full torus but surprisingly low values for $n_\mathrm{cr}$ (even below unity) if one half or less of the torus extends above the boundary. Numerical verifications of the instability for line-tied partial tori found threshold values in the range $n_\mathrm{cr}\approx1.5\mbox{--}2$ \citep{Torok&Kliem2007, Fan&Gibson2007, Aulanier&al2010, Fan2010}. \citet{Demoulin&Aulanier2010} extended the consideration of both catastrophe and instability to arbitrary geometry of the current channel, intermediate between linear and toroidal shapes. They estimated that the instability threshold then typically falls in the range $n_\mathrm{cr}\sim1.1\mbox{--}1.3$ and argued that catastrophe and instability are ``compatible and complementary. In particular, they agree on the position of the instability if no significant current sheets are formed during the long-term evolution of the magnetic configuration.'' Their arguments are based on the facts that catastrophe and instability are related in general and that the investigations cited above employed the same force balance determining the external equilibrium of the current channel. This suggests that torus instability (and its 2D variant) could possibly occur at the critical point in these catastrophe models. Here we perform a detailed consideration of the relationship between catastrophe and instability in toroidal geometry, verifying that torus instability is indeed the instability occurring at the catastrophe studied by Priest, Forbes, Lin and co-workers. The catastrophe point is located exactly at the major torus radius $R$ where $n(R)=n_\mathrm{cr}$, for all cases considered. We also show a case in which the change of a control parameter (i.e., a certain evolutionary scenario) leads to neither a catastrophe nor an onset of instability. However, another control parameter in this system does yield catastrophic/unstable behavior. For simplicity, we will use solar nomenclature in the following, bearing in mind that the situation is generic for eruptions originating in the low-density hot atmosphere of a magnetized, dense star or accretion disk \citep{Yuan&al2009}. Similarly, we will use ``expansion'' of the current channel to represent any change of the current channel's major radius in response to changes at the photospheric boundary. Typically, expansion is observed prior to solar eruptions, and the models considered here all exhibit expansion. We present a discussion of the general relationship between catastrophe and instability in Section~\ref{s:c+i}, introduce the basic eruption model in Section~\ref{s:model}, and then study a number of catastrophe scenarios in bipolar (Section~\ref{s:2p}) and quadrupolar (Section~\ref{s:4p}) ambient field. Section~\ref{s:conclusion} gives the conclusion. | \label{s:conclusion} Using a toroidal flux rope embedded in a bipolar or quadrupolar external field as a model for current-carrying coronal flux and its associated image current, we have demonstrated the occurrence of fold catastrophe by loss of equilibrium when magnetic reconnection can proceed at an X-line under the flux rope. Several evolutionary scenarios have been considered, which include changing the source strength and length-scale of the external field. In each case, the critical point for occurrence of the catastrophe coincides exactly with the threshold for torus instability if the same or compatible approximations are used, a result demonstrated to hold in general for the adopted model. Catastrophe and torus instability are thus equivalent descriptions for the onset of an eruption. They are based on the same force balance for equilibrium and produce an onset of eruption at the same point. Thus, the merits of each description can be exploited while one can be sure that the other description will yield the same onset point of eruption. Analyzing an equilibrium for the occurrence of catastrophe always includes a model for the pre-eruptive evolution and avoids the consideration of unstable equilibria far away from the critical point, which may be impossible to reach in reality. Analyzing the stability of an equilibrium localizes the critical point without the need to model the pre-eruptive evolution and in a formulation independent of the specifics of such a model. Moreover, since only infinitesimally small changes of the parameters must be considered in a stability analysis, the adopted approximations may be better satisfied than during the whole modeled pre-eruptive evolution in an analysis of catastrophe. It is clear, however, that the approximations are equally satisfied in the vicinity of the critical point. | 14 | 4 | 1404.5922 |
1404 | 1404.7382.txt | The disparity between the density profiles of galactic dark matter haloes predicted by dark matter only cosmological simulations and those inferred from rotation curve decomposition, the so-called cusp-core problem, suggests that baryonic physics has an impact on dark matter density in the central regions of galaxies. Feedback from black holes, supernovae and massive stars may each play a role by removing matter from the centre of the galaxy on shorter timescales than the dynamical time of the dark matter halo. Our goal in this paper is to determine constraints on such feedback scenarios based on the observed properties of a set of nearby galaxies. Using a Markov Chain Monte Carlo (MCMC) analysis of galactic rotation curves, via a method developed in a previous paper, we constrain density profiles and an estimated minimum radius for baryon influence, $r_1$, which we couple with a feedback model to give an estimate of the fraction of matter within that radius that must be expelled to produce the presently observed halo profile. We show that in the case of the gas rich dwarf irregular galaxy DDO 154, an outflow from a central source (e.g. a black hole or star forming region) could produce sufficient feedback on the halo without removing the disk gas. We examine the rotation curves of 8 galaxies taken from the THINGS data set and determine constraints on the radial density profiles of their dark matter haloes. For some of the galaxies, both cored haloes and cosmological $\rho \propto r^{-1}$ cusps are excluded. These intermediate central slopes require baryonic feedback to be finely tuned. We also find for galaxies which exhibit extended cores in their haloes (e.g. NGC 925), the use of a split power-law halo profile yields models without the unphysical, sharp features seen in models based on the Einasto profile. | Disk galaxies are presumed by $\Lambda$CDM cosmology to be dominated by dark matter e.g. \citep[e.g.][]{bosma1978}. An understanding of the arrangement of dark matter is therefore necessary for understanding the kinematics and dynamics of these galaxies. Analysis of galactic rotation curves, as well as of N-body cosmological simulations, has produced numerous models describing how dark matter density varies with distance from the centre of a galaxy. Dark matter only cosmological simulations were found by \cite{dubinski1991} and \cite{navarro1996} to produce haloes with an approximately universal density profile, with density proportional to $r^{-1}$ towards $r=0$ and $r^{-3}$ towards $r=\infty$. These haloes follow a set of scaling relations with virial mass such that they behave as a single parameter family of models \citep{bullock2001}. %Early observational work on this theme focused on low surface brightness galaxies, on the basis that the stellar contribution could be ignored entirely to a reasonable approximation. In \cite{vandenbosch2001} it was claimed that it was impossible with the data available at the time to differentiate between flat cores and $r^{-1}$ cusps. They cited the insufficient data range available, and the problem of beam smearing. Both limitations are much less of an issue now, due to improved HI data becoming available in the last decade. %This, and several other observational issues that could lead to erroneous inferences of cored haloes, were investigated and discounted by \cite{deblok2002}, who also showed that for a set of galaxies, several cored profiles provided better fits than the NFW profile. %\cite{bosma2003} claimed to rule out $r^{-1}$ cusps at a 3-sigma level for 17 galaxies, and on this basis, concluded that the slopes predicted by CDM models were Ônot observedÕ. He demonstrated that the position of the slit used at the time to observe rotation curves could not have been a factor in this result, by deliberately imposing such an offset. Due to the paradigm of the time, where there was expected to be a single universal halo, this result was interpreted as excluding cusps entirely. Given that it is now accepted that baryon physics plays a significant role in halo evolution, and the baryon content of galaxies is more stochastic, this is not the conclusion that would now be reasonably drawn from such data. The halo density profiles inferred from observing the rotation of disk galaxies appear to contradict this picture. For example, \cite{gentile2004} inferred the density profiles of 5 spiral galaxies and found them to be consistent with flat cores. Rotation curves of 17 galaxies analysed by \cite{bosma2003} were also found to contradict simulations and exclude $r^{-1}$ cusps. This has become known as the cusp-core problem. The possibility of the difference being due to erroneous inference of cores from observations has been discussed, and refuted, in \cite{deblok2002}. This, coupled with an increase in resolution of kinematic data, has at this point resolved such concerns. High quality data from The HI Nearby Galaxy Survey, THINGS ~\citep{THINGS} has allowed the generation of more detailed rotation curves, that extend to smaller radii than those used in previous treatments of the cusp/core problem ~\citep{deblok2008}. An analysis of these rotation curves by ~\cite{chemin2011} showed that an Einasto profile $\rho \propto \exp(-r^{\rm n})$, provides a better formal fit than cored profiles such as the Burkert profile ~\citep{burkert1995} or the NFW profile. Also using THINGS data, \cite{oh2011} claimed that a selection of dwarf galaxies (including DDO 154, which we studied using an MCMC method in \cite{hw2013}, hereafter HW13) exhibit $r^{-0.29}$ central slopes. They found all the dwarf galaxies in their study to be inconsistent with $r^{-1}$ inner haloes. Simulations have been used to try and resolve the cusp-core problem. \cite{read2005} demonstrated that the baryon physics left out of pure N-body simulations can account for this disparity, in the case of dwarf galaxies, through time asymmetric mass loss (e.g. baryon infall and outflow), and \cite{governato2010} used supernovae feedback to explain both the flattening of the inner dark matter density profile and the absence of bulges in dwarf galaxies. In this paper we attempt to provide an improved modelling of dark matter density profiles in a selection of THINGS galaxies using a more general parameterised density profile, the $\alpha-\beta-\gamma$ profile ~\citep{zhao1996}, and a Markov Chain Monte Carlo (MCMC) method to explore the parameterisation. We also explore the implications of our improved density profiles for out understanding of feedback processes. The structure of this paper is as follows; Section \ref{methodsection} summarises the rotation curve decomposition and MCMC techniques used to derive dark matter density profiles. Section \ref{analysissection} describes a simple analytic model that can be used to constrain formation scenarios for an individual galaxy given its halo density profile and rotation curve. Section \ref{resultssection} discusses the results for individual galaxies, and Section \ref{discussionsection} draws conclusions from the analysis when applied to our full sample of galaxies. | We have applied the MCMC method described in \cite{hw2013} to a number of nearby galaxies and been able to constrain the density profiles of their haloes with less ambiguity than would be possible with simpler statistical methods. From these constraints, we have calculated the values of physical quantities ($r_1$ and $f_{\rm g}$) which can be used to constrain formation scenarios for these galaxies. The sample investigated here is subject to a selection bias. The THINGS galaxies were subsampled for generation of rotation curves by \cite{deblok2008}, based on inclination and other factors, and then subsampled again here on the basis of whether or not they can produce meaningful outputs from our MCMC technique. Our conclusions must be interpreted in this context. The selection biases we experience also apply to any attempt at rotation curve decomposition. The cases where MCMC cannot find a constraint should be taken as an indication that the fitting of an individual profile, that is part of our parameter space or closely approximated by a profile that is, cannot produce a result that is credible without further discussion of the issues that prevent a constraint with MCMC. Our technique has the potential to overcome these bias using different data, or different modelling of the data (that incorporates more well constrained stellar populations for instance.) The behaviour of our MCMC technique with potential future data sets is described in HW13 and is found to be promising. We have identified several degeneracies in the parameter space. Some we are unable to break, such as the degeneracy between $\Upsilon$ and the inner log slope $\gamma_{\rm in}$ for NGC 3621. One of the most important degeneracies we discovered is between $\rho_{\rm s}$ and $r_{\rm s}$, which has been resolved in all cases presented here. This degeneracy precludes these two parameters being independently considered as physical. Our transformation of the parameter $\rho_{\rm s}$ into $v_{\rm max}$ removes this degeneracy, but unfortunately $r_{\rm s}$ still cannot be interpreted as a physically meaningful radius, because its position is degenerate with the shaping parameters $\alpha$, $\beta$ and $\gamma$. Scale radii fixed by the points at which the curve reaches a particular log slope (i.e. $r_n$ where $n$ is the negative log slope) are more useful for a discussion of the actual morphology of dark matter haloes. We chose $r_1$ due to the fact that parts of the halo interior to this distance cannot be modelled by a cosmological halo such as NFW. Thus $r_1$ corresponds to a radius over which baryonic physics must act in order to produce the measured halo. We have shown that $r_1$ is useful and well constrained, and that it can be used to constrain a simple feedback-based formation model. The relevance of $r_1$ is first as a constrainable physical parameter within the data range of the galaxies studied here, secondly as a required scale of mass loss (under reasonable assumptions) and thirdly as a common scaling parameter with which to compare observationally derived haloes to simulated ones in a physically meaningful way. The second reason applies only for $r_1$ and not for other radii. However we recognise that other radii may have similar uses, and such radii may also be constrained well with an MCMC method, as we have used here. The model we use to derive $f_{\rm g}$ is simple, but links a physically viable outflow scenario to a quantity derived by MCMC analysis of observations, and could be refined iteratively by using it as an initial condition in formation simulations. This value cannot be reliably derived from simpler fitting methods due to the complexity of the parameter space, and the low quality of measures such as $\chi^2_{\rm red}$ as absolute goodness of fit statistics for these data. MCMC provides a firm enough constraint, and a confidence that the parameter space has been properly explored, to allow results such as $f_{\rm g}$ to guide simulations. %We have demonstrated a simple model, which links a physically viable outflow scenario to a quantity derived by MCMC analysis of observations. Due to the level of simplification we do not draw any strong physical conclusions from this, but we present it as a demonstration of the viability of using radii such as $r_1$ to constrain formation scenarios. In future work we will apply our method to cosmological simulations in order to quantify its performance further. | 14 | 4 | 1404.7382 |
1404 | 1404.2733_arXiv.txt | We investigate how the observed large-scale surface magnetic fields of low-mass stars ($\sim$0.1 -- 2$\,{\rm M}_\odot$), reconstructed through Zeeman-Doppler imaging (ZDI), vary with age $t$, rotation and X-ray emission. Our sample consists of $104$ magnetic maps of $73$ stars, from accreting pre-main sequence to main-sequence objects ($1 ~{\rm Myr} \lesssim t \lesssim 10$~Gyr). For non-accreting dwarfs we empirically find that the unsigned average large-scale surface field $\bv$ is related to age as {$t^{-0.655 \pm 0.045}$}. This relation has a similar dependence to that identified by Skumanich (1972), used as the basis for gyrochronology. Likewise, our relation could be used as an age-dating method (``magnetochronology''). The trends with rotation we find for the large-scale stellar magnetism are consistent with the trends found from Zeeman broadening measurements (sensitive to large- and small-scale fields). These similarities indicate that the fields recovered from both techniques are coupled to each other, suggesting that small- and large-scale fields could share the same dynamo field generation processes. For the accreting objects, fewer statistically significant relations are found, with one being a correlation between the unsigned magnetic flux $\Phi_V$ and $P_{\rm rot}$. We attribute this to a signature of star-disc interaction, rather than being driven by the dynamo. | Magnetic fields play an important role in stellar evolution. For low-mass stars, the magnetic field is believed to regulate stellar rotation from the early stages of star formation until the ultimate stages of the life of a star. In their youngest phases, the stellar magnetic field lines interact with accretion discs to prevent what would have been a rapid spin-up of the star, caused by accretion of material with high angular momentum and also the stellar contraction \citep[e.g.,][]{2013arXiv1309.7851B}. After the accretion phase is over and the disc has dissipated, the contraction of the star towards the zero-age-main sequence (ZAMS) provides an abrupt spin up. From that phase onwards, `isolated' stars (single stars and stars in multiple systems with negligible tidal interaction, such as the ones adopted in our sample) slowly spin down as they age \citep[e.g.][]{2013A&A...556A..36G}. This fact was first observed by \citet[][S72, from now on]{1972ApJ...171..565S}, who empirically determined that the projected rotational velocities $v \sin(i)$ of G-type stars in the main-sequence (MS) phase decrease with age $t$ as $v\sin(i) \propto t^{-1/2}$. This relation, called the ``Skumanich law'', serves as the basis of the gyrochoronology method \citep{2003ApJ...586..464B}, which yields age estimates based on rotation measurements. The rotational braking observed by \citetalias{1972ApJ...171..565S} is believed to be caused by stellar winds, which, outflowing along magnetic field lines, are able to efficiently remove the angular momentum of the star \citep[e.g.,][]{1958ApJ...128..664P,1962AnAp...25...18S,1967ApJ...148..217W}. Indicators of magnetic activity, such as surface spot coverage, emission from the chromosphere, transition region or corona, have been recognised to be closely linked to rotation \citep[e.g., S72;][]{1984A&A...133..117V,1984ApJ...279..763N,1997JGR...102.1641A,2007LRSP....4....3G,2012A&A...546A.117G,2012LRSP....9....1R}. However, the magnetic activity-rotation relation breaks for rapidly rotating stars, where the indicators of stellar magnetism saturate and become independent of rotation. A saturation of the dynamo operating inside the star, inhibiting the increase of magnetism with rotation rate, has been attributed to explain the activity saturation observed in low-period stars \citep{1984A&A...133..117V}, but alternative explanations also exist \citep[e.g.,][]{1991ApJ...376..204M,1999A&A...346..883J,2007A&A...473..501A}. The average unsigned surface magnetic field $\langle |B_I| \rangle$, as measured by Zeeman-induced line broadening of unpolarised light (Stokes I), also correlates with rotation, in a similar way as the indicators of magnetic activity do (i.e., as one goes towards faster rotating stars, $\langle |B_I| \rangle$ increases until it reaches a saturation plateau; \citealt{2009ApJ...692..538R}). Because $\langle |B_I| \rangle$ is the product of the intensity-weighted surface filling factor of active regions $f$ and the mean unsigned field strength in the regions $B_I$ ($\langle |B_I| \rangle=fB_I$), it is still debatable whether the saturation occurs in the filling factor $f$ of magnetically active regions or in the stellar magnetism itself or in both \citep{1994ASPC...64..477S,1996IAUS..176..237S,2001ASPC..223..292S,2009ApJ...692..538R}. Although Zeeman broadening yields estimates of the average of the total (small and large scales) unsigned surface field strength, it does not provide information on the magnetic topology \citep{2013AN....334...48M}. For that, a complementary magnetic field characterisation technique, namely Zeeman-Doppler Imaging \citep[ZDI, e.g.,][]{1997A&A...326.1135D}, should be employed. The ZDI technique consists of analysing a series of circularly polarised spectra (Stokes V signatures) to recover information about the large-scale magnetic field (its intensity and orientation). In this work, we take advantage of the increasing number of stars with surface magnetic fields mapped through the ZDI technique and investigate how their large-scale surface magnetism varies with age, rotation and X-ray luminosity (an activity index). In the past decade, ZDI has been used to reconstruct the topology and intensity of the surface magnetic fields of roughly one hundred stars \citep[for a recent review of the survey, see][]{2009ARA&A..47..333D}. Since the ZDI technique measures the magnetic flux averaged over surface elements, regions of opposite magnetic polarity within the element resolution cancel each other out \citep{2010MNRAS.404..101J,2011MNRAS.410.2472A}. As a consequence, the ZDI magnetic maps are limited to measuring large-scale magnetic field. Because the small-scale field decays faster with height above the stellar surface than the large-scale field \citep[e.g.,][]{2014MNRAS.439.2122L}, only the latter permeates the stellar wind. If indeed magnetised stellar winds are the main mechanism of removing angular momentum from the star in the MS phase, one should expect the large-scale field to correlate with rotation and age. Likewise, a correlation between rotation and magnetism should also be expected if rotation is the driver of stellar magnetism through dynamo field generation processes. The interaction between magnetism, rotation and age is certainly complex and empirical relations, such as the ones derived in this work, provide important constraints for studies of rotational evolution and stellar dynamos. This paper is organised as follows. We present our sample of stars in Section~\ref{sec.sample}. Section~\ref{sec.relations} shows the empirically-derived trends with magnetism we find within our data. In Section~\ref{sec.discussion}, we discuss how the results obtained using the Zeeman broadening technique compare to the ones derived from Zeeman-Doppler Imaging (Section~\ref{sec.comparison}), we investigate the presence of saturation in the large-scale field (\ref{sec.saturation}), analyse whether stars hosting hot-Jupiters present different magnetism compared to stars lacking hot-Jupiters (\ref{sec.hjhosts}) and discuss the trends obtained for the pre-main sequence (PMS) accreting stars (\ref{sec.accreting}). In Section~\ref{sec.magnetochronology}, we discuss the impact of our findings as a new way to assess stellar ages and as a valuable observational input for dynamo studies and stellar mass loss evolution. Our summary and conclusions are presented in Section~\ref{sec.conclusions}. | 14 | 4 | 1404.2733 |
|
1404 | 1404.4359_arXiv.txt | We analyse light curves covering four years of 39 fast-rotating ($P_\mathrm{rot}\lesssim1d$) late-type active stars from the \textit{Kepler} database. Using time--frequency analysis (Short-Term Fourier-Transform), we find hints for activity cycles of 300--900 days at 9 targets from the changing typical latitude of the starspots, which, with the differential rotation of the stellar surface change the observed rotation period over the activity cycle. We also give a lowest estimation for the shear parameter of the differential rotation, which is $\approx 0.001$ for the cycling targets. These results populate the less studied, short period end of the rotation--cycle length relation. | The 11 year and other, longer activity cycles of the Sun have been known for a long time, and similar multiple cycles have been recovered for many active stars (see \citealt{2009AA...501..703O} and references therein). Systematic studies of stellar cycles began with the Ca H\&K survey at Mount Wilson \citep{1968ApJ...153..221W}, and with the advent of the Automated Photometric Telescopes (APTs, see e.g. \citealt{1997PASP..109..697S}). To study this phenomenon, long-term observations are needed, as the typical timescales of the cycles range from a few years to decades. A correlation has been found between the rotation period and the length of the activity cycle, as shown first by \cite{1996ApJ...460..848B} and recently by \cite{rot-cyc}, namely, that on faster rotating stars the activity cycles tend to be shorter. Planned, and currently developing long-term all-sky surveys, as the Large Synoptic Survey Telescope (LSST, see \citealt{lsst}) the PASS \citep{PASS}, and the Fly's Eye Camera System \citep{flyseye} may give a huge thrust to this field, provided they run for many years, even decades, since not only selected objects (which may contain no suitable targets and miss interesting ones) but the whole sky will be monitored. At present though, the best option for monitoring stars is the \textit{Kepler} space telescope, providing an almost continuous dataset of unprecedented precision from about 160\,000 targets, among them thousands of active stars. The already recovered stellar cycles range from years to decades, while the \textit{Kepler} space telescope operated only for four years. \cite{shortcyc} analysed long-term photometric measurements of ultrafast-rotating ($P_\mathrm{rot}\approx 0.5d$) M-dwarfs, and found activity cycles on three stars with cycle lengths between 300--500 days, which is already within the reach of \textit{Kepler}. Magnetic activity, rotation and differential rotation of \textit{Kepler} stars is in the focus of research lately (see e.g. \citealt{kepleract1,kepleract2,kepleract3}). \cite{keplerrot} developed a robust method using an autocorrelation function to determine rotation periods from light curves and studied more than 2400 stars. The method was applied later by \cite{keplerrot2} to \textit{Kepler} Objects of Interest (KOIs) to study exoplanet-hosting systems. \cite{keplerrot3} used Lomb--Scargle periodograms to search for rotation periods in \textit{Kepler} targets, the authors analyzed 12\,000 F, G and K-type stars. The same method was applied by \cite{keplerdr} to study more than 40\,000 active \textit{Kepler} stars, they also made an effort to estimate the values of the differential rotation shear. Working with \textit{Kepler} data has its own drawbacks. There are instrumental trends during each observing quarter, and shorter term instrumental glitches are also present on a timescale of a few days. Although there are attempts to correct these trends (and not just remove them automatically), the possibility of having a homogeneous light curve ranging many observing quarters seems really hard to achieve. Hence, the information on long-term cycles, which can be basically seen by naked eye on a persistently observed earth-borne light curve from photometry, is lost in the \textit{Kepler} data. Or is it? Are there other properties of the activity cycles, that can help us to trace them? One realisation of the 11-year cycle on the Sun is the butterfly-diagram, i.e., the phenomenon that the sunspots tend to appear on higher latitudes at the beginning of the cycle, and closer to the equator at its end. There have been attempts to recover this migration of typical spot latitudes on other active stars (see e.g. \citealt{2007ApJ...659L.157B}). Lately, \cite{Katsova:2010kt} used wavelet analysis of Ca H\&K data from the Mount Wilson survey to determine the variations in the rotation period of active stars, and studied similar cyclic variation of the solar corona, from a ``Sun as a star'' approach. Recent theoretical dynamo models are able to describe the butterfly diagram reliably for different kinds of active stars. Figure 10. in \cite{emre} shows the modelled spot distribution of a fast-rotating ($P_\mathrm{rot}=2 d$) K0V star during its activity cycles. According to the model, the well known shape of the butterfly diagram changes substantially as a result of the fast rotation. The flux tubes -- even if started from a similar configuration as the Sun -- emerging from the tachocline reach the photosphere at much higher latitudes than on the Sun. Unfortunately, in this fast rotating, late-type stellar case, the latitude distribution also changes: the spots appear in a much thinner latitude stripe (between about $35-45^\circ$) in the model, in contrast with observed solar case (between about $0-40^\circ$). Compared to the Sun, a much smaller modulation of the emerging latitudes is still found in the model during the activity cycle, but most of the emerging spots appear almost at the same latitude. Thus the butterfly diagram in this case resembles much less to a butterfly, as the effect is almost washed away by the overlapping ``butterfly wings" (cf. Figure 9. in \citealt{emre}). With a strong enough differential rotation however, there might be a difference in the rotational period even in the case of the small latitudinal migration of the fast rotating active dwarf stars that is still large enough to be detected by high-precision long-term photometry with good time coverage, such as data of the \textit{Kepler} survey. The signal we have to look for is a small change in the typical latitude of spot emergence of a differentially rotating stellar surface, which would result in a very small quasi-periodic change in the photometric rotational period during an activity cycle. Long-term change of the rotational periods can be revealed by time-series period searching methods. Such effect has already been detected on the long-period giant active star CZ CVn by \cite{tifran-cycle}. In this paper we look for cycles on fast rotating active dwarf stars through the systematic changes of their observed rotational periods due to differential rotation. | \label{sect:discussion} \begin{figure} \centering \includegraphics[width=0.45\textwidth, bb=50 350 554 800]{vida_fig4.pdf} \caption{Correlation between the rotation period and the length of the activity cycle, as in \protect\cite{2009AA...501..703O}. Large black dots, green squares and green triangles stand for the shortest cycles from \protect\cite{2009AA...501..703O}, results from \protect\cite{shortcyc}, and from the present paper, respectively. Smaller grey dots denote data from different surveys, from \protect\cite{2009AA...501..703O}. Smaller triangles mark the less certain periods from this paper (marked with $^\ddagger$ in Table \ref{tab:params}). Red filled squares show data for M dwarf stars from \protect\cite{savanov}. The dotted line represents the fit to all the data from \protect\cite{2009AA...501..703O}, \protect\cite{shortcyc}, plus the results of the present paper excluding M stars; while the parallel line shows the fit to the shortest cycles of that dataset. The slope of the fit to the data from \protect\cite{savanov} is close to 1.0, which means that no correlation is found between rotation and cycle lengths. Error bars on the lower right indicate the typical uncertainty of rotation period and activity cycle determination (error bar of the x axis is smaller than the line itself). See the text for more.} \label{fig:rot-cyc} \end{figure} \cite{keplerrot} studied the rotation of about 2500 {\it Kepler} M dwarfs with a method based on autocorrelation. Their sample with detected rotation contains four of our cycling targets: KIC 4953358, KIC 5791720, KIC 10515986, and KIC 12365719. In all cases their rotation periods derived by an independent method shows very good agreement with our values. \subsection{Estimation of the differential rotation shear} We estimate the $\alpha$ parameter, which is often used in practice to describe the shear of the differential rotation, and is defined as $\alpha= \Delta\Omega/\Omega_\mathrm{eq} = (\Omega_\mathrm{eq}-\Omega_\mathrm{pole} )/\Omega_\mathrm{eq}$. If we suppose that the extrema of the rotation periods ($P_\mathrm{rot,min}$, $P_\mathrm{rot,max}$) we found represent the rotation at the equator and the pole, we can give a lowest estimation of the $\alpha$ parameter using the $P_\mathrm{rot}$ and $\Delta P_\mathrm{rot}$ for each object -- these values are summarized in Table \ref{tab:params}. Note, that by using this method, it is not possible to determine if the differential rotation is solar or anti-solar, since we have no latitude information from where the rotational signal originates. It is possible that the actual $P_\mathrm{rot}$ values span a wider range than we estimate from the extreme positions of the rotation frequency in the STFT diagram -- this can be revealed by detailed Fourier-analysis of segmented light curves for each target, but that is outside the scope of the current paper. This would yield higher values of $\alpha$. A similar method was used by \cite{keplerdr} to study rotation and differential rotation in more than 40,000 active {\it Kepler} targets. The authors used Lomb--Scargle periodograms to find the extrema of the rotation periods during one quarter (Q3). Their sample contains seven targets from this paper\footnote{ KIC 03541346, KIC 04953358, KIC 05791720, KIC 06675318, KIC 08314902, KIC 10515986, and KIC 12365719 }, and in two cases they also detected sign of differential rotation: indeed, they found higher values of $\alpha$, whereas their main rotation periods for the matching targets agree with our values. In the case of KIC 3541346 and KIC 4953358 they found $\alpha=0.0101$, and $\alpha=0.0123$, respectively. The authors did not (and could not) take into account that the active regions might emerge only in a smaller latitude range, thus the differential rotation shear could be even higher. Given the nature of the method, the uncertainty in the spot latitudes does not allow accurate determination of the shear. Note, that the authors used an oversampling of 20 that might result in peaks that are not real, and could change the values of $\alpha$ they found. To give a better estimate, we should know the actual latitude values where the active regions emerge during the cycle, for which we can give only crude guesses. By assuming the usual quadratic differential rotation law of \begin{equation} \Omega(\vartheta)=\Omega_\mathrm{eq}(1-\alpha\sin^2\vartheta), \end{equation} the shear can be determined from known rotation periods at given latitudes using the following equation: \begin{equation} \alpha=\frac {\Omega(\vartheta_2)-\Omega(\vartheta_1)} {\Omega(\vartheta_2)\sin^2\vartheta_1 - \Omega(\vartheta_1)\sin^2\vartheta_2}. \end{equation} If we assume latitudes similar to the solar case, where the spots emerge between $0^\circ$ and $30^\circ$ latitudes, the given $\alpha$ values are higher by a factor of $\approx4$, however this scenario is unlikely (see e.g. \citealt{emre}). In a case based on the fast-rotating ($P_\mathrm{rot}=2d$) K0 dwarf model of \cite{emre}, where the spots emerge between $\approx 35^\circ$ and $\approx 45^\circ$ latitudes (cf. Fig. 10 of that paper), the $\alpha$~values in Table \ref{tab:params} get higher by a factor of $\approx6$ and we get a typical value of $\alpha=0.010$ for our sample. For a more realistic estimate a dynamo model for fast-rotating late-type dwarfs is needed that could more accurately predict the emergence latitudes. \cite{magneticwreath} studied MHD models of a fast rotating Sun, and found wreath-like magnetic structures in the convection zone around 5--25$^\circ$ latitudes. \cite{emre} presented models of solar-like and main sequence K-type stars of different rotation rates, but a model of ultrafast-rotating late-type stars is a real challenge for the theoreticians. Another way for getting more accurate values for $\alpha$ would be to determine directly the active region latitudes from the light curves by analytic modeling or inversion of the light curves. However, the information on the actual latitudes is very limited in photometric data, and is present only in the limb darkening of the spotted surface. \subsection{Rotation--cycle length relation} In \cite{2009AA...501..703O} a new correlation between the cycle length normalized with the rotation, and the inverse rotation period is given in log-log scale, with one single M dwarf star in the sample (EY Dra) with a quite short cycle period, which was not used in determining the slope of the relation. \cite{shortcyc} find that the activity cycles for ultrafast-rotating dwarfs are somewhat shorter than the previous samples would indicate, by extending the relation based on stars of slower rotation. In that work another M dwarf, V405 And, a binary, was added to the stars with known cycles. Using the activity cycles from \cite{2009AA...501..703O}, \cite{shortcyc}, and adding the results of the present paper we studied again the rotation--cycle length relation (see Fig. \ref{fig:rot-cyc}). Two stars from the present sample seem to have double cycles, but the longer ones are uncertain due to the limited length of the dataset, thus only the shortest cycles have been considered. \cite{savanov}, using data from the ASAS survey for a homogeneous set of only M dwarf stars, dis not find any relation between the lengths of rotations and cycles. Looking at Fig. \ref{fig:rot-cyc} we find, that four stars with certain cycles derived in the present paper, and two stars from \protect\cite{shortcyc}, V405 And and EY Dra, (which are M dwarfs), fit well the M dwarf sequence by \cite{savanov}, except one star, KIC 04819564. We thus excluded the M dwarf stars from the fits of Fig. \ref{fig:rot-cyc} but included KIC 04819564. The slope for all the cycles and for the shortest cycles (in case of multiple cycles) is $0.77\pm0.06$ and $0.78\pm0.05$, similarly to the earlier values of 0.74 by \citealt{1996ApJ...460..848B}) and to 0.81 for all the data and 0.84 for the shortest cycles by \cite{2009AA...501..703O}. The existence of a relation between the cycle lengths and rotational periods for a diverse sample of active stars (the sample contains both single and binary stars, giants and dwarfs, of different spectral types) did not change with the exclusion of the M dwarf stars. Already the short period part ($P_\mathrm{rot}<1$\,day) of cycling stars seems to separate by spectral type, and was not evident in \protect\cite{shortcyc} which was prepared before the results of \cite{savanov} was published, without the table cycle lengths. The relation between rotational and cycle periods is extremely important for understanding stellar dynamos (see e.g. \citealt{1996ApJ...460..848B,dynamo2,magneticwreath, dynamo1} for the details). The results presented in this paper, which populate the short period end of the rotation--cycle length relation, give a good impact to this study, showing a clear separation between the K and M dwarfs already at very short rotational periods. The determination of the exact spectral types of cycling stars studied in this work is the subject of a forthcoming paper. \begin{itemize} \item We analyzed light curves of 39 fast-rotating ($P_\mathrm{rot}\lesssim1d$) active stars from the \textit{Kepler} database using time--frequency analysis. \item From the short-term Fourier-transforms (STFT) of the light curves in the region of the rotation frequency and its double, we detected quasi-periodic variations. \item We interpret these variations as a result of stellar butterfly diagram: during the activity cycle the typical latitude of the starspots change, and this, because of the differential rotation of the surface, results in change of the rotation period. \item With our technique, we found hints of activity cycles with periods in the range of 300--900 days in 9 targets. \item To find activity cycles through rotational period variation due to differential rotation and the butterfly diagram is a new method which does not need latitudinal information as input, applicable only for very high precision and (nearly) continuous datasets such as is produced by the Kepler satellite. \item This result populate the short-period part of the rotation--cycle length relation showing clear separation between the K and M dwarf stars with the shortest periods($P_\mathrm{rot}<1$\,day), this is very important in understanding the nature of the cycling dynamos. % \end{itemize} | 14 | 4 | 1404.4359 |
1404 | 1404.4390_arXiv.txt | We present a study of OGLE light curves of red giant stars exhibiting long secondary periods (LSPs) -- an enigmatic phenomenon commonly observed in stars on the upper red giant branch and asymptotic giant branch. We show that the light curves of LSP stars are essentially identical to those of the spotted variables with one dark spot on their photospheres. Such a behavior can be explained by a presence of a dusty cloud orbiting the red giant together with a low-mass companion in a close, circular orbit. We argue that the binary scenario is in agreement with most of the observational properties of LSP variables, including non-sinusoidal shapes of their radial velocity curves. | Long secondary periods (LSPs), observed in at least one third of pulsating red giants and supergiants, are one of the most interesting unsolved problems of modern stellar astrophysics. This phenomenon has been known for decades \citep{oconnell1933,payne1954,houk1963} and it is observed in tens of thousands of long period variables (LPVs) in our and other galaxies. The photometric amplitudes associated with the LSPs are in some cases quite large (up to 1 mag in the {\it V} band), and radial velocity changes during LSP cycles have been detected, but still we cannot even answer the question of whether we are dealing with intrinsic or extrinsic stellar variability. There are two popular hypotheses explaining the LSP phenomenon. The first one assumes that a red giant star has a low-mass companion which, due to interactions with the circumstellar matter, causes the periodic photometric and spectroscopic variations \citep{wood1999,soszynski2007}. The second hypothesis assumes that red giant stars exhibit some kind of radial or non-radial pulsations \citep{hinkle2002,wood2004,derekas2006}, but currently there is no theoretical pulsation model that satisfactorily explains all the observed features of the LSP variables. LSPs range from about 200 to 1500 days and are an order of magnitude longer than the typical pulsation periods of semiregular variables (SRVs) and OGLE small amplitude red giants (OSARGs). It is worth noting that LSPs are not observed in Mira variables, which have the largest-amplitude light curves among pulsating red giants. In the period--luminosity (PL) diagram, LSPs form a well-defined sequence \citep[sequence D;][]{wood1999}, roughly parallel to other PL sequences populated by pulsating red giants. \citet{soszynski2004} noticed that sequence D partly overlaps and is a direct continuation of sequence E, which is formed by close binary systems (eclipsing and ellipsoidal variables) containing a red giant as one of the components. Sequences D and E overlap in all the studied photometric bandpasses, from visual to infrared \citep{derekas2006}, which is a strong argument for the binary explanation of the LSPs. On the other hand, the shapes of the radial velocity curves are interpreted as evidence against the binary scenario. The full velocity amplitudes associated with LSPs range from 2 to 7~km~s$^{-1}$, with a tight clustering around 3.5 km~s$^{-1}$ \citep{nicholls2009}. Assuming a binary origin of the LSP phenomenon, this velocity amplitude would correspond to a secondary component of brown-dwarf mass. The velocity curves are non-sinusoidal, which may be interpreted as a sign of eccentric orbits. However, most of the observed velocity curves have shapes very similar to each other, which implies similar angles of periastron in the majority of the observed LSP variables. Of course, one may expect that the angles of periastron in randomly selected systems should have a uniform distribution. According to \citet{nicholls2009}, the probability that the observed radial velocity curves are consistent with the uniform distribution of angles of periastron is of the order of $10^{-3}$, which practically excludes the possibility that the LSP phenomenon is caused by binarity. Spectroscopic observations gave us information about the changes of the effective temperature during the LSP cycle. The changes are very small, much smaller than expected for radial pulsation \citep{wood2004}. In turn, nonradial oscillations would be difficult to reconcile with the observed movement of the visible surface of the giant stars during their LSP cycle, which is of the order of 30\% of the stellar radius \citep{nicholls2009}. Another important observational fact was discovered by \citet{wood2009b} -- LSP variables are surrounded by significant amounts of cool dust and this circumstellar matter has a non-spherical (clumpy or disk-like) distribution. In this work we argue that the asymmetric radial velocity curve in an LSP variable may be produced by a low-mass companion in a circular orbit just above the surface of the red giant. Such a companion may be followed by a dusty cloud that regularly obscures the giant and causes the apparent luminosity variations. We present a simple model that, at least qualitatively, well reproduces the light and velocity curves observed for LSP stars. \begin{figure} \epsscale{1.1} \plotone{fig1.ps} \caption{Examples of the OGLE {\it I}-band light curves of LSP variables in the LMC and Galactic bulge. The light curves are folded with the LSPs given in the panels. Dotted vertical lines divide each light curve into two equal parts lasting half of the LSP cycle. See the electronic edition of the Journal for a color version of this figure.} \label{fig1} \end{figure} \begin{figure} \epsscale{1.1} \plotone{fig2.ps} \caption{Examples of the OGLE {\it I}-band light curves of variable stars with a dark spots on their photospheres. Dotted vertical lines divide each light curve into two equal parts lasting half of the period. See the electronic edition of the Journal for a color version of this figure.} \label{fig2} \end{figure} \vspace{3mm} | Obviously, the problem of the LSP origin deserves a much more comprehensive analysis than our simple simulation, but it seems that the binary scenario is the only one that is consistent with virtually all the observational facts known for LSPs. A model with a spiral dusty cloud that follows a low-mass object on a circular orbit around the red giant well reproduces the light and radial velocity variations associated with the LSP modulation. This hypothesis naturally explains the observed large movements of the visible surface of the LSP star \citep{nicholls2009}, the mid-infrared excess caused by the circumstellar dust around LSP variables \citep{wood2009}, the lack of significant temperature changes during the LSP cycle \citep{wood2004}, and the PL relation of the LSPs (sequence D) that is a direct continuation of sequence E formed by close binary systems \citep{soszynski2004}. Large blue-to-red amplitude ratios \citep{derekas2006} just reflect the extinction law produced by dusty material obscuring the giant and depend on the physical properties of this matter. Changes of the amplitudes of the LSP modulation observed in some sequence D stars can be explained by variations of the mass-loss rates, which influence the size and density of the dusty cloud orbiting the red giant. The only unclear feature in our model is the reversed phase shift between the light and velocity curves. This inconsistency can be explained by a specific distribution of the circumstellar matter, but more detailed models are needed to address this problem. A natural question that arises is the origin of the brown dwarfs in the close orbits of at least 30\% of red giant stars. These low-mass objects could be former Jupiter-like planets that accreted part of the matter ejected from the giants due to stellar winds, and increased their masses to the brown dwarf range \citep{retter2005,soszynski2007}. If this explanation were true, the LSP giants would be excellent probes of the fraction of planets in different regions of our and other galaxies. Another issue related to the binary explanation of the LSP phenomenon is the mechanism that keeps the low-mass object near the giant surface for a long time and prevents it being swallowed it by the giant companion. A brief discussion of this problem can be found in \citet{soszynski2007b}. We do not have a definitive answer for this question, but we suspect that the low-mass object induces increased mass loss from the giant when its distance is small, which in turn causes the increase of the distance between both components. This feedback mechanism might keep a low-mass companion in a close orbit around a giant for a long time, until the SRV becomes a Mira star, and the changes of the giant radius due to pulsation become very large. Then, the secondary component sinks below the giant surface and it is completely engulfed. Therefore we do not observe LSP modulation in the Mira stars. As a byproduct of this study, we distinguished a group of red giants with periodic variations which we interpret as caused by a dark spot on their surface. These objects also follow a PL relation, spreading between sequence~C (populated by the fundamental-mode pulsators -- Miras and SRVs) and sequence~D (LSP). Note that \citet{soszynski2013b} noticed a dim PL sequence located between sequences C and D for somewhat brighter giants. It is not clear if this sequence has something in common with the spotted variables identified in this work. Undoubtedly, both types of stellar activity -- starspots and LSPs -- deserve special attention in future studies. | 14 | 4 | 1404.4390 |
1404 | 1404.6440_arXiv.txt | Certain regions of Saturn's rings exhibit periodic opacity variations with characteristic radial wavelengths of up to a few hundred meters that have been attributed to viscous overstabilities. The Visual and Infrared Mapping Spectrometer (VIMS) onboard the Cassini spacecraft observed two stellar occultations of the star $\gamma$ Crucis that had sufficient resolution to discern a sub-set of these periodic patterns in a portion of the A ring between 124,000 and 125,000 km from Saturn center. These data reveal that the wavelengths and intensities of the patterns vary systematically across this region, but that these parameters are not strictly determined by the ring's average optical depth. Furthermore, our observations indicate that these opacity variations have an azimuthal coherence scale of around 3000 km. | Saturn's rings consist of many small particles in orbit around the planet. In denser ring regions, the gravitational and collisional interactions among the ring particles give rise to various fine-scale structures. In particular, certain parts of Saturn's rings exhibit periodic opacity variations with characteristic wavelengths between 100 and 500 meters. These patterns have opacity maxima that are nearly perfectly aligned with the azimuthal direction, and so they act like diffraction gratings for radio signals passing through the rings, producing distinctive sidebands in Cassini Radio Science Subsystem occultations. Based on the distribution of these sidebands, \citet{Thomson07} identified periodic structures in several parts of the main rings, including the the inner A ring (123,000-123,400 km and 123,600-124,600 km), the inner B ring (92,100-92,600 km and 99,000-104,500 km) and the outer B ring (110,000-115,000 km). Extremely high-resolution opacity data obtained by the Cassini UVIS instrument during the occultation of the star $\alpha$ Leonis confirmed the existence of optical-depth variations with a characteristic wavelength of $\sim$160 meters in the outer B ring around 114,150 km \citep{Colwell07}. Both of these observations indicated that these periodic variations are almost perfectly azimuthal. \nocite{LO10} These periodic structures have been interpreted as the result of viscous overstabilities in the rings \citep{Thomson07, Colwell07, Colwell09}. Such overstabilities occur when the effective viscosity of the ring increases sufficiently rapidly with increasing particle number density that oscillatory density variations can grow from small initial perturbations (see Schmidt {\it et al.} 2009 for a recent review of this phenomenon, with references to earlier work). In hydrodynamical simulations without self-gravity, the characteristic wavelength of these oscillations initially tends to increase with time \citep{ST95, Schmidt01, SS03}, but if the ring has a finite surface mass density, then non-linear phenomena and the ring's self-gravity limits the range of wavelengths that can be excited, leading to the formation of highly periodic structures with wavelengths around 200 meters, similar to those observed in Saturn's rings (Schmit and Tscharnuter 1999, but see Latter and Ogilvie 2009, 2010 for other possible mechanisms for limiting the waves' growth). While fully self-gravitating N-body simulations have shown that overstabilities can exist in rings with finite mass densities and realistic inter-particle gravitational forces \citep{Salo01}, there is currently not a complete analytic theory for the formation of overstabilities in rings with finite mass densities, which may simultaneously sustain non-radial fine-scale structure such as self-gravity wakes \citep{Schmidt09, LO09, RL13}. Two stellar occultations by the rings of the star $\gamma$ Crucis observed with the Visual and Infrared Mapping Spectrometer (VIMS) instrument onboard Cassini provide new information about the periodic structures in the inner A ring. The observations are described in Section~\ref{data}, while Section~\ref{wave} discusses trends in the wavelength and amplitude of the relevant patterns derived from a wavelet-based analysis of the light-curves. Section~\ref{turn} examines a subset of these data obtained when the star moved nearly azimuthally behind the rings in order to constrain the azimuthal coherence length of these patterns, which turns out to be $\sim10^{4}$ times the radial wavelength. Finally, Section~\ref{discussion} discusses some of the potential implications of these findings. | \label{discussion} Currently, the best explanation available for these periodic, almost purely azimuthal sub-kilometer patterns is that they represent viscous overstabilities. However, additional theoretical and observational work is needed to validate or refute this interpretation. While established linear theories can provide information about the conditions required to initiate overstability, the non-linear processes responsible for determining the final amplitude and wavelength of the patterns are still not perfectly understood, especially for situations where the mutual self-gravity of the particles cannot be ignored \citep{ST99, Salo01, Schmidt09, LO09, RL13}. Since we cannot compare our observations with detailed theoretical predictions for the behavior and distribution of overstabilities, we will instead discuss briefly two ways these measurements could help inform future theoretical work on overstable phenomena. On the one hand, this new information about the radial distribution of periodic patterns could help guide numerical simulations geared towards determining the parameters that influence the expression of overstabilities. On the other hand, our constraints on the patterns' azimuthal coherence lengths will likely require the development of novel theoretical analyses before they can be properly interpreted. \begin{figure*}[tbp] \centerline{\resizebox{6.5in}{!}{\includegraphics{f11.pdf}}} \caption{Sample simulations of small ring patches (700 m$\times$280 m) around 124,000 km with dynamical optical depths of 0.6, 0.8 and 1.0 (corresponding to average photometric optical depths of .68, .88 and 1.07). Each simulation consists of identical particles with coefficient of restitution $\epsilon = 0.1$, particle internal density of 225 kg/m$^3$ and an average surface density of 500 kg/m$^3$. The left panels show snapshots of the simulations after 200 orbit periods viewed from above ($x$=radial direction, $y$=azimuthal direction) when the system has reached a steady state. The middle panels show the same simulation in a side (or edge-on) view, while the right plot shows the average photometric optical depth versus radius. While no overstable pattern is visible in the $\tau=0.6$ case, clear overstable density variations are visible in both higher opacity cases.} \label{simfig} \end{figure*} Most numerical simulations of dense rings consider a small patch of ring material because of limitations on available computer time. Provided the area of the patch is larger than the wavelength of the relevant overstable patterns, such simulations are sufficient to ascertain the conditions under which overstabilities are likely to develop. For example, Figure~\ref{simfig} shows the results of three numerical simulations of a ring with three different optical depths, computed using the algorithms described in \citet{Salo95} and ~\citet{Salo01}, which include the mutual gravitational interactions among the relevant ring particles. These patches all have the same surface mass densities but different ``dynamical optical depths'' $\tau_{dyn}$ (a standardized measure of the total cross sectional area of all particles in the simulation) of 0.6, 0.8 and 1.0, which correspond to average observable normal optical depths of 0.68, 0.88 and 1.07, respectively. All three simulations exhibit an array of tilted features known as self-gravity wakes, which arise from the competition between the particles' mutual gravitational attraction and Keplerian shear. Since the surface density is the same in all three simulations, the radial separation of wake structures (set by Toomre's critical wavelength) is the same. However, in two of the simulations there are also periodic axisymmetric patterns that corresponds to a viscous overstability. These simulations show that there is a relatively sharp transition between optical-depth regimes where the overstability does not occur (e.g. the $\tau_{dyn}$=0.6 case) to those where the opacity variations associated with the overstability are substantial (e.g. the $\tau_{dyn}$=0.8 case). This seems to be consistent with our observations that show rather sharp transitions between regions where the overstability is clear and where it is undetectable (see also Rein \& Latter 2013). For these particular simulations, overstabilities develop when the observed optical depth is around 0.8, which is close to the minimum optical depth where periodic patterns can be detected in the VIMS observations. However, these models assume that the ring particles are all the same size and have a rather low particle internal density of 225 g/cm$^3$, so more work needs to be done to ascertain whether the same threshold can be achieved with higher particle densities and different particle sizes, surface densities, etc. Also, the VIMS observations show that the pattern's distribution across the rings is not strictly a function of the ring's optical depth. For example, no periodic pattern is visible around 124,570 km and 124,720 km, even though the latter region has an optical depth that exceeds 0.8 and appears to be high enough to support patterns elsewhere in this part of the rings. Even if we limit our attention to regions where we can clearly detect a periodic structure, the pattern's wavelength is not always correlated with optical depth. For instance, we observe a minimum in the pattern's wavelength around 124,300 km, where the optical depth undergoes a sharp transition from 1.2 to 0.8. It remains unclear whether these trends can be explained by shifts in the local particle size distribution or other particle properties, or if they require consideration of other aspects of the dynamical environment. Probably the best way to address these issues is by numerically simulating a wide array of conditions in order to thoroughly explore the relevant parameter space. While currently available numerical tools should be able to clarify the radial distribution of the periodic patterns, understanding the azimuthal properties of these structures will likely require different theoretical approaches. Simulating ring regions hundreds or thousands of kilometers across is beyond the abilities of current techniques, so it may be some time before theorists can simulate a region large enough for the overstable regions to exhibit real non-axisymmetric features. While smaller simulations could potentially reveal how localized structures like embedded moonlets could disrupt the overstable patterns, semi-analytical models of how non-circular density ridges evolve over time (analogous to those used to describe density waves and other resonant structures) may also yield useful insights. In lieu of such theoretical advances, we can use the observational data to try and better understand how the patterns' coherence scale depends upon its dynamical environment. Both $\gamma$ Crucis occultations indicate that the azimuthal coherence length of the periodic patterns in the inner A ring is substantial, of order 3000 km. However, such long coherence scales may not be a universal feature of these periodic patterns. For example, UVIS detected periodic structures with a typical wavelength of 160 meters in an occultation with a turnaround radius around 114,150 km in the outer B ring \citep{Colwell07}. Unlike the VIMS occultations, the ingress and egress profiles derived from these UVIS observations are not obviously correlated with each other close to the turnaround point. This suggests the patterns observed by UVIS have a much shorter azimuthal coherence length, perhaps less than 100 km. This reduced coherence length might reflect the particular environment probed by the UVIS occultation. The outer B ring exhibits strong stochastic optical depth variations on a broad range of scales which make the opacity profiles obtained during different occultations very poorly correlated, and the weak correlation between the ingress and egress profiles in the UVIS data could be just another expression of this general behavior. However, it is also possible that the weak correlations in the UVIS data are due to the much higher optical depth in the outer B ring ($\tau_n \sim 3$) compared to the inner A ring ($\tau_n \sim 1$). One potential bit of supporting evidence for this second option is that the periodic patterns seen near the turnaround in the Rev 106 VIMS occultation, where $\tau_n \sim 1.2$, are less well correlated than the patterns seen in the Rev 104 data, where $\tau_n \sim 0.9$. Thus it might be that increasing the opacity of the rings tends to reduce the azimuthal coherence length of the overstable patterns. Probably the best way to confirm or refute this idea would be with additional data from other occultations that turn around at different locations within regions possessing periodic patterns. Another potentially useful tool for understanding the coherence lengths of these patterns are the sidebands \citet{Thomson07} described in the radio occultation data. Since these sidebands occur where a periodic opacity variation acts like a diffraction grating for the radio signal, the intensity of these sidebands depends both on the magnitude of the density variations and their coherence lengths. It is interesting to note that the radio science experiment only detected sidebands out to around 124,400 km, while VIMS detected periodic signals out to 124,800 km. This difference could be due to time-variability in the extent of the periodic patterns between 2005 and 2009, but may also indicate that the patterns beyond 124,400 km are not coherent enough over a large enough region to produce proper sidebands in the radio occultation. If the latter is the case, the radio occultations could provide useful information about the coherence scales of these periodic patterns and how they vary across the rings. | 14 | 4 | 1404.6440 |
1404 | 1404.3579_arXiv.txt | Forecasting the in situ properties of coronal mass ejections (CMEs) from remote images is expected to strongly enhance predictions of space weather, and is of general interest for studying the interaction of CMEs with planetary environments. We study the feasibility of using a single heliospheric imager (HI) instrument, imaging the solar wind density from the Sun to 1 AU, for connecting remote images to in situ observations of CMEs. We compare the predictions of speed and arrival time for 22 CMEs (in 2008-2012) to the corresponding interplanetary coronal mass ejection (ICME) parameters at in situ observatories (\emph{STEREO PLASTIC/IMPACT}, \emph{Wind SWE/MFI}). The list consists of front- and backsided, slow and fast CMEs (up to 2700 \kmsec). We track the CMEs to $34.9 \pm 7.1$ degrees elongation from the Sun with J-maps constructed using the \emph{SATPLOT} tool, resulting in prediction lead times of $-26.4 \pm 15.3$ hours. The geometrical models we use assume different CME front shapes (Fixed-$\Phi$, Harmonic Mean, Self-Similar Expansion), and constant CME speed and direction. We find no significant superiority in the predictive capability of any of the three methods. The absolute difference between predicted and observed ICME arrival times is $8.1 \pm 6.3$~hours ($rms$ value of 10.9h). Speeds are consistent to within $284 \pm 288$~\kmsec. Empirical corrections to the predictions enhance their performance for the arrival times to $6.1 \pm 5.0$~hours ($rms$ value of 7.9h), and for the speeds to $53 \pm 50$~\kmsec. These results are important for \emph{Solar Orbiter} and a space weather mission positioned away from the Sun--Earth line. | Storms from the Sun, known as coronal mass ejections (CMEs), are massive, quickly expanding expulsions of plasma threaded by magnetic fields, originating from both quiescent and active regions in the Sun's corona. Over a distance of a few solar radii, they may accelerate up to speeds of 3000 kilometers per second in rare cases, and subsequently propagate through the solar wind away from the Sun. CMEs are able to reach 1 AU in half a day in the most extreme cases, and are the source of the strongest disturbances in the Earth's magnetosphere \citep[e.g.][]{zha07}. Forecasting their general properties, such as propagation direction and speed close to the Sun and in the interplanetary medium, as well as their arrival time and arrival speed at a given planet or spacecraft, is a major issue in the field of heliophysics. Moreover, the science that underlies our ability to predict CME arrival times and speeds with high precision, which is at the heart of a reliable, real-time space weather forecast, is still not well understood, with average errors of the order of 0.5 to 1 day and several $100$~\kmsec, respectively \citep[e.g.][]{gop01}. Recent advances in analysing multi-point imaging data has improved these classic values for a few CME events by roughly a factor of two \citep{mis13, col13}. While this is clearly of greatest interest for the location of the Earth, predictions and parameters of CMEs impacting Mercury, Venus, Mars, Jupiter and Saturn are also essential for studying their interaction with other planetary environments \citep[e.g.][]{bak13}. The \emph{Solar TErrestrial RElations Observatory} \citep[\emph{STEREO}, ][]{kai08}, launched in late 2006, consists of two spacecraft, one ahead (\emph{STEREO-A}) and one behind the Earth (\emph{STEREO-B}) in orbits around the Sun. Each year, each spacecraft separates from the Earth by about 22\degree in heliocentric longitude. Its \emph{SECCHI} instruments seamlessly image CMEs from the Sun to 1 AU and beyond. We are able to extract CME speeds and directions from the images in order to pin down CME evolution and assess CME predictions \citep[e.g.][]{moe09c,woo10,liu10,lug10, lyn10,sav10,dav11, lie11, moe11, sav12b,rol12, liu13, mis13, col13, dav13}. Even numerical simulations have been employed to enhance our ability to derive the physics of solar wind structures from heliospheric imaging \citep[e.g.][]{lug09a,lug11, xio13b, xio13, rol13}. A concerted campaign to analyse the series of CMEs launched by the Sun on 2010 August 1 has also revealed many details of CME propagation and their 3D evolution for interacting CMEs \citep{liu12,har12,moe12,web13,tem12}. A deceptively simple but persistent problem in the analysis of CMEs has been to find definite connections between the remote images of CMEs \citep{ill85}, taken by coronagraph or heliospheric imager instruments, and the signatures of CMEs in time series of plasma and magnetic field measurements taken directly (in situ) in the solar wind \citep{bur81}. Current space-based coronagraphs on 3 different spacecraft (\emph{STEREO-A/COR1/COR2, STEREO-B/COR1/COR2, and SOHO/LASCO)} can image a CME in its entirety during its ``birth'' and early propagation phase ($1-15$ solar radii). These instruments provide white-light images of CMEs projected into the plane of the sky, i.e.\ the plane perpendicular to the Sun--spacecraft line. As the CME propagates further away from the Sun, heliospheric imager (HI) instruments image, in white--light, its integrated density signature around the so-called ``Thomson surface'' \citep{vou06} or ``Thomson plateau'' \citep{how12b} at elongation angles of 4-88\degree from the Sun (for \emph{STEREO/HI}). Because of the wider viewing angle, the interpretation and analysis of HI data is more complex compared to coronagraphs and not yet fully understood \citep[e.g.][]{rou11rev,how12b}. When a CME hits a spacecraft with in situ instruments onboard that are capable of characterizing the solar wind plasma and magnetic fields, it leads to distinct signatures in the time series of the measured parameters. Often, a shock is followed by a sheath region in front of a magnetic driver, which is either an irregular structure or a large-scale magnetic flux rope \citep[e.g.][]{bur81,bot98,lyn03,lei07,moe09b,ric10,isa13,alh13}. We call the interval including all of these signatures an ``interplanetary CME'' or ``ICME''. Troughout this paper, we use the term ``CMEs'' for events observed in images and ``ICMEs'' for ejecta identified from in situ measurements. However, these measurements of the in situ solar wind give a detailed but otherwise extremely limited and localized view of a CME at the position of the spacecraft near 1 AU. At this distance, a CME has already expanded into an enormous structure, covering up to around 100\degree in heliocentric longitude and several tenths of an AU along the radial direction to the Sun \citep{bur81,bot98,liu05,ric10,woo10,moe12}. Thus, progressing further from the Sun leads to less and less information on the global structure of the CME, which is increasingly hard to interpret, providing a first explanation for the difficulties in linking the datasets. As a background to our study, it needs to be understood that CMEs are almost never really single entities, but they react to their coronal and heliospheric environments \citep[e.g.][]{tem11, kil12b, rol12}. A possible general paradigm of CME propagation through the solar wind has recently emerged. \cite{liu13} state a picture of Sun--to--Earth propagation of fast CMEs, derived from a joint analysis using stereoscopic heliospheric images, radio and in situ observations of three CME events: fast CMEs impulsively accelerate close to the Sun, followed by a rapid deceleration out to about 0.4~ AU, culminating in an almost constant speed propagation phase \cite[see also, e.g.,][for earlier, similar ideas]{gop01}. Our paper addresses the problem of seamlessly connecting CMEs from the Sun to 1 AU in two ways. First, we establish a list of suitable CME events from 2008-2012, using observations by coronagraphs, heliospheric imagers and in situ instruments onboard the \emph{STEREO} and Wind spacecraft, and model the imaging observations using single-spacecraft state-of-the-art-``geometrical modeling'' methods. Secondly, we use these connections to enhance our understanding of CME propagation and their prediction, focusing on the improvement of methods to extract CME parameters from heliospheric imager data. Our study builds on the results of \cite{lug12}, who analyzed CMEs in \emph{STEREO/HI} data that impacted the other \emph{STEREO} spacecraft during the interval 2008--2010. This study established that predictions of speeds and arrival times for slow CMEs are roughly consistent with corresponding in situ parameters, and demonstrated the possibility for succesfully predicting CMEs that propagate behind the limb or on the backside of the Sun as viewed from HI. However, our paper goes further along several, critical avenues: we included modeling with the new Self-Similar Expansion Fitting (SSEF) technique \citep{dav12}, which allows more flexibility for the CME width in the solar equatorial plane than previous models, which were either point-like \citep[Fixed-$\Phi$, ][]{she99,rou08} or extremely wide \citep[Harmonic Mean, ][]{lug09a,lug10}. In addition, we now have \emph{STEREO} data of very fast CMEs ($> 2000$~\kmsec) available, and we mainly discuss Earth-directed events. The \emph{STEREO} separation from Earth increased from 22\degree in early 2008 to 120\degree in mid 2012, thus we include in our study backsided events (from the point of view of a \emph{STEREO} spacecraft), similar to \cite{lug12}. Several lines of research have recently converged to make this work possible, apart from having available the remote \emph{STEREO} observatories in conjunction with the Wind spacecraft (the latter at the Sun-Earth Lagrangian 1 or L1 point): (1) the existence of software packages (i.e., \emph{SATPLOT} and croissant modeling) to easily extract and fit CMEs in \emph{STEREO/COR2} and HI data, (2) the development of mature models to obtain CME speeds and directions from heliospheric imagers, and (3) the rise of solar cycle 24 which culminated in several very fast coronal mass ejections. All this now gives us the opportunity to study the potentially most geoeffective events with multi--point in situ and imaging data \citep[e.g.][]{liu13,dav13}. The connections established in our paper may be used by other researchers to benchmark any empirical or numerical propagation model of CMEs. We need to emphasize that our paper focuses on establishing connections between the datasets, which means that we track CMEs as far as possible through the HI data, up to 30--40\degree elongation from the Sun. For this reason the prediction lead times, which are the differences between the last data points used for extracting CME parameters, and the actual in situ arrival times, are relatively short, of the order of one day. This should be kept in mind when discussing our results for the errors in CME speeds and arrival times. Shorter tracks in HI must be used in order to increase the prediction lead time to values suitable for real time forecasting, namely from more than one day for fast CMEs to several days for slow CMEs. Such an analysis was carried out by \cite{moe11} for a case study, and is the aim of future studies that will exploit our full dataset, consisting of 22 CME events. The differences in speeds and arrival times that we derive from comparing the HI data to the in situ data thus show how well a HI system configured as on \emph{STEREO} can perform for CME forecasting. | We have presented a study in which we have connected white light to in situ observations of a set of 22 near-equatorial CMEs. Their parameters cover a wide range of initial and propagation speeds (260 to 2715 \kmsec), and a variety of principal CME directions with respect to the HI observer (40\degree to 170\degree in heliocentric longitude). This is the first study to do such an analysis of such a large and diverse set of events. Here, we summarize our results and their implication for space weather prediction and the evolution of CMEs between the Sun and 1~AU separately, emphasizing our main conclusions in italics. First, concerning space weather prediction, we have mainly tested methods for predicting CME directions, speeds and arrival times based on J-maps produced using observations from a single-spacecraft heliospheric imager instrument. These data were provided by HI on \emph{STEREO-A/B}, which, for the CMEs under study, were positioned well outside the Sun-Earth line, on heliocentric longitudes between 30\degree and 120\degree away from the Earth. \begin{enumerate} \item \textbf{Event selection}: We have selected CME events with clear interplanetary CME signatures (shock, sheath and ejecta) in \WIN and \STB in situ observations near 1 AU, and which we could easily track in the HI J-maps. This set of CMEs covers a wide range of initial speeds, so it is suitable for statistical analysis, although there are actually many more CMEs in the data during this time range. The events in our list occurred during the rise of solar cycle 24, between 2008-2012, and \emph{STEREO} progressed towards and beyond opposition during this time. Therefore, our dataset contains mostly slow frontsided and fast backsided CMEs. Our results must be considered carefully with this in mind, and are likely to be different for different datasets. \item \textbf{Tracking CMEs and prediction lead times:} We tracked CMEs as far as possible in the J--maps, resulting in an average track length of $34.9\pm7.1$\degree elongation. Depending on the CME speed, its direction and the model applied, this corresponds to different distances each CME has traveled away from the Sun at the time of the last HI observation. This distance is on average $0.86 \pm 0.28$ AU, thus we have tracked most CMEs almost up to 1 AU. The prediction lead times also depend on several of the aforementioned parameters, and are on average $-26 \pm 15$~hours, about $- 1$~day. This is considerably longer than those provided by a solar wind monitor at L1 (on the order of 1 hour, e.g.\ the current \emph{ACE} mission), but definitely shorter than lead times using corongraphs only \citep[on the order of CME transit times of a few days, e.g.][]{kil12b}. The work presented here should rather be seen as an attempt to establish connections between CME-related phenomena detected in different data sets (coronagraph, heliosphere, in situ), which is strongly desirable for benchmarking various empirical or numerical CME prediction models. \item \textbf{CME directions}: The three different geometrical models used in this study do not provide consistent CME directions, with differences of up to 50\degree in heliocentric longitude for fast CMEs. For this reason, we derived the direction from multi-viewpoint applications of the croissant model to coronagraph images as a well constrained reference for the initial CME direction. The FPF direction was shown to be, on average, consistent to within a few degrees with the croissant direction. This means that \emph{if CMEs propagate radially away from the Sun above 15 solar radii, the FPF method is superior over the others in deriving the CME principal direction}. However, there is also considerable scatter, of the order of $\pm 30$\degree heliocentric longitude around the average direction. The directions provided by the SSEF and HMF models, which assume an extended CME front, differ by about $30$\degree from the croissant direction. These methods show a bias in the direction to values further away from the HI observer, with larger differences for faster CMEs, confirming theoretical predictions by \cite{lug13}. \item \textbf{CME arrival time and speed predictions:} Using geometrical modeling to predict CME speed and arrival time, with a lead time of roughly 1 day, results in average absolute differences from observed ICME sheath speeds and arrival times of $|\Delta V|=284 \pm 288$~\kmsecc and $|\Delta t| = 8.1 \pm 6.3$h, respectively, averaged over all three methods. The arrival time difference given by the root-mean-square method is $\Delta t_{RMS} =10.3$h. Conserving the sign of the differences, similar numbers for calculated minus observed speeds and arrival times are $\Delta V=275 \pm 297$~\kmsecc and $\Delta t = -3.8 \pm 9.6$h, respectively. \emph{In summary, predicted ICME speeds at 1 AU are, on average, overestimated, and consequently, predicted arrival times are too early compared with the in situ observations}. Correlating the interplanetary CME speed in the direction of the in situ observatory with the in situ speeds, and, independently, with the differences in observed and predicted arrival times, we obtained new empirical relationships between these variables, based on linear fits. These allow us to predict the CME speed and arrival time with better accuracy for, at least, the present dataset. \emph{Applying these empirical corrections in the prediction of CME speeds and arrival times, $|\Delta V|=53 \pm 50$~\kmsec ($\Delta V=0 \pm 73$~\kmsec), and $|\Delta t| = 6.1 \pm 5.0$h ($\Delta t = 0.0 \pm 7.9$h, $\Delta t_{RMS} = 7.9$h), averaged over all events and methods.} More specifically, 88\% (or roughly 9 out of 10) of all in situ ICME sheath region speeds in our dataset were predicted to within $|\Delta V| < 100$~\kmsec. In 71\% of cases (or roughly 3 out of 4), ICME arrival times are predicted within $|\Delta t| < 8$~hours. Moreover, we quantified the relationship between the maximum magnetic field $B_{max}$ in the ICME and the interplanetary propagation speed, which lets us predict $B_{max}$ to within $\pm 5$~nT in 2 out of 3 cases. \item \textbf{Comparison to stereoscopic modeling}: \cite{col13} found similar results for CME arrival time and speed prediction using the results of methods applied to two heliospheric imager instruments, such as fitting the stereoscopic croissant model to \emph{STEREO/COR2/HI1/HI2} and \emph{SOHO/LASCO} images, for heliocentric distances up to about 0.9 AU. Similar to our study, they also applied corrections for the apex and flank parts of the CMEs impacting the in situ observatory. They found that for 78\% of cases, $\Delta t < 6$~hours, and for 55\% of CMEs, $\Delta V < 100$~\kmsec, although for all events $\Delta V < 140$~\kmsec. \cite{col13} fitted the height-time data in several different ways, and they found a linear fit between $50$~$R_{\odot}$ (0.23 AU) and 1~AU and thus assuming a constant speed to produce the best predictions, even though they also concluded that CMEs clearly decelerate. It is interesting to note that an equivalent assumption of constant speed between 0.07 to 0.85 AU in our geometrical modeling methods yields a similar level of predictive performance. \end{enumerate} Second, we summarize our results in terms of the physical evolution of CMEs between the Sun and 1 AU. In general, we find that, using single-spacecraft HI observations, it is much more difficult to generalise the behavior of CMEs in terms of such properties as propagation direction, speed variation and global shape evolution when compared to the use of stereoscopic HI measurements \citep[e.g.][]{liu10, lug10, liu11, col13, mis13, liu13, dav13}. \begin{enumerate} \item \textbf{CME radial propagation:} A major unsolved question is whether CMEs propagate radially away from the Sun, or undergo any significant change of direction as they travel through the interplanetary (IP) medium. CMEs are known to be deflected in the corona by coronal holes \citep{gop09} and possibly through CME-CME interaction in IP space \citep{lug12}. \cite{liu13} and \cite{dav13} showed the CME direction for a few events to stay within about $\pm 15$\degree (heliocentric longitude) from the corona to the IP medium. This can still be considered as consistent with a radial propagation. With our own dataset, CME deflections are difficult to assess without further analysis. As discussed above, the HI methods can give very different answers for a single event - \emph{CME principal directions are not well defined using single-spacecraft HI methods.} Note also that we assume constant direction in IP space in contrast to the stereoscopic methods, so we can only assess deflections by comparing directions derived from coronagraph and HI measurements. However, there is considerable scatter between these initial and IP directions (of the order of $\pm 30$\degreee, about twice the level derived from stereoscopic methods), pointing indeed to the possibility that some CMEs may significantly change in direction between the corona and the IP medium. While the croissant model constrains the CME direction well close to the Sun, there is no straightforward way to constrain the CME direction using single-spacecraft in situ data, and thus we leave further analysis for future work. Our results on CME direction in IP space clearly point out that its calculation is always influenced by the strongly idealized shapes of the CME front which we assume in the first place. The geometrical definitions we use make it possible to describe CME front shapes analytically, and form very useful tools. However, our study casts some doubts on their use in defining a CME's central propagation direction in the interplanetary medium, because its calculation depends so strongly on the assumption of its frontal geometry. Consequently, we propose that \emph{future work should quote ranges of heliocentric longitude that will be affected by a CME, rather than a central direction}. This would be especially helpful when describing distorted or asymmetric CME front shapes \citep[e.g.][]{sav10,moe12}. \item \textbf{CME speed profiles}: CMEs are well known to decelerate in the solar wind out to 1 AU, mainly due to a force equivalent to aerodynamic drag \citep[e.g.][]{gop01, kil12b, vrs13,liu13}, and we can see this clearly in our data. We can compare stepwise a CME initial speed ($< 15~R_\odot$, or $< 0.07$ AU) to its average IP propagation speed (from $\approx 0.07$ to $0.86 \pm 0.28$ AU), and to the speed of the ICME sheath region observed in situ near 1~AU. FPF and SSEF suggest that CMEs decelerate from the corona to IP space, while HMF yields a constant speed. CMEs are clearly slower when observed in situ near 1 AU than in IP space, and the in situ sheath region speeds can be reasonably well predicted by multiplying the IP speeds with $\approx 0.2$ and adding $320$~\kmsec, which is independent of the model used. The speed of $320$~\kmsecc is reminiscent of the slow solar wind, and this relationship is also consistent with early work by \cite{lin99}. However, we cannot definitely say where most of the deceleration occurs, because of our assumption of constant IP speed. Recent analyses with stereoscopic methods by \cite{liu13} showed that much of the deceleration of fast CMEs occuring up to about 80 solar radii (0.37 AU), but there is probably no general distance by which the deceleration ceases, as a case has been found where a CME almost does not decelerate out to 1 AU \citep{moe10}. \item \textbf{Evolution of the global CME shape}: We expected that there would be clear differences concerning the prediction performance of different geometrical models, giving us hints which one better describes the CME front shape in the plane perpendicular to the HI images. In particular, we expected the SSEF model, as it is the most mature, with a well defined CME width, to perform best. But surprisingly, we did not find any significant difference in its performance for predicting CMEs compared to the other models. We think that this is caused by their assumptions of constant speed and constant direction, and their high sensitivity to a violation of these assumptions \citep{lug13}. In summary, \emph{the current state of the art of geometrical modeling of CMEs with single-spacecraft instruments (i.e.\ fitting methods) in comparison to single-spacecraft in situ data precludes inferences to be made regarding the large--scale geometry of CME fronts in planes perpendicular to the HI images, such as the ecliptic plane.} \end{enumerate} We conclude that predicting CME speeds and arrival times with heliospheric images gives more accurate results than using projected initial speeds from coronagraph measurements. These improvements are on the order of 12 hours for the arrival times \citep{col13}, and our results are consistent with those found with other space weather models in the \ST era \citep[see also][]{gop13,mis13,mis14}. Independent of the specific methods used, we can derive an average of the CME interplanetary propagation speed when we track a CME out to 1 AU. This average speed includes to some extent the background solar wind, which is known to play a significant role in modulating CME propagation \citep[e.g.][]{gop01,vrs07, tem11, kil12b}. The same is true for interacting CMEs, although it can be very difficult to differentiate and decipher different density tracks in HI when CMEs are launched close together in time and space \citep{har12, web13}. It is clear that the information contained in heliospheric images does indeed improve space weather prediction. However, the compromise between prediction accuracy ($\Delta t$) and prediction lead times ($t_{lead}$) needs to be better studied. Future modeling should thus focus on modeling CME tracks in J-maps for elongations from the Sun of $< 35$\degreee, which will result in longer prediction lead times than one day in the current study. It needs to be assessed how the predictions for speed and arrival time become less accurate as the prediction lead time is increased, and the best balance for space weather prediction purposes needs to be found. Another possibility for future work is to actually include deceleration into the geometrical fitting methods for single-spacecraft HI instruments. This is expected to further improve the accuracy of predicting CME arrival times and speeds through use of a more realistic approach than the current assumption of constant speed. Such an approach, applied to the different model geometries, could provide clues to the CME global front shape, in particular when constrained by multi-point in situ measurements. Another solution would be to send a mission equipped with a heliospheric imager in a polar orbit around the Sun to look down onto the ecliptic plane \citep{lie08}. In this way, information on the global shape of a CME in the ecliptic, as it approaches Earth, would be revealed, and the CME propagation characteristics could be provided by the geometrical models as used in our paper. However, for effectively predicting geo-effectiveness it is also necessary to know the components of the interplanetary magnetic field, which cannot be derived from white-light images, and require new ideas like the Faraday-rotation technique \citep[e.g.][]{xio13}. Moreover, the \emph{Solar Orbiter} \citep[e.g.][]{mue13} and \emph{Solar Probe Plus} missions are currently under development and will approach the Sun closer than ever before by the end of the decade. The results and methods presented in this paper may provide both the scientific background and tools for analyzing the data from these exciting future missions. \begin{table*}[t]\label{tab:imaging} \begin{center} \caption{Imaging: Croissant and geometrical modeling (SSEF) results} \begin{tabular}{ccrrrrrrcc} \tableline\tableline (1) & (2) & (3) & (4) & (5) & (6) & (7) &(8) & (9) &(10)\\ CME & \emph{t$_{COR2}$} & $\Phi_{\mathrm{init;Earth}}$ & \emph{V$_{\mathrm{init}}$} & $\Phi_{\mathrm{IP;Earth}}$ & $\Phi_{\mathrm{IP;HI}}$& \emph{V$_{\mathrm{IP}}$} & \emph{V$_{\mathrm{IPo}}$} & \emph{t$_a$} & spacecraft\\ \tableline 1 & 2008 Apr 26 14:53 & -20& 523&-45&-70& 656&611& 2008 Apr 29 13:21 &STEREO-B\\ 2 & 2008 Jun 01 21:23&-37&260 & -15&-44 &384& 375 & 2008 Jun 06 22:34& STEREO-B\\ 3 & 2008 Jun 02 02:07& \nodata\tablenotemark{a}& \nodata &-44&-73&398& 369&2008 Jun 07 12:39 &STEREO-B\\ 4 & 2008 Dec 12 07:37&8& 497&10&55&421&414&2008 Dec 16 11:01&Wind\\ 5 & 2008 Dec 27 05:23& -32& 405 &-79 &-122&603&452&2008 Dec 31 05:01 &STEREO-B\\ 6& 2009 Feb 13 06:37& \nodata\tablenotemark{b}& \nodata & -75 & -119 & 396 &329& 2009 Feb 18 11:11&Wind\\ 7 & 2010 Apr 03 09:54& 4 & 829 & -19 &-86 &991 &915& 2010 Apr 05 06:35 &Wind\\ 8& 2010 Apr 08 03:54& 3 & 511 & -34& -102& 555& 407& 2010 Apr 12 07:19 &Wind\\ 9& 2010 May 23 17:39& 10 & 381 & 8 &-63& 440& 433 &2010 May 27 17:02& Wind\\ 10& 2010 Jun 16 11:24& -16 & 297 & 13& -62& 376& 364& 2010 Jun 21 08:00& Wind\\ 11& 2010 Aug 01 08:24& -28 & 1160 & -43 & -122 & 980 &808 & 2010 Aug 03 13:18& STEREO-B\\ 12& 2010 Aug 01 08:24& -28 & 1160 & -43 &-122 & 980 &525 & 2010 Aug 04 14:34& Wind\\ 13& 2011 Feb 15 02:09& 23 & 557 & -40 &-127& 867 &536 & 2011 Feb 18 04:21& Wind\\ 14& 2011 Aug 02 06:39& -29 & 1050 & -25 &-125& 714 &617 & 2011 Aug 05 00:14& Wind\\ 15& 2011 Sep 06 22:39& 34 & 1160 & -24 &-127& 838 &731 & 2011 Sep 09 08:11& Wind\\ 16& 2011 Oct 22 01:09& 19 & 692 & -15 &-120& 813 &772 & 2011 Oct 24 07:52& Wind\\ 17& 2012 Jan 19 15:09& -37 & 1335 & -36 &-144& 1097& 767 & 2012 Jan 21 19:03& Wind\\ 18& 2012 Jan 23 03:09& 21 & 1708 & -33 &-141& 2181& 1644 & 2012 Jan 24 03:54& Wind\\ 19& 2012 Mar 05 04:09& -53 & 974 & -41 &-150& 1347& 807 & 2012 Mar 07 06:37& Wind\\ 20& 2012 Mar 07 01:39\tablenotemark{c}& -35 & 2585 & -42 &-151& 2202& 1265 & 2012 Mar 08 08:34& Wind\\ 21& 2012 Mar 10 17:54& 27 & 1265 & -6 &-116& 1297& 1286 & 2012 Mar 12 00:44& Wind\\ 22& 2012 Apr 19 16:24& -26 & 639 & -20 &-133& 785 & 713 & 2012 Apr 22 01:46& Wind\\ 23& 2012 Jun 14 14:09& 0 & 1102 & -28 &-145& 1453 & 1205 & 2012 Jun 16 00:02& Wind\\ 24& 2012 Jul 12 16:45& -1 & 1277 & -22 & -142& 1486 & 1336 & 2012 Jul 13 23:50& Wind\\ \tableline \end{tabular}\tablenotetext{1}{This event is the core or trailing part of the CME on June 1, so it is not fitted with the croissant model.} \tablenotetext{2}{This CME was too faint to be fitted with the croissant model.} \tablenotetext{3}{This is the 2nd CME of a double eruption of the same active region, with another CME first observed at 00:39 UT in COR2A. We quote the croissant results for the 2nd event because it is mainly directed in the ecliptic plane and thus more likely to impact Earth, whereas the first CME is directed mainly northward.} \tablecomments{Explanation of parameters: (1) Number of CME event. (2) Date and time (UT) of the first image in COR2A when the CME is observed. (3) The initial direction (in degrees) in heliocentric longitude (\emph{Heliocentric Earth Equatorial} or \emph{HEEQ} coordinates) of the CME from croissant modeling (2.5-15.6~$R_{\odot}$). Earth is at 0\degree longitude, angles $> 0$\degree corresponds to solar west. (4) The initial speed of the CME from croissant modeling, in \kmsec. (5) The interplanetary direction (in degrees) of the CME in heliocentric longitude (close to but not exactly in the solar equatorial plane, see Section 2.2), from geometrical SSEF modeling with 45\degree half width (Earth at 0\degreee). (6) The interplanetary direction of the CME apex in degrees, measured from the HI observer (at 0\degreee). (7) The CME interplanetary propagation speed, for the apex of the front (for the SSEF model), in \kmsec. (8) The speed of the point along the CME front that travels towards the in situ spacecraft (for the SSEF model), in \kmsec. (9) Date and time (UT) of the predicted arrival at the in situ spacecraft, from SSEF modeling. (10) Name of the in situ spacecraft for which the predicted arrival time $t_a$ is calculated. } \end{center} \end{table*} \begin{table*}[t] \begin{center} \caption{In situ ICME parameters} \begin{tabular}{ccrrrrrrrr} \tableline\tableline (1) & (2) & (3) & (4) & (5) & (6) & (7) &(8) & (9) &(10)\\ CME & spacecraft & $d_i$ & $\Phi_{\mathrm{IP;insitu}}$ &\emph{t$_{\mathrm{insitu}}$} & \emph{V$_{\mathrm{sheath}}$} & \emph{N$_{\mathrm{sheath}}$} & \emph{B$_{\mathrm{max}}$} & min \emph{B$_z$} & min Dst\\ \tableline 1 & STEREO-B & 1.0280 & 21 &2008 Apr 29 14:10 & 430$\pm$11 & 16$\pm$6 & 14.0 & -9.5 & \nodata\\ 2 & STEREO-B & 1.0542 & -11 &2008 Jun 06 15:35 & 403$\pm$16 & 15$\pm$7 & 14.6 & -8.6 & \nodata\\ 3 & STEREO-B & 1.0548 & 19 &2008 Jun 07 12:07 & 384$\pm$17 & 13$\pm$7 &12.5 &-11.3 &\nodata\\ 4 & Wind& 0.9840 & -10 &2008 Dec 16 06:36 &355$\pm$9 &16$\pm$4 &10.0 &-7.6 &\nodata\\ 5 & STEREO-B & 1.0263 & 34 &2008 Dec 31 01:45 & 447$\pm$10 &7$\pm$3 &9.5 &-6.7 &\nodata\\ 6 & Wind & 1.0023& 28 & 2009 Feb 18 10:00 &350$\pm$8 &22$\pm$4 &12.3 &-9.4 &\nodata\\ 7 & Wind & 1.0004& 19&2010 Apr 05 07:58 &735$\pm$18 &10$\pm$2 &21.5 &-14.6 &-81\\ 8 & Wind & 1.0021& 34&2010 Apr 11 12:14 &431$\pm$18 &10$\pm$1 &12.7 &-8.6 &-51\\ 9&Wind & 1.0132& -8&2010 May 28 01:52& 370$\pm$10 &19$\pm$4 &13.7 &-12.9 &-85\\ 10&Wind & 1.0161& -13&2010 Jun 20 23:02 & 400$\pm$6 &8$\pm$3 &8.6 &-2.8 &\nodata\\ 11&STEREO-B & 1.0604& -28 &2010 Aug 03 05:00& 632$\pm$47 &4$\pm$4 &33.2 &-30,2 &\nodata\\ 12&Wind & 1.0146& 43 &2010 Aug 03 17:05& 581$\pm$16 &10$\pm$2 &19.2 &-11.2 &-67\\ 13&Wind & 0.9881& 40 &2011 Feb 18 00:48& 497$\pm$27 &25$\pm$11 &31.8 &-24.3 &\nodata\\ 14&Wind & 1.0145& 25 &2011 Aug 04 21:18& 413$\pm$12 &6$\pm$1 &10.1 &-8.1 &-107\\ 15&Wind & 1.0072& 24 &2011 Sep 09 11:46& 489$\pm$47 &12$\pm$14 &23.3 &-21.4 &-69\\ 16&Wind & 0.9946& 15 &2011 Oct 24 17:38& 503$\pm$15 &26$\pm$4 &24.3 &-22.1 &-132\\ 17&Wind &0.9841 & 36 &2012 Jan 22 05:28& 415$\pm$18 &26$\pm$17 &30.8 &-27.9 &-69\\ 18&Wind & 0.9844& 33&2012 Jan 24 14:36& 638$\pm$34 &8$\pm$2 &30.5 &-15.7 &-73\\ 19&Wind & 0.9924& 41 &2012 Mar 07 03:28& 501$\pm$65 &14$\pm$5 &18.8 &-18.2 &-74\\ 20&Wind & 0.9927& 42&2012 Mar 08 10:24& 679$\pm$44 &12$\pm$4 &30.4 &-18.4 &-131\\ 21&Wind & 0.9938& 6 &2012 Mar 12 08:28& 489$\pm$23 &24$\pm$9 &29.2 &-23.6 &-50\\ 22&Wind & 1.0055& 20 &2012 Apr 23 02:14& 383$\pm$8 &24$\pm$7 &15.9 &-15.3 &-108\\ 23&Wind & 1.0160& 28 &2012 Jun 16 19:34& 494$\pm$29 &50$\pm$24 &41.0 &-21.0 &-71\\ 24&Wind & 1.0165& 22 &2012 Jul 14 17:38& 617$\pm$39 &16$\pm$6 &27.7 &-18.3 &-127\\ \tableline \end{tabular}\tablecomments{Explanation of parameters: (1) Number of CME event. (2) The spacecraft which detected the ICME, using data from the \emph{PLASTIC} (plasma) and \emph{IMPACT} (magnetic field) instruments on \emph{STEREO-B}, and \emph{SWE} (plasma) and \emph{MFI} (magnetic field) on Wind. (3) Heliocentric distance of the in situ spacecraft at ICME arrival, in AU. (4) Difference between the interplanetary CME direction (heliocentric longitude, from the SSEF model) and the HEEQ longitude of the in situ spacecraft, in degree (Earth at 0\degreee). Small angles indicate central hits, larger angles flank hits. For angles $>0$\degree ($< 0$\degreee), the in situ observer is west (east) of the CME apex derived from SSEF. (5) The date and time (UT) of the in situ detection of the shock, or a significant increase in density ahead of a magnetic structure, if no shock is present. (6) The mean proton bulk speed in the ICME sheath region, and its standard deviation, in \kmsec. (7) The mean proton density in the sheath region, and its standard deviation, in cm$^{-3}$. (8) The maximum magnetic field (nT) in the ICME, including the sheath and ejecta intervals. (9) The minimum value of $B_Z$ (nT) in the ICME, the component of the magnetic field normal to the ecliptic plane (for Wind) or the solar equatorial plane (for \emph{STEREO-B}). (10) The minimum value of the $Dst$ index (nT), provided by Kyoto, during the geomagnetic storm following the arrival of the ICME at Earth. Values $> -50$~nT and events directed towards \emph{STEREO-B} are ignored. } \end{center} \label{tab:insitu} \end{table*} \begin{table*}[t] \begin{center} \caption{Performance of HI geometrical models in connecting remote observations of CMEs to in situ data at 1 AU} \begin{tabular}{lccrrrr} \tableline\tableline method & variable & unit & FPF & SSEF & HMF & average \\ \tableline Speed of model apex &$\Delta V$ & \kmsec & 298 $\pm$ 296 & 443 $\pm$ 445 & 541 $\pm$ 567 & 427 $\pm$ 455\\ Speed in direction of in situ observatory &$\Delta V$ &\kmsec & 298 $\pm$ 296 & 252 $\pm$ 302 & 274 $\pm$ 304 & 275 $\pm$ 297 \\ Speed with empirical correction &$\Delta V$ &\kmsec & 0 $\pm$ 69 & 0 $\pm$ 79 & 0 $\pm$ 74 & 0 $\pm$ 73\\ Speed of model apex &$|\Delta V|$ & \kmsec & 303 $\pm$ 290 & 446 $\pm$ 442 & 544 $\pm$ 564 & 431 $\pm$ 451\\ Speed in direction of in situ observatory &$|\Delta V|$ &\kmsec & 303 $\pm$ 290 & 267 $\pm$ 289& 282 $\pm$ 296 & 284 $\pm$ 288 \\ Speed with empirical correction &$|\Delta V|$ &\kmsec & 50 $\pm$ 47 & 57 $\pm$ 53 & 53 $\pm$ 51 & 53 $\pm$ 50\\ \tableline Arrival time in direction of in situ observatory &$\Delta t$ &hours & -6.7 $\pm$ 7.6 & -1.4 $\pm$ 11.1 & -3.3 $\pm$ 9.5 & -3.8 $\pm$ 9.6 \\ Arrival time with empirical correction (=version 1) &$\Delta t$ & hours & 0.0 $\pm$ 7.0 & 0.0 $\pm$ 9.2 & 0.0 $\pm$ 7.8 & 0.0 $\pm$ 7.9 \\ Arrival time with transit time relationship (=version 2) &$\Delta t$ & hours & -1.9 $\pm$ 6.6 & 1.2 $\pm$ 9.8 & -2.0 $\pm$ 8.3 & -0.9 $\pm$ 8.4\\ Arrival time in direction of in situ observatory & $|\Delta t|$ &hours & 8.5 $\pm$ 5.4 & 8.4 $\pm$ 7.2 & 7.5 $\pm$ 6.6 & 8.1 $\pm$ 6.3 \\ Arrival time with empirical correction (=version 1) &$|\Delta t|$ &hours & 5.6 $\pm$ 4.1 & 6.8 $\pm$ 6.0 & 5.9 $\pm$ 4.9 & 6.1 $\pm$ 5.0\\ Arrival time with transit time relationship (=version 2) &$|\Delta t|$ & hours & 5.7 $\pm$ 3.8 & 7.7 $\pm$ 6.1 & 6.6 $\pm$ 5.3 & 6.6 $\pm$ 5.1\\ \tableline \end{tabular} \tablecomments{Explanation: For each method, the differences $C-O$ (calculated $-$ observed) between the parameters from geometrical modeling and the corresponding in situ parameters is given. The speed and arrival time from geometrical modeling are compared to the average proton bulk speed of the ICME sheath region, and the in situ arrival time of a shock or significant density jump, respectively. The numbers in the table correspond to the variables $\Delta V$ and $\Delta t$ in the text, and errors quoted correspond to $\pm 1$ standard deviation. } \end{center} \label{tab:performance} \end{table*} | 14 | 4 | 1404.3579 |
1404 | 1404.5958_arXiv.txt | In previous work we have presented Schwarzschild models of the Sculptor dSph, demonstrating that this system could be embedded in dark matter halos that are either cusped or cored. Here we show that the non-parametric distribution function recovered through Schwarschild's method is bimodal in energy and angular momentum space for all best fitting mass models explored. We demonstrate that this bimodality is directly related to the two components known to be present in Sculptor through stellar populations analysis, although our method is purely dynamical in nature and does not use this prior information. It therefore constitutes independent confirmation of the existence of two physically distinct dynamical components in Sculptor and suggests a rather complex assembly history for this dwarf galaxy. | Sculptor was the first dwarf spheroidal (dSph) galaxy discovered \citep{Shapley1938}, and it may be considered an archetype of the class of dSph as it is a rather featureless system \citep[compared to e.g. Fornax,][]{deBoer2011AA}. Nonetheless, Scl has proven to be more complex than originally thought. Photometric surveys starting from \cite{DaCosta1984}, \citep[and later by][]{Light1988PhDT, HurleyKeller1999ApJ, Majewski1999ApJ}, have revealed that its horizontal branch morphology changes with radius. More recently, thanks to large spectroscopic surveys, it has been possible to relate the differences in the spatial distribution of the blue and red horizontal branch (BHB/RHB) to differences in chemical composition and kinematics of its stars \citep{Tolstoy2004ApJ}, as well as to age gradients \citep{deBoer2011AA}. The picture that has emerged from this body of work is that Sculptor has two populations or components. The first population is centrally concentrated, metal rich, younger, is represented in RHB stars and has colder kinematics, with a decreasing line-of-sight velocity dispersion with distance from the centre. The second population is less concentrated, metal poor, older, is prominent in BHB stars, has hotter kinematics and a more constant velocity dispersion profile. It was not clear until now whether this could simply be due to a population gradient. dSph have been the target of many kinematic surveys in the past decade because of their very high dynamical mass-to-light ratios. The aim of these studies has been to provide constraints on the nature and distribution of dark matter, however no firm conclusions have yet been drawn. This is because of limitations in the data (only access to line-of-sight velocities) and also in the models. For example, the most-widely used modeling technique is based on the Jeans Equations and requires making assumptions about the orbital structure of the system \citep[see e.g.][]{Walker2009}, although recent work by \citet{Richardson2013,Richardson2014} using higher moments and the virial equations, seems to be able to circumvent this degeneracy. A more powerful approach is to use orbit-based dynamical modeling, also known as Schwarzschild's method. \cite{Breddels2012arXiv} have shown that the data on Scl does not constrain the inner slope of its dark matter density profile very strongly, and that neither cored nor cuspy \cite[of the NFW-type,][]{NFW1996ApJ...462..563N} profiles are favoured. On the other hand, it has been argued that the multiple components present in Sculptor should be used to model this system dynamically and that this ought to lead to much tighter constraints. This is because these components are hosted by the same underlying potential and their presence effectively would reduce the available parameter space of plausible dynamical models \citep{Battaglia2008ApJ}. Several studies have attempted this using e.g. the virial equations \citep{Agnello} or constraints based on Jeans modeling \citep{Walker2011ApJ, Amorisco2011}, and concluded that NFW-like profiles are strongly disfavoured. All these works \citep[with the exception of ][]{Walker2011ApJ} have assumed that the two populations are split in the same way in photometry and kinematics/chemistry, although this is a priori not guaranteed, as the kinematics (and split in metallicity) are obtained from the RGB while the photometry is fit for the BHB and RHB stars independently. Perhaps more importantly, all these models based on a single estimate of the mass at a given radius (e.g. either through Jeans or through the virial equations) have assumed the components to follow the same functional form of the light distribution (with different characteristic parameters). As we shall show below, this is not necessarily a valid asssumption. In this {\it Letter} we analyse the phase-space structure of the best fitting Schwarzschild dynamical models of Sculptor from \citet{Breddels2013arXivb} and \citet{BreddelsThesis}. Our spherical orbit based dynamical models are non-parametric in the distribution function (e.g. no assumptions are made on the anisotropy) and provide good fits to the global kinematics and light distribution of Scl. The dark matter distribution follows specific parametric profiles \citep[c.f.][]{Jardel2012Dra}, which all produce very similar mass distributions in a finite region around the half-light radius of Scl. As we shall show below, the orbit weights (which correspond to the distribution function of the galaxy) show a bimodal distribution for all the best fit models of Sculptor, even though this is not a priori assumed. | \label{sec:conclusions} We have shown that the distribution function of Sculptor for several best fitting mass models is bimodal in energy and angular momemtum space. The two components may be split in a low and high angular momentum parts using the watershed method. The properties of the low and high angular momentum components are similar to the metal rich and metal-poor components respectively, known to be present in this galaxy, in terms of their velocity dispersion profile and their light distribution \citep{Battaglia2008ApJ}. This result is quite remarkable since we have not assumed at any point the existence of multiple components in the Sculptor dwarf. It therefore suggests that the metal-rich and metal-poor stars indeed are dynamically distinct, and that Sculptor is not simply a system with a radial gradient in stellar populations. This finding highlights the full power of the Schwarzschild's dynamical approach, and would not have been possible if we had taken a parametric approach to model the distribution function. The fact that our models naturally recover the bimodality present in Sculptor, for all dark matter profiles explored, and even for the NFW form, would seem to be at odds with the results of \citet{Agnello} and \citet{Walker2011ApJ}. In these works, Sculptor was modeled as a two-component system with light distributions that followed similar profiles. The use of the virial equations or the robust estimator of the mass at the half-light radii of each component was used to argue that NFW profiles could be ruled out with high significance. Our modeling however, shows this is not the case and why. The assumption of similar light profiles appears to be crucial to reach those conclusions, and would seem to introduce a systematic bias that none of these works have taken into account. In the resulting non-parametric dynamical models we have obtained, the light distribution for the two components is quite different and cannot be parametrized well by Plummer profiles as Fig.~~\ref{fig:light} shows. Walker (2014, private communication) repeated the analysis of \citet{Walker2011ApJ}, but now allowing the metal rich profile to follow an exponential form. While still excluding a cusp with $p>98.4\%$ instead of $p>99.8\%$, it demonstrates the bias caused by the assumed parametric form of the light profiles. It is natural to wonder whether other dwarfs also exhibit multiple dynamical components. Fornax would be a natural candidate but its complex light distribution \citep[e.g. the presence of shells, non-axisymmetries in the centre,][]{Battaglia2006AA} and the hints of misaligned kinematics \citep[see e.g.][]{2012ApJ...756L...2A} require the use of a more general (non-spherical) Schwarzschild modeling approach. On the other hand, it would be desirable to have larger datasets for e.g. Carina and Sextans to be confident in the robustness of the analyses. More generally, an interesting challenge will be to understand how such complex systems can form on the smallest galaxy scale, i.e. on the scale of the dwarf spheroidals. | 14 | 4 | 1404.5958 |
1404 | 1404.2055_arXiv.txt | Using Fermi statistics, a formalism was developed by L.H. Thomas and E. Fermi to obtain the charge distribution and also the distribution of electric field in the extra-nuclear space inside heavy atoms \cite{TF1,TF2}. This proposed formalism is the so called Thomas-Fermi model. The electrons inside the atoms are assumed to be a degenerate Fermi gas. In this model the electron density is found to be nonuniform inside the atom, i.e., $n_e=n_e(\vec r)$, where $\vec r$ is the radial distance vector of the point from the nucleus situated at the center of the atom. The electric potential $\phi (\vec r)$ and the corresponding electric field $\vec E(\vec r)$ within the atom also vary with the radial distance. The electron density has been observed to be a smoothly varying function of radial coordinate $r$ (the atoms are assumed to be of spherical in shape), instead of having peaks according to shell model. The model was successful in predicting the binding energies of the atoms \cite{LIEB}. With some suitable modification the model has been successfully applied to molecules, solids and also to nuclei \cite{MARCH} to explain some of the experimental values. The electronic shell effect was also incorporated in the model. The model could also satisfactorily explain the thermodynamic properties of dense degenerate electron gas. For very high density matter, the electron gas surrounding the nucleus is assumed to be enclosed in a region, called WS cell \cite{LY}. Therefore in such situation, instead of atoms, there are regularly spaced WS cells, which are assumed to be charge neutral and spherically symmetric. There are also relativistic generalization of TF model for very high energy electron gas and the model was found to be successfully to investigate the thermodynamic properties of such igh density degenerate electron gas\cite{REMO}. Generalized versions of non-relativistic as well as relativistic form of Thomas-Fermi equations in presence of strong quantizing magnetic field, when the Landau levels for the electrons are populated have also been obtained \cite{NAG,NAG1,NAG2}. The thermodynamic properties of matter inside the magnetically deformed WS cells have also been investigated. In presence of strong quantizing magnetic field, the electron pressure becomes anisotropic inside the WS cells. As a result they will be deformed to ellipsoidal shape from their usual spherical structure \cite{GHOSH}. However, all these investigations are associated with the three dimensional degenerate electron gas, enclosed inside the WS cells. There are only a few reported results on the study of two dimensional electron gas using Thomas-Fermi model \cite{R1,R2,R3}. Further, to the best of our knowledge, no studies have been reported on the two dimensional Thomas-Fermi model for electron gas in presence of strong quantizing orthogonal magnetic field, in which the Landau levels are populated for the electrons. Again, in the three dimensional case, incorporating electron-electron exchange interaction, a modified form of Thomas-Fermi equation, called Thomas-Fermi-Dirac equation has been developed both for non-relativistic as well as relativistic electron gas with or without the presence of magnetic field \cite{LY,ST,NAG,REMO,NAG1}. Unfortunately, no such formalism has been developed in the case of two dimension. To the best of our knowledge, the first reported result on two dimensional Thomas-Fermi model for degenerate electron gas is by Bhaduri et. el. \cite{R1} (see also \cite{R2,R3}). Two dimensional electron gas has a lot of important applications in modern days condensed matter physics. The electrons in 2D are constrained to move in two dimensional sheet embedded in a three dimensional space. Such two dimensional electron gas may be realized in many semi-conductor devices \cite{R4}. There are also possibility of having two dimensional electron gas on the surface of materials, e.g., liquid He \cite{R5}. In such system electrons are free to move on the surface of liquid He but rigidly attached with the He atoms. There are also a kind of solid insulators, e.g., topological insulators \cite{R6}, the surface of which supports conducting states of free electrons. During the present days the most interesting two dimensional system in condensed matter physics is the so called called graphene. It is an almost ideal two dimensional material developed in the laboratory using graphite \cite{R7,R8,R9}. It has also been observed that the graphene can also support 2-D electron gas. This has become a topic of current interest due to a large number of application of graphene. There are also a lot of academic interest to study graphene theoretically. In particular application of quantum electrodynamics and the study of the physics of mass-less electrons or chiral electrons using two component Dirac equation. In the present article we have investigated the properties of electron gas enclosed in two-dimensional WS cells, which are embedded in a three-dimensional space. The WS cell is assumed to be in $x-y$ plane and the strong magnetic field is along $z$-axis. The electrons are constrained to move on $x-y$ plane. The presence of strong magnetic field along $z$-direction makes electron energy eigen value discrete. The motion of the electrons on $x-y$ plane are in quantized form. This is the well known Landau quantization in 2D. The electron energy therefore does not depend on $p_z$, the component of momentum along $z$-direction. however, the momentum component on $x-y$ plane changes in a discrete manner. We have organized various sections of this article in the following manner: In the next section we have developed the basic formalism for two dimensional Thomas-Fermi model for degenerate electron gas in presence of strong quantizing orthogonal magnetic field. In section 3 we have studied the thermodynamic properties of 2D degenerate electron gas inside a WS cell in presence of a strong quantizing magnetic field. In section 4 we have considered the electron-electron exchange interaction in absence of magnetic field and incorporate this result in Thomas-Fermi condition to obtain Thomas-Fermi-Dirac equation satisfied by degenerate electron gas in 2D. In section 5 we have shown explicitly that the same technique can not be followed to obtained Thomas-Fermi-Dirac equation for degenerate electron gas in presence of strong quatizing magnetic field. However, for the conventional three dimensional case, one can obtain exchange energy for electrons \cite{NAG1}. Finally we present the conclusion of this work. | It is quite surprising that the form of Thomas-Fermi differential equation in presence of strong quantizing magnetic field is exactly identical with that of zero field case. The exchange part of electron energy does not exist in 2D in presence of strong quantizing magnetic field. The Fermi momentum obtained in this case is along $z$-direction, which is suppressed in ideal 2D case. The Thomas-Fermi-Dirac equation therefore can not be obtained for a 2D electron gas in presence of a strong quantizing magnetic field. However, in absence of magnetic field, exchange energy can be obtained assuming a quasi 2D structure. Hence one can formulate Thomas-Fermi-Dirac model in 2D scenario for an electron gas. We have noticed that the radius of a two dimensional charge neutral WS cell is infinitely large. On the other hand it is finite if $N/Z <1$, i.e., the cell is ionized or positively charged. In usual three dimensional case also the radius of an atom can not be finite in Thomas-Fermi model. However, in Thomas-Fermi-Dirac model the radius of a two dimensional charge neutral WS cell is found to be finite. We have also noticed that the size of circular shape WS cell does not depend on the strength of magnetic field, even if it is of astrophysical order. Because of two dimensional structure, there is no distortion of circular type WS cells to elliptical form. On the other hand, in the usual three dimensional case, because of pressure anisotropy within the WS cells, a distortion to ellipsoidal shape may occur in presence of strong quantizing magnetic field. In the usual three dimension, The anisotropy increases with the increase of the strength of magnetic field. Then in the extrim case, it can be shown that an atom becomes needle shape with its length alon the direction of magnetic field. | 14 | 4 | 1404.2055 |
|
1404 | 1404.7393_arXiv.txt | We present detections of the CO($J=$ 1--0) emission line in a sample of four massive star-forming galaxies at $z\sim1.5-2.2$ obtained with the Karl G. Jansky Very Large Array (VLA). Combining these observations with previous CO(2--1) and CO(3--2) detections of these galaxies, we study the excitation properties of the molecular gas in our sample sources. We find an average line brightness temperature ratios of $R_{21}=0.70\pm0.16$ and $R_{31}=0.50\pm0.29$, based on measurements for three and two galaxies, respectively. These results provide additional support to previous indications of sub-thermal gas excitation for the CO(3--2) line with a typically assumed line ratio $R_{31}\sim0.5$. For one of our targets, BzK-21000, we present spatially resolved CO line maps. At the resolution of $0.18''$ (1.5 kpc), most of the emission is resolved out except for some clumpy structure. From this, we attempt to identify molecular gas clumps in the data cube, finding 4 possible candidates. We estimate that $<40\%$ of the molecular gas is confined to giant clumps ($\sim1.5$ kpc in size), and thus most of the gas could be distributed in small fainter clouds or in fairly diffuse extended regions of lower brightness temperatures than our sensitivity limit. | The physical processes behind gas supply, and subsequent star formation, in early galaxies, remain key uncertainties in our understanding of galaxy formation. Study of the demographics and gas depletion timescales show that most star forming galaxies at $z>1$ form a tight correlation between their star formation rates (SFR) and stellar masses. Such correlation, usually termed as the `main-sequence' of galaxies, suggests that the star formation is typically a long-lived process, likely occurring over timescales of $\sim0.7$ Gyr \citep[e.g., ][]{Daddi2005,Daddi2007}. Major gas rich mergers, typically lying above such main-sequence, are unlikely to be the primary driving mechanism for such continuous star formation, since they would lead to short timescale, nuclear starbursts as it is seen in local Ultra Luminous IR Galaxies \citep[ULIRGs; e.g., ][]{Solomon1997, Downes1998}. Two of the major challenges for understanding the mechanisms of gas accretion and stellar build up in these galaxies is to spatially and kinematically resolve the star formation and molecular gas components down to kpc scales \citep{Shapiro2008}, as well as targeting several molecular gas emission lines in order to characterize the physical state of the interstellar medium \citep[ISM;][]{Carilli2013}. High-resolution observations of the ionized gas (H$\alpha$) kinematics and the stellar component have shown that a majority of these galaxies are consistent with clumpy rotating disks with sizes of order 10 kpc \citep{Genzel2006, Genzel2008, ForsterSchreiber2009, ForsterSchreiber2011}. % However, these observations do not directly trace the cold molecular gas from which stars are formed, and could be prone to obscuration within the host galaxy. Direct high resolution observations of the molecular gas are thus necessary. \begin{table*} \centering \caption{Observational parameters\label{tab:0}} \begin{tabular}{lcccccccc} \hline Source & $\alpha_{\rm CO(1-0)}$ $^{\rm a}$& $\delta_{\rm CO(1-0)}$ $^{\rm a}$& Array $^{\rm b}$& $\nu_{\rm obs}$ $^{\rm c}$& Beam $^{\rm d}$& P.A. $^{\rm d}$& rms $^{\rm e}$& Chan $^{\rm f}$\\ & (J2000) & (J2000) & & (GHz) & & (deg) & ($\mu$Jy) & (km s$^{-1}$)\\ \hline\hline BzK-21000 & $12^{\rm h}37^{\rm m}10.69^{\rm s}$ & $+62^\circ22'34.3''$ & B/D & 45.656 & $0.18''\times0.17''$ & $-178$ & 91 & 50 \\ BzK-4171& $12^{\rm h}36^{\rm m}26.61^{\rm s}$ & $+62^\circ08'35.6''$ & D & 46.765 & $2.50''\times2.25''$ & $+47$ & 220 & 80 \\ BzK-16000 & $12^{\rm h}36^{\rm m}30.09^{\rm s}$ & $+62^\circ14'27.7''$ & C/D & 45.708 & $1.46''\times1.31''$ & $-46$ & 130 & 80 \\ BX610 & $23^{\rm h}46^{\rm m}09.45^{\rm s}$ & $+12^\circ49'19.3''$ & D & 35.905 & $1.65''\times1.46''$ & $+28$ & 180 & 80 \\ \hline \end{tabular} \begin{flushleft} \begin{footnotesize} \noindent {\bf Notes:} $^{\rm a}$ Right ascension and declination of the measured CO(1--0) positions; $^{\rm b}$ VLA array configuration used in the observations; $^{\rm c}$ Observed frequency; $^{\rm d} $Synthesized beam size (major and minor axis) and position angle (P.A.); $^{\rm e}$ Average noise level reached in the data cube at a velocity resolution per channel given in $^{\rm f}$. \end{footnotesize} \end{flushleft} \end{table*} Recently, observations of the molecular gas, through CO line emission, in optical/IR color-selected star-forming galaxies at $z=1-3$ have revealed significant molecular gas reservoirs, comparable to their stellar component ($\sim10^{10}$ M$_\odot$) in systems which typically show SFRs in the range $50-400$ M$_\odot$ yr$^{-1}$ \citep{Daddi2008, Daddi2010a, Tacconi2010, Tacconi2013}. This indicated that these galaxies have low star formation efficiencies and long gas depletion timescales, compared to that seen in extreme starbursting submillimeter galaxies (SMGs) and quasars, and suggest their integrated properties may follow a different star-formation law \citep{Daddi2010b, Genzel2010}. Furthermore, their implied CO luminosity to gas mass conversion factors resemble local disk galaxies \citep{Daddi2010a, Magdis2011, Magdis2012,Magnelli2012}. These studies, however, focused on the observation of $J>1$ CO line emission. One of the major assumptions encountered when observing $J>1$ CO lines in main-sequence galaxies has been the the adoption of an ``average'' constant ratio between the $J>1$ CO line and CO(1--0). Determination of these ratios are required in order to convert the high-J CO line luminosities into CO(1--0) luminosities, for which the conversion factors of CO luminosity to gas mass have been calibrated \citep{Bolatto2013}. Thus, observations of the CO(1--0) line in statistical samples of star-forming galaxies at $z>1$ are necessary for calibrating such line ratios. As Bauermeister et al. point out, calibration of the line ratios is particularly important for the CO(3--2) line for two main reasons: (1) this line ($\nu_{\rm rest}=345.538$ GHz) is shifted to the 2mm and 3mm atmospheric windows at $z=1-3$, being directly accessible with the most powerful (sub)millimeter facilities that can easily access these kind of galaxies, namely the Atacama Large Millimeter/submillimeter Array (ALMA) and the Plateau de Bureau Interferometer (PdBI). Hence, observations of the CO(3--2) line will (and have) become routine and constitute the first direct attempt to characterize the molecular gas properties of these objects \citep[e.g., ][]{Tacconi2010,Tacconi2013}; (2) The cosmic time spanned by redshifts $z=1-3$, 6 Gyr, corresponds to the important period when most of the stars in the Universe where created and where most of the galaxies were assembled. To date, only a few main-sequence galaxies at cosmological distances ($z>0.1$) have observations in two or more CO lines \citep{Dannerbauer2009, Aravena2010b, Bauermeister2013}, and generally only a handful of these main-sequence galaxies have spatially resolved CO observations down to $<10$ kpc scales \citep{Tacconi2013, Genzel2013}. Follow-up CO(1--0) observations of three representative $z\sim1.5$ galaxies in the CO(1--0) line emission suggest that the molecular gas in these systems is already sub-thermally excited at the CO(3--2) transition similar to what is found in local disks \citep{Dannerbauer2009, Aravena2010b}, with typical line brightness temperature ratios between both lines of $\sim0.5$. This is also similar to what is found in SMGs \citep{Harris2010, Ivison2011, Bothwell2013}, but substantially different to high-redshift QSOs, which appear to have highly excited gas with line temperature ratios close to unity \citep[e.g.,]{Riechers2006,Weiss2007,Ao2008,Riechers2011c, Ivison2012}. Recent observations of $z\sim0.3$ disk galaxies support these findings, indicating that the molecular gas content, as traced by CO(1--0), is two times larger than expected from $J>3$ CO measurements, comparable to $z>2$ SMGs \citep{Papadopoulos2002, Harris2010, Ivison2011, Riechers2011b}. In this paper, we present observations of the CO(1-0) emission line in four main-sequence star forming galaxies at $z\sim1.5-2.2$ obtained with the Karl G. Jansky Very Large Array (VLA). The angular resolution of our observations for one of these sources, $0.18''$, allows us to spatially resolve the distribution of the molecular gas. The new correlator system at the VLA permits us to expand the bandwidth and velocity resolution of the previous CO(1--0) detections in three of our targets, and to detect the CO emission in a new object at $z=2.2$. We adopt a standard $\Lambda$CDM cosmology throughout \citep{Komatsu2011}. \begin{figure*} \includegraphics[scale=0.35]{bzk21000_imclean_ave440_robust0.8_ORI_6x6.ps}% \includegraphics[scale=0.35]{bzk21000_imclean_ave440_robust0.8_6x6_0.30as.ps}% \includegraphics[scale=0.35]{bzk21000_imclean_ave440_robust0.8_6x6_0.8as.ps}% \caption{VLA CO(1--0) maps averaged over 440 km s$^{-1}$ for BzK-21000, shown at the native resolution of $\sim0.18''$ (left), tapered to $0.4''$ (middle), and tapered to $1.1''$ (right). Contour levels are given in steps of $\pm1\sigma$, starting at $\pm2\sigma$, with $\sigma\approx25, 32$ and 42 $\mu$Jy beam$^{-1}$. The red cross indicates the VLA 1.4 GHz position (Morrison et al. 2010). All windows have identical axis. \label{fig:1}} \end{figure*} | We have presented detections of the CO(1--0) line emission in four massive star-forming galaxies in the redshift range $z=1.5-2.2$. Our observations allow us to confirm previous measurements of the brightness temperature line ratio between the CO(2--1) to CO(1--0) lines in three BzK galaxies. We measure average line ratios of $R_{21}=0.70\pm0.16$ (based on the 3 BzK galaxies) and $R_{31}=0.50\pm0.29$ (based on two objects). These findings indicate that the molecular gas is, on-average, likely sub-thermally excited already in the CO(2--1). We find that the gas is sub-thermal in both cases at the CO(3--2) line, and support the widely assumed line ratio $R_{31}\sim0.5$ \citep{Tacconi2010, Tacconi2013, Genzel2013}. Since $R_{31}$ ranges from $\sim$ 0.4 to 0.6, we note that care must be exercised in assuming the average line ratio for individual cases. Finally, we took advantage of the high angular resolution achieved for BzK-21000, and searched for gas clumps in the CO data cube. We found 4 clump candidates with estimated gas masses that can account for up to 40\% of the total molecular gas mass of this system. | 14 | 4 | 1404.7393 |
1404 | 1404.7500_arXiv.txt | In contrast to radial velocity surveys, results from microlensing surveys indicate that giant planets with masses greater than the critical mass for core accretion ($\sim 0.1~M_{\rm Jup}$) are relatively common around low-mass stars. Using the methodology developed in the first paper, we predict the sensitivity of M-dwarf radial velocity (RV) surveys to analogs of the population of planets inferred by microlensing. We find that RV surveys should detect a handful of super-Jovian ($>M_{\rm Jup}$) planets at the longest periods being probed. These planets are indeed found by RV surveys, implying that the demographic constraints inferred from these two methods are consistent. We show that if total RV measurement uncertainties can be reduced by a factor of a few, it is possible to detect the large reservoir of giant planets ($0.1-1~M_{\rm Jup}$) comprising the bulk of the population inferred by microlensing. We predict that these planets will likely be found around stars that are less metal-rich than the stars which host super-Jovian planets. Finally, we combine the results from both methods to estimate planet frequencies spanning wide regions of parameter space. We find that the frequency of Jupiters and super-Jupiters ($1\lesssim m_p\sin{i}/M_{\rm Jup}\lesssim 13$) with periods $1\leq P/{\rm days}\leq 10^4$ is $f_{\rm J}=0.029^{+0.013}_{-0.015}$, a median factor of 4.3 ($1.5-14$ at 95\% confidence) smaller than the inferred frequency of such planets around FGK stars of $0.11\pm 0.02$. However, we find the frequency of all giant planets with $30\lesssim m_p\sin{i}/M_{\oplus}\lesssim 10^4$ and $1\leq P/{\rm days}\leq 10^4$ to be $f_{\rm G}=0.15^{+0.06}_{-0.07}$, only a median factor of 2.2 ($0.73-5.9$ at 95\% confidence) smaller than the inferred frequency of such planets orbiting FGK stars of $0.31\pm 0.07$. For a more conservative definition of giant planets ($50\lesssim m_p\sin{i}/M_{\oplus}\lesssim 10^4$), we find $f_{\rm G'}=0.11\pm 0.05$, a median factor of 2.2 ($0.73-6.7$ at 95\% confidence) smaller than that inferred for FGK stars of $0.25\pm 0.05$. Finally, we find the frequency of all planets with $1\leq m_p\sin{i}/M_{\oplus}\leq 10^4$ and $1\leq P/{\rm days}\leq10^4$ to be $f_p=1.9\pm 0.5$. | The ever-increasing number of exoplanet discoveries has enabled the characterization of the underlying population of planets in our galaxy. Planet frequencies have been determined by multiple detection methods: RV \citep[e.g.][]{2005ApJ...622.1102F,2008PASP..120..531C,2008A&A...487..373S,2009A&A...493..639M,2010PASP..122..905J,2010Sci...330..653H,2011arXiv1109.2497M,2013A&A...549A.109B}, transits \citep{2006ApJ...644L..37G,2011ApJ...736...19B,2011ApJ...742...38Y,2011ApJ...738..151C,2012ApJS..201...15H,2012ApJ...745...20T,2013ApJ...764..105S,2013ApJ...767...95D,2013ApJ...766...81F}, microlensing \citep{2002ApJ...566..463G,2010ApJ...720.1073G,2010ApJ...710.1641S,2011Natur.473..349S,2012Natur.481..167C}, and direct imaging \citep{2010ApJ...717..878N,2011ApJ...733..126C,2012A&A...541A.133Q}. These studies have provided interesting results, but, individually, are constrained to limited regions of parameter space (i.e. some given intervals of planet mass and period). Synthesizing detection results from multiple methods to derive planet occurrences that cover larger regions of parameter space would provide much more powerful constraints on demographics of exoplanets than is provided by individual techniques. Such synthesized data sets will better inform formation and migration models of exoplanets. Perhaps surprisingly, M dwarf hosts are the best characterized sample in terms of exoplanet demographics. RV surveys are most sensitive to planets on orbits smaller than a few AU (ultimately depending on the duration and cadence of a given survey). At large separations, from $\sim 10$ to $100~$AU, direct imaging is currently the only technique with the capability to provide information, and then, only for young stars. The only method capable of deriving constraints on the demographics of exoplanets in the intermediate regime of separations from a few to $\sim 10~$AU is microlensing. However, for a range of lens distances, $dD_l$, the contribution to the rate of microlensing events scales as $\propto n\left(D_l\right)M_l^{1/2}$, where $n\left(D_l\right)$ is the number density of lenses and $M_l$ is the lens mass. Thus, the integrated microlensing event rate is explicitly dependent on the mass function of lenses. The slope of the mass function for $M_l\lesssim M_{\odot}$ is such that there are roughly equal numbers of lens stars per logarithmic interval in mass. Thus, lower mass objects are more numerous and more often act as lenses in a microlensing event. Indeed, \citet{2010ApJ...720.1073G} (hereafter GA10) report the typical mass in their sample of microlensing events to be $\sim 0.5~M_{\odot}$. This means that constraints on exoplanet demographics at ``intermediate'' separations (few to $\sim 10~$ AU) exist primarily for M dwarfs, as that is the population best probed by microlensing. The low giant planet frequencies around M dwarfs inferred from RV surveys have been been heralded as a victory for the core accretion theory of planet formation, which makes the generic prediction that giant planets should be rare around such stars \citep{2004ApJ...612L..73L,2005ApJ...626.1045I,2008ApJ...673..502K}. However, microlensing has found an occurrence rate of giant planets, albeit planets that are somewhat less massive than those found by RV (but nevertheless still giant planets), that is more than an order of magnitude larger than that inferred from RV. On the other hand, microlensing is sensitive to larger separations than RV, typically detecting planets beyond the ice line. If the microlensing results are correct, they imply that giant planets do form relatively frequently around low mass stars, but do not migrate, perhaps posing a challenge to core accretion theory. Table~\ref{tab:freq_constraints} lists the constraints on giant planet occurrence rates around M dwarfs from the microlensing survey of GA10 and the RV surveys of \citet{2010PASP..122..905J} (hereafter JJ10) and \citet{2013A&A...549A.109B} (hereafter BX13), including the planetary mass and orbital period intervals over which the frequency measurements are valid. \begin{table*} \centering \caption{\label{tab:freq_constraints} Planet frequency around M dwarfs from microlensing and RV surveys. The mass and period intervals for the microlensing measurement were estimated using the typical lens mass of $M_l\sim 0.5~M_{\odot}$ and the typical mass ratio $q\sim 5\times10^{-4}$. The mass limit for the CPS sample assumes a $0.5~M_{\odot}$ host at an orbital separation of 1~AU. See \S~\ref{sec:sample_properties} for details.} \begin{tabular}{@{\extracolsep{0pt}}lcccc@{\extracolsep{0pt}}} \hline \hline \rule{0pt}{2.6ex}\rule[-1.8ex]{0pt}{0pt} & $\frac{d^2N}{d\log{\left(m_p\sin{i}\right)}d\log{\left(a\right)}}$ $\left[{\rm dex^{-2}}\right]$& Period Interval [days] & Mass Interval $\left[M_{\oplus}\right]$ & Reference \\ \hline \hline Microlensing & $0.36\pm 0.15$ & $560\lesssim P \lesssim 5600$ & $10\lesssim m_p\sin{i} \lesssim 3000$ & GA10 \\ \hline HARPS (RV) & $0.0080^{+0.0077}_{-0.0043}$ & $P \lesssim 2000$ & $m_p\sin{i}\gtrsim100$ & BX13 \\ \hline CPS (RV) & $0.0085\pm 0.0041$ & $P \lesssim 2000$ & $m_p\sin{i}\gtrsim150$ & JJ10 \\ \hline \end{tabular} \end{table*} There are several potential reasons for this large difference in inferred giant planet frequency. The properties and demographics of the observed sample of host stars observed with microlensing could well be different from the targeted (local) M dwarfs monitored with RV. RV studies have shown a clear trend of planet occurrence with metallicity \citep{2005ApJ...622.1102F,2010PASP..122..905J,2013A&A...551A..36N,2014ApJ...781...28M} and the slope of the Galactic metallicity gradient \citep[see e.g.][and references therein]{2012ApJ...746..149C,2013arXiv1311.4569H} suggests that the metallicity distribution of local M dwarfs is systematically lower than that of the GA10 microlensing sample. Furthermore, some of the lenses in the GA10 microlensing sample could be K or G dwarfs, or even stellar remnants, although the fraction of events with such lenses to all events is expected to be relatively low \citep[e.g.][]{2000ApJ...535..928G}. It could also be that the population of planets orbiting local M dwarfs differs from the population orbiting M dwarfs in other parts of the galaxy, and in particular, planets orbiting stars in the Galactic bulge. However, perhaps the simplest potential explanation for the large discrepancy in the observed giant planet frequency around M dwarfs is the different ranges of orbital period and planet mass probed by the two discovery methods. Indeed, \citet{clanton_gaudi14a} suggest that the slope of the planetary mass function is sufficiently steep that even a small difference in the minimum detectable planet mass can lead to a large change in the inferred frequency of planetary companions. Thus, motivated by the order-of-magnitude difference in the frequency of giant planets orbiting M dwarfs inferred by microlensing and RV surveys, we have developed in a companion paper \citep{clanton_gaudi14a} the methodology necessary to statistically compare the constraints on exoplanet demographics inferred independently from these two very different discovery methods. We also justify the need for a careful statistical comparison between these two datasets by showing an order of magnitude estimate of the velocity semi-amplitude, $K$, and the period, $P$, of the ``typical'' microlensing planet, which we define as one residing in the peak region of sensitivity for the GA10 microlensing sample. This typical planet has a host star mass of $M_l\sim 0.5~M_{\odot}$, a planet-to-star mass ratio of $q\sim 5\times10^{-4}$, and a projected separation of $r_{\perp}\sim 2.5~$AU, corresponding to a planet mass of $m_p \sim 0.26~M_{\rm Jup} \sim{\rm M_{\rm Sat}}$. We find that for $\sin{i}\approx 0.866$ (the median value for randomly distributed orbits) and a circular orbit, the typical microlensing planet will have a period of about 7~years and produce a radial velocity semi-amplitude of $5~{\rm m~s^{-1}}$. We further demonstrate that for a fiducial RV survey with $N=30$ epochs, measurement uncertainties of $\sigma = 4~{\rm m~s^{-1}}$, and a time baseline of $T=10~$years, the typical microlensing planet would then be marginally detectable with a signal-to-noise ratio (SNR) of 5. This suggests that there is at least some degree of overlap in the planet parameter space probed by RV and microlensing surveys. In \citet{clanton_gaudi14a}, we then predict the joint probability distribution of RV observables for the whole planet population inferred from microlensing surveys. We find that the population has a median period of $P_{\rm med} \approx 9.4~$yr with a 68\% interval of $3.35\leq P/{\rm yr}\leq 23.7$ and a median RV semi-amplitude of $K_{\rm med}\approx 0.24~{\rm m~s^{-1}}$ with a 68\% interval of $0.0944\leq K/{\rm m~s^{-1}}\leq 1.33$. The California Planet Survey (CPS) includes a sample of 111 M dwarfs \citep{2014ApJ...781...28M} (hereafter MB14) which have been monitored for a median time baseline of over 10~years. The RV survey of HARPS includes 102 M dwarfs (BX13) that have been monitored for longer than 4~years. Thus, at least in terms of orbital period, these surveys should be sensitive to a significant fraction of the planet population inferred from microlensing. However, the fact that a majority of these planets produce radial velocities $K\lesssim 1~{\rm m~s^{-1}}$ means that many will remain undetectable by current generation RV surveys; this is primarily due to the steeply declining planetary mass function inferred by microlensing, $dN/d\log{q}\propto q^{-0.68\pm 0.20}$ \citep{2010ApJ...710.1641S}. The results of \citet{clanton_gaudi14a} thus, qualitatively, indicate that the constraints on giant planet occurrence around M dwarfs inferred independently from microlensing and RV surveys are consistent. However, because the planetary mass function inferred by microlensing is so steep, the level of consistency is, quantitatively, very sensitive to the actual detection limits of a given RV survey. The primary aim of this paper is then to make an actual quantitative comparison of the planet detection results from microlensing and RVs. We start with a simulated population of microlensing-detected planets, the properties and occurrence rates of which are consistent with the actual population inferred from microlensing surveys for exoplanets \citep[GA10;][]{2010ApJ...710.1641S}, and map these into a population of analogous planets orbiting host stars monitored with RV. We next use the detection limits reported by BX13 for the HARPS M dwarf sample to predict the number of planets they should detect and compare this with the number of detections they report. We perform the same comparison with the CPS sample (MB14), but because they have yet to fully characterize the detection limits for each of their stars, this comparison is not as robust. For both comparisons, we also predict the number and magnitude of long-term RV trends that should be found and compare with the reported values. In doing so, we show that microlensing predicts that RV surveys should see a handful of giant planets around M dwarfs at the very longest periods to which they are sensitive. These planets have indeed been found. Because the detection results of these two discovery techniques are consistent, we are able to synthesize their independent constraints on the demographics of planets around M dwarfs to determine planet frequencies across a very wide region of parameter space, covering the mass interval $1<m_p\sin{i}/M_{\oplus}<10^4$ and period interval $1<P/{\rm days}<10^5$. We quote integrated planet frequencies over the period range $1<P/{\rm days}<10^4$ since our statistics are more robust in this interval. Readers who are mainly interested in our results, but not necessarily the details, need only refer to figure~\ref{fig:freq_plot} and read the summary and discussion in \S~\ref{sec:discussion}. The full paper is organized as follows. We begin with a discussion of what exactly we mean by the term ``giant planet'' in \S~\ref{sec:giant_planet_def}. In \S~\ref{sec:sample_properties} we describe the sample properties of the microlensing and RV surveys we compare. We summarize the methodology developed in \citet{clanton_gaudi14a} to map the observable parameters of a planet detected by microlensing to the observable parameters of an analogous planet orbiting a star monitored with RV and describe the application of this methodology to this paper in \S~\ref{sec:methods}. We present our results, comparing our predicted numbers of detections and trends with the reported values of RV surveys in \S~\ref{sec:results}. \S~\ref{sec:uncertainties} details sources of uncertainty in our analysis. We derive combined constraints on the planet frequency around M dwarfs from RV and microlensing surveys in \S~\ref{sec:synthesis} and conclude with a discussion of our results in \S~\ref{sec:discussion}. Finally, we examine the properties of the planets accessible by both techniques in the Appendix. | The general procedure detailed in \citet{clanton_gaudi14a} is comprised of a two steps. The first step is the mapping $\left(q,s\right) \rightarrow \left(m_p,r_{\perp}\right)$ using a Galactic model. Here, $q$ and $s$ are the planet-to-star mass ratio and the planet-star projected separation in units of the Einstein radius ($\theta_E$), respectively, and are the quantities measured in a microlensing planet detection. The mapping between these measurements and the true planet mass, $m_p=qM_l$, and the projected separation in physical units, $r_{\perp}=sD_l\theta_E$, requires a Galactic model because the precise forms of the distributions of physical parameters of microlensing systems are unknown. In particular, we do not know the true distribution of lens masses, $M_l$, or distances, $D_l$, nor do we know with certainty whether the lens lies in the disk or the bulge in a given microlensing event. We account for this by drawing these parameters from basic priors and weighting by the corresponding microlensing event rate, $\Gamma$, assuming a Galactic model. The second step is the mapping $\left(m_p,r_{\perp}\right)\rightarrow \left(K,P\right)$, where $K$ and $P$ are the velocity semi-amplitude and the orbital period, respectively. This is accomplished by adopting priors on, and marginalizing over, the Keplerian orbital parameters (i.e. inclination, eccentricity, mean anomaly, and argument of periastron) of the microlensing-detected systems to get a distribution of semimajor axes, which then immediately gives the $P$ distribution by way of Kepler's third law. Combining the period distribution with $m_p$ and the distribution of inclinations, we are able to derive the distribution of $K$. Figure \ref{fig:marg_dist} shows the resultant joint distribution of $K$ and $P$ for a population of planets analogous to that inferred from microlensing, marginalized over all planet and host star properties inferred from microlensing, as well as all orbital parameters \citep{clanton_gaudi14a}. The median values we found are $P_{\rm med} \approx 9.4~$yr and $K_{\rm med}\approx 0.24~{\rm m~s^{-1}}$. The 68\% intervals in $P$ and $K$ are $3.35\leq P/{\rm yr}\leq 23.7$ and $0.0944\leq K/{\rm m~s^{-1}}\leq 1.33$, respectively, and their 95\% intervals are $1.50\leq P/{\rm yr}\leq 94.4$ and $0.0422\leq K/{\rm m~s^{-1}}\leq 16.8$, respectively. In \citet{clanton_gaudi14a}, we demonstrated how to compute the expected number of planets an RV survey should detect, as well as the number of long-term RV trends (due to planets) that should be seen, by parameterizing RV detection limits in terms of a SNR threshold. \begin{figure*} \epsscale{0.9} \plotone{fig1.eps} \caption{Mapping of microlensing planets into RV observables, from \citet{clanton_gaudi14a}. Shown in greyscale are contours of the probability density of $K$ and $P$, marginalized over the entire microlensing parameter space. The contour levels, going from grey to black, are $1\%$, $10\%$, $25\%$, $50\%$ and $80\%$ of the peak density. The filled yellow circle represents where the typical microlensing planet lies in this parameter space at the median inclination and mean anomaly and on a circular orbit ($K_{\rm typ}\sim 5~{\rm m~s^{-1}}$, $P_{\rm typ}\sim 7~$yr). The blue and red colored line represent the median RV detection limit curves for the surveys of BX13 and JJ10, respectively. Planets that lie above these lines and have periods less than the duration of the RV survey are detectable, while those with longer periods might show up as long-term RV trends. The colored histograms represent the the total numbers of detections plus trends for the HARPS sample (blue curve) and the CPS sample (red curve) as a function of $P$ (top panel) and $K$ (right panel). It is clear from these colored histograms that RV surveys are beginning to sample the full period distribution of the planet population inferred from microlensing, but are only able to catch the tail of the $K$ distribution towards higher values, or equivalently, the high-mass end of this planet population. \label{fig:marg_dist}} \end{figure*} We showed that the phase-averaged SNR, which we designate as $\mathcal{Q}$, assuming uniform and continuous sampling of the RV curve, is \begin{align} \mathcal{Q} = & {} \left(\frac{N}{2}\right)^{1/2}\left(\frac{K}{\sigma}\right) \nonumber \\ & {} \times \left\{1-\frac{1}{\pi^2}\left(\frac{P}{T}\right)^2\sin^2{\left(\frac{\pi T}{P}\right)}\right\}^{1/2}\; , \label{eqn:snr_full} \end{align} where $N$ is the average number of epochs per star, $\sigma$ is the average RV precision and $T$ is the time baseline of the RV survey. In the limit where the period is much less than the time baseline, $P\ll T$, this reduces to \begin{equation} \mathcal{Q} \approx \left(N/2\right)^{1/2}\left(K/\sigma\right)\; , \label{eqn:snr_small_p} \end{equation} which is also a good approximation for periods up to $P\sim T$ when approaching from $T$ from small $P$. We assume an effective sensitivity for our fiducial RV survey by assuming a SNR threshold, $\mathcal{Q}_{\rm min}$, above which planets can be detected. Solving equation (\ref{eqn:snr_full}) for $K$ in terms of $P$, we find a sensitivity of \begin{align} K_{\rm min} = & {} \mathcal{Q}_{\rm min}\sigma\left(\frac{2}{N}\right)^{1/2} \nonumber \\ & {} \times \left\{1-\frac{1}{\pi^2}\left(\frac{P}{T}\right)^2\sin^2{\left(\frac{\pi T}{P}\right)}\right\}^{-1/2} \; , \label{eqn:k_sens_first} \end{align} meaning that the RV survey will be sensitive to planets that produce velocity semi-amplitudes greater than or equal to $K_{\rm min}$ at SNRs of $\mathcal{Q}_{\rm min}$ or greater. We further make the approximation that only planets with periods $P\leq T$ will be detected, whereas planets with periods $P>T$ can possibly be identified as long-term RV trends. In this study, to compute the expected number of detections and long-term trends for the RV survey of BX13, we approximate the detection limit curves they provide for each star in their sample by fitting equation (\ref{eqn:k_sens_first}) to their curves with $\mathcal{Q}_{\rm min}$ as a free parameter. We provide more information on our approximation of the detection limits of both the HARPS and CPS samples in \S~\ref{subsec:method_application} and \S~\ref{subsubsec:bonfils_detailed_comparison}. Figure \ref{fig:marg_dist} shows a couple examples of such a sensitivity curve, given by equation (\ref{eqn:k_sens_first}), over-plotted on top of our joint distribution of $K$ and $P$. The blue curve represents the median detection limit as a function of period for the HARPS sample (BX13), which has the median values $N_{\rm med}=8$, $\sigma_{\rm med}\approx 4.2~{\rm m~s^{-1}}$, $T_{\rm med}\approx 4.1~$yr, $M_{\star, {\rm med}}=0.27~M_{\odot}$, and $\mathcal{Q}_{\rm min, med}\approx 8.9$, and the red curve is that of the CPS sample (MB14), which has the median values $N_{\rm med}=28$, $\sigma_{\rm med}\approx 4.1~{\rm m~s^{-1}}$, $T_{\rm med}\approx 11.1~$yr, $M_{\star, {\rm med}}=0.43~M_{\odot}$, and $\mathcal{Q}_{\rm min, med}\approx 8.3$. We can rewrite equation (\ref{eqn:k_sens_first}) in terms of a minimum $m_p\sin{i}$ by substituting the velocity semi-amplitude equation for $K$ and solving, to yield an equivalent sensitivity in terms of planetary mass \begin{align} \left.m_p\sin{i}\right|_{\rm min} = & {} \; \mathcal{Q}_{\rm min}\sigma M_{\star}^{2/3}\left(\frac{2}{N}\right)^{1/2}\left(\frac{P}{2\pi G}\right)^{1/3} \nonumber \\ & {} \times \left\{1-\frac{1}{\pi^2}\left(\frac{P}{T}\right)^2\sin^2{\left(\frac{\pi T}{P}\right)}\right\}^{-1/2} \label{eqn:mpsini_sens_first} \end{align} which evaluates to \begin{align} \left.m_p\sin{i}\right|_{\rm min} \approx & {}\; 69~M_{\oplus}\left(\frac{P}{\rm 7~yr}\right)^{1/3}\left(\frac{M_{\star}}{0.5~M_{\odot}}\right)^{2/3} \nonumber \\ & {} \times \left(\frac{\mathcal{Q}_{\rm min}}{5}\right)\left(\frac{\sigma}{4~{\rm m~s^{-1}}}\right) \nonumber \\ & {} \times \left(\frac{N}{30}\right)^{-1/2} \end{align} in the approximation $P\ll T$. Also plotted in the top and right panels of figure~\ref{fig:marg_dist} are colored histograms representing the total numbers of detections plus trends for the HARPS sample (blue curve) and the CPS sample (red curve) as a function of $P$ (top panel) and $K$ (right panel). It is clear from these colored histograms that RV surveys are beginning to sample the full period distribution of the planet population inferred from microlensing, but are only able to catch the tail of the $K$ distribution towards higher values, or equivalently, the high-mass end of this planet population. \subsection{Application: Comparing with Real RV Surveys} \label{subsec:method_application} The application of this methodology to compare microlensing detections to those reported by real RV surveys is a little more involved than our description above. In that simple estimate, we assumed each star had the same number of epochs, the same measurement uncertainties at each epoch, and that each star was observed over the same time baseline. The reality is that RV surveys have varying sensitivities for each of their monitored stars which need to be included in a direct comparison. We must also take care to construct a microlensing sample that is consistent with that of real RV surveys, i.e. one with the same distribution of host star masses. In this section, we describe how we do this in order to perform independent statistical comparisons of planet detection results from microlensing with each of the RV surveys of HARPS and CPS. When comparing with the HARPS survey, we begin with an ensemble of microlensing events for a sample of planet-hosting stars in the mass interval $0.07\leq M_l/M_{\odot}\leq 1.0$ for which we have numerically determined the joint distributions of the RV observables $K$ and $P$. In order to force the microlensing sample to be consistent with that of HARPS, we consider only microlensing detections around lenses with $\left|M_l-M_{\star}\right|\leq \sigma_{M_{\star}}$ for each star in the RV sample, where $M_l$ is the lens mass for a given microlensing event, $M_{\star}$ is the mass of the RV monitored star, and $\sigma_{M_{\star}}$ is the uncertainty on the measurement of $M_{\star}$. This yields a set of distributions of $K$ and $P$, each corresponding to a particular microlensing planet detection that has been mapped into these observables. We then sum up all the joint $K$ and $P$ distributions for each set of events with lens star masses within $\pm \sigma_{M_{\star}}$ of $M_{\star}$. The summation and weighting of these distributions is done in exactly same manner as described in \S~\ref{subsec:mapping_summary} (and in more detail in \citet{clanton_gaudi14a}), except that now, rather than marginalizing over the entire mass interval $0.07\leq M_l/M_{\odot}\leq 1.0$, we have instead marginalized over all lens masses within $\pm \sigma_{M_{\star}}$. We are left with a single distribution, $d^2N_{\rm pl}/(dKdP)$, for each star in the RV sample. We note that by matching the host mass distribution of our simulated sample to that of HARPS, we are implicitly assuming that the microlensing planet distribution is independent of host mass, $M_{\star}$. This is unavoidable because the microlensing sample is not large enough to subdivide and determine the planet frequency dependence on host mass. In order to compute the expected number of detections and trends for each star in the HARPS RV sample, we must first model the sensitivity of their survey for each star, in terms of $K$ and $P$. For each star in their sample, BX13 graphically provide detection limit curves, i.e. the minimum $m_p\sin{i}$ to which they are sensitive as a function of $P$. They generate these detection limits by systematically injecting known (fictitious) planetary signals into their data and determining the subset of these signals that are detectable (see \S~6 of BX13 for a more detailed explanation). We approximately reproduce these detection limits by parameterizing in terms of a minimum SNR. We use the values of $\sigma$, $M_{\star}$, $T$, and $N$ for each star provided by BX13, including $\mathcal{Q}_{\rm min}$ as a free parameter, to match (by eye) equation (\ref{eqn:mpsini_sens_first}) to the detection limit curves for each star. We describe the RV measurement uncertainties we adopt in \S~\ref{subsubsec:bonfils_detailed_comparison}. Many of these curves are quite noisy (see figure 18 of BX13), so we match to the approximate mean of the noise in these curves by eye. This parameterization of their detection limits can be interpreted as computing the minimum SNR to which the survey can detect a planet or identify a long-term RV trend. The distribution of $\mathcal{Q}_{\rm min}$ we find for the HARPS sample is shown in figure \ref{fig:sn_fig}. The fact that $\mathcal{Q}_{\rm min}$ varies from star to star is a reflection of the non-uniformity of the HARPS M dwarf sample, i.e. each star has a different number of epochs, and spans a different time baseline, resulting in differing detection limits within the sample. The four stars with $\mathcal{Q}_{\rm min}\geq 50$ shown in figure~\ref{fig:sn_fig} are from stars with just four epochs that span relatively short time baselines. These SNR values are used in conjunction with equation (\ref{eqn:k_sens_first}) to compute the number of detections and trends we expect the HARPS M dwarf survey to find in the same manner as described in \S~{\ref{subsec:mapping_summary}} and illustrated in figure \ref{fig:marg_dist}. These expected numbers of detections and trends are then compared with the actual numbers reported by BX13. The results and comparison is presented in \S~\ref{subsec:bonfils_comparison}. \begin{figure}[t!] \epsscale{1.2} \plotone{fig2.eps} \caption{Distribution of SNR thresholds ($\mathcal{Q}_{\rm min}$) we find for the HARPS and CPS M dwarf samples. The median values for these surveys are 8.9 and 8.3, respectively. These values represent the minimum SNRs to which a given RV survey can detect a planet or identify a long-term RV trend, and are used to approximate the detection sensitivities of these two RV surveys for each star in their samples. \label{fig:sn_fig}} \end{figure} We follow an identical procedure for computing the expected numbers of detections and trends for the CPS survey, except for the way in which we estimate their detection limits. The CPS team has not yet determined the individual detection sensitivities for their sample, so to roughly estimate their detection limits (in terms of $\mathcal{Q}_{\rm min}$) we assume the sensitivities of their stars are similar to those of stars with similar systematics in the HARPS sample. We compute values of $\sigma_i/N^{1/2}$ for all stars in both RV samples, where $\sigma_i$ is the RV measurement precision (not including ``external'' noise sources, e.g. stellar jitter) and $N$ is the number of epochs. Each star in the CPS sample is ``matched'' to the star in the HARPS sample with the nearest value of $\sigma_i/N^{1/2}$. We assume the matched pairs of stars have similar sensitivities, and assign the stars in the CPS sample the same sensitivities (i.e. the same minimum SNR, $\mathcal{Q}_{\rm min}$) as that of the star in the HARPS sample to which they are matched. Since the CPS team reports stellar jitter values of $3-6~{\rm m~s^{-1}}$ for all stars in their sample, we only ``match'' them to stars in the HARPS sample which have consistent ``external'' errors of $\sigma_e\leq6~{\rm m~s^{-1}}$. The resultant distribution of $\mathcal{Q}_{\rm min}$ we obtain for the CPS sample is displayed against that of the BX13 in figure \ref{fig:sn_fig}, and has a median value of 8.3. The expected number of planet detections and long-term RV trends is calculated in the same manner as those for the HARPS survey. Our results and comparison with the CPS sample is presented in \S~\ref{subsec:johnson_comparison}. Ideally, we would like to do this comparison more accurately once the CPS determines their detection limits for their sample. In \citet{clanton_gaudi14a}, we derive the planetary mass-ratio and projected separation function \begin{align} \frac{d^2N_{\rm pl}}{d\log{s}~d\log{q}} = & {} \left(0.23\pm 0.10\right)~{\rm dex^{-2}} \nonumber \\ & {} \times \left(\frac{q}{q_0}\right)^{-0.68\pm 0.20} \; , \label{eqn:planetary_mass_function} \end{align} where $q_0=5\times10^{-4}$. We adopt the slope of the planetary mass-ratio function $dN_{\rm pl}/d\log{q} \propto q^{p}$, where $p=-0.68\pm 0.20$, from \citet{2010ApJ...710.1641S} and normalize it using the integrated frequency measurement of $d^2N_{\rm pl}/(d\log{q}~d\log{s})\equiv \mathcal{G}=(0.36\pm0.15)~{\rm dex}^{-2}$ by GA10. We assume planets are uniformly distributed in $\log{s}$ since the distribution of projected separations from the sample of GA10 is consistent with such a distribution. As we will show in \S~\ref{sec:uncertainties}, the main uncertainties in our results arise from the uncertainties in $p$ and $\mathcal{G}$. Mathematically, the total number of planet detections we expect a RV sample to yield for a given realization $i$ in our simulation (corresponding to given values of $p_i$ and $\mathcal{G}_i$) is \begin{equation} N_{\rm det, i}=\displaystyle \sum_k N_{\rm det, i, k}\; , \end{equation} where $N_{\rm det, i, k}$ is the number of expected planet detections for a given star $k$, \begin{align} N_{\rm det, i, k} = & {} \displaystyle \int dM_l \int dD_l \int d\log{q} \int d\log{s} \nonumber \\ & {} \times \int dK \int dP \left.\frac{d^6N_{\rm pl}}{dKdPdM_ldD_ld\log{q}~d\log{s}}\right|_{i} \nonumber \\ & {} \times \Phi_{{\rm det}, k}\left(\mathcal{Q}\right)\Phi_{{\rm det}, k}\left(P\right)\Phi_k\left(M_l\right)\; , \label{eqn:n_det_analytic} \end{align} where $\Phi_{{\rm det},k}\left(\mathcal{Q}\right)$ and $\Phi_{{\rm det},k}\left(P\right)$ are selection functions on a given star constraining the detections to those planets which have SNRs larger than the threshold value (i.e. $\mathcal{Q}_{\rm min}$) and periods smaller than the time baseline of observations, $T$, for that particular star in the RV sample with which we are comparing. The functional forms of these are $\Phi_{{\rm det},k}\left(\mathcal{Q}\right)=\Theta\left(\mathcal{Q} - \mathcal{Q}_{{\rm min},k}\right)$ and $\Phi_{{\rm det},k}\left(P\right)=\Theta\left(T_k-P\right)$, respectively, where $\Theta$ is the Heaviside step function. In equation (\ref{eqn:n_det_analytic}), $\Phi_k\left(M_l\right)$ is the selection function on lens masses that we employ to force our microlensing sample to have the same stellar mass distribution as the RV survey to which we are comparing, having the functional form $\Phi_k\left(M_l\right)=\Theta\left[M_l - \left(M_{\star, k}-\sigma_{M_{\star, k}}\right)\right]\Theta\left[\left(M_{\star, k}+\sigma_{M_{\star, k}}\right)-M_l\right]$. The integrand of equation (\ref{eqn:n_det_analytic}) (not including the selection functions) represents the distribution of $K$ and $P$ for a single system, i.e. only one $M_l$, $D_l$, $\log{q}$, and $\log{s}$, marginalized over all possible orbital configurations. Integrating this distribution marginalizes over all planet and host star properties inferred from microlensing. Multiplying this distribution by selection functions of RV detectability and on the host star mass, as in equation (\ref{eqn:n_det_analytic}), and integrating yields the number of RV detectable planets for a given host star mass. As we showed in \citet{clanton_gaudi14a}, the distribution function is given formally as \begin{align} & {} \left.\frac{d^6N_{\rm pl}}{dKdPdM_ldD_ld\log{q}d\log{s}}\right|_{i} = \mathcal{F}_i\displaystyle \int_{\left\{\alpha\right\}}d\left\{\alpha\right\} \nonumber \\ & {} \hspace{0.8in} \times \frac{d^n{\rm N_{pl}}}{d\left\{\alpha\right\}}\delta\left(K\left(m_p, i, M_l, a\right)-K'\right)\nonumber \\ & {} \hspace{0.8in} \times \delta\left(P\left(M_l, m_p, a\right)-P'\right)\delta\left(M_l-M_l'\right) \nonumber \\ & {} \hspace{0.8in} \times \delta\left(D_l-D_l'\right)\delta\left(q-q'\right)\delta\left(s-s'\right)\; ,\label{eqn:planet_dist_function} \end{align} where $\left\{\alpha\right\}$ is the set of all $n$ intrinsic, physical parameters on which the frequency of planets fundamentally depends. We assume the form \begin{align} \frac{d^n{\rm N_{pl}}}{d\left\{\alpha\right\}} = & {} \frac{d{\rm N_{pl}}}{di}\frac{d{\rm N_{pl}}}{da}\frac{d{\rm N_{pl}}}{dM_0}\frac{d^2{\rm N_{pl}}}{d\log{q}~d\log{s}} \nonumber \\ & {} \times \frac{d{\rm N_{pl}}}{dM_l}\frac{d{\rm N_{pl}}}{dD_l}\frac{d{\rm N_{pl}}}{d\omega}\frac{d{\rm N_{pl}}}{de}\; , \label{eqn:orb_marg_function} \end{align} and we note that \begin{equation} \frac{dN_{\rm pl}}{dM_l}\frac{dN_{\rm pl}}{dD_l} \propto \displaystyle \int \int \frac{d^4d\Gamma}{dD_ldM_ld^2\boldsymbol{\mu}}\Phi\left(t_E\right)d^2\boldsymbol{\mu}\; , \end{equation} where $d^4d\Gamma/(dD_ldM_ld^2\boldsymbol{\mu})$ is the event rate of a given microlensing event, $\Phi\left(t_E\right)=\Theta\left(t_E/{\rm days} - 10\right)$ is a selection function on the event timescale, $t_E$, and $\boldsymbol{\mu}$ is the lens-source relative proper motion. Finally, the $\mathcal{F}_i$ in equation (\ref{eqn:planet_dist_function}) represents the effective number of planets per star in the area over which our simulated planetary microlensing evetns are sampled, i.e., the integral over that area weighted by the joint distribution function $d^2N_{\rm pl}/(d\log{q}~d\log{s})$, \begin{equation} \mathcal{F}_i = \mathcal{A}_i\displaystyle \int_{\log{0.5}}^{\log{2.5}} \int_{-5}^{-2}\left(\frac{q}{q_0}\right)^{p_i}d\log{q}~d\log{s}\; .\label{eqn:f_a_n} \end{equation} We find a mean value and 68\% confidence interval of $\mathcal{F}=1.5\pm 0.6$. For our final results, we adopt the mean value of the number of detections from all realizations (i.e the expectation value) and the 68\% confidence intervals to represent our errors. Uncertainties in $p$ and $\mathcal{G}$ are numerically propagated through our simulations and are responsible for the uncertainties in our final results. Similarly, the total number of expected long-term RV trends per star for an RV survey is given by equation (\ref{eqn:n_det_analytic}), but with the new selection function $\Phi_{{\rm det}, k}\left(P\right)\rightarrow\Phi_{{\rm tr}, k}\left(P\right)=\Theta\left(P-T_k\right)$, such that only planets with periods larger than the time baseline of observations for a given star are counted as trends. Refer to \citet{clanton_gaudi14a} for a more complete description of the mathematical formalism presented here. \label{sec:discussion} In this paper, we map the observable parameters ($q,s$) of the population of planets inferred from microlensing into the observables ($K,P$) of an analogous population of planets orbiting a stellar sample monitored with RV. We derive joint distributions of these RV observables for simulated samples of microlensing systems with similar stellar mass distributions as the M dwarf RV surveys of HARPS (BX13) and CPS (MB14). We then apply the actual RV detection limits reported by BX13 to predict the number of planet detections and long-term RV trends we expect the HARPS survey to find, and we apply roughly estimated detection limits to make predictions for the CPS sample. Comparing our predictions with the actual numbers reported by these RV surveys, we find consistency. We predict that HARPS should find $N_{\rm det}=1.4\pm 0.8$ planets right at the edge of their survey limit, and indeed, they find one such planet around Gl 849 (BX13). This star also appears in the CPS sample, where this very same planet was originally discovered \citep{2006PASP..118.1685B}. We expect the CPS survey to detect $N_{\rm det}=4.7^{+2.5}_{-2.8}$ planets with periods $P\gtrsim 100~$days and masses $m_p\sin{i}\gtrsim 10^2~M_{\oplus}$. The number of such planets they actually detect is four, around the stars Gl 179, Gl 317, Gl 649, and Gl 849 \citep{2010ApJ...721.1467H,2007ApJ...670..833J,2010PASP..122..149J,2006PASP..118.1685B}. The fact that our predicted numbers of detections and the actual numbers are consistent implies that microlensing and RV surveys are largely disjoint, with only a small amount of overlap for orbital periods between roughly $100-10^3~$days and planetary masses larger than about a Jupiter mass. This limited overlap is such that, due to the steeply declining planetary mass function, RV surveys infer low giant planet frequencies around M dwarfs, detecting only the high-mass end of the giant planet population ($m_p\gtrsim M_{\rm Jup}$) inferred by microlensing. For RV surveys to be sensitive to the majority of this population, measurement precisions of $\sim 1~{\rm m~s^{-1}}$ (including instrumental errors and stellar jitter) over time baselines of $\sim 10~$years are required. The frequency of Jupiters and super-Jupiters around metal-rich stars is already found to be very high from current RV surveys, which implies that the large population of giant planets with $0.1\lesssim m_p\sin{i}/M_{\rm Jup}\lesssim 1$ inferred from microlensing (and not currently detected by RV surveys) would either be detected by future, more sensitive RV surveys around stars with lower metallicities or in multi-planet systems around the metal-rich M dwarfs. However, we are left with a puzzle concerning the scaling of the frequency of Jovian planets ($1\lesssim m_p\sin{i}/M_{\rm Jup}\lesssim 13$) with stellar metallicity inferred from the CPS M dwarf sample \citep{2014ApJ...781...28M}. We estimate the metallicity distribution of our simulated microlensing sample using the bulge MDF of \citet{2013A&A...549A.147B} and the Galactic metallicity gradients from \citet{2013arXiv1311.4569H} and find a median metallicity of ${\rm [M/H]} = 0.17~$dex with a 68\% confidence interval of $-0.23<{\rm [M/H]}/{\rm dec}<0.41$. Using this metallicity distribution, we find that the occurrence rate implied by the scaling inferred by MB14 is over-predicted by a median factor of 13 ($4.4-44$ at 95\% confidence) relative to the actual frequency found by microlensing surveys. This could suggest that the MB14 relation is incorrect or perhaps incomplete. A significantly shallower scaling with metallicity seems to be required for agreement (more in line with that reported by \citealt{2010PASP..122..905J} or perhaps \citealt{2013A&A...551A..36N}), or perhaps the metallicity dependence saturates at some value, with (e.g.) a flat distribution for metallicities above the saturation value. We also investigate another possibility. What if giant planets do not form around bulge stars \citep[e.g.][]{2013MNRAS.431...63T}? We show that if this were true, the occurrence rate for the microlensing sample implied by the MB14 relation moves closer to agreement with the measured value (a median factor of 9.1, or $3.0-30$ at 95\% confidence, discrepant), but probably does not account for the full difference. This solution would also be attractive because it could partially explain the difference in the lens distance distributions between our simulated microlensing sample and the GA10 sample. We also point out that it seems unlikely the relations between planet frequency and metallicity hold for giant planets with masses $0.1\lesssim m_p\sin{i}/M_{\rm Jup}\lesssim 1$ given the fact that RV surveys are not sensitive to the bulk of the giant planet population inferred from microlensing surveys. This suggests that the scaling of giant planet frequency with host metallicity is a function of planetary mass. This hypothesis is supported by the results of \citet{2013A&A...551A..36N}, which suggest that the scaling of planet frequency with host metallicity is significantly different between Jovian and Neptunian hosts. Finally, since we have demonstrated that the giant planet frequencies measured by microlensing and RV surveys are actually consistent, we are able to combine their constraints to determine planet frequencies across a very wide region of parameter space. The combined constraints on the giant planet occurrence rate around M dwarfs as a function of orbital period and planet mass are summarized in table~\ref{tab:synthesized_fs} and plotted in figure~\ref{fig:freq_plot}. We also show that the planet frequencies in the mass range $1\leq m_p\sin{i}/M_{\oplus}\leq 10$ and period range $1\leq P/{\rm days}\leq 10^2$ are consistent with the detection results from the \emph{Kepler} M dwarf sample reported by \citet{2013ApJ...767...95D} and \citet{2013ApJ...764..105S}. We can integrate over various regions of this plane to compute total planet frequencies. We find the frequency of giant planets with $30\lesssim m_p\sin{i}/M_{\oplus}\lesssim 10^4$ and $1\leq P/{\rm days}\leq 10^4$ to be $f_{\rm G}=0.15^{+0.06}_{-0.07}$. For a more conservative definition of giant planets ($50\lesssim m_p\sin{i}/M_{\oplus}\lesssim 10^4$), we find $f_{\rm G'}=0.11\pm 0.05$. The frequency of Jupiters and super-Jupiters ($1\lesssim m_p\sin{i}/M_{\rm Jup}\lesssim 13$) with periods $1\leq P/{\rm days}\leq 10^4$ is $f_{\rm J}=0.029^{+0.013}_{-0.015}$, consistent with the measurement by MB14 of $f_{\rm J}=0.065\pm 0.030$. We find the frequency of all planets with $1\leq m_p\sin{i}/M_{\oplus}\leq 10^4$ and $1\leq P/{\rm days}\leq10^4$ to be $f_p=1.9\pm 0.5$. These planet frequencies are closer to lower limits on the planet frequency, because our combined constraints on the planet frequency include the lower limits in the period range $10^2-10^3~$days, where the sensitivity of microlensing surveys declines. This is a very broad result, covering four orders of magnitude in planetary mass and four orders of magnitude in orbital period. But perhaps more importantly, it demonstrates that it is possible to get a more complete picture of the demographics of exoplanets by including constraints from multiple discovery methods. In a future paper, we plan to compare and synthesize the planet detection results found here with those from direct imaging surveys. | 14 | 4 | 1404.7500 |
1404 | 1404.5952_arXiv.txt | { In supersymmetric theories without $R$-parity, the gravitino can play the role of a decaying Dark Matter candidate without the problem of late NLSP decays affecting Big Bang Nucleosynthesis. In this work, we elaborate on recently discussed limits on $R$-parity violating couplings from decays to antideuterons and discuss the implications for two classes of flavor symmetries: horizontal symmetries, and Minimal Flavor Violation. In most of the parameter space the antideuteron constraints on $R$-parity violating couplings are stronger than low-energy baryon-number-violating processes. Even in the absence of flavor symmetries, we find strong new limits on couplings involving third-generation fields, and discuss the implications for LHC phenomenology. For TeV scale superpartners, we find that the allowed MFV parameter space is a corner with gravitino masses smaller than $\OO(10)$ GeV and small $\tan\beta$. } \begin{document} | In supersymmetric theories, \rpa \cite{Farrar:1978xj,Bento:1987mu} is usually introduced to remove unwanted dimension four operators that would lead to fast proton decay; the renormalizable \rpving superpotential is: \beq W_{RPV}=\mu_i L_i\phi_u+\lambda_{ijk} L_iL_j\bar\ell_k +\lambda'_{ijk}L_iQ_j\bar d_k+\lambda_{ijk}''\bar u_i\bar d_j\bar d_k\,, \eeq where the indices are generation indices, $i,j,k=1,\ldots,3$, and only antisymmetric combinations of $i,j$ (respectively, $j,k$) are allowed in $\lambda$ (respectively, $\lambda''$). The first three operators violate lepton number while the last violates baryon number, and both types of operators are involved in proton decay. It is then possible for the proton to be stable if only one type of operators is allowed, leaving $B$ (or $L$) as an accidental symmetry of the theory \cite{Ibanez:1994ig,Dreiner:2005rd}. This is an aspect of the flavor problems associated with low energy Supersymmetry (SUSY): generic soft terms give large contributions to flavor-changing neutral currents (FCNCs), which can be suppressed by assuming that flavor symmetries govern the structure of the Minimal Supersymmetric Standard Model (MSSM) Lagrangian. Two particularly well motivated types of flavor symmetries are Abelian horizontal symmetries ({\it a la} Froggatt-Nielsen \cite{Froggatt:1978nt,Leurer:1992wg,Nir:1993mx}) and Minimal Flavor Violation (MFV) \cite{Nikolidakis:2007fc,Csaki:2011ge}, according to which the Higgs Yukawa operators are spurions of a $\sut^5$ flavor symmetry under which the full MSSM Lagrangian is invariant. Under the assumption of these flavor symmetries, definite structures of the RPV couplings are predicted: \begin{itemize} \item with a horizontal \uone\ symmetry, the relative structure of the RPV couplings is completely determined by the fermion masses and mixings alone \cite{Monteux:2013mna,Joshipura:2000sn,Florez:2013mxa,Sierra:2009zq}; the baryon number violating (BNV) or lepton number violating (LNV) operators are allowed or forbidden independently. In \cite{Monteux:2013mna}, it was argued that, in order not to disagree with LHC null results, LNV operators should be forbidden altogether when considering sub-TeV SUSY. The BNV couplings $\lambda''_{ijk}$ are written in terms of % an overall scale $\lambda''_{323}% $ and depend on the horizontal charges (we denote the charge of a field by the field symbol itself, $\Phi\equiv q_\Phi$, and the inter-generational difference between two fields as $\Phi_{ij}\equiv q_{\Phi_i}-q_{\Phi_j}$): \beq &\lijk=\l''_{323}\eps^{{u_{i3}}+d_{j2}+d_{k3}}, \qquad \left(\text{where }\eps\equiv V^{CKM}_{12}\simeq \sin\theta_C\right), \\\label{LHOR} &\qquad\left(\begin{array}{ccc} \lambda''_{112} & \lambda''_{212} & \lambda''_{312} \\ \lambda''_{113} & \lambda''_{213} &\lambda''_{313} \\\lambda''_{123} & \lambda''_{223} & \lambda''_{323} \end{array}\right) = \lambda''_{323} \left(\begin{array}{ccc} 3\times10^{-5}& 3\times10^{-3}&5\times10^{-2}\\ 1\times10^{-4}&1\times10^{-2}&2\times10^{-1}\\6\times10^{-4}&5\times10^{-2}&1\end{array}\right). \eeq \item in the MFV framework \cite{Nikolidakis:2007fc,Csaki:2011ge}, the baryon number violating couplings depend just on $\tan\beta$ and an overall scale factor $w''$, while the lepton number violating operators are naturally suppressed. For $\tan\beta\gtrsim1$ we have: \beq &\lambda''_{ijk}=w'' \tan^2\beta\, m_i^{(u)}m_j^{(d)}m_k^{(d)}\epsilon_{jkl}V^*_{il}/v^3,\\\label{LMFV} &\qquad\left(\begin{array}{ccc} \lambda''_{112} & \lambda''_{212} & \lambda''_{312} \\ \lambda''_{113} & \lambda''_{213} &\lambda''_{313} \\\lambda''_{123} & \lambda''_{223} & \lambda''_{323} \end{array}\right)= w''\tan^2\beta\left(\begin{array}{ccc}3\times10^{-12}&1\times10^{-8}&4\times10^{-5}\\6\times10^{-9}&1\times10^{-5}&6\times10^{-5}\\5\times10^{-7}&4\times10^{-5}&2\times10^{-4} \end{array}\right). \eeq The coefficient $w''$ is not constrained by the flavor structure and should be an $\OO(1)$ number. \end{itemize} We take these examples as a justification to consider scenarios in which only Baryonic \rpv\ (BRPV) is allowed, while lepton number is conserved (at least to a good approximation). This is the scenario that will be studied in the rest of this paper. It should be noted that in both models (eqs. \eqref{LHOR} and \eqref{LMFV}), $\l''_{223}$ is the largest coupling that does not involve a top in the final state. Implicit in \rpa\ scenarios is stability of the lightest supersymmetric particle (LSP) which can provide a viable relic Dark Matter (DM) candidate. With a neutralino LSP, this is the usual SUSY WIMP scenario, and problems can arise from late time gravitino decays to the LSP \cite{Khlopov:1984pf}, disturbing the predictions of Big Bang Nucleosynthesis (BBN). Alternatively, for a gravitino LSP, it is the NLSP decay to the gravitino that is suppressed by the Planck scale $M_P$ and can interfere with BBN. In contrast, \rpv\ allows superpartners to decay directly and quickly into SM particles,\footnote{As noted above, we consider only baryonic RPV in this paper. Then, late NLSP decays are not a problem for a neutralino or squark NLSPs, but they can be for a stau NLSP. In the second case, heavy superapartners and/or light gravitinos would be needed.} solving this problem but at the same time eliminating dark matter candidates from the theory. If, however, the gravitino is the LSP, its decay (see Figure \ref{grvudd}) is suppressed by the SUSY breaking scale $F$ (or equivalently, by $M_P$),\footnote{For a comprehensive review of gravitino interactions, see Ref. \cite{Moroi:1995fs}.} by the \rpving couplings, and by the superpartner scale $\mt$. This naturally allows for lifetimes longer than the age of the universe \cite{Takayama:2000uz}. Because the gravitino is unstable, its decays will generate cosmic-rays and high-energy $\gamma$-ray emission which can potentially be detected by modern indirect-detection experiments. Given the non-observation of gravitino decay products, we will proceed to set limits on RPV couplings and will compare them to bounds coming from low-energy baryon-number-violating processes (which are especially weak for couplings involving third generation fields). Although this has been studied in the literature, many groups have focused only on the bilinear RPV coupling $\mu_i L_i\phi_u$ \cite{Takayama:2000uz,Ishiwata:2008cu,Grefe:2014bta,Bobrovskyi:2010ps,Bertone:2007aw} with just Refs. \cite{Lola:2007rw,Lola:2008bk,Bomark:2009zm,Dal:2014nda} discussing the trilinear interactions; weak scale supersymmetry was also frequently assumed. In this paper, we do not set the superpartner scale, we discuss the connection to models with flavor symmetries, which has been unexplored so far, and we show that the limits can be stronger than those from low-energy flavor physics. Following Ref. \cite{Moreau:2001sr}, the decay rate of Figure \ref{grvudd} can be written as \beq\label{32gamma} \Gamma_{3/2}\simeq \frac{19}{60\cdot 768\pi^3}\lambda''^2_{ijk}\frac{\mtr^3}{M_P^2}{\frud{\mtr}{\mt}}^4 \eeq in the limit of vanishing masses for the final state particles and at leading order in $\mtr/\mt$. The lifetime is \beq \label{32lifetime} \tau_{\tilde G\to u_id_jd_k}=2.9\times 10^{14} \text{sec} \left(\frac{\text{10 GeV}}{\mtr}\right)^3\frac1{\lambda''^2_{ijk}}\frud{\mt}{\mtr}^4. \eeq In this equation $\mt$ is the common mass scale of the squarks which participate in the process; it is slightly modified in presence of a large hierarchy between different squarks. In particular, the detailed dependence on the squark masses is recovered by substituting the factor $19\mtr^4/\mt^4$ in \eqref{32gamma} with \beq \frac{\mtr^2}{m_{\tilde u_i}^4}\left(3+2n_d\frac{m_{\tilde u_i}^2}{m_{\tilde d_j}^2}+3n_d^2\frac{m_{\tilde u_i}^4}{m_{\tilde d_j}^4} \right), \eeq where we have denoted by $\tilde d_j$ the lightest down squark, and $n_d$ is the number of down squarks participating in the process, $n=\system{1, \ m_{\tilde d_j}\ll m_{\tilde d_k}\\2,\ m_{\tilde d_j}\sim m_{\tilde d_k}}$. \begin{figure} \begin{center}\includegraphics[width=5cm]{grvdecay}\end{center} \caption{Gravitino RPV decay; the white vertex marks the $1/M_P$-suppressed interaction, while the RPV interaction $\lambda''_{ijk}\tilde{\bar u}_i\bar d_j\bar d_k$ is marked by a black dot.} \label{grvudd} \end{figure} With the pre-inflationary gravitino abundance washed out during inflation, gravitinos are produced by thermal scattering at reheating and by decays of other fields (such as moduli, or the inflaton). We will show overclosure limits coming from the overproduction of gravitinos, and in the following we will assume $T_R>\mt>\mtr$ for the reheating temperature. As a conservative choice, we will assume that the full DM relic abundance is generated {\it in toto} at reheating;\footnote{If the universe reheats below $\mt$, gravitinos are not produced thermally. Still, a gravitino relic abundance might be produced by moduli or inflaton decay.} the second class of processes will just strengthen the overclosure bounds that we are considering.\footnote{On the other hand, these limits can be relaxed with a late entropy injection diluting the relic abundance.} The thermal scattering, with a cross section of order $\sigma\approx g_3^2 \frac{\mt^2}{M_P^2\mtr^2}$, overcloses the universe unless (see \cite{Moroi:1995fs,Hall:2013uga} for the precise expression) \beq\label{grvclose} 10^{-3}\frac{T_R\mt^2}{\mtr}\lesssim M_PT_{eq}. \eeq where the equality holds if the gravitino forms all of the dark matter, as we will assume in the following, and $T_{eq}\sim 1.5$ eV is the temperature of matter-radiation equality. \bigskip This paper is organized as follows: in Section \ref{grvdecay}, we review the importance of \antid s for the indirect detection of dark matter candidates and the coalescence model of \antid \ formation. We then compute and discuss the \antid \ injection spectrum. In Section \ref{rpvlimits} we derive the upper limits on the RPV coupling $\l''_{223}$ from the lack of antideuterons and discuss the dependence on the SUSY and SUSY mediation scales. We apply these limits in Section \ref{flavor}, where we discuss the implications for models with flavor symmetries. Finally, we conclude in Section \ref{conclusions}. | In this work, we studied how the non-observation of antideuterons cosmic rays places significant constraints on gravitino dark matter in baryonic \rpving models with flavor symmetries. We studied a selected number of decay channels and presented limits on the RPV couplings $\l''_{223}$ and $\l''_{323}$, which are almost everywhere stronger than bounds from baryon-number-violating low-energy processes. If flavor symmetries can be used as guides, these are the largest couplings and severe bounds can be cast. While the limits on horizontal flavor symmetries are not as strong, in the minimal flavor violating case the gravitino mass is forced to $\mtr\lesssim 20\gev$ for TeV-scale SUSY. The AMS-02 experiment will be able to reduce this bound below 10\gev. A suggestive implication (which could hold at least for the MFV scenario) is that the gravitino might be effectively stable, not because of a discrete symmetry such as \rpa, but because decays are not kinematically allowed.\footnote{If the gravitino is lighter than the proton, the proton can decay to it $p\to K^+ \tilde G$. This was considered in Refs.~\cite{Choi:1996nk,Choi:1998ak}), with the most relevant bounds being: \beq \l''_{112}\leq 5\times 10^{-16}\fru \mt{300\gev}^2\fru{\mtr}{1\text{ eV}},\qquad \l''_{323}\leq 5\times 10^{-8} \fru \mt{300\gev}^2\fru{\mtr}{1\text{ eV}} \eeq For models with a horizontal symmetry, this corresponds to $\l''_{323}\lesssim 10^{-2} \fru \mt{300\gev}^2\fru{\mtr}{\text{100 MeV}}$, which should be compared to the limits in figure \ref{Lhoriz}. In the MFV scenario, the gravitino mass has to be above $\OO(100 \text{ keV}) \times \tan^2\beta $ (a similar bound was also studied in ref. \cite{Csaki:2011ge}, resulting in a dependence on $\tan^4\beta$). } Further studies, especially at gravitino masses between 1 and 10 GeV, are needed. In this range, the best constraints on the RPV coupling will come from antiprotons, positrons and gamma rays. This would also imply a somewhat suppressed mediation scale for SUSY breaking, lower than $M_P$ or $M_{GUT}$, providing a suggestive hint for more new physics at intermediate energies. In a forthcoming publication \cite{futureUS}, we are comprehensively exploring all the different decay and detection channels, the uncertainties related to propagation and DM halo profile, as well as the full dependence on the SUSY spectrum. \paragraph{Note Added} While the write-up of this paper was being completed, reference \cite{Savastio:2014wva} was submitted to the arXiv, which puts similar limits on gravitino DM in the MFV framework by analyzing the antiproton and $\gamma$ fluxes and has no mention of the SUSY scale. In the present work, the source of the bounds is the lack of observation of antideuterons, which is less sensitive to astrophysical uncertainties. In addition to analyzing other types of flavor symmetries and a larger range of gravitino masses, we extensively discuss sensitivity to the superpartner scale and limits from overclosure. | 14 | 4 | 1404.5952 |
1404 | 1404.6160_arXiv.txt | We introduce a cosmological invisible decay of the sterile neutrino with the eV-scale mass indicated by short-baseline neutrino oscillation experiments in order to allow its full thermalization in the early Universe. We show that the fit of the cosmological data is practically as good as the fit obtained with a stable sterile neutrino without mass constraints, which has been recently considered by several authors for the explanation of the observed suppression of small-scale matter density fluctuations and for a solution of the tension between the Planck and BICEP2 measurements of the tensor-to-scalar ratio of large-scale fluctuations. Moreover, the extra relativistic degree of freedom corresponding to a fully thermalized sterile neutrino is correlated with a larger value of the Hubble constant, which is in agreement with local measurements. | 14 | 4 | 1404.6160 |
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1404 | 1404.3090_arXiv.txt | The injections of energetic hadrons could have occurred in the early universe by decays of hypothetical long-lived exotic particles. The injections induce the showers of nonthermal hadrons via nuclear scattering. Neutrons generated at these events can react with $^7$Be nuclei and reduce $^7$Be abundance solving a problem of the primordial $^7$Li abundance. We suggest that thermal neutron injection is a way to derive a model independent conservative limit on the relation between abundances of D and $^7$Li in a hadronic energy injection model. We emphasize that an uncertainty in cross sections of inelastic $n+p$ scattering affects the total number of induced neutrons, which determines final abundances of D and $^7$Li. In addition, the annihilations of antinucleons with $^4$He result in higher D abundance and trigger nonthermal $^6$Li production. It is concluded that a reduction of $^7$Li abundance from a value in the standard big bang nucleosynthesis (BBN) model down to an observational two $\sigma$ upper limit is necessarily accompanied by an undesirable increase of D abundance up to at least an observational 12 $\sigma$ upper limit from observations of quasi-stellar object absorption line systems. The effects of antinucleons and secondary particles produced in the hadronic showers always lead to a severer constraint. The BBN models involving any injections of extra neutrons are thus unlikely to reproduce a small $^7$Li abundance consistent with observations. | \label{sec1} Many environments have been considered regarding the origin of deuterium~\cite{Epstein1976Natur.263..198E}. They include pregalactic cosmic rays (CRs) from quasars and collapsing objects, shock waves, and neutron stars. In general, the CRs induce nuclear reactions producing D, $^3$He, Li, Be, and B nuclides~\cite{Reeves1970Natur.226..727R,Meneguzzi1971A&A....15..337M,Reeves1974ARA&A..12..437R}. Pregalactic CRs or cosmological CRs generated before the Galaxy formation also produce $^{6,7}$Li (via the $\alpha+\alpha$ fusion~\cite{Montmerle1977ApJ...216..177M}) and $^3$He (via $^4$He+$p$ nuclear spallation~\cite{Montmerle1977ApJ...217..878M}). $^6$Li productions have been calculated for the CRs in specific environments: the CRs accelerated in structure formation shocks at the Galaxy formation epoch~\cite{2002ApJ...573..168S} and the CRs from supernova remnants at the pregalactic epoch~\cite{Rollinde:2004kz,Rollinde:2006zx}. Since a metal pollution proceeds along with a stellar activity in the universe, the CRs would come to contain metals such as C, N, and O. Therefore, the pregalactic CR nucleosynthesis would also produce Be and B through reactions of (C, N, or O)+($p$ or $\alpha$)~\cite{Kusakabe2008,Rollinde2008} and ($^3$He or $\alpha$)+$\alpha\rightarrow (^6$He or $^{6,7}$Li)+$a$ followed by ($^6$He or $^{6,7}$Li)+$\alpha\rightarrow ^9$Be+$b$ with byproducts $a$ and $b$~\cite{Kusakabe:2012sh}. Another possible source of the CR is an energy injection at decay and annihilation of exotic long-lived particles~\cite{Lindley1979MNRAS.188P..15L,1982NCimR...5j...1C,Khlopov:1984pf,Balestra:1984cu,Ellis:1984er,Lindley:1986wt,Sedelnikov:1987ef,Reno:1987qw,Levitan:1988au,Dimopoulos:1987fz,Dimopoulos:1988zz,Dimopoulos:1988ue,Terasawa:1988my,Kawasaki:1993gz,Khlopov:1993ye,Kawasaki:1994af,Holtmann:1996cq,Jedamzik:1999di,Kawasaki:2000qr,Cyburt:2002uv,Kawasaki:2004yh,Kawasaki:2004qu,Jedamzik:2004er,Jedamzik:2004ip,Jedamzik:2005dh,Ellis:2005ii,Kusakabe:2006hc,Kanzaki:2006hm,Jedamzik:2006xz,Cumberbatch:2007me,Kusakabe:2008kf,Kawasaki:2008qe,Kawasaki:2009ex,Cyburt:2009pg,Pospelov:2010cw,Pospelov:2010kq,Cyburt:2010vz,Ellis:2011sv,Kang:2011vz,Olive:2012xf,Kusakabe:2013sna,Ishida:2014wqa}. A constraint on the mass of a hypothetical stable heavy neutrino has been derived through calculation of its present cosmological energy density~\cite{Hut:1977zn,Lee:1977ua}. An unstable heavy neutrino was then considered, and constraints on its mass and lifetime were derived~\cite{Sato:1977ye,Dicus:1977nn,Vysotsky:1977pe}. The electromagnetic decay of the unstable particle is constrained through distortions in the energy spectrum of cosmic microwave background radiation~\cite{Sato:1977ye}. The constraints on hypothetical heavy neutrino~\cite{Miyama:1978mn} and primordial black holes~\cite{Miyama:1978mp} were then derived from the effect on light element abundances through energy densities in detailed calculations of big bang nucleosynthesis (BBN). The decay of unstable heavy neutrinos also affects nuclear abundances through nonthermal photodissociation of nuclei~\cite{Lindley1979MNRAS.188P..15L}. The radiative decay induces electromagnetic cascades of energetic photons, electrons, and positrons during the propagation of the nonthermal photon emitted at the decay~\cite{Ellis:1984er}. Effects of hadronic injections at the decay were studied~\cite{Levitan:1988au,Dimopoulos:1987fz,Dimopoulos:1988ue,Dimopoulos:1988zz,Reno:1987qw}. Levitan {\it et al.} investigated hadronic cascades of proton and antiproton and dissociations of $^4$He~\cite{Levitan:1988au}. Dimopoulos {\it et al.}~\cite{Dimopoulos:1987fz,Dimopoulos:1988ue,Dimopoulos:1988zz} extensively studied the effects on abundances of nuclei up to $^7$Li and $^7$Be. They considered the reaction, i.e., $^1$H($n,\gamma$)$^2$H, for D production, and the reaction, i.e., $^7$Be($n,p$)$^7$Li, for $^7$Be destruction, where 1(2$,$3)4 stands for a reaction $1+2\rightarrow 3+4$. Antiprotons injected at decays of exotic long-lived particles could dissociate $^4$He and produce D and $^3$He~\cite{1982NCimR...5j...1C,Khlopov:1984pf,Balestra:1984cu}. The cross sections of $\bar{p}+^4$He annihilation have been measured~\cite{1988NCimA.100..323B}, and the yields of D, $^3$H, and $^3$He at the annihilation were calculated as a function of energy of antiproton~\cite{Sedelnikov:1999km}. Effects of exotic particles on nuclear abundances through hadronic showers have been extensively studied with realistic initial spectra of injected hadrons~\cite{Kawasaki:2004qu,Jedamzik:2006xz}. The standard BBN (SBBN) model explains primordial light element abundances inferred from astronomical observations well~\cite{2011ARNPS..61...47F}. Modifications of the BBN model are then constrained from the consistency between theoretical predictions and observations of abundances. Among light elements produced during the BBN, however, the lithium has an unexplained discrepancy between SBBN prediction and observational determinations of its primordial abundances~\cite{Melendez:2004ni,Asplund:2005yt}. Spectroscopic observations of metal-poor stars (MPSs) indicate an abundance measured by number relative to hydrogen, i.e., $^7$Li/H$=(1-2) \times 10^{-10}$~\cite{Spite:1982dd,Ryan2000,Melendez:2004ni,Asplund:2005yt,bon2007,Shi:2006zz,Aoki:2009ce,Hernandez:2009gn,Sbordone2010,Monaco:2010mm,Monaco:2011sd,Mucciarelli:2011ts} \footnote{Surface Li abundances of metal-poor red giant branch stars do not depend on parameters of standard stellar models as much as dwarf stars do. Mucciarelli {\it et al.}~\cite{Mucciarelli:2011ts} determined Li abundances of metal-poor halo red giant branch stars, and estimated initial abundances, which were also $\sim$2--3 lower than SBBN prediction.} \footnote{Monaco {\it et al.}~\cite{Monaco:2011sd} reported that one star, $\sharp$37934, among 91 stars of the globular cluster M4 has a high lithium abundance ($^7$Li/H=$7.4^{+3.1}_{-2.2}\times 10^{-10}$) consistent with the abundance of the SBBN model.}. This abundance is a factor of 2--4 higher than the SBBN prediction when we adopt the baryon-to-photon ratio determined from the observation of the cosmic microwave background radiation with Wilkinson Microwave Anisotropy Probe (WMAP)~\cite{Hinshaw:2012aka}. After the lithium problem was recognized, the neutron injection during the BBN was suggested to be a solution since it can reduce $^7$Be abundance via $^7$Be($n,p$)$^7$Li($p,\alpha$)$^4$He, although it increases D abundance via $^1$H($n,\gamma$)$^2$H simultaneously~\cite{Jedamzik:2004er,Vasquez:2012dz}. Such a neutron injection is realized in the hadronic decay of exotic long-lived massive particles~\cite{Jedamzik:2004er,Kawasaki:2004qu,Jedamzik:2006xz}. Important reactions caused by injected nonthermal hadrons have been identified in a statistical study, which are shown to be closely associated with resulting elemental abundances~\cite{Cyburt:2010vz}. A wide parameter region of the lifetime and the abundance of a long-lived particle was studied, and a parameter region for $^7$Li reduction has been found~\cite{Kawasaki:2004qu,Jedamzik:2006xz,Cyburt:2009pg} \footnote{If long-lived exotic particles of sub GeV-scale mass exist, and their decay products do not include nucleons, another route of additional neutrons operates~\cite{Pospelov:2010cw}. When mesons such as $\pi$ and $K$ are generated by the particle decays, they can convert protons to neutrons, and a reduction of $^7$Li abundance realizes along with an enhancement of D abundance. When the decays do not generate any mesons, and muons and neutrinos are generated, on the other hand, induced electron antineutrinos convert protons to neutrons. In this case, the dissociation of once enhanced D by nonthermal photons can reduce D abundance to the level consistent with observations.}. In this paper, we focus solely on the parameter region for $^7$Li reduction, and derive a model independent constraint on a relation between abundances of D and $^7$Li, by using recent D abundance data. In Sec.~\ref{sec2}, we describe input physics and assumptions adopted in this paper. We prove that the assumption of thermal neutron injection (TNI) leads to a conservative lower limit on the ratio of the increase of D abundance to the decrease of $^7$Li abundance. In Sec.~\ref{sec3}, we describe the TNI model and the BBN model, as well as adopted observational constraint on primordial nuclear abundances. The TNI is assumed to occur instantaneously, and the injection time and the abundance of injected neutron are used as parameters in this model. In Sec.~\ref{sec4}, results of the BBN calculations are shown, and a relation between abundances of D and $^7$Li is derived. In Sec.~\ref{sec5}, we estimate an effect of antinucleon annihilation with $^4$He on the abundance relation. In Sec.~\ref{sec6}, we estimate amounts of $^6$Li production induced by the antinucleon+$^4$He annihilation. In Sec.~\ref{sec7}, conclusions are done finally. In Appendix~\ref{app1}, we list important nuclear reactions which work in a parameter region for the reduction of primordial $^7$Li abundance. In Appendix~\ref{app2}, approximate analytic estimates of D and $^7$Li abundances are shown. In this paper, we adopt notation of $a(n)=a\times 10^n$ with a real number $a$ and an integer $n$, and $Q_{,b}=Q/b$ with a parameter $Q$ and a real number $b$. The Boltzmann's constant ($k_{\rm B}$), the reduced Planck's constant ($\hbar$), and the light speed ($c$) are normalized to be unity. | \label{sec7} The injections of energetic hadrons could have occurred in the early universe by hypothetical events of decays or annihilations of long-lived exotic particles, or evaporations of exotic objects. The injections cause scattering of thermal nuclei by energetic hadrons, and showers of nonthermal nucleons, antinucleons, and nuclei can develop. Neutrons generated at the exotic events can react with $^7$Be and reduce final abundances of $^7$Li (which are mainly produced via the electron capture of $^7$Be). It has been suggested that the $^7$Be reduction can be a solution to a discrepancy between theoretical $^7$Li abundances of the SBBN model and that inferred from observations of Galactic metal-poor stars. The theoretical abundance is about a factor of three larger than the observational one. Based on an analysis of related physical processes, we prove that the assumption of instantaneous thermalization of injected neutron provides the way to derive a conservative limit on the relation between abundances of D and $^7$Li in the hadronic energy injection model, which is independent of uncertainties in generations and reactions of nonthermal hadrons originating from the injections (Sec.~\ref{sec2}). Furthermore, two important points are stressed: 1) An uncertainty in cross sections of inelastic $n+p$ scattering [Eqs. (\ref{eq6}), (\ref{eq7}), and (\ref{eq8})] affects the total number of neutrons generated from the primary neutron injection, which is critical for resulting abundances of D and $^7$Li. 2) One must include effects of annihilations of antinucleons with $^4$He on a primordial D abundance even if antinucleons generated with neutron were instantaneously thermalized. We then consider a simple model in which extra thermal neutrons are injected in a late epoch of the BBN. We estimate the probability that primordial abundances of $^7$Li in this model can be consistent with observed abundances. Relations between primordial abundances of D and $^7$Li are obtained in a manner to conserve the probability securely. We perform a BBN calculation, and find a very small parameter region of the neutron injection time ($t_{\rm inj}$) and the number density ($\Delta n_{\rm inj}$) of injected neutron in which $^7$Li abundances are within the 2 $\sigma$ uncertainty range determined from observation and changes in D abundance are minimum. In the preferred parameter region, the injection time is $t_{\rm inj}\sim 800$~s, and its number density is $10^{-5}$ times as large as that of total baryonic matter. A typical pattern of nucleosynthesis in the parameter region is analyzed (Appendix~\ref{app1}). Situations of D production and $^7$Li reduction are observed especially (Appendix~\ref{app2}). We derive a model-independent result [Eq.~(\ref{eq17})] that a reduction of $^7$Li abundance from the SBBN value down to the observational two $\sigma$ upper limit is necessarily accompanied by an undesirable increase of D abundance up to at least the 12 $\sigma$ upper limit (best observed value) and the 5 $\sigma$ upper limit (mean observed value). When effects of antinucleons+$^4$He annihilations are considered utilizing a possible example case, the preferred parameter regions become narrower in the present model. BBN models involving any injections of extra neutron are, therefore, not likely to accommodate alone a reduction of primordial $^7$Li abundance to the observed level. \appendix | 14 | 4 | 1404.3090 |
1404 | 1404.7656.txt | Metal absorption systems are products of star formation. They are believed to be associated with massive star forming galaxies, which have significantly enriched their surroundings. To test this idea with high column density \civ\ absorption systems at $z{\sim}5.7$, we study the projected distribution of galaxies and characterise the environment of \civ\ systems in two independent quasar lines-of-sight: J103027.01+052455.0 and J113717.73+354956.9. Using wide field photometry (${\sim} 80 {\times}60 {\it h}^{-1}$ comoving Mpc), we select bright (M$_{\rm UV}(1350$\AA$)\simlt{-}21.0$ mag.) Lyman break galaxies (LBGs) at $z{\sim}5.7$ in a redshift slice $\Delta z {\sim}0.2$ and we compare their projected distribution with \zlbg\ narrow-band selected Lyman alpha emitters (LAEs, $\Delta z {\sim}0.08$). We find that the \civ\ systems are located more than 10${\it h}^{-1}$ projected comoving Mpc from the main concentrations of LBGs and no candidate is closer than ${\sim}5{\it h}^{-1}$ projected comoving Mpc. In contrast, an excess of LAEs --lower mass galaxies-- is found on scales of ${\sim}10{\it h}^{-1}$ comoving Mpc, suggesting that LAEs are the primary candidates for the source of the \civ\ systems. Furthermore, the closest object to the system in the field J1030+0524 is a faint LAE at a projected distance of 212${\it h}^{-1}$ physical kpc. However, this work cannot rule out undiscovered lower mass galaxies as the origin of these absorption systems. We conclude that, in contrast with lower redshift examples ($z{\simlt}3.5$), strong \civ\ absorption systems at \zlbg\ trace low-to-intermediate density environments dominated by low-mass galaxies. Moreover, the excess of LAEs associated with high levels of ionizing flux agrees with the idea that faint galaxies dominate the ionizing photon budget at this redshift. | There is significant observational evidence that cosmic reionization of hydrogen is largely completed by $z{\sim}5.7$ \citep[e.g.][]{ouchi2010, kashikawa2011,larson2011,komatsu2011,caruana2012,finkelstein2012b,zahn2012,jensen2013}. \citet{zahn2012} combined WMAP7 and South Pole Telescope data to model the duration of the epoch of reionization (EoR) by including the kinetic Sunyaev-Zel'dovich effect in their analysis. They report for the most conservative case that the EoR begins at $z_{EoR}{<}13.1$ and is over by $z_{EoR}{>}5.8$ at $95\%$ confidence level. Moreover, studies of narrow-band selected \Lya\ emitters (LAEs) have found that the normalisation of the \Lya\ luminosity function of LAEs is higher at $z{\sim}5.7$ than $z{\sim}6.5$ \citep[e.g.][]{ouchi2010,hu2010,clement2012}. Since \Lya\ is a resonant line, a small amount of neutral hydrogen in the intergalactic medium (IGM) is able to reduce the number of \Lya\ photons that are transmitted. Therefore, a higher transmission of \Lya\ photons at $z{=}5.7$ would result from a lower fraction of neutral-to-ionized hydrogen in the IGM than at $z\sim6.5$, suggesting that the main reionization process took place at $z_{EoR}{\simgt}6$. \citet[][2011]{stark2010} reported a decrease in the fraction of Lyman break galaxies \citep[LBGs,][]{steidel1996} with \Lya\ in emission from $z{=}6$ to $z{=}3$, at fixed luminosity, in line with the observational and theoretical expectation of the evolution of star-forming galaxies over this period. However, several spectroscopic campaigns for the identification of $z{\simgt} 7$ LBGs have shown very low numbers of \Lya\ detections \citep{fontana2010, pentericci2011, schenker2012a, ono2012a, caruana2012, bunker2013, treu2013}. This suppression of the \Lya\ emission could indicate a more neutral IGM at $z{>}6$ \citep[although see][]{bolton2013}. Finally, a classic piece of evidence that cosmic reionization was probably complete by $z{\sim}6$ comes from the \Lya\ forest in the spectra of high redshift QSOs. They show several examples of complete Gunn--Peterson troughs \citep{gunnpeterson1965} at $z{>}6$ and an optical depth decreasing with cosmic time \citep[e.g.][]{becker2001, fan2006a, goto2011, mortlock2011}. \citet{becker2007} show that the distribution of optical depths in the \Lya\ forest is better reproduced by models that account for an inhomogeneous ionizing background and non-uniform IGM temperature, which implies that reionization was certainly not homogeneous nor instantaneous \citep[e.g.][]{schroeder2013}. Moreover, a heterogeneous reionization is also predicted by theoretical studies \citep[e.g.][]{trac2008,mesinger2009, finlator2009b, choudhury2009, griffen2013}. Hydrodynamical simulations combined with high redshift \Lya\ forest data suggest an extended process of reionization that occurs in a ``photon-starved'' regime \citep{bolton2007}. Semi-numerical simulations have explored the implications of this result on the topology of the reionization process. \citet{choudhury2009} find a two stage process starting with an ``inside-out'' topology in which high-density regions hosting ionizing sources are the first to be ionized. From there, reionization proceeded directly into voids while dense regions which hosted no ionizing sources and had remained neutral to this point, were slowly ionized from the outside (``outside-in''). After reionization is complete, the relative flux of ionizing radiation that is left over could trace the history of reionization of the large-scale structure. In particular, the scatter in the intensity of the UV background is affected by the distribution of sources of the ionizing field \citep[e.g.][]{mesinger2009} and the evolution on the mean free path of ionizing photons \citep[e.g.][]{miralda-escude2003, bolton2007, faucher-giguere2008}. \citet{mesinger2009} compare analytic, semi-numeric and numeric calculations of inhomogeneous flux fields and found a highly variable ionization state predicted to persist after reionization at $z{=}5$--6. For example, if reionization proceeded in a fully inside-out geometry, a highly ionized IGM is expected to exist in regions where the density of matter is higher than the average \citep[e.g.][]{trac2008}, leading to a possible direct observational test for the challenging question of which regions were the first ones to be permanently ionized. A highly ionized IGM can be detected through metal absorption systems. A typical signature is the presence of strong triply ionized carbon absorption (\civ, ionization energy${=}47.89$eV). In the redshift range $5.3{<}z{<}6.2$, only four \civ\ absorption systems with column densities \nciv${>}10^{14}$\cm\ have been reported from a sample of 13 sight-lines towards high-redshift QSOs \citep{ryan-weber2009, simcoe2011b,dodorico2013}. Interestingly, two of them lie at similar redshift ($z{\sim}5.72$--5.73). One strong \civ\ absorption system at $z_{\rm abs}{=} 5.7244$ in the line-of-sight towards QSO J1030+0524 \citep{ryan-weber2009, simcoe2011b} is accompanied by a weaker system at $z_{\rm abs}{=}5.7440$ \citep[][]{simcoe2011b,dodorico2013}. The second example is found at redshift $z_{\rm abs}{=}5.7383$ towards QSO J1137+3549 \citep{ryan-weber2009}. The redshift of these three systems is in co-incidence with an atmospheric transmission window at $\lambda {\sim}8180$\AA\ ($z_{\rm Ly\alpha}{\sim}5.73$) and sets the possibility to search for galaxies in their vicinity using ground based observations. Conveniently located at $z{\sim}5.72$--5.73, these three \civ\ systems provide an opportunity to study the connection between the ionization state of the intergalactic medium shortly after the EoR and the population of galaxies in their environment on different scales. The evolution with time of the comoving mass density of \civ\ ($\Omega_{\text \civ}(z)$) shows a rapid rise between $z{\sim}6$ and $z{\sim}5$ \citep{ryan-weber2009, becker2009,simcoe2011b}. This is unlikely to be solely due to a sharp rise in the metal content of the Universe as the star formation rate density is reasonably smooth over this short period of time \citep[e.g.][]{bouwens2007,stark2009,stark2013}. More recently, \citet{dodorico2013} revisited the evolution of $\Omega_{\text \civ}(z)$ and find it to be smoothly rising from $z{\sim}6$ to $z\sim1.5$, as expected from a progressive accumulation of metals. Nevertheless, they also report that the column density distribution function of \civ\ is lower at $5.3{<}z{<}6.2$ than $1.5{<}z{<}5.3$, which suggests a change in the number density and/or the physical size of the \civ\ absorption systems. Furthermore, the evolution of the \siiv /\civ\ column density ratios towards lower redshift currently suggest a change in the ionization conditions of the absorbing gas at $z{<}5$ \citep{dodorico2013}. Therefore, it is possible that the observed evolution of the abundance of high ionization absorption systems is the result of a change in the ionization balance driven by the evolution of the ionizing UV background after the EoR. If the distribution of sources dominates the ionizing field at that time, then the environment of high redshift highly ionized absorption systems contains information not only on the origin of the enrichment of the Universe but also on the nature of the ionizing sources. Recent studies suggest that sub-L$^{\star}$ galaxies most likely dominate the ionizing photon budget at $z{\simgt}6$ \citep{cassata2011, dressler2011, kuhlen2012, jaacks2012, finkelstein2012b, ferrara2013, robertson2013, cai2014, fontanot2014}. Moreover, many authors have observed an anti-correlation between UV luminosity and the strength of the \Lya\ emission line, with fainter objects showing larger \Lya\ equivalent widths \citep[e.g.][]{shimasaku2006, ouchi2008, vanzella2009, ouchi2010}; and an anti-correlation between the UV luminosity and the fraction of galaxies with \Lya\ emission \citep{stark2010, stark2011}, with fainter objects being more likely to show \Lya\ emission. Because at high redshift the UV luminosity of star forming galaxies correlates with the stellar mass \citep[e.g.][]{mclure2011, gonzalez2011}, the interpretation of these trends suggest that is possible to use LAEs to preferentially select low-mass galaxies. The two goals of this work are: a) to identify the galaxies associated to the nearby environment of highly ionized \civ\ absorption systems shortly after the EoR; and b) to characterise the matter density distribution at larger scales using galaxies as tracers of the large-scale structure. First, if the change in $\Omega_{\text \civ}(z)$ is driven only by the metal content of the IGM, meaning that at \zlbg\ the IGM is simply less enriched, then it is reasonable to expect that strong \civ\ systems are associated with regions of earlier star formation episodes where the IGM was polluted first and for longer times. This is found at lower redshift, $2{\simlt} z {\simlt} 3$ \citep[e.g.:][]{adelberger2005b, steidel2010}, where galaxies in denser environment are more likely to have a strong \civ\ system within 1${\it h}^{-1}$ comoving Mpc. Thus, if the absorbing gas at \zlbg\ is not affected by changes in the IGM ionization state, then we would expect \zlbg\ \civ\ absorption systems near over-densities of LBGs similar to that found at $z{\simlt} 3$. Second, if the change in $\Omega_{\text \civ}(z)$ results from the evolution in the ionizing flux density background fluctuations, then \civ\ systems at \zlbg\ would trace regions of high flux density of ionizing radiation. In this case, a simple prediction from an inside-out reionization process is a positive correlation between mass distribution and the ionization level of the IGM. Under this scenario, rare highly ionized strong absorption systems would be expected to reside in dense structures that collapsed earlier and were reionized first. Finally, a third scenario involving the reversal of the topology of reionization is also possible. If young low-mass galaxies forming away from the main over-densities provide a final push for the cosmic reionization, then these will be the regions that, at large scales, will present a higher ionizing flux density that favours the detection of \civ\ in absorption. We report that \civ\ absorption systems are found in low-to-intermediate density environments populated by low mass galaxies and are not associated with over-densities of massive galaxies, which is in tension with the expectation from a fully inside-out reionization, but in agreement with an outside-in reionization during the last stage of the EoR. This work supports the idea that, although reionization is complete by $z{\sim}5.7$, the predicted inhomogeneous ionizing flux density of the IGM affects the detection of high ionization metal absorption systems. In this case, the finding that the immediate environment of highly-ionized absorption systems at \zlbg\ is dominated by low-mass galaxies is a new piece of evidence that these galaxies are an important sources of ionizing radiation at $z{\sim}6$. This paper is organised as follows: Section \ref{s:obs-red} describes the observations, Section \ref{s:sel} explains the photometric selection of the galaxies for the study, Section \ref{s:results-colours} presents the colours and magnitudes of the LBGs and LAEs candidates, Section \ref{s:results-num} reports the number density of each sample, and Section \ref{s:results-sd} describes in detail their surface density distribution. The discussion on the origin of the \civ\ and the reionization of the IGM can be found in Section \ref{s:discussion}. Finally, a summary of the work and the conclusions are presented in Section \ref{s:conclusion}. Throughout this work we use AB magnitudes and assume a flat universe with $H_{0}{=}70$\kms Mpc$^{-1}$ (${\it h}{=}0.7$), $\Omega_{m}{=}0.3$ and $\Omega_{\lambda}{=}0.7$. \section[]{Observations and data reduction}\label{s:obs-red} \subsection{Subaru data} This section presents the observational data and the reduction process. The present work is based on broad-band and narrow-band photometry obtained with Suprime-Cam \citep{miyazaki2002} on the Subaru Telescope. We use broad-band R$_c$, i' and z' filters covering the wavelength range ${\sim}5800$--$10 000$\AA\ and a custom-made narrow-band filter to detect \Lya\ in emission at redshift $z{=}5.71\pm0.04$ (NB\civ , $\lambda_c{=}8162$\AA, FWHM${=}100$\AA). Observations with the NB\civ, R$_c$ and i' band were acquired the nights 07--08 March 2011 and images in the z' band were obtained 31 March and 01 April 2011. We observed two fields centred on QSOs SDSS J103027.01+052455.0 ($z_{em} {=} 6.309$, R.A.=10:30:27.01 , DEC.=05:24:55.0) and SDSS J113717.73+354956.9 ($z_{em}{=}6.01$, R.A.=11:37:17.73, DEC.=35:49:56.9) \citep{fan2006a}, here after J1030+0524 and J1137+3549. The total exposure time of the final images and the full width half maximum (FWHM) of the point-spread function (PSF) are presented in Table \ref{t:obs}. Note that the z' band images have the best resolution in both cases. These values were measured in science images resulting from the reduction process described next. The data were processed with the software SDFRED2 \citep{yagi2002,ouchi2004a} designed to reduce Suprime-Cam data. The reduction process includes bias subtraction and overscan, flat field correction, distortion correction, PSF-equalization of different exposures (when needed), masking of bad regions (e.g. satellite tracks and saturated pixels), alignment of all frames and stacking to create the final combined image. Detection and extraction of objects was carried out using the source extraction software \textsc{sextractor} 2.5.0 \citep{bertin1996}. In order to have consistent photometry, first we matched the PSF of the field J1030+0524 to PSF=0.87" and the field J1137+3549 to PSF=1.13", which equates to the PSF of the filter with the poorest seeing. The catalogue of broad-band detected objects was obtained running \textsc{sextractor} in dual mode using the best resolution z' band image for detection and the PSF-matched images for aperture photometry. The two samples of LBGs analysed in this work (sections \ref{s:sel-lbg} and \ref{s:sel-idrop}) are extracted from this catalogue. Similarly, the catalogue of narrow-band selected objects used to identify LAEs (section \ref{s:sel-LAE}) was obtained running \textsc{sextractor} in dual mode with the NB\civ\ image for detection and the PSF-matched images for aperture photometry. The following \textsc{sextractor} parameters that regulate the detection of sources were used: DETECT\_MINAREA${=}5$, DETECT\_THRESHOLD${=}2.0$, ANALYSIS\_THRESHOLD${=}2.0$ and DEBLEND\_MINCON${=}0.005$. For both detection and measurement images, the corresponding {\it rms-map} of the background was converted to a weight-map ($WEIGHT{=}1/RMS^2$) and provided to \textsc{sextractor} using WEIGHT\_TYPE${=}$MAP\_WEIGHT. Colours were computed from magnitudes measured in a 2.0" aperture (MAG\_APER) in J1030+0524 and a 2.4" aperture in J1137+3549, and MAG\_AUTO was used for the total magnitude of an object. Considering the z' filter samples the UV continuum (rest frame 1350\AA) of galaxies at redshift $z{\sim}5.7$, the continuum magnitude of an object is measured from the best resolution z' band image. \begin{table} \caption{Exposure time and PSF of science images.} \label{t:obs} \begin{tabular}{@{}lcrc} \hline \hline Field & Filter & Exposure & PSF \\ & & Time (min) & (") \\ \hline & NB\civ\ & 240 & 0.79 \\ & R$_c$ & 80 & 0.87 \\ J1030+0524 & i' & 90 & 0.81 \\ & z' & 116 & 0.69 \\ \hline & NB\civ\ & 226 & 1.31 \\ & R$_c$ & 100 & 1.11 \\ J1137+3549 & i' & 90 & 1.13 \\ & z' & 114 & 0.67 \\ \hline \end{tabular} \\ \end{table} \subsection{Photometric calibrations} The zero-point magnitude in each broad-band image was tested in each field against point-like sources from the Sloan Digital Sky Survey (SDSS) as both of our fields are covered by the survey. Stars were selected with magnitudes in the range ${\sim}18$--22 and cross-matched with a total of 690 (545), 1034 (665) and 576 (385) point sources in R$_c$, i' and z' band in the J1030+0524 (J1137+3945) field. The best fit to the Sloan magnitudes was found after applying a three sigma-clipping process. Zero-point magnitudes in the J1030+0524 and J1137+3549 field are R$_{c\,zp}{=}34.57{\pm}0.11$ and R$_{c\,zp}{=}34.52{\pm}0.14$, i'$_{zp}{=}34.62{\pm}0.11$ and i'$_{zp}{=}34.50{\pm}0.11$, z'$_{zp}{=}33.52{\pm}0.07$ and z'$_{zp}{=}33.82{\pm}0.09$, respectively. Figure \ref{f:zpoint} shows the residuals after the zero-point correction of the stars selected from SDSS. Magnitudes in all filters in both fields are in good agreement within ${\pm}0.2$--0.3 magnitudes with respect to the SDSS magnitudes. Note the increment in the vertical scatter is due to the increase in the uncertainty in SDSS as we approach its point source limiting magnitude. The zero-point magnitudes for the NB\civ\ band were derived from photometric standard stars observed the same nights. The stars are GD50 for the field J1030+0524 and HZ44 for the field J1137+3549. The zero-point magnitudes are NB\civ$_{zp}{=}32.28$ (J1030+0524) and NB\civ$_{zp}{=}32.22$ (J1137+3549). Galactic extinction from the dust map of \citet{schlegel1998} is $E(B-V){=}0.024$ in the field J1030+0524 and 0.018 in the field J1137+3549. We apply a correction of 0.064 (0.048) magnitudes in R$_c$, 0.050 (0.038) magnitudes in i' and NB\civ , and 0.035 (0.027) magnitudes in z' for the field J1030+0524 (J1137+3549). Aperture corrections in the four bands were estimated from the flux of isolated point sources in 20 apertures from 0.4" (2.0 pixels) to 6.0" (29.7 pixels). The measured fluxes level off in a 5.0" (5.5") aperture in the field J1030+0524 (J1137+3549). Therefore, the fractional flux is estimated as the ratio between the flux in the aperture and the flux in a $5.0$" ($5.5$") aperture. We then searched for an aperture with a fractional flux close to $90\%$ in all four bands and find good compromise with a 2.0" (10 pixels) aperture in the field J1030+0524 and a 2.4" (12 pixels) aperture in the field J1137+3549. In particular, we find that in the field J1030+0524 the fractional fluxes in an aperture of 2.0" in the R$_c$, i', NB\civ\ and z' bands are $86.8\%$, $89.2\%$, $89.1\%$ and $89.6\%$, respectively, implying aperture corrections of -0.15 mag, -0.12 mag, -0.11 mag and -0.11 mag. In the same way, in the field J1137+3549 the fractional fluxes in an aperture of 2.4" are $90.7\%$, $89.9\%$, $75.6\%$ and $94.7\%$. The corrections for this case are -0.10 mag, -0.11 mag, -0.24 mag and -0.05 mag. \begin{figure} \includegraphics[width=84mm]{f-zeropoint.ps} \caption{ Difference between zero-point corrected magnitudes and SDSS magnitudes of stars selected from SDSS. From top to bottom, residuals in the R$_c$, i' and z' band photometry from Suprime-Cam. Diamond points are used to estimate the correction and asterisks represent stars rejected after a $3\sigma$-clipping used in the fitting process.} \label{f:zpoint} \end{figure} \subsection{Limiting magnitudes} \label{s:limitmag} Since the sources of interest are very faint, the magnitude error is dominated by the sky background level. Therefore, the limiting magnitude of each PSF-matched image used for aperture photometry is important to understand the limits of the photometric selection criteria described in Section \ref{s:sel}. To estimate the $5\sigma$-limiting magnitude due to the sky level, the background level is measured in 10\,000 apertures placed randomly on the sky. The same diameter as for the aperture photometry was used in the {\it measurement} images: 2.0" in the field J1030+0524 and 2.4" in the field J1137+3549. For z'-band {\it detection} images (best PSF), a 2.0" aperture was used in both fields. Then, the FWHM of a Gaussian fit to the distribution of background counts is used to estimate $\sigma{=}$FWHM$/2.35482$ and finally obtain the $5\sigma$-limiting magnitude $m_{5\sigma}{=}m_{zp}{-}2.5\log_{10}(5\sigma)$. The resulting values and the aperture sizes used on the process are reported in Table \ref{t:mlim}. Other ways to explore the detection limits of the data are presented and compared to $m_{5\sigma}($z'$)$ in Appendix \ref{app:limitmag}. \begin{table} \caption{5$\sigma$-limiting magnitude of science images.} \label{t:mlim} \begin{tabular}{@{}llccc} \hline \hline Field & Image & Filter & m$_{5\sigma}\,$ & Aperture\\ & & & magnitudes & (``)\\ \hline J1030+0524 & Detection & NB\civ\ & 25.60$^a$ & 2.0 \\ & Detection & z' & 25.66$^a$ & 2.0 \\ & Measurement & NB\civ\ & 25.65$^b$ & 2.0 \\ & Measurement & R$_c$ & 26.60$^b$ & 2.0 \\ & Measurement & i' & 26.29$^b$ & 2.0\\ & Measurement & z' & 25.74$^b$ & 2.0\\ \hline \hline J1137+3549 & Detection & NB\civ\ & 25.30 & 2.4 \\ & Detection & z' & 25.85$^a$ & 2.0\\ & Measurement & NB\civ\ & 25.32 & 2.4 \\ & Measurement & R$_c$ & 26.24$^b$ & 2.4 \\ & Measurement & i' & 25.87$^b$ & 2.4\\ & Measurement & z' & 25.64$^b$ & 2.4\\ \hline \end{tabular} \\ $^{\it (a)}${Before PSF-matching.}\\ $^{\it (b)}${After PSF-matching.}\\ \end{table} | \label{s:conclusion} This is a study of the environment of high column density \civ\ systems (\nciv${>}10^{14}$\cm ) at $z{\sim}5.72$--5.74, in the fields J1030+0524 and J1137+3549. Using wide field photometry in the R$_c$, i' and z' bands, and a narrow-band filter NB\civ\ we select LBGs using broad-band colours, and LAEs using narrow-band excess and colours. Our results and conclusions are summarised as follows: \begin{itemize} \renewcommand{\labelitemi}{$\bullet$} \item We find the selection criteria for LAEs to be reliable and stable within the photometric uncertainty. We confirm that strong \Lya\ emission can affect the broad-band colours of the LBG population at the redshift of interest. \item We have tested a selection criteria based on broad-band colours that aims for a sample statistically dominated by bright star-forming galaxies with EW(\Lya) $\simlt 25$\AA\ (see Section \ref{s:sel}), in a redshift slice $\Delta z {\sim}0.2$. This $z{\sim}5.7$ LBG selection criteria is predicted to be more effective at selecting galaxies at the redshift of the \civ\ systems than the $z{\sim}6$ i'-dropout criteria. In general, the number of objects detected is consistent with expectations from the $z{\sim}6$ luminosity function (Section \ref{s:results-num}). \item We compare the projected distribution of LBGs ($\Delta z {\sim}0.2$) with narrow-band selected LAEs ($\Delta z {\sim}0.08$). A direct comparison of the clustering of the sources is possible thanks to the narrow volume that is sampled. In both fields-of-view, we find bright UV LBGs in clustered associations and LAEs distributed in the surroundings areas. The structure detected in the distribution of galaxies is consistent, although not definite, with a possible dependence of the EW(\Lya) with environment. \item The local environment of \civ\ absorption systems in the fields J1030+0524 and J1137+3549 presents an excess of LAEs and a deficit of \zlbg\ LBGs per arcmin$^2$ on several scales. In the field J1137+3549, LAEs are low in number but the surface density at a scale of $10{\it h}^{-1}$ comoving Mpc is higher than the mean of the field. \item i'-dropouts are found in excess towards both QSO lines-of-sight and are likely related to the background ($z{\simgt}6$) QSO environment instead of the foreground ($z{\sim}5.72$--5.74) absorption systems of interest. This is in agreement with the expectation that QSOs inhabit massive haloes in the centre of large-scale over-densities, and that large-scale over-densities can be traced by LBGs. \item Our results suggest that strong \civ\ absorption systems at the end of the EoR are not related to over-densities of bright and massive (L${>}$L$^\star$) LBGs with low or no \Lya\ emission. Therefore, the environment of strong $z{\sim}5.7$ \civ\ systems is different to the examples at lower redshift ($z{\leq}3.5$). Instead, \civ\ absorption systems are found in regions dominated by LAEs, which are younger (recent star formation), fainter and lower mass systems than LBGs. This would imply that $z{\sim}5.7$ \civ\ systems trace low-to-intermediate density environments and are distant from the oldest star-forming regions of each field. \item We report one LAE that lies at ${\sim}212{\it h}^{-1}$ physical kpc from the line-of-sight in the J1030+0524 field. The close proximity suggests the faint galaxy is the progenitor of one of the two \civ\ systems in this sight-line. This result supports the idea that LAEs are the most favourable candidates for the physical origin of the \civ\ systems at $z{\sim}5.7$. Spectroscopic redshift determination is required to test a galaxy-absorption system connection and we will address this topic in more detail in a forthcoming paper. \item The results support the idea that the detection of high ionization absorption systems after the EoR depends on the fluctuations of the ionizing flux density. In this case, the excess of LAEs found in the field J1030+0524 is related to high levels of ionizing flux that allow the detection of \civ . This result implies that faint galaxies are important sources of ionizing radiation, in agreement with many other findings in the literature that propose that faint galaxies are the primary sources driving the end of cosmic hydrogen reionization. \end{itemize} More work on the environment of metal absorption lines in the EoR is needed. Recently, \oi\ absorption systems have been proposed as probes of the physical state of neutral filamentary over-densities in the later stages of the EoR \citep{keating2014}. If this is the case, at $z{\geq} 5.7$ strong \civ\ absorption system with no low ionization metal lines are the complement to \oi\ absorption systems. It could be possible to combine low ionization and high ionization metal absorption lines to study the EoR, because \oi\ are expected to trace the haloes of the galaxies that produced the cosmic reionization \citep[e.g.][]{finlator2013}, whereas \civ\ are likely tracing diffuse recently ionized IGM. | 14 | 4 | 1404.7656 |
1404 | 1404.2814_arXiv.txt | Angular power spectra are calculated and presented for the entirety of the Canadian Galactic Plane Survey polarization dataset at 1.4 GHz covering an area of 1060 deg$^2$. The data analyzed are a combination of data from the 100-m Effelsberg Telescope, the 26-m Telescope at the Dominion Radio Astrophysical Observatory, and the Synthesis Telescope at the Dominion Radio Astrophysical Observatory, allowing all scales to be sampled down to arcminute resolution. The resulting power spectra cover multipoles from $\ell \approx 60$ to $\ell \approx 10^4$ and display both a power-law component at low multipoles and a flattening at high multipoles from point sources. We fit the power spectrum with a model that accounts for these components and instrumental effects. The resulting power-law indices are found to have a mode of 2.3, similar to previous results. However, there are significant regional variations in the index, defying attempts to characterize the emission with a single value. The power-law index is found to increase away from the Galactic plane. A transition from small-scale to large-scale structure is evident at $b= 9^{\circ}$, associated with the disk-halo transition in a 15$^{\circ}$ region around $l=108^{\circ}$. Localized variations in the index are found toward \ion{H}{2} regions and supernova remnants, but the interpretation of these variations is inconclusive. The power in the polarized emission is anticorrelated with bright thermal emission (traced by H$\alpha$ emission) indicating that the thermal emission depolarizes background synchrotron emission. | Magnetic fields permeate the Interstellar Medium (ISM) of the Milky Way. They carry significant energy \citep{beck11} and play important roles in interstellar processes. On the large scale, magnetic fields somehow mirror the structure of the Galaxy, approximately following the spiral arms \citep{brown10} and they determine the thickness of the disk by supporting it against gravity. Within the arms, on the small scale, they also counter gravity and thereby regulate star formation. They participate in the return of radiation and matter from stars to the ISM through stellar winds and supernova explosions. In supernova blast waves, magnetic fields are responsible for the acceleration of relativistic particles, and the large-scale fields ultimately control the distribution of these particles in the disk and halo. One of the best tracers of the magnetic field is synchrotron radio emission because it is generated throughout the Galaxy. The polarized fraction of the emission is particularly rich in information, since the polarization angle carries the imprint of the field at the point of origin, and is further affected by Faraday rotation as it propagates through the magnetized ISM. Indeed, Faraday rotation effects dominate the appearance of the polarized sky at decimeter wavelengths. It should, then, be possible to use images of polarized radio emission to understand the distribution, strength and structure of the Galactic magnetic field. \citet{landecker12} reviews the available data sets, discusses their limitations, and what has been learned to date from radio polarization data about the role of magnetic fields in ISM processes. There are several approaches to describing the polarized sky. First, there is the classical approach of searching for objects, or searching for polarization manifestations of objects seen in other tracers (for example \ion{H}{2} regions or stellar-wind bubbles). A second possibility is to search for the products of various depolarization phenomena, differential Faraday rotation (or depth depolarization), or beam depolarization arising from internal or external Faraday dispersion within the ISM \citep{burn66,soko98} and thereby to derive physical conditions from these manifestations. In this paper we take a third approach, using statistical methods to examine the spatial scales of polarization structures. Such analysis has been done before with focus on calculating the angular power spectra or the structure functions of the polarized emission \citep{tucci00,giar01,tucci02, bruscoli02,giar02,have03,have04,have06, have08,lapo06,carr05,carr10} . More recently, the work of \citet{gaensler11} demonstrated that the statistics of the gradient of polarized emission provided clear measurements of the magnetoionic medium. Structure functions and power spectrum analyses nominally yield equivalent information from the images. Structure functions are computationally intensive for large maps but can be employed in cases where large fractions of the domain lack data as is often the case for rotation measure data toward point sources. In contrast, angular power spectra can leverage computationally efficient Fourier analysis but require continuously sampled data. Below, we present an angular power spectrum analysis of the continuously sampled polarization maps from the Canadian Galactic Plane Survey. This investigation presents an unprecedented spatial dynamic range by including both aperture-synthesis and single-antenna data to cover all structural scales from the largest to about one arcminute. Furthermore, the area of sky is large, over 1000 square degrees along the northern Galactic plane. Finally, we adopt a model and processing which explicitly accounts for instrumental effects and the presence of point sources in the data. This work expands on the treatment first presented in \citet{stutz-thesis}. In Section \ref{data} we give a brief description of the data used in this work and outline the technique used in our analysis. We present maps of the spectral indices in Section \ref{sn:spectral_index_results}. In Section \ref{discussion} we compare our results with other work of this kind. | We present a spatial power spectrum analysis of the polarized emission from the Galactic plane as mapped in the CGPS by \citet{landecker10}. The CGPS is unrivalled in its combination of Galactic longitude coverage, angular resolution, and full inclusion of a wide range of angular scales. This power spectrum analysis is the largest such analysis to date, and we are able to resolve significant spatial variations in the index of the power spectrum at a resolution of 2.67$^{\circ}$. We have examined instrumental effects and spurious contributing signals and developed a model which accounts for these contaminants. We find significant, large-scale variations in the slope of the power spectrum associated with different features of the interstellar medium. There are pronounced shifts toward large-scale structure in the direction of \ion{H}{2} regions, which are likely the result of the Faraday rotation eliminating polarized signal from behind the ionized region. We find no difference between the spatial power spectrum index calculated for the Stokes $Q$ and $U$ data and that calculated for the polarized intensity. We interpret this similarity as evidence that the structure in the 1.4 GHz polarized emission arises mostly from Faraday depolarization effects. Lines of sight with large Faraday depths have contributions from many different regions and the emission is Faraday rotated in transmission, leading to a change in the structure. Additionally, there are sharp changes in the slope of the power spectrum at high Galactic latitudes. These changes can represent both a change in the structure of the emitting medium and short lines of sight through the disk arising above $b>10^{\circ}$ in the 15$^{\circ}$ longitude range centered at $l\sim 108^{\circ}$. Finally, we note an anticorrelation between the brightness of the diffuse polarized emission and the Stokes $I$ 21-cm continuum emission as well as the H$\alpha$ emission. The polarized sky still holds much to be discovered, and a full classification of the features in the polarized sky may soon be possible as large surveys such as the CGPS reveal polarization structure on all scales. Decoupling small-scale magnetic field variation and electron densities from the regular component of the magnetic field remains difficult at 1.4 GHz. Recent progress in parameterizing the resulting emission properties from generalized magnetohydrodynamic turbulence theory \citep[e.g.,][]{lp12} offers some possibility for interpreting such data. However, the theoretical framework currently assumes constant electron density and will need generalization to include fluctuations in electron density to capture Faraday rotation effects and thus be directly applicable to these data. The results of our angular power spectrum analysis find real features captured in the structure of the polarized emission, and we expect that these results can soon be translated into a characterization of the turbulent magneto-ionic medium. | 14 | 4 | 1404.2814 |
1404 | 1404.0811_arXiv.txt | We compare predictions of cooled masses and cooling rates from three stripped-down Semi-Analytic Models (SAMs) of galaxy formation with the results of N-body+SPH simulations with gas particle mass of $3.9 \times 10^6$ {\hMsun}, where radiative cooling of a gas of primordial composition is implemented. We also run a simulation where cooling is switched on at redshift $\sim$2, in order to test cooling models in a regime in which their approximations are expected to be valid. We confirm that cooling models implemented in SAMs are able to predict the amount of cooled mass at $z=0$ to within $\sim$20 per cent. However, some relevant discrepancies are found. (i) When the contribution from poorly resolved halos is subtracted out, SAMs tend to under-predict by $\sim$30 per cent the mass that cools in the infall-dominated regime. (ii) At large halo masses SAMs tend to over-predict cooling rates, though the numerical result may be affected by the use of SPH. (iii) As found in our previous work, cooling rates are found to be significantly affected by model details: simulations disfavour models with large cores and with quenching of cooling at major mergers. (iv) When cooling is switched on at $z\sim2$, cold gas accumulates very quickly in the simulated halos. This accumulation is reproduced by SAMs with varying degrees of accuracy. | \label{introduction} The formation of galaxies within the $\Lambda$CDM cosmological model involves a large number of physical processes, many of which are still poorly understood. The hierarchical build-up of DM halos, resulting from the non-linear evolution of primordial perturbations under their own gravity, provides the backbone of the whole process of galaxy formation. Thanks to advances in N-body techniques and to the very accurate constraints available on cosmological parameters \citep[e.g.,][]{Planck13}, the evolution and properties of DM halos can be computed with very good accuracy \citep[e.g.][]{Reed13}. Despite baryonic processes are known to affect the build-up of DM halos to some extent \citep[e.g.][]{Stanek09, Duffy10, Saro10, Cui12}, the modeling of baryonic physics still provides the major source of uncertainty. A purely collisionless simulation thus remains a good starting point for a galaxy formation model. Galaxy formation in the cosmological context has been historically addressed with two main tools. SAMs are applied to the backbone of DM halo merger trees, taken from an N-body simulation or equivalent tools \citep[e.g.][]{Monaco13}. They use a set of simplified or phenomenological models to describe the various processes that involve baryons. Hydrodynamic simulations consist of numerically solving the equations of motion of DM and gas particles in a realization of a cosmological volume. Two fundamental processes take place on scales that are within reach of presently available simulations. Gravity and hydrodynamic forces are responsible for infalling of gas and heating to the halo virial temperature. Radiative cooling down to $\sim10^4$ K, which is computed based on the density and temperature of the heated gas, is responsible for the condensation of gas into the inner regions of the halo. There, the gas can fragment into stars and thus form a galaxy, but star formation and all the processes triggered by it (stellar feedback, chemical evolution, galaxy winds, black hole seeds), not to mention the accretion of gas onto black holes, take place at much smaller scales. To properly follow these processes, the range of scales that must be resolved (from sub-pc scale of star formation to cosmological scales) is so vast and the involved physics so complex that their effects need to be treated through simplified, sub-resolution models. The modeling of cooling in SAMs is based on the assumption that the gas settles into a hot atmosphere in hydrostatic equilibrium within the potential well of the DM halo. This allows the computation of a cooling time as a function of radius. Whenever the central cooling time is longer than the halo dynamical time \citep[``cooling-dominated regime'';][]{Rees77,Binney77,White91}, the deposition of cold gas into the central galaxy is assumed to be regulated by cooling; otherwise, the timescale for gas to condense into the galaxy is assumed to be of the order of the halo dynamical time (``infall-dominated regime''). Using hydrodynamical simulations that included radiative cooling and star formation (but no efficient stellar feedback), \cite{Keres05} reported that at $z\ga2$, or at any redshift for halos smaller than $\sim10^{11}$ {\msun} \citep[see also][]{Dekel06}, gas tends not to shock to the virial temperature but to condense directly into the galaxy via a cold flow. As a caveat, the deposition of gas through cold flows is known to depend on the hydrodynamic scheme \citep{Nelson13} and to be affected by feedback processes connected to galaxy formation \citep{Benson11,Murante12}. To check to what level the two techniques, SAMs and hydrodynamical simulations, give a consistent description of the deposition of cold mass into the ``galaxies'', many authors \citep{Benson01,Yoshida02,Helly03,Cattaneo07,Viola08,Saro10,Lu11,Hirschmann12} performed comparisons of the predictions of SAMs and simulations. All of these papers presented comparisons performed using stripped-down SAMs, where all processes beyond gas cooling were switched off and simulations where either no star formation or no (effective) feedback from star formation was present. The first papers \citep{Benson01,Yoshida02,Helly03,Cattaneo07} compared one SAM with simulations and reported that SAMs are able to reproduce the gas mass that cools in DM halos to a level, to cite \cite{Benson01}, {\it ``better than a pessimist might have expected''}. More recent papers focused on some discrepancies between the two kinds of modeling. \cite{Viola08} simulated cooling in isolated, hydrostatic DM halos and compared the resulting cooling mass with two models: an implementation from \cite{Cole00} and the one used in the MOdel of the Rise of Galaxies And Agn \citep[MORGANA][]{Monaco07}. They found that the former model underestimates the amount of cooled mass when cooling is suddenly switched on, while the latter model produced a much better fit. \cite{Saro10} compared the galaxy populations in a massive galaxy cluster predicted by SPH simulations with those from the SAM described in \cite{DeLucia07}. Both models included gas cooling and a simple prescription for star formation (as we will do in this study). The resultant object-by-object comparison revealed important differences between the two methods. In particular, the star formation history of BCGs in the SPH simulations is characterized by a more prominent high redshift peak and lower level of recent star formation with respect to predictions from the SAM. As noticed by \cite{Saro10}, this is due to the assumption of an isothermal gas density distribution for the hot gas in the SAM, which differs from the actual gas distribution in the simulation. In \citet[][hereafter Paper I]{DeLucia10} we compared the results of stripped-down versions of three independently developed SAMs, ``Durham'' \citep{Cole00,Benson01}, ``Munich'' \citep{DeLucia07,Saro10} and Morgana \citep{Monaco07}. We ran them on the same set of merger trees taken from the Millennium simulation \citep{Springel05}. We concentrated on two mass scales, selecting 100 halos as massive as the Milky Way at $z=0$ and 100 as abundant as SCUBA galaxies at $z\sim2$. We found that the resulting cold masses and cooling rates were in good agreement at the Milky Way mass scale, but we noticed that the ``Durham'' model predicted systematically lower cooling rates in halos of the SCUBA set. We showed that this difference is again due to different assumptions on the gas profile, which is isothermal in the ``Munich'' model and cored in the ``Durham'' model. A comparison of the results of the same models in a configuration where star formation and stellar feedback is active was presented in \cite{Fontanot13}. More recently, \cite{Lu11} compared the results of several implementations of semi-analytic cooling models with 1D simulations of both an isolated halo and an accreting halo, and with a simulation of a cosmological volume including inefficient stellar feedback. They reported that different models give predictions of gas accretion rates that can vary by up to a factor of 5. With respect to simulations, semi-analytic models under-predict gas accretion rates in small halos and over-predict them in massive halos. They also showed that the predicted cooling-dominated and infall-dominated regimes do not closely correspond to the regimes where cold flows or hot atmospheres were found to dominate in their simulation. A similar setting was used in \cite{Hirschmann12}, with the aim of comparing the predictions of simulations and SAMs when feedback and star formation are used. They used a set of resimulations of dark-matter halos \citep[see][]{Oser10} run with the {\sc gadget} code, but they implemented primordial cooling and inefficient stellar feedback, and compared the results with several versions of the model of \cite{Somerville08}, including a stripped-down one with no stellar feedback. This work shows that, while stripped-down SAMs and simulations agree rather well (with some discrepancies consistent with those found in the papers cited above), SAMSs predict that the deposition of cold gas takes place mostly in the cooling-dominated regime, while the contribution from simulated cold flows is significant at all redshifts and dominant at $z\ga1-2$. To perform an accurate comparison of simulations with SAMs, the SAMs should be run on merger trees extracted from the same simulation, as was done in \cite{Yoshida02}, \cite{Helly03}, \cite{Cattaneo07}, \cite{Saro10} and \cite{Hirschmann12} but not in \cite{Benson01} and \cite{Lu11}. Proper time sampling of merger trees is also relevant: \cite{Benson12} demonstrated that a SAM gives a convergent description of the formation of galaxies if merger trees are sampled at least $\sim128$ times, a factor of two higher than, e.g., the time sampling of the Millennium simulation. Finally, the condensation of gas into the central ``galaxy'' is governed not only by cooling but also by the time required for progenitor halos to merge with the central object. As demonstrated in Paper I, different SAMs do not use consistent predictions of galaxy merging times, and this should be properly taken into account. A further important issue is related to the runaway nature of cooling of self-gravitating gas. When no feedback from stars is present, gas (over-)cools in the small DM halos that form at high redshift, so cooling takes place in poorly resolved halos, and in the infall-dominated regime where the cooling models we are aiming to test do not apply. Increasing the resolution would imply resolving smaller halos at higher redshift, thus worsening the over-cooling problem. Results showing a reasonable agreement of SAMs and simulations at $z=0$ may simply reflect the fact that both predict that most baryons have (over-)cooled. We are convinced that a satisfactory numerical test of semi-analytic cooling models is still missing. An ideal test should have the following characteristics: (i) the study should be limited to cooling in well resolved halos; (ii) a clear assessment of the accumulation of cold gas in the cooling-dominated regime, independent of (over-)cooling at high redshift, should be performed; (iii) the analysis should include several SAMs; (iv) SAMs should be run on merger trees extracted from the same simulation; (v) time sampling should be fine enough to guarantee convergence of SAM predictions; (vi) measured cooling rates should be independent of the accuracy with which merger times are predicted by SAMs. In this paper we present a comparison of SAMs and numerical (SPH) simulations that meets all the above criteria. Finding a numerical solution of cooling in cosmological halos is not a straightforward task. To face this problem we use the {\sc gadget} Tree-PM$+$SPH code. The specific implementation used in this paper is shortly described in Section~\ref{section:code}. While this project was in progress, \cite{Keres12} published a comparison of {\sc gadget} with the new moving-mesh code {\sc arepo} \citep{Springel10}, run on the same initial conditions and with a setting similar to that of \cite{Lu11}, though at higher resolution. They reported that galaxy stellar mass functions obtained with the two hydrodynamic schemes tend to be quite similar in the low-mass end but exhibit significant differences in the high mass end. They traced the origin of this difference to the different efficiencies of dissipative heating from gas accretion onto halos, which cause cooling to be partially offset in SPH with respect to the moving--mesh hydrodynamic scheme. The issue was readdressed by \cite{Nelson13}, who showed that the strucuture of cold filaments penetrating into hot halos is very different for the two hydro solvers. While a detailed comparison of different hydrodynamical schemes is beyond the aims of this paper, we stress that some of our results might be affected by the use of SPH. We will comment on this below. As in Paper I, we use here three stripped-down SAMs. The model of \cite{DeLucia07}, denoted the {\it Munich} model in Paper I, will be called here {\del}, while {\mor} of \cite{Monaco07} will retain its acronym. In place of the {\it Durham} model we use the highly modular {\gal} model of \cite{galacticus} in a configuration that closely resembles that of \cite{Bower06}. We run the three SAMs on merger trees extracted from a collisionless N-body simulation, and compare them with the results of a simulation run on the same initial conditions but including gas hydrodynamics and radiative cooling for a primordial composition. We set merger times to zero in SAMs, and compute cooled masses in simulations by summing over all substructures in simulated FoF halos. We run the hydrodynamical simulation in two configurations: we allow cooling to be active from the start, or we run the simulation without radiative cooling down to redshift $z\sim2$, and then switch cooling on. This second configuration allows us to test cooling models exactly in the range of redshift and halo mass where their approximations are expected to be valid: when cooling is switched on, no (over-)cooling has taken place in the infall-dominated regime and all the baryons associated with halos are in hot atmospheres; the contribution of cooling from small halos (that are poorly resolved and where gas mostly cools in the infall-dominated regime) is much smaller. We use a relatively small box (36 \hMpc on a side, 50 Mpc for $h=0.72$) sampled with $512^3$ DM particles and an equal number of gas particles, and use a force resolution of 1.5 comoving \hkpc. With these choices, we prioritize resolution over statistics and test for the first time cooling at a resolution that is sufficient to resolve the morphology of a galaxy when star formation and feedback are properly taken into account \citep[e.g.][]{Scannapieco12}. The DM halo masses we test range from small galaxies ($3\times10^{11}\ {\rm M}_\odot$) to rich galaxy groups ($5\times10^{13}\ {\rm M}_\odot$). Merger trees have been sampled at 128 time-steps \citep[uniformly in the log of scale factor;][]{Benson12}, with the time interval between two snapshots roughly corresponding to half the dynamical time of DM halos. Moreover, following \cite{Viola08} and \cite{Saro10} we use a ``star formation'' algorithm to remove cooled gas particles from hydrodynamics, with the result of speeding up the simulation and strongly reducing numerical artifacts at the interface of cold and hot phases. We will be mainly concerned with cooling rates and cooled masses, neglecting for the time being whether gas has cooled on the main substructure of the halo or on a satellite. Other important issues, like the density profiles of gas in cooling halos, the quantification of cooling on non-central galaxies, or the delineation between cold-flow and hot-flow modes, will be addressed in future works. This paper is organized as follows. Section~\ref{section:sim} describes the simulations run for this project and the post-processing analysis used to obtain cooling rates and cooled masses. Section~\ref{section:sam} presents the three SAMs used in the paper. Section~\ref{section:results} reports the comparison of results from simulations and SAMs. Finally, Section~\ref{section:comparison} compares the results with those presented in previous papers, and Section~\ref{section:discussion} gives a summary of the main results and a discussion. \begin{figure} \centering{\includegraphics[width=.45\textwidth]{mah0.eps}} \caption{Mass accretion history of the main progenitor of Halo 0, the most massive halo in our box. Black continuous line: {\mtwoh} from the PUREDM simulation. Blue dotted line: {\mfof} from the PUREDM simulation. Green dashed line: {\mtwoh} from the COOL simulation. Red dot-dashed line: {\mtwoh} from the COOLZ2 simulation. Vertical dashes denote major mergers with mass ratios of merging halos larger than 1:10, the length being proportional to the mass ratio.} \label{fig:mah0} \end{figure} | \label{section:discussion} We have tested cooling models embedded in three widely used SAMs \citep{galacticus,Monaco07,DeLucia07} by comparing their predictions to N-body hydrodynamical (SPH) simulations of radiative cooling in cosmological DM halos. With respect to previous papers that performed similar tests \citep{Benson01,Yoshida02,Helly03,Cattaneo07,Viola08,Saro10,Lu11,Hirschmann12}, our simulations are improved in several ways: (i) we used a mass and force resolution sufficient to fully resolve the cooling region in all halos larger than $5\times10^{10}\ {\rm M}_\odot$; (ii) we computed cooling rates and cooled masses subtracting out the contribution of cooling in poorly resolved halos; (iii) by also running a simulation where cooling is switched on at $z\sim2$, we were able to test cooling models exactly in the redshift range where they are expected to be valid, with no influence from high-redshift over-cooling; (iv) using a suitable formulation of SPH and a ``star formation'' algorithm \citep[as in][]{Viola08,Saro10} to treat cooled particles as collisionless, we were able to limit numerical cooling and speed up the simulation considerably. As a word of caution, we recall that the simulations that we compare to SAMS have been carried out using an SPH hydrodynamical solver. Significant differences have been reported for the amount of star formation predicted by a simulation based on the {\sc arepo} code that uses an Eulerian scheme \citep{Keres12,Nelson13}, so some of our results, especially those relative to massive halos, may be affected by the specific hydro solver we use. We confirm that, overall, cooling models are able to approximately predict the correct amount of cooled mass. When cooling is active since the start of the simulation (the COOL simulation), median values are recovered at $z=0$ to within 20 per cent and with a similar scatter. At higher redshift, median values agree to within 40 per cent. For individual halos, the worst discrepancies are rarely larger than a factor of two. However, when the cooled mass in the COOL simulation is limited to properly resolved halos, cooling models in SAMs underestimate the amount of cooled mass in the infall-dominated regime by $\sim20-40$ per cent at $z=2$. This difference is much less visible when the contribution of poorly resolved halos is included, as the numerical underestimate happens to compensate the theoretical one. In some models ({\del} and {\mor}, and {\gal} when an isothermal gas profile is used), cooled masses for more massive halos tend to be higher than those found in the simulations at $z=0$. While this difference is found in the same range of halo masses where Eulerian and Lagrangian codes give different results \citep{Keres12}, this confirms the findings of \cite{Saro10} (see also \citet{Hirschmann12}), who compared predictions from the {\del} model with cooling rates from a simulation with very similar setting as our COOL simulation. This is a very relevant point: late cooling in massive halos deposits mass in the central galaxy, which is typically a bright elliptical galaxy. The stellar populations of these galaxies are observed to be very old \citep[e.g.][]{Thomas05}, so quenching this cooling is necessary for any successful galaxy formation model. AGN feedback in the so-called radio mode \citep{Croton06,Bower06} it typically advocated to produce this quenching; however, the fraction of galaxies with detectable radio emission associated with the AGN activity necessary to perform this quenching is higher than what it is observed and shows the wrong dependence as a function of halo mass \citep{Fontanot11}. As noticed also in Paper I, a cooling model that produces too strong a cooling flow at late times would require stronger AGN feedback to maintain quenching. For the {\del} model, \cite{Saro10} showed that the higher cooling rates with respect to results from simulations are due to the assumption of isothermal gas density profile. The same trend is shown by {\mor}, which assumes a hydrostatic density profile with a shallow inner slope. Clearly, the different type of integration used in the {\mor} cooling model causes the same trend without assuming a singular profile. However, before reaching a firm conclusion on this point it is necessary to fully understand the role of the hydrodynamic scheme. Consistently with the results of Paper I, the {\gal} model with a cored gas profile under-predicts cooling flows in massive halos at late times with respect to simulations. This prediction depends significantly on the assumed gas density profile: using an isothermal gas density profile generates predictions that are very similar to the {\del} model and in much better agreement with the simulation, while large core radii are strongly disfavoured. Cooling rates found in the simulations are recovered in the models with larger scatter, about a factor of two. Scatter is larger for the {\mor} model, and part of it is due to the assumption in {\mor} that cooling is quenched during major mergers. We find no such trend in the simulations, and this is likely due to the persistence of cooled condensations during mergers. When the assumption of quenching at major mergers is dropped, {\mor} predicts cooling rates with less scatter, but it still larger than the other models. \begin{figure} \centering{\includegraphics[width=.45\textwidth]{scattergrams_morganaMM.eps}} \caption{Cooled masses and cooling rates for all halos in the COOL simulation at $z=0$. Results of the {\mor} model are shown for two different assumptions on the behavior at major mergers. Left panels: standard cooling model; right panels: cooling is not quenched at major mergers.} \label{fig:morgana2} \end{figure} Comparing models and simulations when cooling is switched on at $z \sim 2$ probably represents the cleanest test of the cooling model. In this case, in both the simulation and models, the baryons associated with halos are not pre-processed by runaway cooling, they are all located in the hot atmospheres when cooling is switched on. Also, the contribution of cooling from poorly resolved halos is very small for several halo dynamical times, and the deposition of cold gas is much less affected by all the numerical issues connected with the infall-dominated regimes. In our COOLZ2 simulation, the cooled mass is found to accumulate rapidly. At $z=1.5$, {\mor} is able to predict the right amount of cooled mass, though with substantial scatter; {\del} is biased low by $\sim20-30$ per cent; and {\gal} is low by a factor of 2, even when an isothermal gas profile is assumed. This confirms the findings of \cite{Viola08}, obtained with static halos and using gas profiles that closely matched the simulated ones just before cooling is switched on. Although switching on cooling at a given redshift provides a clean test of cooling models, one can wonder whether such conditions occur in realistic cases, and therefore, whether the difference among models, which is much less evident in the COOL simulation, should be a cause for concern. When cooling is active since the beginning, most baryons have already cooled by $z=2$ (especially in relatively small halos). The effect of this overcooling is visible, for instance, in Fig.~\ref{fig:trees}, where cooling rates in the example halos 0 and 1 hardly exceed the value of $\sim200$ M$_\odot$ yr$^{-1}$. These deposition rates can translate at best into star formation rates of the same order, which would be typically lower than the several hundreds M$_\odot$ yr$^{-1}$ measured for massive star forming galaxies at the same redshift. In the COOLZ2 simulation, cooling rates are higher by a factor of $\sim5$ when cooling is suddenly switched on. Feedback from massive stars and accreting black holes is responsible for limiting overcooling at high redshift, and this makes more gas available at lower redshift. Moreover, as commented in Section~\ref{section:majormergers}, halo mergers or, more likely, feedback from star formation and AGN will likely be responsible for episodic quenching of catastrophic cooling, so the setting of the COOLZ2 simulation may be a good approximation for cooling flows in massive halos at the peak of cosmic star formation, after a quenching event. This is the first time that several cooling models run on the same merger trees are compared with a cosmological hydrodynamical simulation. Despite the simplified setting used in these simulations, we believe that they provide an important benchmark test for cooling models embedded in SAMs. Indeed, while energetic feedback from stars and AGN, which almost certainly plays a crucial role in shaping the properties of galaxies, is the most important contributor to the variance among model predictions \citep{Fontanot13}, an accurate calibration of the condensation of gas in the central galaxy is desirable to remove unwanted sources of inaccuracies. Merger trees and results from the simulations presented in this paper are available to interested modelers upon request. | 14 | 4 | 1404.0811 |
1404 | 1404.0166_arXiv.txt | {In this first chapter we present the properties of the most massive stars known by the end of 2013. We start with a summary of historical claims for stars with masses in excess of several hundreds, even thousands of solar masses. We then describe how we determine masses for single stars. We focus on the estimates of luminosities and on the related uncertainties. We also highlight the limitations of evolutionary models used to convert luminosities into masses. The most luminous single stars in the Galaxy and the Magellanic Clouds are subsequently presented. The uncertainties on their mass determinations are described. Finally, we present binary stars. After recalling some basics of binary analysis, we present the most massive binary systems and the estimates of their dynamical masses. } | \label{s_conc} In this chapter we have presented the observational evidence for the existence of very massive stars. Mass estimates of single stars are mainly obtained from the conversion of luminosities to evolutionary masses. We have highlighted the uncertainties in the determination of luminosities: crowding, accurate photometry, distance, extinction, atmosphere models all contribute to render uncertain luminosity estimates. The other source of error comes from evolutionary tracks. Different calculations produce different outputs depending on the assumptions they are built on. Even if the luminosity was perfectly well constrained, its transformation to masses relies on the predictions of evolutionary models. With these limitations in mind, there are several stars that can be considered as good candidates for a VMS status. They are manily located in the massive young clusters NGC~3603, R136 and the Arches. In R136, the brightest members may reach initial masses higher than 200 \msun. In the other two clusters, masses between 150 and 200 \msun\ are not excluded. A few binary systems may also host stars with masses in excess of 100 \msun. NGC~3603 A1 seems to be the best candidate, with a M $\sim$ 115 \msun\ primary star, but a better analysis of the light curve is needed to refine the analysis. In conclusion, very massive stars may be present in our immediate vicinity. They usually look like WN5-9h stars, i.e. hydrogen rich mid to late WN stars. Super star clusters -- the best places to look for VMS -- being impossible to resolve with the current generation of instruments, these local VMS have to be re-observed and re-analyzed in order to minimize the uncertainties involved in their mass determination. This is important to understand the upper end of the initial mass function and the formation process of massive stars in general. \begin{acknowledgement} The author thanks Paul Crowther for discussions on the mass determination of the R136 stars. \end{acknowledgement} | 14 | 4 | 1404.0166 |
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1404 | 1404.4059_arXiv.txt | {It has been suggested that the bow shocks of runaway stars are sources of high-energy gamma rays (E\,>\,100\,MeV). Theoretical models predicting high-energy gamma-ray emission from these sources were followed by the first detection of non-thermal radio emission from the bow shock of \bd and non-thermal X-ray emission from the bow shock of AE Aurigae.} {We perform the first systematic search for MeV and GeV emission from 27 bow shocks of runaway stars using data collected by the Large Area Telescope (LAT) onboard the \textit{Fermi Gamma-ray Space Telescope (Fermi)}.} {We analysed 57 months of \lat~data at the positions of 27 bow shocks of runaway stars extracted from the Extensive stellar BOw Shock Survey catalogue (E-BOSS). A likelihood analysis was performed to search for gamma-ray emission that is not compatible with diffuse background or emission from neighbouring sources and that could be associated with the bow shocks.} {None of the bow shock candidates is detected significantly in the \lat~energy range. We therefore present upper limits on the high-energy emission in the energy range from 100\,MeV to 300\,GeV for 27 bow shocks of runaway stars in four energy bands. For the three cases where models of the high-energy emission are published we compare our upper limits to the modelled spectra. Our limits exclude the model predictions for \zetaoph~by a factor $\approx 5$. } {} | Runaway stars with strong winds can produce bow shocks in the surrounding interstellar medium (ISM) when moving supersonically with respect to the material. The runaway stars sweep up the ISM in the direction of motion, and arc-shaped features develop ahead of the stars. Thermal emission from many bow shocks of runaway stars has been detected at infrared wavelengths. The mid- to far-infrared radiation originates in the dust that is swept up by the supersonic movement of the stars through the ISM and heated by the stellar radiation, as well as by the radiation from the shocked gas. Stellar bow shocks were discovered by \cite{vanBuren88} using data from the \textit{Infrared Astronomical Satellite} (IRAS), and the first survey was performed by \cite{vanBuren95}. The most recent survey of bow shocks of runaway stars is the Extensive stellar BOw Shock Survey catalogue \citep[ ][E-BOSS]{eboss}. It summarizes a systematic search for bow shocks around runaway OB stars in the newest infrared data releases, mainly using data from the Midcourse Space eXperiment (MSX) and the Wide-field Infrared Survey Explorer (WISE). Their search around 283 early-type stars, selected to be closer than 3\,kpc, results in a sample of 28 bow shock candidates. Bow shocks can thus be detected around roughly 10\% of the runaway OB stars. \cite{eboss} do not find any correlation between the detection of a bow shock and either stellar mass, age or position. Introducing a non-thermal emission model, \cite{bd_benaglia} suggest that bow shocks are emitters of high-energy gamma rays (HE, E\,>\,100\,MeV). Moreover, it was shown that the emission could be detectable by current gamma-ray experiments \citep{Valle_model_zeta}. Bow shocks can accelerate particles up to relativistic energies via Fermi shock acceleration. \cite{bd_benaglia} have detected non-thermal radio emission from the bow shock of \bd, which is produced by accelerated electrons that emit synchrotron radiation. The same electrons upscatter photons from the stellar and dust photon fields via the inverse Compton process, which leads to high-energy gamma-ray emission. The search for an X-ray counterpart of the bow shock of \bd~performed by \cite{terada_bd} using a 99\,ks exposure with \textit{Suzaku} only resulted in upper limits. They measure an enhanced X-ray count rate in the bow shock region, but taking the systematic errors on the non X-ray and cosmic-ray background into account, they argue that the X-ray count rate in the bow shock region is compatible with that of the background region. The first detection of non-thermal X-ray emission from a bow shock produced by a runaway star was recently claimed by \cite{ae_aurigae_LopezSantiago} for AE Aurigae (HIP 24575). Although the XMM-\textit{Newton} data do not allow distinguishing between a very hot thermal and a non-thermal origin, the latter seems more likely for two reasons: there is no counterpart in the infrared and optical wavelengths for the putative thermal source, which could be a foreground or background stellar object, and the temperature would have to be extremely high. The good spatial correlation of the X-ray and IR emission from the bow shock also promotes the bow shock hypothesis. The first potential detection of a bow shock from a runaway star in high-energy gamma rays was published by \cite{Valle_pulsar}. The bow shock of HD 195592, listed in the \eboss~as HIP 101186, is spatially coincident with the \fermi~source 2FGL~J2030.7+4417 \citep{2fgl}. Under some energetic assumptions \cite{Valle_pulsar} conclude that 2FGL~J2030.7+4417 might be associated with the bow shock from HIP 101186. However, this \fermi~source has been identified as a gamma-ray pulsar by \cite{Pletsch}. In the Second \fermi~Large Area Telescope Catalog of Gamma-ray Pulsars \citep{2013ApJS..208...17A}, it is listed among the pulsars with no significant off-peak emission. The absence of off-pulse emission is a clear indicator that the observed LAT photons predominantly originate in the pulsar. A possible gamma-ray signal from the bow shock of HIP 101186 is below the current sensitivity threshold of the LAT. Gamma rays from the bow shock might be detected with deeper LAT observations or by observations with future instruments like the Cherenkov Telescope Array that feature better angular resolution than the LAT. In this paper we describe the \lat~observation and data analysis of 27 bow shock candidates in Section\,2. The results of the analysis of 57 months of \lat~data are presented in Section\,3, which also includes a comparison of the calculated \lat~upper limits with published model predictions for the three cases where these are available. We conclude with some implications of the non-detections and a short look at which instruments might be able to detect or further constrain the high-energy emission from the bow shocks of runaway stars. | We performed the first systematic study to search for high-energy gamma-ray emission from the bow shocks of runaway stars collected in the \eboss. There is no evidence for high-energy gamma-ray emission in any of the cases. The existing model is challenged by the presented upper limits for one of the bow shock candidates. The spectral energy distributions for the non-thermal emission of bow shocks, computed by \cite{Valle_model_zeta}, mainly depend on the assumptions for the particle acceleration, the magnetic field, and the dust emission. One way to interpret our results is that the particle acceleration is not efficient enough, and the maximum energies of the accelerated electrons are less than predicted or that the photon density provided by the dust is lower. Another explanation is that the magnetic fields in these systems are not as turbulent as in other non-thermal emitters like pulsar wind nebulae and supernova remnants \citep[as also pointed out in][]{terada_bd}. Further analyses with more data and improved event selection and calibration leading to an improved sensitivity of the LAT \citep[as e.g. outlined in][]{2013arXiv1304.5456B} might constrain the model predictions for \bd. Also, long exposures with current ground-based Cherenkov telescope systems and observations with future Cherenkov telescopes like the Cherenkov Telescope Array \citep[see e.g.][]{Hinton20131}, which will be more sensitive than the \lat~above $\sim$100\,GeV, will be able to test the predictions. Recently, \cite{2014arXiv1401.3255D} have shown that runaway massive stars can be variable gamma-ray sources on time scales of one to a few years with significant intensity variations between the high and the low states. The variability time scale depends on the size of the density inhomogeneities of the traversed ambient gas and the stellar velocity. A dedicated search for such time variations might help improve the sensitivity of future bow shock searches. The upper limits presented in this first systematic search provide important constraints on the nature of particle acceleration processes in bow shocks and the environment in which they happen. It therefore helps to improve future emission models for these objects. \\ \textbf{Acknowledgements} The \textit{Fermi}~LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT, as well as scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States, the Commissariat \`a l'Energie Atomique, and the Centre National de la Recherche Scientifique / Institut National de Physique Nucl\'eaire et de Physique des Particules in France, the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK), and Japan Aerospace Exploration Agency (JAXA) in Japan, and the K.~A.~Wallenberg Foundation, the Swedish Research Council and the Swedish National Space Board in Sweden. Additional support for science analysis during the operations phase is gratefully acknowledged from the Istituto Nazionale di Astrofisica in Italy and the Centre National d'\'Etudes Spatiales in France.\\ This publication makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration. \\ This research has made use of the SIMBAD database, operated at the CDS, Strasbourg, France. | 14 | 4 | 1404.4059 |
1404 | 1404.1483_arXiv.txt | Ultra-high energy cosmic rays interacting with the radiation fields in the universe cause electromagnetic cascades resulting in a flux of extragalactic gamma rays, detectable to some 100 GeV. Recent precise measurements of the extragalactic gamma ray flux by Fermi-LAT, coupled with estimates of the background from active galactic nuclei of various types, allows limits to be set on the cascade component. By comparison with prediction and, making various assumptions, ie taking a particular model, limits can be set on the maximum energy to which ultra-high energy particles can be accelerated. If our model is correct, it is unlikely that the maximum energy is above 100 EeV, in turn, the apparent `GZK' cut-off in the measured ultra-high energy spectrum could instead be due to a fall-off in the intrinsic emergent particle spectrum. However, it is not possible to be dogmatic at the present time because of uncertainty in many of the parameters involved. We have used recent estimates of the range of parameters and have found that although our model has parameters in the allowable ranges the uncertainties are so large that our result is not unique, although the method is satisfactory. The result must thus, so far, be taken as an indication only. | Some decades ago [1] it was pointed out that there is a constraint on the energy spectrum of the ultra-high energy cosmic ray (UHECR) intensity caused by the electromagnetic cascade of photons and electrons initiated by the initial interaction of the UHECR with the cosmic microwave background (CMB). Later interactions with both the CMB and the starlight and infra-red fields cause the cascade to extend down to the MeV gamma ray region. Comparison of the expected flux for various (proton) production scenarios [2] with the then measured extragalactic (EG) gamma flux [3] allowed limits to be put on the former. With more recent estimates of the EG gamma flux by Fermi-LAT [4] and superior estimates of the contribution from unresolved sources (active galactic nuclei, AGN) [5] an improved production scenario can be derived. Our particular interest is the maximum energy achievable at the sites of acceleration, the analysis being made for both primary protons and iron nuclei. Regarding the mass composition at the highest energies, the case for heavy nuclei was made early on (see, eg, [6]) and recent analysis give some support [7,8,9]. In what follows, we start by assuming that our initial calculations [1,2] were correct and follow them through with the Fermi-LAT gamma ray spectrum [4] to establish the method and arrive at tentative conclusions. This is followed by an examination of the limits that can be put on the various input parameters, and on the consequent result using a recent analysis [9]. Of relevance is the observation by the Pierre Auger Observatory (PAO) that above 55 EeV, some 24\% of the particles come from the giant Cen-A radiogalaxy within a direction of 40 degrees [10] to a significance level of 4\%. Others [11,12] have developed theories assuming this identification. The relation of this result to the problem in hand will also be examined. | 14 | 4 | 1404.1483 |
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1404 | 1404.6576_arXiv.txt | We present a kinematic analysis of three triple stellar systems belonging to two open clusters: CPD$-$60$^\circ$961 and HD\,66137 in NGC\,2516, and HD\,315031 in NGC\,6530. All three systems are hierarchical triples with a close binary bound to a third body in a wider orbit, whose presence is detected through velocity variations of the close binary barycentre. Orbital parameters are derived from radial velocity curves. Absolute parameters for all stars are estimated assuming cluster membership. Some dynamical and evolutionary aspects of these systems are discussed, particularly the possible influence of Kozai cycles. The two systems of NGC\,2516 have similar orbital configurations with inner periods of 11.23~d and 8.70~d and outer periods of 9.79~yr and 9.24~yr. The young system HD\,315031 in the cluster NGC~6530 has an inner binary with a period of 1.37~d and a very eccentric ($e$=0.85) outer orbit with a period of 483~d. We report also radial velocity measurements of the components of the visual binary CPD$-$60$^\circ$944 in NGC\,2516. Including results from previous works, this cluster would harbor 5 hierarchical triples. Possible dynamical evolutionary scenarios are discussed. Long-term radial velocity monitoring is highlighted as strategy for the detection of subsystems with intermediate separations, which are hard to cover with normal spectroscopic studies or visual techniques. | 14 | 4 | 1404.6576 |
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1404 | 1404.6081_arXiv.txt | We investigate the tensor perturbation in the inflation model driven by a massive-scalar field in Eddington-inspired Born-Infeld gravity. For short wave-length modes, the perturbation feature is very similar to that of the usual chaotic inflation. For long wave-length modes, the perturbation exhibits a peculiar rise in the power spectrum which may leave a signature in the cosmic microwave background radiation. | Recently, the evolution of the Universe driven by a massive scalar field was investigated in Ref.~\cite{Cho:2013pea} in Eddington-inspired Born-Infeld (EiBI) gravity \cite{Banados:2010ix}. The action for this model is given by \begin{eqnarray}\label{action} S_{{\rm EiBI}}=\frac{1}{\kappa}\int d^4x\Big[~\sqrt{-|g_{\mu\nu}+\kappa R_{\mu\nu}(\Gamma)|}-\lambda\sqrt{-|g_{\mu\nu}|}~\Big]+S_{\rm M}(g,\phi), \end{eqnarray} where $\lambda$ is a dimensionless parameter related with the cosmological constant by $\Lambda = (\lambda -1)/\kappa$, and $\kappa$ is the only additional parameter of the theory. In this theory the metric $g_{\mu\nu}$ and the connection $\Gamma_{\mu\nu}^{\rho}$ are treated as independent fields (Palatini formalism). The Ricci tensor $R_{\mu\nu}(\Gamma)$ is evaluated solely by the connection, and the matter field is coupled only to the gravitational field $g_{\mu\nu}$. The matter action is in the usual form used for the chaotic inflation model \cite{Linde:1983gd} in general relativity (GR), \be \label{S:chaotic} S_{\rm M}(g,\phi) = \int d^4 x \sqrt{-|g_{\mu\nu}|} \left[ -\frac12 g_{\mu\nu} \partial^\mu\phi \partial^\nu \phi -V(\phi) \right], \qquad V(\phi) = \frac{m^2}{2} \phi^2. \ee In EiBI gravity, there exists an upper bound in pressure due to the square-root type of the action. When the energy density is high, the maximal pressure state (MPS) is achieved, for which the Universe undergoes an exponential expansion from a nonsingular initial state. It was investigated that this MPS is the past attractor from which all the classical evolution paths of the Universe originate. Although the energy density is high in the MPS, the curvature scale remains constant since the Hubble parameter becomes $H_{\rm MPS} \approx 2m/3$. Therefore, quantum gravity is not necessary in describing the high-energy state of the early universe. The MPS is unstable under the global perturbation (zero-mode scalar perturbation) and evolves to an inflationary attractor stage. The succeeding inflation feature is the same with the ordinary chaotic inflation in GR, but it is not chaotic at the high-energy state because the pre-inflationary stage can have a finite low curvature. Depending on the initial conditions, the evolution of the Universe can acquire the 60 $e$-foldings in the late-time inflationary attractor period. If the sufficient $e$-foldings are not acquired in this period, it must be complemented in the exponentially expanding period at the near-MPS in order to solve the cosmological problems. Once an inflation model has been introduced in EiBI gravity, it is worthwhile to investigate the density perturbation. % The density perturbation has been studied in the EiBI universe filled with perfect fluid in Refs.~\cite{EscamillaRivera:2012vz,Avelino:2012ue,Lagos:2013aua,Yang:2013hsa}. (Other work has been investigated in the cosmological and astrophysical aspects in Refs.~\cite{Cho:2012vg,Pani:2011mg,Pani:2012qb,DeFelice:2012hq,Avelino:2012ge,Avelino:2012qe,Casanellas:2011kf, Liu:2012rc,Delsate:2012ky,Pani:2012qd,Cho:2013usa,Scargill:2012kg,Kim:2013nna,Kim:2013noa,Du:2014jka}.) In particular, the very recent observational result of BICEP2 has put an increasing importance on the tensor-mode perturbation in the inflationary scenario \cite{Ade:2014xna}. In this paper, we investigate the tensor perturbation in the EiBI inflation model introduced above. We shall consider the perturbation analytically at the two stages: ``the near-MPS stage" which is described by the globally perturbed solution of the MPS, and ``the attractor stage" which is similar to the ordinary chaotic inflation in GR. | We investigated the tensor perturbation of the inflation model in Eddington-inspired Born-Infeld gravity developed in Ref.~\cite{Cho:2013pea}. The background universe is driven by a massive scalar field as in the usual chaotic inflation model in GR. There are three stages in the background evolution. At the early stage of the background evolution, there is the near-MPS stage which is described by the globally perturbed {\it maximal pressure solution} investigated in Ref.~\cite{Cho:2013pea}. At this stage, the scale factor increases exponentially in cosmological time. This stage is followed by the intermediate stage. For most this stage, the first slow-roll condition is satisfied, but the analytic form of the background evolution is not available. At late times, the attractor stage appears in which the first and the second slow-roll conditions are satisfied. The background evolution is the same with the one in the usual chaotic inflation. Therefore, there are two exponentially expanding stages in EiBI inflation. In EiBI gravity, as one can see from the field equation \eqref{mueq}, the tensor perturbation is described by the conformal time $\tau$ and the scale factor $Y$ of the auxiliary metric $q_{\mu\nu}$ (not of the metric $g_{\mu\nu}$). At the attractor stage, $\tau$ is identified with $\eta$ which is the conformal time of the metric. The scale factors are related by $Y=Y_0a$, where $Y_0$ is almost constant. Therefore, the perturbation story is very similar to that of the usual chaotic inflation, with a very small EiBI correction implied in $Y_0$. The perturbation produced at this stage provides a scale invariant power spectrum. When the attractor stage does not provide 60 $e$-foldings, one needs to consider the perturbation produced at the near-MPS stage in order to explain the low angular modes in the power spectrum. At the near-MPS stage, $Y(\tau)$ behaves very differently from that at the attractor stage. For short wave-length (high $k$) modes, the minimum energy condition imposed on the initial perturbation picks only the positive energy state. It evolves adiabatically at the intermediate stage and is continued to the attractor stage. The perturbation feature is the same with the one investigated at the attractor stage. For long wave-length (low $k$) modes, however, the minimum energy condition requires the mixed energy state of the initial perturbation. The perturbation can evolve adiabatically at the intermediate stage for which the WKB solution is applied. By matching the WKB solution with the near-MPS and the attractor solutions, we could evaluate the power spectrum at the attractor stage. For very low $k$, there is a peculiar rise in the spectrum while for the rest the spectrum is scale invariant. This low $k$ behavior may leave a signature in CMB, which can distinguish the EiBI inflation model from others. The recent detection of the $B$-mode polarization by BICEP2 invoked the importance of the tensor perturbation in the inflationary scenario \cite{Ade:2014xna}. According to the result, the tensor-to-scalar ratio is best fit by the usual $\phi^2$ chaotic inflation model. Since our EiBI inflation model is very similar to the usual chaotic inflation model at the attractor stage, we expect that the tensor-to-scalar ratio is also very similar. We shall investigate the scalar perturbation in the EiBI inflation in order to confirm this. | 14 | 4 | 1404.6081 |
1404 | 1404.1945_arXiv.txt | \grb was extremely bright as a result of occurring at low redshift whilst the energetics were more typical of high-redshift gamma-ray bursts (GRBs). We collected well-sampled light curves at 1.4 and 4.8~GHz of \grb with the Westerbork Synthesis Radio Telescope (WSRT); and we obtained its most accurate position with the European Very Long Baseline Interferometry Network (EVN). Our flux density measurements are combined with all the data available at radio, optical and X-ray frequencies to perform broadband modeling in the framework of a reverse-forward shock model and a two-component jet model, and we discuss the implications and limitations of both models. The low density inferred from the modeling implies that the \grb progenitor is either a very low-metallicity Wolf-Rayet star, or a rapidly rotating, low-metallicity O star. We also find that the fraction of the energy in electrons is evolving over time, and that the fraction of electrons participating in a relativistic power-law energy distribution is less than $15\%$. We observed intraday variability during the earliest WSRT observations, and the source sizes inferred from our modeling are consistent with this variability being due to interstellar scintillation effects. Finally, we present and discuss our limits on the linear and circular polarization, which are among the deepest limits of GRB radio polarization to date. | \label{section:intro} Gamma-ray bursts (GRBs) are a broadband phenomenon, covering many orders of magnitude in observing frequency, from radio frequencies below 1~GHz to gamma-ray energies of tens of GeV. They also cover many orders of magnitude in observed timescales, from millisecond variability in the gamma-ray light curves up to months or even years at radio frequencies. Much of our understanding of the physics behind GRBs is based on multi-frequency and multi-timescale observations. In the case of long-duration GRBs \citep[i.e, with a duration $>2$~seconds;][]{kouveliotou1993} a picture has emerged in which a relativistic collimated outflow, or jet, is produced by a central engine, due to the collapse of a massive star \citep{woosley1993}; for short-duration GRBs most likely due to a binary merger of two compact objects \citep{eichler1989,narayan1992}. The prompt gamma-ray emission at keV to MeV energies is believed to be produced by particles accelerated in shocks internal to the outflow, while the later time afterglow emission (from X-ray to radio frequencies, and arguably also the long-lasting GeV gamma-ray emission), is due to the interaction of the jet with the ambient medium \citep[see][for recent reviews]{kouveliotou2012}. At the front of the jet, matter is swept up and a forward shock is formed, accompanied by a short-lived reverse shock moving back into the outflow. The forward shock is initially moving at relativistic speeds but decelerating, while the reverse shock can be either relativistic or Newtonian. The observed afterglows are usually dominated by emission from the forward shock, but occasionally the reverse shock causes a bright optical flash peaking in the first minutes and a radio flare in the first days after the GRB onset \citep[e.g.][]{akerlof1999,kulkarni1999}. Radio observations are important for constraining the spectra and evolution of the forward and reverse shocks, and follow the evolution of the GRB jet up to much later times than at higher frequencies \citep[for a recent review on GRB radio observations and their implications for GRB jet physics, see][]{granot2014}. Over the last decade new ground- and space-based observatories have provided broadband GRB data sets, e.g. the {\it Fermi Gamma-ray Space Telescope} for detecting high-energy gamma-rays, the {\it Swift} satellite for X-ray light curves, robotic optical telescopes for early-time light curves, and improved and new facilities for observations at radio frequencies. However, it is quite rare that excellent broadband coverage is accompanied with great temporal sampling, in particular at the extreme ends of the spectrum \citep[e.g.][]{cenko2011}; conversely, some GRBs with extremely well sampled light curves do not have comparable spectral coverage \citep[e.g.][]{racusin2008}. The recent, extremely bright, long-duration \grb was the exception that brought all these observational capabilities together, from its detection in gamma-rays to its multi-wavelength follow-up observations. Most long-duration GRBs occur at high redshifts, with a mean redshift at $z\simeq2$ \citep{fynbo2009,jakobsson2012}; the current record holder is at $z\simeq9.4$ \citep{cucchiara2011}. For a small group of these at low redshifts ($z<0.4$), we are able to detect and identify spectroscopically their associated supernovae, although this does not always appear to be the case \citep[e.g.,][]{fynbo2006,gehrels2006}. A significant fraction of that group has intrinsic luminosities and energetics lower than those of GRBs at higher redshifts \citep[e.g.][]{kaneko2007,starling2011}; even the most luminous one to date, GRB\,030329, is at the low end of the energetics distribution for the total GRB sample \citep{kaneko2007}. \grb is exceptional in that, although it is at a low redshift of $z=0.34$, with an accompanying supernova of the same type as the other GRB-associated supernovae \citep[SN\,2013cq;][]{levan2013,xu2013}, it is comparable in luminosity to the majority of long GRBs. At gamma-ray energies this is a record-breaking GRB, with the highest observed fluence in 29 years, the longest lasting high-energy gamma-ray afterglow (i.e. 20~hours), and the highest energy gamma-ray photon ever detected \citep[95~GeV;][]{ackermann2014}. Compared to the entire GRB sample, the \grb X-ray and optical observed brightness are amongst the highest, while its intrinsic luminosities are just above or around the average \citep{perley2014}. Given the extremely well sampled light curves for \grbnos, and the fact that the light curves at X-ray and optical frequencies are comparable to those of other high-luminosity GRBs, this source provides a unique opportunity to study not only the physics of this particular GRB in great detail \citep[e.g.,][]{kouveliotou2013,preece2014}, but also to make inferences for GRBs at more typical redshifts. A remarkable feature of \grb is the early-time peak at optical frequencies, $\sim10-20$~seconds after the GRB onset, for which an optical flash due to the reverse shock has been suggested as the most likely explanation \citep{vestrand2014}. At radio frequencies the light curves display a peak on a day timescale, which has also been attributed to the reverse shock \citep[][]{laskar2013,perley2014,anderson2014}. Broadband modeling efforts have shown that the light curves from radio to X-ray frequencies, and also the high-energy gamma-ray light curves, can indeed be interpreted as a combination of emission from the forward and reverse shocks \citep{laskar2013,panaitescu2013,maselli2014,perley2014}. In this paper we present radio observations of \grb with the Westerbork Synthesis Radio Telescope (WSRT) at two radio frequencies (Section~\ref{sec:wsrt}), resulting in well sampled light curves and enabling more detailed modeling than previous efforts. We also show the results from Very Long Baseline Interferometry (VLBI) observations with the European VLBI Network (EVN), which set constraints on the source size and provide the best localization of this GRB (Section~\ref{sec:vlbi}). We revisit the modeling of the broadband light curves to set more stringent constraints on the evolution of the forward and reverse shock spectra, and present a two-component jet model as an alternative to describe all the available data from radio to X-ray frequencies (Section~\ref{sec:model}). Since our WSRT observations have long durations, we also present radio brightness variations at relatively short timescales to study variability of the source and possible scintillation effects (Section~\ref{sec:shvar}). Furthermore, due to the source brightness we can put very tight constraints on the linear and circular radio polarization, and discuss those in the context of GRB afterglow emission models (Section~\ref{sec:pola}). Finally, we summarize our results and draw some conclusions (Section~\ref{sec:concl}). | \label{sec:concl} \grb was a record-breaking GRB in many respects, and its broadband follow-up from GHz radio frequencies to GeV gamma-ray energies has resulted in very well sampled light curves. In this paper we have presented radio observations with the WSRT at 1.4 and 4.8~GHz, significantly enhancing the temporal coverage at these two frequencies. We have combined our WSRT observations with data published in the literature and performed broadband modeling. We have shown that the reverse-forward shock model put forward by other authors can not fit all the light curves well, plus the obtained dependence of the outflow Lorentz factor on radius is not physical. As an alternative we have shown that the addition of a second jet component provides a good description of the light curves from radio to X-ray frequencies, in particular that the very early steep decay and subsequent flattening in the optical light curve can be described well by adding the extra free parameters of a second forward shock emission component. In this model only the very early optical peak originates in the reverse shock, while the rest of the optical emission, and also the radio and X-ray emission, are produced by a narrow fast jet surrounded by a slower and wider jet component. We can not determine which one of the two models is statistically better, but we can draw conclusions on the physics of the jet and its surroundings that are true for both models. We have put constraints on the physical parameters, and found that the density is very low and structured like a stellar wind. The low density indicates a very low mass-loss rate from the progenitor star, which implies either a low-metallicity ($<10^{-3}$ of solar metallicity), nitrogen-rich Wolf-Rayet star; or a rapidly rotating, low-metallicity O star. We have also determined the microphysical parameters describing the energetics of the electrons and magnetic field. To explain the fast evolution of the spectral peak frequency, we have invoked a moderate temporal evolution of $\varepsilon_{\rm{e}}$. Furthermore, we find that the fraction of electrons participating in a relativistic power-law energy distribution is $<15\%$. We note that one issue with the two-component jet model is that the temporal evolution of $\varepsilon_{\rm{e}}$ is slightly different for the narrow and wide jet components, and that they are only equal to each other at $\sim1$~s after the GRB onset. Besides radio flux density measurements we have also performed VLBI observations to constrain the source size at 6.55~d. Unfortunately the source became too faint for VLBI observations at later times, when measuring the source size with this technique would have been feasible, but we did obtain the most accurate localization of this GRB. Because of the long observations at 4.8~GHz and the brightness of the source we were able to study intraday variability within the first days after the GRB onset. In particular the observation at $\sim1.5$~d showed fast variations which were not intrinsic to the source, and most likely caused by strong ISS. We showed that this is indeed a plausible explanation by comparing the source image size inferred from broadband modeling with the characteristic angular scales for ISS. Finally, we have presented some of the most constraining upper limits of radio polarization. These limits, of only a few percent on both linear and circular polarization, are at the peak of the 4.8~GHz radio emission. If one interprets this peak as emission from the reverse shock, these would be the deepest reverse shock radio polarization measurements. In our modeling work, however, we have shown that the radio peak can also be caused by the narrow core component of the jet, and although these polarization limits are still among the lowest ones to date (except for GRB\,030329), a non-detection of radio polarization at a few percent level is not unexpected (even for reverse shock emission). Pushing these limits further down in future GRB observations will allow us to put constraints on jet models, in particular the role and structure of magnetic fields in the jet and in the shocks producing the emission. | 14 | 4 | 1404.1945 |
1404 | 1404.2177_arXiv.txt | {The Helix Nebula (NGC\,7293) is the closest planetary nebulae. Therefore, it is an ideal template for photochemical studies at small spatial scales in planetary nebulae.} {We aim to study the spatial distribution of the atomic and the molecular gas, and the structure of the photodissociation region along the western rims of the Helix Nebula as seen in the submillimeter range with {\it Herschel}.} {We use 5 SPIRE FTS pointing observations to make atomic and molecular spectral maps. We analyze the molecular gas by modeling the CO rotational lines using a non-local thermodynamic equilibrium (non-LTE) radiative transfer model.} {For the first time, we have detected extended OH$^+$ emission in a planetary nebula. The spectra towards the Helix Nebula also show CO emission lines (from $J=4$ to 8), [N\,{\sc ii}] at 1461 GHz from ionized gas, and [C\,{\sc i}] ($^3\rm{P}_2-$$^3\rm{P}_1$), which together with the OH$^+$ lines, trace extended CO photodissociation regions along the rims. The estimated OH$^+$ column density is $\sim 10^{12}-10^{13}$ cm$^{-2}$. The CH$^+$ (1-0) line was not detected at the sensitivity of our observations. Non-LTE models of the CO excitation were used to constrain the average gas density ($n{\rm (H_2)}\sim (1-5)\times 10^5$ cm$^{-3}$) and the gas temperature ($T_{\rm k}\sim 20-40$ K).} {The SPIRE spectral-maps suggest that CO arises from dense and shielded clumps in the western rims of the Helix Nebula whereas OH$^+$ and [C\,{\sc i}] lines trace the diffuse gas and the UV and X-ray illuminated clumps surface where molecules reform after CO photodissociation. [N\,{\sc ii}] traces a more diffuse ionized gas componnent in the interclump medium.} | \indent\par {Planetary nebulae (PNe) represent the final stage in the evolution of low- and intermediate-mass stars like the Sun. These stars lose matter during the asymptotic giant branch (AGB) phase, and form an expanding circumstellar envelope. While the central stars evolve from AGB phase to planetary nebula (PN) phase, the effective temperatures of the stars rise, increasing the UV radiation. Molecules previously ejected in mass loss episodes from the progenitor star are photodissociated by the UV photons as the dissociation front advances through the gas. When the central star becomes hotter than $\sim 30,000$ K, the circumstellar gas is ionized. The nebular gas cools radiatively, i.e. by visible line emission. However, not all the envelope is ionized and neutral atoms and molecules dominate the gas cooling in photodissociation regions (PDRs) and in the shielded gas. In PNe, the neutral and molecular material form fragmented rims around the ionized nebula. Their infrared spectrum is characterized by [C\,{\sc i}], [O\,{\sc i}], [C\,{\sc ii}] atomic fine structure lines, and rotational lines of CO and H$_2$. } \par{The Helix Nebula (NGC 7293) is the closest PN at a distance of $219\pm 30$ pc \citep{Harris07}, therefore it is a unique template to resolve the different structures expected in a planetary nebula (i.e. H\,{\sc ii} region, PDRs, and shielded molecular gas). The central star of the Helix Nebula is a white dwarf with an effective temperature $T_{\rm eff}\sim 120,000$ K, a luminosity of $L\sim 76$ $L_{\odot}$, and a mass of $M\sim 0.57$ $M_{\odot}$ \citep{Napiwotzki99, Traulsen05}. The central star is a source of X-rays at energies $\sim 0.25$ keV that arise from the stellar photosphere. In addition, {\it Chandra} and ROSAT observations revealed X-ray emission near $\sim 1$ keV \citep{Leahy94,Guerrero01}. Its origin remains uncertain.\\ } \begin{table*} \begin{center} \caption{Observational parameters. \label{tab1}} \renewcommand{\arraystretch}{1.2} \begin{tabular}{lccccccc} \hline\hline ObsId$^a$ & Date&Target& Proposal & RA$_{\rm (J2000)}$$^b$& Dec$_{\rm (J2000)}$$^c$& Total time$^d$& v$_{\rm rad}$$^e$\\ &&&&&&(s) &(km s$^{-1})$ \\ \hline 1342256097 & 2012-11-25& T1&DDT\_mustdo\_7&$22^{\rm h}29^{\rm m}10.03^{\rm s}$ & $-20^{\rm o}48\arcmin 10.04\arcsec$ & 3612& -26.78\\ 1342256098 &2012-11-25 &T2&DDT\_mustdo\_7&$22^{\rm h}29^{\rm m}22.84^{\rm s}$ & $-20^{\rm o}49\arcmin 18.79\arcsec$ & 3612&-26.77\\ 1342256099& 2012-11-26&T3&DDT\_mustdo\_7&$22^{\rm h}29^{\rm m}22.84^{\rm s}$ & $-20^{\rm o}52\arcmin 30.81\arcsec$ & 3612&-26.78 \\ 1342256100 & 2012-11-25&T4&DDT\_mustdo\_7&$22^{\rm h}29^{\rm m}10.03^{\rm s}$ & $-20^{\rm o}51\arcmin 22.00\arcsec$ & 3612&-26.79\\ 1342257353 & 2012-12-17&T5 &OT2\_pvanhoof\_2 & $22^{\rm h}29^{\rm m}10.02^{\rm s}$ & $-20^{\rm o}49\arcmin 53.77\arcsec$ & 6992&-24.27\\ 1342256744& 2012-12-08 & SPIRE 250 $\mu$m image & DDT\_mustdo\_7&$22^{\rm h}29^{\rm m}35.24^{\rm s}$ & $-20^{\rm o}50\arcmin 40.51\arcsec$ & 2047 & ...\\ \hline \end{tabular} \end{center} \begin{list}{}{} \item[$^a$]Observation identification number \item[$^{b}$]Right ascension of the central detectors SLWC3 and SSWD4 \item[$^{c}$]Declination of the central detectors SLWC3 and SSWD4 \item[$^d$]Total integration time of each observation \item[$^e$]Radial velocity of the {\it Herschel} telescope along the line of sight \end{list} \end{table*} \begin{figure*} \resizebox{\hsize}{!}{\includegraphics{Figure1.eps}} \caption{Footprint of the five SPIRE FTS observations over the SPIRE 250 $\mu$m photometric image. White circles show the layout of the unvignetted field of view (FoV$\sim$ 2.0 arcmin in diameter) of the four mustdo observations, and white-dashed circle shows the FoV of the pvanhoof observation. The total area coverage by the five observations is $\sim 6\times8$ arcmin$^2$. Layout of the FTS detector arrays (the SLW in green and the SSW in red) and the FoV (black) is shown in the lower right corner. The circle sizes of the detectors correspond to the FWHM of the beam. Black contours trace levels: 10, 12.5, 15, 17.5 and 20 MJy sr$^{-1}$} \label{fig1} \end{figure*} \par{Low-$J$'s CO and H$_2$ observations of the Helix Nebula show dense, neutral knots with ionized cometary tails located in the central region of the nebula \citep{Huggins02,ODell05,Hora06,Matsuura07}. \citet{Matsuura09} showed that it is in the inner region of the Helix, towards the central star, where tails are observed from the neutral globules probably created by the stellar winds from the central star \citep{Meaburn10,Matsuura09,Speck02}. The ionized cavity is surrounded by a double rim of dust, and molecular and atomic gas (see Figure~\ref{fig1}). The inner rim is a circular and fragmented ring around the central star \citep{Young99} with an inner radius $\sim 175$\arcsec ($\sim 0.2$ pc). The outer rim has an inner radius of $\sim 340\arcsec$ ($\sim 0.35$ pc). Knots at the envelope are difficult to resolve and seem to form clumps. The clumpiness and the strong UV fields in the envelope determine much of the physical and chemical conditions. } \par{The Helix is probably an oxygen-rich planetary nebula (C/O= $0.87\pm 0.12$, \citet{Henry99}), with a high abundance of neutral carbon, $N$[C\,{\sc i}]$/N{\rm (CO)}\sim $ 6 measured towards the outer western rim \citep{Cox98}. The Helix molecular envelope is devoid of PAH's, which is consistent with its C/O ratio \citep{Hora06}. } \par{So far, the lower energy levels of OH$^+$ emission lines have been detected in the ultra-luminous galaxies Mrk\,31 \citep{vanderWerf10} and NGC\,1068 \citep{Spinoglio12}. Most recently, \citet{vanderTak13} presented the first detection of extended OH$^+$ line emission in the galaxy, toward the Orion Bar, using the HIFI instrument onboard {\it Herschel}. } \par{In this paper, we report the first detection of extended OH$^+$ emission in a circumstellar envelope, a key ion precursor for the oxygen chemistry. Simultaneously to this detection, \citet{Aleman13} also detected OH$^+$ emission in three planetary nebulae: NGC\,6445, NGC\,6720, and NGC\,6781 obtained in the {\it Herschel} Planetary Nebulae Survey (HerPlaNS) \citep{Ueta12}. Their work is also published in this volume. We also detected OH$^+$ in emission in NGC \,6853 planetary nebula. This nebula was also observed as part of the OT2 project (PI: P. van Hoof). The Helix Nebula and NGC\,6853 present very similar features in the SPIRE FTS spectra, showing emission lines of [N\,{\sc ii}], CO rotational lines (from $J=4-3$ to $J=8-7$), [C\,{\sc i}], and OH$^+$ along the molecular rims. A detailed analysis of the NGC\,6853 nebula will be presented in a forthcoming paper. } \par{In this work, we study the physical and chemical conditions in the western rims of the Helix Nebula by analyzing the submm spectra from 447 GHz to 1550 GHz taken with the {\it Herschel} SPIRE Fourier Transform Spectrometer (FTS). The SPIRE FTS spectral maps allow us to study the molecular gas by modeling the CO rotational line emission and to study the distribution of the atomic and the molecular gas along the western rims. } | \indent\par{We have reported the first detection of extended OH$^+$ line in emission in a planetary nebula. Independently and simultaneously, OH$^+$ lines in emission have been detected in several oxygen-rich planetary nebula, by \citet{Aleman13}, observed as part of the HerPlans project. Their work is also presented in this volume. } \par{{\it Herschel} SPIRE FTS spectra display several atomic and molecular emission lines along the western rims of the Helix Nebula. The intensity maps of the atoms and molecules detected trace the dissociation of CO molecules and the stratification of the PDR along the outer western rims. CO arises from dense and shielded clumps in the western rims of the Helix Nebula. OH$^+$ and [C\,{\sc i}] likely trace the clumps surface where molecules reform after being photodissociated. Both, the OH$^+$ and [C\,{\sc i}] distributions are spatially coincident peaking at the same position in the outer western rim. [N\,{\sc ii}] traces the diffuse ionized gas in the interclump medium.} \begin{acknowledgement} We thank ASTROMADRID for funding support through the grant S2009ESP-1496, the consolider programme ASTROMOL: CSD2009-00038 and the Spanish MINECO (grants AYA2009-07304 and AYA2012-32032). FK is supported by the FWF project P23586 and the ffg ASAP project HIL. PvH and PR acknowledges support from the Belgian Science Policy Office (Belspo) through the ESA PRODEX program. HIPE is a joint development by the {\it Herschel} Science Ground Segment Consortium consisting of ESA, the NASA {\it Herschel} Science Center, and the HIFI, PACS, and SPIRE consortia. SPIRE has been developed by a consortium of institutes led by Cardiff University (UK) and including University of Lethbridge (Canada); NAOC (China); CEA, LAM (France); IFSI, Univ. Padua (Italy); IAC (Spain); Stockholm Observatory (Sweden); Imperial College London, RAL, UCL-MSSL, UKATC, Univ. Sussex (UK); and Caltech, JPL, NHSC, Univ. Colorado (USA). This development has been supported by national funding agencies: CSA (Canada); NAOC (China); CEA, CNES, CNRS (France); ASI (Italy); MCINN (Spain); SNSB (Sweden); STFC, UKSA (UK); and NASA (USA). \end{acknowledgement} | 14 | 4 | 1404.2177 |
1404 | 1404.2800_arXiv.txt | In this paper, we investigate the no-boundary wave function and the complex-valued instantons for two-field inflation models that have different masses. If there is a relatively massive direction, to classicalize the massive field, the solution should start from the slow direction with relatively larger vacuum energy. Therefore, the existence of the massive direction implies the increase of expected $e$-foldings. The most probable $e$-foldings are approximately $\mathcal{N} \simeq (m_{2}/m_{1})^{2} \times \mathcal{O}(1)$ in the $m_{1} \ll m_{2}$ limit. Therefore, as long as there is a sufficient mass hierarchy, the no-boundary wave function can reasonably explain large $e$-foldings, so to speak more than $50$ $e$-foldings. | Understanding the beginning of our universe is the important task of modern physics and cosmology. The theory of quantum gravity and the application to cosmology should resolve the problem of the initial singularity \cite{Hawking:1969sw} and also should give a reasonable probability to explain the initial conditions for our universe, especially the initial conditions for inflation \cite{Guth:1980zm}. Now, we are getting data from cosmological observations and soon after we will be able to understand the detailed mechanism for inflation. Perhaps, the recent tension between the Planck data \cite{Ade:2013uln} and the BICEP2 results \cite{bicep2} may require multi-field inflation or complication of a single field inflation model, though it is not possible to conclude yet. In this context, now this is a natural question: \textit{can the multi-field inflation reasonable to explain our inflationary universe in terms of quantum gravity?} Following the canonical quantization \cite{DeWitt:1967yk}, the master wave function that contains all information of our universe, so-called the wave function of the universe, is governed by the Wheeler-DeWitt equation. The solution depends on the boundary condition. Perhaps one natural assumption is the ground state, where the ground state wave function can be obtained by the Euclidean path integral \cite{Hartle:1983ai} (there can be alternative boundary conditions, e.g., \cite{Vilenkin:1986cy}). This wave function is known as the \textit{no-boundary wave function} and this is called by the no-boundary proposal. The Euclidean path integral is approximated by sum-over on-shell solutions, so-called instantons\footnote{Since we are using the instanton method, in other words a kind of semi-classical methods, this approach may lose a truly wave nature of the entire wave function, e.g., a resonant structure \cite{Maydanyuk:2010qb}. However, as long as the quantum state is in the ground state and the parameters allow a regime where the steepest-descent approximation is still sound, the instanton approximations will be a good description that describes the no-boundary wave function.}. In general, these instantons are complex-valued \cite{Halliwell:1989dy}. After a long Lorentzian time, the instanton should return to real-valued functions \cite{Lyons:1992ua,Hartle:2007gi,Hartle:2008ng}. This condition is called by the \textit{classicality}; note that in this paper we use the terminology `classicality' for the classicalization of all matter fields and the metric, while sometimes the same terminology is used to explain the classicalization of inhomogeneous perturbations generated during inflation. To impose the classicality, each history needs a period of slow-roll inflation \cite{Hartle:2008ng}; and the boundary of the classicalizable region forms a \textit{cutoff} near the local minimum such that if the initial condition is inside the cutoff, the history cannot be classicalized. However, one traditional problem of the no-boundary wave function (with Einstein gravity and single field inflation) is that the result does not prefer large $e$-foldings. For classicality, we only need just order one $e$-foldings. To explain large $e$-foldings, e.g., more than $50$ $e$-foldings, we need further additional assumptions. For example, Hartle, Hawking and Hertog weighted the volume factor to enhance the initial conditions for large $e$-foldings \cite{Hartle:2007gi,Hawking:2002af}. Apart from this \textit{ad hoc} assumption, one may introduce other reasonable assumptions that can enhance large $e$-foldings \cite{Hwang:2013nja}, e.g., introducing a (perhaps, Planck scale) pre-inflation era before the primordial inflation of our universe, finely tune the shape of the potential, introducing the multi-field inflation scenario \cite{Hwang:2012bd}, or using new contributions that can come from modified gravity \cite{Sasaki:2013nka}. However, these previous analysis in \cite{Hwang:2013nja} relied on the single field inflation. Even for the multi-field inflation case, we only analyzed for the single mass case that is effectively equivalent to single field inflation. On the other hand, more realistic inflation model will be cooperated by the contributions of many fields with various potential shapes. In this paper, to investigate this issue, as a toy model, we study classicalized instantons for two-field inflation models with different mass parameters. We observe that the cutoff structure drastically changes and hence we have to change the naive intuitions that come from the result of the single field inflation. In Section~\ref{sec:int}, we describe the formulation of the no-boundary proposal for the two-field inflation model. In Section~\ref{sec:cla}, we discuss the motivations of this paper. In Section~\ref{sec:two}, we study the no-boundary wave function for the two-field inflation model by using analytic and numerical methods. Finally, in Section~\ref{sec:con}, we summarize our conclusions. | 14 | 4 | 1404.2800 |
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1404 | 1404.0728_arXiv.txt | Investigating the outflows emanating from young stellar objects (YSOs) on sub-arcsecond scales provides important clues to the nature of the underlying accretion-ejection process occurring near the central protostar. We have investigated the structures and kinematics of the outflows driven by the YSO DG Tauri, using the Near-infrared Integral Field Spectrograph (NIFS) on Gemini North. The blueshifted outflow shows two distinct components in [Fe II] 1.644 $\mu$m emission, which are separated using multi-component line fitting. Jet parameters are calculated for the high-velocity component. A stationary recollimation shock is observed, in agreement with previous X-ray and FUV observations. The presence of this shock indicates that the innermost streamlines of the high-velocity component are launched at a very small radius, $0.01\textrm{--}0.15\textrm{ AU}$, from the central star. The jet accelerates and expands downstream of the recollimation shock; the `acceleration' is likely a sign of velocity variations in the jet. No evidence of rotation is found, and we compare this non-detection to previous counter-claims. Moving jet knots, likely the result of the jet velocity variations, are observed. One of these knots moves more slowly than previously observed knots, and the knot ejection interval appears to be non-periodic. An intermediate-velocity component surrounds this central jet, and is interpreted as the result of a turbulent mixing layer along the jet boundaries generated by lateral entrainment of material by the high-velocity jet. Lateral entrainment requires the presence of a magnetic field of strength a few mG or less at hundreds of AU above the disc surface, which is argued to be a reasonable proposition. In H$_2$ 1-0 S(1) 2.1218 $\mu$m emission, a wide-angle, intermediate-velocity blueshifted outflow is observed. Both outflows are consistent with being launched by a magnetocentrifugal disc wind, although an X-wind origin for the high-velocity jet cannot be ruled out. The redshifted outflow of DG Tau takes on a bubble-shaped morphology, which will be discussed in a future paper. | It is likely that the outflows driven by accreting young stellar objects (YSOs) play a critical role in solving the angular momentum problem of star formation by removing angular momentum from circumstellar disc material. The nature of this coupled accretion-ejection mechanism remains poorly understood. Magnetic fields are almost certainly integral to this process \citep{MO07}, but the ejection mechanism is still a matter of debate. Outflows could be launched from the stellar surface \citep[e.g.,][]{ST94,MP05}, from points near the truncation radius of the disc, as in the X-wind model \citep{Se94}, or from a range of disc radii via magnetocentrifugal acceleration \citep{BP82,PN83}. Indeed, multiple launch mechanisms may act in concert \citep{L03,FDC06,SLH07}. Determining the nature of the outflow mechanism is critical in order to understand the underlying accretion process \citep{E09}. Magnetic fields are believed to drive these outflows, and they may also be responsible for inducing disc turbulence via the magnetorotational instability \citep[MRI;][]{BH91,B10}. Both of these processes extract angular momentum from the disc, enabling mass accretion onto the central protostar \citep{MO07}. It is therefore important to determine the physical processes that lead to jet launching, and link these with the properties of the resulting outflow. Direct observation of the jet launching region is not possible with current optical/near-infrared telescope technology. However, constraints on the jet launching mechanism can be inferred from observations of the outflows close to the central star. For low-mass stars, this takes the form of observing the `microjets' of optically-visible classical T Tauri stars (CTTS). These microjets, which make up the first $\sim 200\textrm{--}300\textrm{ AU}$ ($1\farcs 4$--$2\farcs 1$ at 140 pc) of the outflow, are thought to be largely unaffected by ambient gas, as the jet is expected to clear a channel much wider than the jet via a wide bow shock as it emerges \citep{RCC95}. Most models predict that jet collimation and acceleration occur within $\lesssim 50\textrm{ AU}$ of the star \citep{C07}. Significant effort has been expended over the previous two decades observing these YSO microjets at high angular resolution, first with the space-based Hubble Space Telescope (HST), and later with ground-based adaptive-optics (AO) systems \citep[see, e.g.,][and references therein]{Raye07}. One of the most intensely studied T Tauri stars is DG Tauri, which drives the HH 158 and HH 702 outflows \citep{MF83,MRF07}. The accretion and outflow rates determined for this object are amongst the highest of any CTTS \citep{Be02}, with accretion rates approaching $10^{-6}\textrm{ }M_\odot\textrm{ yr}^{-1}$ at some epochs \citep{WG01,WH04}. A multi-velocity structure is observed in the first $\sim$ 300 AU of the approaching outflow, consisting of a well-collimated high-velocity flow near the axis of the system, confined within slower, more spatially extended material. The absolute line-of-sight velocities of the high-velocity component (HVC) are in the range $200$--$400\kms$, with the highest-velocity material positioned closest to the central jet axis and showing bright, shock-excited regions \citep[e.g.,][]{Le97,Be00,Pe03b}. The intermediate-velocity component (IVC) typically shows much broader line widths than the HVC, and is centered around a line-of-sight velocity of $\sim 100\kms$ \citep{Pe03b}. It is important to understand whether the presence of multiple velocity components in the outflow is the result of multiple launch mechanisms and/or locations, or if it can be described through a single outflow model. For example, \citet{Pe03b} suggested a dual-origin model for the DG Tau outflow, combining a magnetospheric jet with a disc wind. However, it was suggested in the same paper that at least part of the DG Tau IVC could be due to entrainment of this disc wind by the HVC. It would also be possible for a single-component jet to exhibit a double-peaked line profile if, for example, the ionisation of the outflow material varied greatly between inner and outer streamlines, as demonstrated by \citet{Pe04} with analytical models of magnetohydrodynamic disc winds. Therefore, higher-quality data on both velocity components, especially regarding spatial positions, accurate radial velocities, and relative intensities between the components, are required in order to constrain these scenarios. Improved line velocity determination, coupled with spatial information, will also provide improved constraints on jet rotation. Not only would the unambiguous detection of rotation provide direct evidence that the outflows are extracting angular momentum from the circumstellar disc, but it may also be used to place constraints on the launch radius of the outflow, assuming an MHD disc wind scenario \citep{MO07}. Since the first claims of jet rotation in the DG Tau outflow from HST Space Telescope Imaging Spectrograph (STIS) data \citep{Be02}, many CTTS outflows have been investigated for this signature \citep[e.g.,][]{Ce04}, including a repeat investigation of DG Tau \citep{Ce07}. Radial velocity differences observed across the DG Tau jet have been interpreted as rotation \citep{Be02,Ce07} having the same sense as the rotation inferred for the DG Tau circumstellar disc \citep{Tes02}. The claimed rotation in the IVC is consistent with an MHD disc wind launched from a radius of $\sim$ 3 AU \citep{Be02,Pe04}, whilst the velocity differences across the HVC match a disc wind launched from $\sim 0.2\textrm{--}0.5\textrm{ AU}$ under the assumption that the entire outflow is an MHD disc wind \citep{Ce07}. However, if the IVC results at least partially from entrainment, the line-of-sight velocities could be skewed at any one position by the turbulent motions of shocked gas. In a recent observation of the extreme T Tauri star RW Aurigae, \citet{Ce12} found that the apparent rotation signatures in the outflows from that object change direction over time, and occasionally disappear, indicating that other effects overwhelm any rotation signal present. It is therefore important to understand how the velocities of each component are expected to evolve due to the natural progression of the outflow, and compare this with the observational evidence. We have obtained three epochs of integral-field spectrograph data of the DG Tau system in the $H$-band over a four-year period (2005--2009). Each epoch provides images of the outflows in [Fe II], in particular the 1.644 $\mu$m line, over an approximately 3\arcsec $\times$ 3\arcsec\ field of view. [Fe II] is one of the strongest forbidden lines present in the near-infrared spectrum, and is less affected by extinction than optical lines \citep{Pe03b}. In this paper, we present the data from the initial observing epoch (2005), and a small amount of data from the 2006 and 2009 observing epochs. In a future paper, we will introduce the full data from the 2006 and 2009 observing epochs, and discuss the time-evolution of the DG Tau outflows in more detail. The outflows of DG Tau were most recently investigated in [Fe II] emission by \citet{A-Ae11}, using the SINFONI instrument on the Very Large Telescope. Their data, obtained in 2005 Oct, one month prior to our observations, demonstrate the potential of high-angular resolution spectroimaging for explaining the origin of various outflow components. Here we use our significantly longer ($\sim 20\times$) on-source exposure time, our increased sensitivity to extended structure due to our use of a stellar occulting disc, and our resulting higher signal-to-noise ratio, to rigorously separate the emission from different jet components (Appendix \ref{app:Ftest}), and examine the physical parameters of each one in detail. This paper is organised as follows. The observations and data reduction methods are described in \S\ref{sec:obsdata}. The results of the data reduction are detailed in \S\ref{sec:results}. We analyse and then remove the stellar spectrum from the data cube, revealing the extended emission structure of the DG Tau outflows. We use multi-component Gaussian line fitting to separate the blueshifted emission into high- and intermediate-velocity components. We analyse each of these components in detail in \S\ref{sec:discuss}. The blueshifted high-velocity component denotes the high-velocity jet driven by DG Tau. The knot ejection period of DG Tau cannot be conclusively determined from our data; we suggest that knot ejections in this object are less periodic than previously thought (\S\ref{sec:D-blueknots}). A stationary recollimation shock is detected at the base of the outflow (\S\ref{sec:D-recoll}), which implies that the innermost streamlines of the jet are initially launched at a high velocity, $\sim 400\textrm{--}700\kms$, from a small launch radius, $\sim 0.01\textrm{--}0.15\textrm{ AU}$ (\S\ref{sec:D-launch}). Following this rapid deceleration, the jet velocity increases beyond the point where magnetocentrifugal acceleration ceases (\S\ref{sec:D-bluepower}), probably as a result of intrinsic velocity variations (\S\ref{sec:D-blueaccel}). There is no indication of rotation in the jet (\S\ref{sec:D-bluerot}). The intermediate-velocity blueshifted component emanates from a turbulent entrainment layer which forms between the jet and either the ambient medium, or the wider-angle molecular wind observed in H$_2$ emission (\S\ref{sec:D-blueH2}). A magnetic field of strength a few hundreds of $\mu$G to a few mG is expected at these heights above the circumstellar disc, and would facilitate this entrainment (\S\ref{sec:D-entrainreq}). We summarise these results in \S\ref{sec:concl}. | \label{sec:concl} We have investigated the YSO DG Tauri, and its associated outflows, in detail using $H$- and $K$-band data from the NIFS instrument at Gemini North taken on 2005 Oct and Nov. The $H$-band stellar spectrum shows significant photospheric absorption features, in contrast to previous studies of DG Tau that showed a veiled continuum spectrum. The $K$-band stellar spectrum also shows significant photospheric absorption features, as well as CO $\Delta v=2$ bandheads in absorption. These bandheads appear to oscillate between absence, emission and absorption, depending upon the observing epoch. The lack of a veiling continuum, and the absence of CO bandheads in emission, suggests that DG Tau was in a low accretion rate phase during this observation epoch. This is consistent with our observation epoch being between periodic outflow episodes. Two regions of extended emission were detected about the central star, on opposing sides of the circumstellar disc. Three distinct emission components were observed in the blueshifted, or approaching, outflow, out to a distance of $1\farcs 5$ from the central star: \begin{description} \item[{\bf High-velocity jet.}] A high-velocity, well-collimated central jet is seen as the high-velocity component (HVC) of [Fe II] 1.644 $\mu$m line emission. A stationary emission knot is observed at the base of the outflow, $\sim 0\farcs 2$ from the central star. We interpret this feature as a jet recollimation shock, based on comparison with X-ray \citep{Ge05,Ge08,Ge11,SS08,GML09} and FUV \citep{Sce13} observations. The entire jet shocks to a temperature of $\sim 10^{6}\textrm{ K}$, but only a small region of this shock emits strongly in X-rays \citep{Be11}. The jet material then cools as it flows downstream. Using the pre-shock flow velocity inferred from X-ray observations of $\sim 400\textrm{--}700\kms$, we calculate that the innermost streamlines of the jet are launched from a radius of $0.01\textrm{--}0.15\textrm{ AU}$ from the central star, assuming an MHD disc wind. This range of launch radii could correspond to either a disc wind or an X-wind. The post-recollimation-shock jet is seen as the HVC of [Fe II] emission, having been decelerated to $\lesssim 215\kms$. The jet follows a non-linear path in the NIFS field, and changes in both velocity and diameter along its length. After accounting for the wandering jet trajectory, we find no evidence of rotation in the jet, which is consistent with the effects of passage through a strong recollimation shock. Two moving jet knots are detected, and labelled knots B and C. Knot B is seen to move at $0\farcs 17\pm 0\farcs 01\textrm{ yr}^{-1}$, much slower than previously observed knots in the DG Tau jet. Knot C is only observed in our 2005 epoch data, and hence we are unable to reliably constrain the proper motion and launch date of that feature. Our data suggest that the interval between knot ejections is non-periodic, and the velocity of the ejected knot varies between ejection events. The jet velocity increases from $215\kms$ to $315\kms$ deprojected between the moving knots, which after the elimination of alternative explanations we interpret to be the result of intrinsic jet velocity variations. These velocity variations are likely the cause of the formation of the moving knots. \item[{\bf Entrainment region.}] A second outflow component in [Fe II] 1.644 $\mu$m emission was separated from the jet emission, using a multi-component Gaussian line fitting routine based on the statistical $F$-test. This intermediate-velocity component (IVC) takes the appearance of a wider-angle flow. Comparison to the molecular wind detected in the $K$-band (see below), as well as consideration of the excitation method of the forbidden [Fe II] lines, suggests that this component represents a shocking, turbulent entrainment layer between the central jet and the wide-angle molecular wind. A magnetic field of with a strength of $\lesssim$ a few mG allows for entrainment to occur by destabilising the jet-wind interface, although careful analysis of the effects of field orientation is required. The presence of lateral entrainment in a YSO outflow provides an interesting alternative driving mechanism for large-scale CO outflows in younger-type YSOs. An analytical model of this entrainment will be presented in a future paper (White et al.~2014c, in preparation). \item[{\bf Molecular outflow.}] Wide-angle H$_2$ 1-0 S(1) 2.1218 $\mu$m emission was observed on the near side of the DG Tau circumstellar disc, as reported by \citet{Be08}. Line velocity mapping of this emission indicates that it is most likely due to a wide-angle molecular wind, which agrees with the conclusions of \citeauthor{Be08} and \citet{A-Ae14}. \end{description} A receding outflow was detected on the far side of the DG Tau circumstellar disc. This disc obscures our view of this outflow out to $\sim 0\farcs 7$ from the central star, corresponding to an outer disc radius of $\sim 160\textrm{ AU}$. The redshifted outflow takes the form of a bubble-like structure in [Fe II] 1.644 $\mu$m line emission. There is tentative evidence for the presence of an underlying jet, although this cannot be confirmed without further data from later epochs. We will discuss the nature of this structure in a future paper \citep{MCW13b}. Many of the above conclusions depend on time-varying mechanisms. Further multi-epoch data are therefore required in order to validate these findings. In particular, confirmation of the knot launch period and proper motions requires multi-epoch data taken in the same fashion. It is also of interest to see how the velocity differences across the jet evolve with time, and if any trend attributable to rotation can be identified. Multi-epoch data will also help to settle the question of whether the mass flux and kinetic power of the approaching jet are constant or time-varying. In the future, the advent of 30 m-class telescopes such as GMT will allow for a finer cross-jet sampling, which is necessary to detect complex velocity structures within the jet. | 14 | 4 | 1404.0728 |
1404 | 1404.1384.txt | We present the results of a numerical study based on the analysis of the {\tt MUSIC-2} N-body/hydrodynamical simulations, aimed at estimating the expected concentration-mass relation for the CLASH cluster sample. We study nearly 1400 halos simulated at high spatial and mass resolution, which were projected along many lines-of-sight each. We study the shape of both their density and surface-density profiles and fit them with a variety of radial functions, including the Navarro-Frenk-White, the generalised Navarro-Frenk-White, and the Einasto density profiles. We derive concentrations and masses from these fits and investigate their distributions as a function of redshift and halo relaxation. We use the X-ray image simulator X-MAS to produce simulated {\em Chandra} observations of the halos and we use them to identify objects resembling the X-ray morphologies and masses of the clusters in the CLASH X-ray selected sample. %In order to do so, we use a set of X-ray morphological estimators to quantify the degree of X-ray regularity in the halo projections. This is then compared to analogous measurements consistently made on the X-ray images of the CLASH clusters. We construct a sub-sample of simulated halos reproducing the distribution of X-ray regularities observed in the CLASH X-ray selected sample, and we use it to derive the concentration-mass relation expected from CLASH. We also derive a concentration-mass relation for strong-lensing clusters. We find that the sample of simulated halos which resemble the X-ray morphology of the CLASH clusters is composed mainly by relaxed halos, but it also contains a significant fraction of un-relaxed systems. For such a heterogeneous sample we measure an average 2D concentration which is $\sim 11\%$ higher than found for the full sample of simulated halos. After accounting for projection and selection effects, the average NFW concentrations of CLASH clusters are expected to be intermediate between those predicted in 3D for relaxed and super-relaxed halos. Matching the simulations to the individual CLASH clusters on the basis of the X-ray morphology, we expect that the NFW concentrations recovered from the lensing analysis of the CLASH clusters are in the range $[3-6]$, with an average value of $3.87$ and a standard deviation of $0.61$. Simulated halos with X-ray morphologies similar to those of the CLASH clusters are affected by a modest orientation bias. | Gravitational lensing is one the most powerful methods to investigate the distribution of matter (either dark or baryonic) in galaxy clusters. It is well known that this class of objects is particularly important in cosmology for several reasons. First, in a hierarchical model of structure formation, galaxy clusters are the latest bound structures to form in the universe. They are often captured in the middle of violent dynamical processes like mergers between smaller structures, allowing us to study in detail how structure formation proceeds. Second, each of them is a miniature universe, i.e. their composition closely reflects the matter composition of the universe at large. Last but not least, they trace the exponential tail of the structure mass function. Tiny variations of the cosmological parameters are reflected in dramatic changes of their mass function and of its evolution. The lensing effects produced by galaxy clusters are sometimes spectacular. The light emitted by galaxies in the background of these objects interacts with the immense gravitational fields of these large cosmic structures and is deflected. Occasionally, if a background galaxy lays at small angular distance from the cluster center, the lensing effects are highly non linear, leading to the formation of {\em giant} arcs and multiple image systems. This regime is often called {\em strong lensing}. However, even at large angular distances the light feels the gravitational pull of the cluster. In this case, where the lensing distortion changes on scales much larger than the size of the sources, the shape of the distant galaxies is only weakly distorted. In this {\em weak lensing} regime, the lensing effects are described by means of an additional image ellipticity. Every cluster produces a weak lensing signal, while strong lensing events are rare and often observed only in the cores of the most massive clusters or in systems with enhanced shear fields. \cite{HE07.1} and \cite{2010A&A...519A..90M} illustrated with the help of numerical simulations how peculiar the population of strong-lensing clusters is. Clusters forming in the context of CDM typically have oblate triaxial dark matter halos \citep{1988ApJ...327..507F,1991ApJ...378..496D,2011MNRAS.411..584M,2013SSRv..177..155L,2012ApJ...752..141L,2013MNRAS.431.1143D} and, among them, strong lenses tend to have their major axes preferentially oriented along the line-of-sight. Additionally, as described in \cite{TO04.1}, the cluster's ability to produce strong lensing features is boosted by dynamical events such as mergers or, more generally, by substructures orbiting around their host halo and occasionally crossing the cluster cores in projection \citep{2014ApJ...783...41B}. For these reasons, the selection of clusters based on their ability to produce strong lensing events is likely to generate a sample affected by biases. Since lensing is sensitive to the total mass projected on the lens plane, the halo structural parameters inferred from the lensing analysis of clusters affected by an orientation bias will be biased as well. In particular, for clusters elongated along the line of sight, we expect to measure higher masses and concentrations \citep[see e.g.][]{2009ApJ...699.1038O,2009MNRAS.392..930O,HE07.1,2010A&A...519A..90M,2011ApJ...737...74G}, while the opposite is expected for clusters whose major axes are perpendicular to the line-of-sight. To avoid this, a selection based on the cluster X-ray morphology is often advocated. The thermal X-ray emission by galaxy clusters originates in the Intra-Cluster-Medium (ICM), which is ionized gas heated to temperatures up to 100 keV emitting in the X-ray via thermal Bremsstrahlung \citep[e.g.][]{SA86.1}. In absence of processes inducing non-thermal pressure contributions, like e.g. perturbations induced by dynamical events like mergers or ICM turbulence, we do expect the ICM to be nearly in hydrostatic equilibrium with the cluster gravitational potential. As an indication for such equilibrium, or {\em relaxation}, the X-ray surface-brightness is expected to be symmetric and its iso-contours ``round" and concentric \citep[see e.g.][]{2013AstRv...8a..40R}. Following this philosophy, the CLASH cluster sample \citep{2012ApJS..199...25P} has been constructed by selecting 20 massive clusters from X-ray based compilations of massive relaxed clusters. The the relaxation state has been established on the basis of X-ray morphological estimators applied to {\em Chandra X-ray Observatory} images. Are these selection criteria really leading to a sample which is unbiased in terms of lensing masses and concentrations? \cite{2012MNRAS.426.1558G} have recently pointed out that, for randomly selected cluster samples, the concentration-mass relation derived from a two-dimensional lensing analysis is expected to have a lower amplitude compared to the intrinsic 3D concentration-mass relation. The reason is identified in the prolate triaxial shape of the cluster halos. Due to their prolateness, the probability of observing them elongated on the plane of the sky is higher than the probability of viewing them with their major axes pointing towards the observer \cite[some examples are shown in Fig.~10 of][]{2012MNRAS.425.2169G}. \cite{2013ApJ...776...39R} showed that selecting clusters according to their X-ray luminosity not only increases the normalisation of the $c-M$ relation with respect to a control sample but also returns a steeper slope. This behaviour is explained by the fact that at fixed mass, the most luminous clusters are also the most concentrated. In this paper, we aim at using a set of numerical simulations of galaxy cluster sized halos, the {\tt MUSIC-2} simulation set, to better understand the expected properties of a sample of clusters having X-ray morphologies similar to the CLASH sample. In particular, we wish to quantify the possible residual biases on the mass and on the concentration estimates due to the CLASH selection function. This work has two companion papers\footnote[1]{To appear on arXiv/astro-ph the same day as this work.}: the strong-lensing and weak-shear study of CLASH clusters by Merten et al. (2014) and the weak-lensing and magnification study of CLASH clusters by Umetsu et al. (2014), where a comparison between our results and the observational analysis of the CLASH sample is presented. The paper is structured as follows: in Section 2, we introduce the simulation set used in our analysis and we describe the methods used to measure the shape of density profiles in simulated halos; in Section 3, we introduce the CLASH cluster sample to which the simulations will be compared; in Section 4, we describe the morphological parameters used to construct a sample of X-ray selected clusters resembling the properties of the CLASH clusters; in Section 5, we describe the general properties of the halos in the simulated set and discuss their concentration-mass relation; in Section 6, we discuss the concentration-mass relation of strong lensing and X-ray selected halos; in Section 7, we use the X-ray morphology of the simulated clusters to predict the concentrations of the individual CLASH clusters. Finally, Section 8 contains our summary and conclusions. | In this paper, we used a large set of 1419 cluster-sized halos evolved in N-body/hydrodynamical simulations and distributed over the redshift range $0.25\leq z \leq 0.67$, to make predictions about several properties of the clusters included in the CLASH sample \citep{2012ApJS..199...25P}. The simulations used here, which are taken from the {\tt MUSIC-2} sample \citep{2013MNRAS.429..323S}, intentionally do not include radiative physics to avoid an artificial boost of the halo concentrations due to the well known over-cooling problem. First, we characterised the halos by studying their total density profiles. We fitted the profiles using three fitting models: the NFW, the gNFW, and the Einasto profiles. We derived concentration-mass relations and we quantified their dependence on the degree of relaxation. By fitting with the gNFW and with the Einasto profiles, we could also investigate the distribution of the inner slopes and of the shape parameter of the density profiles. We combined our work with measurements of concentrations and masses taken from Vega et al. (in prep.). These measurements were obtained by fitting the surface-density profiles extracted from hundreds of projections of the {\tt MUSIC-2} halos. The fits were performed with the same codes used to measure the surface-density profiles recovered from the strong and weak lensing analyses of the CLASH cluster sample, as described in Merten et al. (2014). The radial ranges over which the fits were performed are compatible with those used in the observational analysis. Using the X-MAS code \citep{GA04.1,2011ApJ...729...45R}, we produced simulated {\em Chandra} observations for three orthogonal lines-of-sight to each halo above the {\tt MUSIC-2} mass completeness limit. These simulated observations were processed using the same routines employed in Donahue et al. (in prep.) to carry out the X-ray morphological analysis of the CLASH clusters. The X-ray morphology of the simulated halos was quantified by means of five morphological parameters, which we combined to define a global regularity parameter. Using the concentrations and masses derived from the analysis of the surface-density profiles, we derived lensing-like concentration-mass relations including the effects of selection functions aimed at reproducing some observational properties of the CLASH clusters. In particular, we focused on their ability to produce strong lensing effects and their X-ray regularity. For this purpose, we created two sub-samples of {\tt MUSIC-2} halos. The first includes halos with Einstein radii in the range of those of the CLASH clusters. The second is constructed such to reproduce the distribution of X-ray regularity parameters of the CLASH clusters. Our results can be summarised as follows: \begin{itemize} \item We find that a large fraction of {\tt MUSIC-2} halos has density profiles which are better fitted by gNFW and Einasto profiles than by NFW profiles. Not surprisingly, the halos which mostly deviate from the NFW model are the least relaxed. For these halos more flexible profiles are needed to better reproduce the shape of the density profiles. The analysis based of the gNFW model shows that the inner slopes of these profiles are distributed over a wide range of values. On average, the logarithmic inner slope is largely consistent with the NFW slope, though. The Einasto profile fits the halos slightly better than the gNFW model; \item when seen in projection, the distribution of the inner slopes widens further, and a large fraction of halos is fitted with profiles that are flatter than the NFW at small radii. On average, the inner logarithmic slopes derived from the gNFW fits of the surface-density profiles is $\sim15\%$ smaller than found fitting the density profiles. About $15\%$ of the halos have inner logarithmic slopes smaller than 0.5; \item the masses derived from the fits of the density profiles match quite well the true masses of the halos, with a scatter which is of only few percent. When they are recovered from the projected mass distributions, mimicking the results obtainable from the analysis of surface-density fields reconstructed via lensing, the masses are smaller than the true masses by less than $5\%$ on average. As discussed in \cite{2012MNRAS.426.1558G} a mass bias is expected for randomly oriented prolated triaxial halos. However, the amplitude of the bias for this sample is $\sim 50\%$ smaller than expected from semi-analytical calculations. The bias is even smaller for relaxed halos, because their shapes are more spherical; \item the concentrations derived from the fits of the density profiles with different models are rather similar. However, we find that Einasto concentrations are smaller by $10-15\%$ compared to the NFW and gNFW concentrations; \item we find that the {\tt MUSIC-2} halos follow an intrinsic concentration-mass relation characterised by a slightly larger normalisation compared to other concentration-mass relations recently proposed in the literature for the NFW model. The redshift evolution is rather weak. \item when we mimic the selection of clusters on the basis of their strong lensing signal, we find that the concentration-mass relation derived from the analysis of the projected mass distributions is considerably steeper than expected for non-strong lenses. It also has a larger normalisation. This result holds for all the fitting models used in this work; \item using the X-ray regularity parameter $M$ to select halos with regular X-ray morphologies leads to the inclusion of both relaxed and un-relaxed halos in the sample. Therefore, the X-ray morphology, especially if evaluated in a relatively small region around the cluster centre, is not ideal at identifying relaxed halos; \item the parameter $M$ is correlated to the halo 2D concentration. The most regular halos have higher mass concentrations compared to the full sample of simulated halos, as they could be measured from a lensing analysis. The excess of concentration is explained in terms of 1) the higher fraction of super-relaxed objects in the X-ray selected sample and 2) to the presence, among the selected halos, of un-relaxed systems which happen to be well aligned with the line-of-sight. For a regularity parameter $M$ equal to the median value measured for the CLASH sample, we expect that the concentration will be higher than the average of all halos in the simulated set by $\sim 11\pm3\%$; \item measuring the concentration-mass relation and its redshift evolution in a sub-sample of {\tt MUSIC-2} halos which reproduces the distribution of X-ray regularity parameters of the clusters in the CLASH X-ray selected sample, we find that this has an amplitude and mass dependence similar to those of the concentration-mass relation of strong-lensing clusters. We verified that the sample of X-ray selected halos is largely composed by strong lensing clusters, and contains a fraction of only $8\%$ of halos which do not have extended critical lines for sources at $z\sim2$. \item the sample of X-ray selected halos is in large fraction composed by relaxed halos. These amount to $\sim70\%$ of sample. \end{itemize} These results suggest that the CLASH clusters are prevalently relaxed and likely to be modestly affected by strong lensing bias. Once accounted for projection and selection effects, their NFW concentrations are expected to scale with mass as $c\propto M^{-0.16\pm0.11}$ for the NFW model, resulting in average concentrations which are intermediate between those predicted in 3D for relaxed and super-relaxed halos in the mass range $2\times10^{14}\lesssim M_{200}\lesssim 10^{15}h^{-1}M_{\odot}$. Matching the simulations to the individual CLASH clusters on the basis of the X-ray morphology, we expect that the NFW concentrations recovered from the lensing analysis of the CLASH clusters are in the range $[3-6]$, with an average value of $3.87$ and a standard deviation of $0.61$. The median value of the concentrations in the simulated sample is $3.76$ and the first and third quartiles of the concentration distribution are 3.62 and 3.93, respectively. As shown in \cite{2010A&A...519A..90M} and in \cite{2008AJ....135..664H}, strong lensing clusters are expected to be frequently elongated along the line of sight. For the simulated CLASH sample, the median angle between the major axis of the halos and the lines of sight selected from the X-ray analysis is $54 \deg$. This indicates that the orientation bias is very modest. It is consistent with the results based on the analysis of the halos from the {\tt MareNostrum Universe} presented in \cite{2010A&A...519A..90M}. | 14 | 4 | 1404.1384 |
1404 | 1404.3084_arXiv.txt | We test 16 bibliometric indicators with respect to their validity at the level of the individual researcher by estimating their power to predict later successful researchers. We compare the indicators of a sample of astrophysics researchers who later co-authored highly cited papers before their first landmark paper with the distributions of these indicators over a random control group of young authors in astronomy and astrophysics. We find that field and citation-window normalisation substantially improves the predicting power of citation indicators. The two indicators of total influence based on citation numbers normalised with expected citation numbers are the only indicators which show differences between later stars and random authors significant on a 1\,\% level. Indicators of paper output are not very useful to predict later stars. The famous $h$-index makes no difference at all between later stars and the random control group. | Any indicator should actually indicate what it is made for. If an indicator is used for evaluation it should not provide an incentive for an unwanted behaviour. In scholarly publishing we know salami and multiple publications, unjustified assignment of co-authorship, and different practices of tactical citation behaviour. Bibliometricians should strive to develop valid research indicators which have no unwanted adverse effects~\cite{kreiman_nine_2011}. Most bibliometric indicators are not developed for the evaluation of individual researchers~\cite[p.\ 1565]{costas_bibliometric_2010}, however individuals are increasingly being evaluated using such indicators. We test selected indicators with respect to their validity at the level of the individual researcher by estimating their power to predict later successful researchers. For this reason, we compare bibliometric indicators of a sample of astrophysics researchers who later co-authored highly cited papers (later stars, for short) before their first landmark paper with the distributions of these indicators over a random control group of young authors in astronomy and astrophysics. Results obtained with some standard basic indicators have been presented on a poster at ISSI 2013.\footnote{ \textit{14th International Society of Scientometrics and Informetrics Conference} in Vienna, Austria, 15th to 20th July 2013 \cite{havemann2013cls}} Here we extend the study to more sophisticated measures with the aim to find the best indicators for predicting later stars. We imagine that later stars apply for a job in an astrophysical research institute five years after their first paper in a journal indexed in Web of Science~(WoS). Do they perform better bibliometrically than the average of applicants with the same period of publishing? | Our results underline the necessity to correct citation indicators for the age of the cited papers and also for varying citation behaviour.\footnote{ It would be interesting---from a theoretical point of view---to determine the influence of each of both corrections separately.} The two indicators of total influence based on citation numbers normalised with expected citation numbers are the only indicators among a total of 16 which show significant differences between later stars and random authors on a 1\,\% level. Thus, normalised citation indicators of total influence can indeed help to predict later successful authors. Despite this relative good performance of normalised citation indicators of total influence we cannot recommend to use them as the only basis for an evaluation of young authors in astrophysics and in similar fields of natural sciences. Normalisation at the field level cannot correct for a variability in citation numbers between different topics. \citeN{opthof_differences_2011} analysed the citation density in different topics of cardiovascular research papers and concluded that even normalised citation indicators ``should not be used for quality assessment of individual scientists'' (cf.\ his abstract).\footnote{ Topics in physics as in astrophysics also differ substantially in citation density \cite{radicchi_rescaling_2011,pepe_measure_2012}.} In each case, bibliometrics can only support evaluation and cannot replace individual peer review. None of the two output indicators have a significant difference below the 5\,\% level.\footnote{ This is in accordance with the result obtained by \citeN[cf.\,p.\,9]{neufeld_peer_2013} when comparing successful with non-successful applicants of a funding programme for young researchers.} Thus, it is very unlikely to discover a later star in astrophysics by comparing her productivity with the productivity of a random author (Figures~\ref{Fig-rank11:12} and \ref{Fig-rank13:14}). The Hirsch index makes no difference at all~($p = 21\,\%$, Figure~\ref{Fig-rank15:16}). This is in agreement with conclusions drawn by % \citeN{lehmann_measures_2006} and also by \citeN{kosmulski_calibration_2012} who analysed small samples of mature scientists and found that the number of publications ``is rather useless'' as a tool of assessment and that also the $h$-index is not really helpful. In contrast to these findings, \citeN{pudovkin_research_2012} found that $h$-index and number of papers are indicators which differ most significantly between group leaders and other scientists at a medical research institution. This can surely be explained by real output differences of elder and younger researchers but maybe partly also by the assumption that group leaders have more often been working at the institute over the whole analysed 5-years period than other researchers. We could have analysed the generalised $h$-index proposed by \citeN{radicchi_universality_2008} who use normalised citation and paper numbers. We did not because $h$ performs much worse than indicators of total influence. The $g$-index proposed by \citeN{egghe_improvement_2006} to improve the $h$-index performs indeed better than the original~($p = 3.7\,\%$, Figure~\ref{Fig-rank9:10}). The same holds for the analysed three $h$-type indices which are based on fractional counting. They have been introduced by \citeN{egghe_mathematical_2008} and by \textcolor{blue}{Schreiber} \citeyear{schreiber2008share,schreiber_fractionalized_2009} to account for varying collaboration behaviour. There is no significant difference between the two samples when we compare citation indicators which are designed to reflect the mean influence of an author's papers. We calculated three of them: the arithmetic mean of citation numbers ($p = 11.7\,\%$, Figure \ref{Fig-rank13:14}), fractionally counted citations per paper ($p = 6.2\,\%$, Figure~\ref{Fig-rank11:12}), and the median of the fractionally counted citations~($p = 26\,\%$, Figure~\ref{Fig-rank15:16}). We wondered whether for a later star a large maximum of (fractional) citations is more typical than a large value of any measure of central tendency of citation numbers. The answer is yes. The maximum of fractional citations is a better indicator of typical influence ($p = 3\,\%$, Figure~\ref{Fig-rank7:8}). We could have analysed normalised indicators of typical influence, too. We did not because indicators of typical influence do not perform better than those of total influence. We do not exclude self-citations when calculating citation indicators. There are arguments for their exclusion in evaluative bibliometrics but we assume that it would be difficult for young authors to massively cite their own papers within their first five years of publishing. We expect that weighting (fractional) paper numbers with a measure of journal reputation would improve the predictive power of output indicators. We did not test this because the only journal-reputation indicator available for us was the \textit{journal impact factor} which is not useful here---albeit often used for weighting paper numbers \cite[s.\ also the references of these papers]{Seglen1997impact-factor,lozano_weakening_2012}. Analysing 85 researchers in oncology \citeN{honekopp2012future} found that ``a linear combination of past productivity and the average paper's citation'' is a better predictor of future publication success than any of the single indicators they had studied. We did not consider combinations of indicators of productivity and of mean influence because the simpler indicators of total influence also reflect productivity---as far as the produced papers have been cited. Neglecting uncited papers is a wanted effect that is also quoted in favour of the $h$-index. \citeN{hornbostel_funding_2009} found only small differences in numbers of publications and citations between approved and rejected applicants to a German funding programm for young researchers. In an earlier study, \citeN{nederhof_peer_1987} compared 19 PhD graduates in physics with best degrees to 119 other graduates with lower grade. They considered the total number of papers before and after graduation and their total and average (short time) impact. The 19 best graduates performed significantly better but, interestingly, the impact of their papers declined and reached the level of the control-group papers a few years after graduation. The authors speculate about the reason of this phenomenon and suggest that better students could have been engaged for hot and therefore highly cited research projects. They conclude, that maybe ``the quality of the research project, and not the quality of the particular graduate is the most important determinant of both productivity and impact figures''~\cite[p.\,348]{nederhof_peer_1987}. This hypothesis could also hold for the young astrophysicists analysed by us. Its confirmation would further diminish the weight of bibliometric indicators in the evaluation of young researchers. | 14 | 4 | 1404.3084 |
1404 | 1404.1879_arXiv.txt | A new data product from the \textit{Helioseismic and Magnetic Imager} (HMI) onboard the \textit{Solar Dynamics Observatory} (SDO) called Space-weather HMI Active Region Patches ({\sf SHARP}s) is now available. SDO/HMI is the first space-based instrument to map the full-disk photospheric vector magnetic field with high cadence and continuity. The {\sf SHARP} data series provide maps in patches that encompass automatically tracked magnetic concentrations for their entire lifetime; map quantities include the photospheric vector magnetic field and its uncertainty, along with Doppler velocity, continuum intensity, and line-of-sight magnetic field. Furthermore, keywords in the {\sf SHARP} data series provide several parameters that concisely characterize the magnetic-field distribution and its deviation from a potential-field configuration. These indices may be useful for active-region event forecasting and for identifying regions of interest. The indices are calculated per patch and are available on a twelve-minute cadence. Quick-look data are available within approximately three hours of observation; definitive science products are produced approximately five weeks later. {\sf SHARP} data are available at \href{http://jsoc.stanford.edu}{{\sf jsoc.stanford.edu}} and maps are available in either of two different coordinate systems. This article describes the {\sf SHARP} data products and presents examples of {\sf SHARP} data and parameters. | \label{s:Introduction} This article describes a data product from the \textit{Solar Dynamics Observatory's Helioseismic and Magnetic Imager} (SDO/HMI) called Space-weather HMI Active Region Patches ({\sf SHARP}s). {\sf SHARP}s follow each significant patch of solar magnetic field from before the time it appears until after it disappears. The {\sf SHARP} data series presently include 16 indices computed from the vector magnetic field in active-region patches. These parameters, many of which have been associated with enhanced flare productivity, are automatically calculated for each solar active region using HMI vector magnetic-field data with a 12-minute cadence. The indices and other keywords can be used to select regions and time intervals for further study. The active-region patches are automatically identified and tracked for their entire lifetime \cite{Turmon2013}. In addition to the indices, the four {\sf SHARP} data series include the photospheric vector magnetic-field data for the patches, as well as co-registered maps of Doppler velocity, continuum intensity, line-of-sight magnetic field, and other quantities. Measurements of the photospheric magnetic field provide insight into understanding and possibly predicting eruptive phenomena in the solar atmosphere, such as flares and coronal mass ejections. For example, it is generally accepted that large, complex, and rapidly evolving photospheric active regions are the most likely to produce eruptive events \cite{zirin,priest}. As such, it is an active area of research to seek a correlation (or its rejection) between eruptive events and quantitative parameterizations of the photospheric magnetic field. Many studies have found a relationship between solar-flare productivity and various indices: magnetic helicity (\textit{e.g.} \opencite{tian}; \opencite{torokkliem}; \opencite{labonte}), free energy proxies (\textit{e.g.} \opencite{moore44}), magnetic shear angle (\textit{e.g.} \opencite{hagyard1984}; \opencite{lekabarnes2003}, \citeyear{lekabarnes2}, \citeyear{lekabarnes2007}), magnetic topology (\textit{e.g.} \opencite{Cui2006}; \opencite{lekabarnes2006}, \opencite{grust}), or the properties of active-region polarity inversion lines (\textit{e.g.} \opencite{mason}; \opencite{falconer56}; \opencite{schrijverR}). However, when \inlinecite{lekabarnes2003} conducted a discriminant analysis of over a hundred parameters calculated from vector magnetic-field measurements of seven active regions, they could identify ``no single, or even small number of, physical properties of an active region that is sufficient and necessary to produce a flare." Larger statistical samples show correlations between some vector-field non-potentiality parameters and overall flare productivity \cite{lekabarnes2007,Yang2012}, as well as correlations between the parameters themselves. Still, characteristics have yet to be identified that uniquely distinguish imminent flaring in an active region. The {\sf SHARP} data series will provide a complete record of all visible solar active regions since 1 May 2010. {\sf SHARP} data are stored in a database and readily accessible at the Joint Science Operations Center (JSOC). JSOC data products from SDO, as well as source code for the modules, can be found at \href{http://jsoc.stanford.edu}{{\sf jsoc.stanford.edu}}. Continuously updated plots of near-real-time parameters are available online (see Table~\ref{tab:urls} for URLs). We describe how the {\sf SHARP} series are created and show results for two representative active regions. We also present examples of four active-region parameters for 12 X-, M-, and C-class flaring active regions. | \label{s:analysis} {\begin{table} \caption{Flare-Producing Active Regions} \renewcommand{\arraystretch}{1.5} \renewcommand{\tabcolsep}{0.2cm} \begin{tabular}{ l r r c c } Flare Peak [TAI] & Class & HARP & NOAA AR & \parbox{1.7cm}{(Lat., Lon.)\\in Degrees} \\ \hline 2011.02.15\_01:56:00&X2.2&377&11158& (-20.20, 12.77) \\ 2011.03.09\_23:23:00&X1.5&401&11166& (8.86, 10.30) \\ 2011.09.06\_22:20:00&X2.1&833&11283& (15.13, 14.19) \\ 2012.03.07\_00:24:00&X5.4&1449&11429& (17.72, -25.90)\\ 2012.11.21\_15:30:00&M3.5&2220&11618& (7.88, -5.19) \\ 2012.11.27\_21:26:00&M1.0&2227&11620& (-13.40, 41.18) \\ 2013.01.13\_00:50:00&M1.0&2362&11652& (19.49, 12.28) \\ 2013.02.17\_15:50:00&M1.9&2491&11675& (12.43, -22.75) \\ 2012.12.25\_06:43:00&C1.8&2314&11635& (11.07, 6.60) \\ 2013.01.01\_09:06:00&C1.2&2337&11640& (27.21, -0.38) \\ 2013.01.31\_04:34:00&C1.1&2420&11663& (-10.96, 9.63) \\ 2013.02.03\_18:01:00&C1.5&2433&11665& (10.66, -2.94) \\ \end{tabular} \caption*{The following active regions that produced X-, M-, and C-class flares were used in our sample data. In the table, we list the time and position of the active region during the GOES X-Ray flux peak; however, we analyzed a five-day time series of data per active region. The latitude and longitude are given in Stonyhurst coordinates and correspond to the latitude and longitude of the flux-weighted center of active pixels at the time of the GOES X-Ray flux peak. These correspond to keywords {\sc lat\_fwt} and {\sc lon\_fwt}.} \label{tab:ar} \end{table}} {\begin{figure} \centering \caption{Active Region Profiles} \renewcommand{\tabcolsep}{0.0018\textwidth} \begin{tabular}{cc} \includegraphics[angle=90,width=0.496\textwidth]{usfluxtest10-eps-converted-to.pdf} & \includegraphics[angle=90,width=0.496\textwidth]{absnjzhtest10-eps-converted-to.pdf} \\ \includegraphics[angle=90,width=0.496\textwidth]{totpottest10-eps-converted-to.pdf} & \includegraphics[angle=90,width=0.496\textwidth]{meangamtest10-eps-converted-to.pdf} \\ \end{tabular} \caption*{Clockwise from top left, temporal profiles of the total unsigned flux [{\sc usflux}], the modulus of net the current helicity [{\sc absnjzh}], the mean value of the inclination angle [{\sc meangam}], and the integrated total free-energy density per active region [{\sc totpot}]. The entire sample is color coded: Active regions associated with X-class flares are represented with red-purples, M-class by blue-greens, and C-class by yellow-browns. For clarity a larger symbol is plotted every three hours, \textit{i.e.} every 15th point. The legend is in the top-left panel. The time profiles are adjusted to align the flare peaks a little after the start of Day 5, as denoted by the red dotted--dashed line. Error bars are plotted for all points; however, in most cases, they are smaller than the point size. Scatter in the active-region parameters for NOAA AR\,11429 for a few points following the flare peak is due to poor data quality following an eclipse: thermal changes in the HMI front window affect the focus. Periodicities in some of the parameters, most prominently in some temporal profiles of unsigned flux, are systematic effects due to the daily variation of the radial velocity of the spacecraft inherent to the geosynchronous orbit.} \label{fig:arprofiles} \end{figure}} For illustrative purposes, Figure \ref{fig:arprofiles} shows the evolution of a few {\sf SHARP} parameters for selected active regions associated with X-, M-, and C-class flares (Table \ref{tab:ar}). A more complete analysis with comprehensive statistics is left for a future publication. Region selection was based on the following criteria. i) To minimize the effects of the increased noise in limb-ward data, we require that (a) the active region must be within 45 degrees of central meridian during the GOES X-Ray flux peak, and (b) for active regions that produced multiple flares, we chose the flare that occurred while the region was closest to disk center. ii) In some cases the identification and extraction algorithm \cite{Turmon2013} identifies as one coherent magnetic structure -- \textit{i.e.}, one HARP -- a region associated with multiple NOAA active regions. For simplicity such HARPs were excluded from this sample. iii) We selected the largest flare class associated with that active region (\textit{e.g.} a multi-flaring active region chosen for a C-class flare would not be associated with an M- or X-class flare). From that list we then arbitrarily selected four regions of each flare class to show as a demonstration of the presently available {\sf SHARP} parameters. Figure \ref{fig:arprofiles} shows temporal profiles for each active region, color-coded by flare class, for the unsigned flux, the absolute value of the net current helicity, the mean of the absolute value of the inclination angle, and a proxy for the total free-energy density. These and other active region parameters appear as keywords in the {\sf SHARP} data series and so can be displayed, retrieved, or used in a query with the JSOC data-handling tools without having to retrieve the image data. A link to examples that can be used interactively with the JSOC {\sf lookdata} program can be found at the magnetic field portal (see Table \ref{tab:urls}). The temporal profiles are adjusted to align the flare occurrence time to a little after the start of Day 5, as indicated by the red dotted-dashed line. The {\sf SHARP} data can be used to create temporal profiles of the parameters for any active region since 1 May 2010. Note that at the time of writing, the HMI analysis pipeline is running as fast as practical to close the remaining gap in {\sf SHARP} coverage by mid-2014. We chose the four parameters in Figure \ref{fig:arprofiles} to suggest possible uses of {\sf SHARP} indices for quickly and easily comparing regions of interest. Magnetic flux has been well correlated with flaring activity (\textit{e.g.} \opencite{barnesleka2008}; \opencite{komm2011}; \opencite{welsch}; and \opencite{g2012}), although the line-of-sight magnetic field data are known to suffer from bias. Region 11429 was much greater in both total unsigned flux (upper left panel of Figure \ref{fig:arprofiles}) and in flare magnitude (Class X\,5.4). Small flux regions showed little flare activity. It is easy to track the growth rate of total flux, \textit{e.g.} region 11620 grows rapidly during its disk transit. Statistical studies of flare-related magnetic field configurations, including the best determinations of the true total magnetic flux, have been performed with vector magnetic data (\textit{e.g.} \opencite{lekabarnes2007}, \opencite{barnesleka2008}, \opencite{barnesleka2007}), albeit with the recognized limitations of ground-based data sources, many of which are now ameliorated with the SDO/HMI {\sf SHARP} series. Several studies use line-of-sight magnetogram data to show that the photospheric magnetic field can store up to 50\,\% of the total magnetic energy (\textit{e.g.} \opencite{ForbesPriest2002} and references therein); however, this percentage may change when considering the transverse component of the vector magnetic field. The integrated free-energy density {\sc totpot}, shown in the lower-left panel, seems to increase significantly for most, but not all, of the large-flare regions; the exception was region 11283. \inlinecite{fan} and \inlinecite{fang} suggest that some eruptive flares result in an imbalance of magnetic torque at the photosphere; this may have implications for the photospheric current helicity. Two of the largest regions, 11429 and 11158, had a large net current helicity and showed abrupt changes at the time of their X-class flares (upper right panel). C\,1.8-class region 11631 also had reasonably high net current helicity. A more comprehensive analysis is required to see if a significant relationship exists. \inlinecite{hudson} noted that explosive events should decrease coronal magnetic energy and thus lead the coronal field to contract, increasing the inclination angle or the angle between the vertical and horizontal photospheric field. Indeed, several studies (\opencite{liudelta}; \opencite{Petrie2012}, \citeyear{Petrie2013}; \opencite{sun}; \opencite{wangpil}) show that the horizontal component of the magnetic field changes within select areas of an active region -- in particular, near the polarity inversion line. However, the mean inclination angles shown in the lower-right panel give no indication of an obvious systematic relationship to flare size or timing. Such field changes may not be detectable in the large-scale {\sf SHARP} averages shown in Figure \ref{fig:arprofiles}. We have implemented an interface to automatically submit {\sf SHARP} parameters, as well as HARP geometry and location keywords, to the Heliophysics Events Knowledgebase (HEK; \opencite{hurlburt2012}). The HEK is a web-based tool designed to aid researchers in finding features and events of interest. Various features extracted or extrapolated from HMI data, such as the location of sunspots, polarity-inversion lines, and non-linear force-free numerical models, are already available in the HEK (see Sections 13\,--\,15 of \opencite{martens2012}). The list of active-region parameters in the {\sf SHARP} data series is by no means exhaustive. We plan to include additional parameters, including those that characterize polarity-inversion lines and field morphologies of varying complexity. Several studies show a relationship between flaring activity and properties of the polarity-inversion line. For example, \inlinecite{schrijverR} defined a parameter [$R$] that measures the flux contribution surrounding polarity-inversion lines. After determining $R$ for 289 active regions using line-of-sight magnetograms from the \textit{Solar and Heliospheric Observatory's Michelson Doppler Imager} (SOHO/MDI), he found that ``large flares, without exception, are associated with pronounced high-gradient polarity-separation lines." \inlinecite{mason} developed a similar parameter, called the Gradient-Weighted Inversion Line Length (GWILL), applied it to 71\,000 MDI line-of-sight magnetograms of 1075 active regions, and found that GWILL shows a 35\,\% increase during the 40 hours prior to an X-class flare. \inlinecite{falconer56} devised a similar parameter [WL$_\textit{sg}$] and computed it for 56 vector magnetic field measurements of active regions. Using WL$_\textit{sg}$, they could predict CMEs with a 75\,\% success rate. Two additional approaches have been widely used to characterize active regions in the context of energetic-event productivity. One is to model the coronal magnetic field from the observed photospheric boundary and parametrize the results in order to gauge the coronal magnetic field complexity and morphology. Examples of relevant parameterizations include descriptions of the magnetic connectivity ({\it e.g.} $\phi_{ij}$ from \opencite{lekabarnes2006}, and $B_{\rm eff}$ from \opencite{grust}), and topological descriptions (\opencite{lekabarnes2006}; \opencite{barnes2007}; \opencite{uu2007}; \opencite{cook2009}). The results are fairly convincing that parameters based on models of the coronal magnetic field can add unique information to what is otherwise available from characterizing the photosphere. Secondly, the fractal spectrum and related parameterizations of the photospheric field provide additional measures of the magnetic complexity, although the event-predictive capabilities of such measures require additional research. While \inlinecite{mcateer2005} and \inlinecite{abra} found a relation between fractal dimension and the range of multifractality spectra and flare productivity, respectively, \inlinecite{g2012} found that ``both flaring and non-flaring active regions exhibit significant fractality, multifractality, and non-Kolmogorov turbulence, but none of the three tested parameters manages to distinguish active regions with major flares from the flare-quiet ones." More study is required using these analysis approaches. As the database of {\sf SHARP} active-region parameters grows, it will include parameters derived from these and other relevant studies. | 14 | 4 | 1404.1879 |
1404 | 1404.1562_arXiv.txt | NGC 4194 is a post-merger starburst known as The Medusa for its striking tidal features. We present here a detailed study of the structure and kinematics of ionized gas in the central 0.65 kpc of the Medusa. The data include radio continuum maps with resolution up to $0.18\arcsec$ (35 pc) and a $12.8\mu$m [NeII] data cube with spectral resolution $\sim4$\kms: the first {\it high resolution, extinction-free} observations of this remarkable object. The ionized gas has the kinematic signature of a core in solid-body rotation. The starburst has formed a complex of bright compact \HII~regions, probably excited by deeply embedded super star clusters, but none of these sources is a convincing candidate for a galactic nucleus. The nuclei of the merger partners that created the Medusa have not yet been identified. | The most luminous starbursts appear to be caused by major mergers of galaxies \citep[e.g.,]{1988ApJ...328L..35S} and are rare because major mergers are infrequent. Minor mergers create LIRGS; slightly less luminous but much more common, and important to galaxy evolution due to their sheer numbers \citep{KA10}. Minor mergers, like major mergers, appear to instigate intense star formation in compact regions and create concentrated sources. But minor mergers evolve differently from major mergers, so the characteristics of star formation are likely to be different. How does star formation develop in a minor merger? How will these starbursts evolve and how do they affect their surroundings as they contribute to the newly formed galaxy? To answer those questions we need to understand the structure and kinematics of the gas ionized by the embedded stars with the highest possible spectral and spatial resolution. We consider here the case of NGC~4194, ``The Medusa", a galaxy with distorted morphology and luminous star formation that appears to be the result of an unequal merger between an elliptical and a smaller spiral. This is the fourth paper in a series on high resolution spectroscopy of intense extragalactic star formation sources in the middle infrared \citep{BT10,BT12, BT13}. We use mid-infrared lines of metal ions to trace the kinematics and spatial distribution of ionized gas in Galactic {\HII} regions and in starburst galaxies \citep{{AC95},{ZH08},{BT13}} because they are little affected by extinction and permit us to attain true spectral resolution, including thermal effects, much higher than is possible with any hydrogen line. The 'Medusa galaxy', NGC 4194 (a.k.a. Arp 160 and Mkn 201) is a starburst galaxy at 39 Mpc % distance (1\arcsec = 190 pc) with striking tidal features; it has been variously classed as Magellenic, Sm(pec) and BCG. The central kpc of NGC 4194 is a powerful infrared source with 60\um/100\um $\approx 1$, typical of starburst heating. Spitzer IRS spectra (from the Heritage Archive) show a spectrum typical of a starburst-dominated galaxy, with little if any contribution from an AGN. NGC 4194 is believed to be a merger remnant, with the favoured history being a small gas-rich spiral falling into an elliptical four times it mass \citep{MA08}. The central region of NGC 4194 is the site of intense star formation: \citet{WE04} and \citet{HA06} find numerous bright optical and UV knots that they identify as very young globular cluster precursors. But the structure of this central starburst has not been probed. The observations are either too low in spatial resolution (e.g. the 2Mass survey) or too affected by the deep extinction \citep{HA04} to determine the structure. \citet{BE05} mapped the center of NGC 4194 at 21 cm with sub-arcsecond resolution and found two compact sources separated by only 0.35\arcsec~, which they identify with the galactic nucleus, and which \citet{MA08} appear to tentatively accept as the nuclei of the progenitor galaxies, but the nature of these source and their relation to the merger history have not been explored. We report here on radio continuum maps of NGC 4194 with sub-arcsecond spatial resolution and on spectra of the 12.8\um~emission line of [NeII] with velocity resolution better than 5\kms. The radio maps are at short cm wavelengths, which are sensitive to both the thermal emission of {\HII} regions and the non-thermal emission of SNR. The fine-structure line of $Ne^+$ at 12.8\um~ is usually one of the strongest mid-infrared emission lines in {\HII}~ regions and is a preferred kinematic probe because of its low susceptibility to thermal broadening; in a $T_e =7500 K$ {\HII} region the FWHM from thermal effects will be $4.1$\kms~ compared to $18$\kms~ for $H^+$. | We have presented high-resolution radio continuum maps at 6, 3.6 and 2 cm, and a high spectral-resolution velocity-position cube in the [NeII] $12.8\mu$m emission line, of the central $1.3~kpc$ of NGC 4194. These maps are the first high resolution, extinction-free, measurements of ionized gas in the center of this galaxy and trace the star formation regions with resolution up to 0.18\arcsec ($\sim35~pc$). We find that: \begin{itemize} \item NGC 4194 hosts a nuclear starburst that has formed multiple compact sources, apparently groups of embedded super star clusters, within a ~3\arcsec ~radius. The low-level radio emission suggets a 'nuclear spiral' but that is not confirmed by the kinematics. \item Based on the thermal radio emission at 2 cm, which agrees well with previous observations at 2.7mm, we find for the central $\sim$10\arcsec\ region a thermal free-free flux of $S_{2cm}^{thermal} = 5.6 \pm 1~\rm mJy$, which implies a Lyman continuum rate of $N_{Lyc} = 1.0 \times 10^{54}~(D/\rm 39~Mpc)^2~s^{-1}$. For a Kroupa IMF and a 3~Myr starburst, this implies a star formation rate of $\sim$10~$M_\odot~\rm y^{-1}$, and a luminosity in massive young stars of $L_{OB} = 3 \times 10^{10}~\rm L_\odot$, about a third of the total infrared luminosity of $L_{IR} = 8.5 \times 10^{10}~\rm L_\odot$. The star formation in this galaxy is dispersed widely over the inner 10\arcsec~(1.9 kpc) region. Our radio observations are not sensitive to regions with 2 cm fluxes less than $\sim 0.1$~mJy, or $N_{Lyc} < 2 \times 10^{52}~(D/\rm 39~Mpc)^2~s^{-1}$, so it is possible that the remaining infrared luminosity arises in smaller, and widely dispersed, star forming regions within the system. \item Of the compact emission sources that are bright enough to analyze, one has a pure thermal or slightly rising spectrum, typical of a very young embedded \HII~region. The others are older and have a mix of thermal and significant non-thermal emission. The [NeII] line velocity dispersions are consistent with the gravitational effects of many dense star clusters. \item The ionized gas has a smooth N-S velocity gradient of 390 \kms kpc$^{-1}$ across the observed region, consistent with a core in solid body rotation. \item None of the radio sources can be convincingly identified with a galactic nucleus. The nuclei of the original merger partners have not been identified. \item The CO velocity field shows that a mass concentration is present at $\alpha=12^h14^m09.5^s, \delta= +54^o 31^{'} 36^{''}$. This location is in between and roughly equidistant from the three star formation regions, and there is no star formation detected there. \end{itemize} How can the last two items on this list be reconciled with the scenario that the Medusa is a minor merger? Each of the merger partners presumably hosted a nucleus of mass $10^6-10^8M_\odot$ that would be detected via their influence on the kinematics. It is possible, and would be consistent with the simulations, to have both original nuclei now included in the mass concentration detected in the isovelocity contours. But in this case the nuclei must be devoid of star formation and ionised gas, or they would be detected in the radio and [NeII]. The gas and stars in the center of NGC 4194 have not come to equilibrium and the starburst may continue in regions now quiescent. Measurements of ionised and molecular gas with higher spatial resolution, and simulations exploring the central kpc, could perhaps find more clues to the behaviour of this remarkable galaxy. \bigskip \bigskip TEXES observations at the IRTF were supported by NSF AST-0607312 and by AST-0708074 to Matt Richter. This research has made use of the NASA\&IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, Caltech, under contract with NASA. We thank an anonymous referee for careful and thoughtful comments. | 14 | 4 | 1404.1562 |
1404 | 1404.5946_arXiv.txt | We consider the vacuum energy of massive quantum fields in an expanding universe. We define a conserved renormalized energy-momentum tensor by means of a comoving cutoff regularization. Using exact solutions for de Sitter space-time, we show that in a certain range of mass and renormalization scales there is a contribution to the vacuum energy density that scales as nonrelativistic matter and that such a contribution becomes dominant at late times. By means of the WKB approximation, we find that these results can be extended to arbitrary Robertson-Walker geometries. We study the range of parameters in which the vacuum energy density would be compatible with current limits on dark matter abundance. Finally, by calculating the vacuum energy in a perturbed Robertson-Walker background, we obtain the speed of sound of density perturbations and show that the vacuum energy density contrast can grow on sub-Hubble scales as in standard cold dark matter scenarios. | \label{intro} Since the discovery of the accelerated expansion of the Universe \cite{SNIa}, we have learned that most of the Universe content is a kind of cosmic fluid with negative pressure known as dark energy. Furthermore, even the dominant contribution to the matter content is to a high degree unknown, being described by a weakly interacting component which has received the name of dark matter. This present knowledge about the composition of the Universe has been possible thanks to precise measurements including for instance CMB temperature power spectrum \cite{Planck_WMAP7}, large-scale structures correlation functions (BAOs \cite{Eisenstein}) or high-redshift type Ia supernovae \cite{SNIa}. To the best knowledge of the authors a theoretical explanation of the values or even the presence of these dark components is absent. Considering the simplest model of dark energy, i.e.\ a cosmological constant, it is believed that this term has classical and quantum contributions \cite{Shapiro1,Shapiro2,Sola,Martin}. The classical one may just be taken as a parameter of the theory since the most general form of the General Relativity equations may include this contribution without breaking any of the fundamental assumptions of the theory such as general covariance or energy-momentum conservation \cite{Lovelock,Wald,HE}. On the other hand, the quantum contribution is expected from quantum field theory grounds. However, as it is widely known, the theoretical predictions of its value and the measured one differ in many orders of magnitude. This difference may be compensated by the classical contribution leaving us with the observed value. The fine tuning necessary for this to happen is one of the drawbacks that have brought us to the cosmological constant problem. However, many of the standard arguments about the contribution of the zero-point quantum fluctuations to the cosmological constant are based on calculations performed in flat space-time, in which the vacuum state is assumed to respect the Lorentz invariance of the Minkowski space-time. In fact, when taking into account that the actual geometry of the Universe is not Minkowskian and moving to a Robertson-Walker background, new contributions to the vacuum energy-momentum tensor appear \cite{Birrell} and new aspects of the problem are revealed which were not apparent in the flat space-time calculations \cite{Maggiore,Hollenstein}. One of the major problems in calculating the vacuum energy density is the divergent integral over the Fourier modes appearing in the canonical quantization procedure. Several methods have been proposed in the literature in order to obtain finite renormalized results. Thus in general, the physical renormalized vacuum expectation value of the energy-momentum tensor $\langle 0\vert T_{\mu \nu}\vert 0\rangle_{\text{ren}}$ is obtained from the divergent bare quantities by subtracting the regularized divergences by means of appropriate counterterms, i.e \begin{eqnarray} \langle 0\vert T_{\mu \nu}\vert 0\rangle_{\text{ren}}=\langle 0\vert T_{\mu \nu}\vert 0\rangle_{\text{bare}}+\langle 0\vert T_{\mu \nu}\vert 0\rangle_{\text{count}}\,. \end{eqnarray} Different schemes have been proposed to obtain the regularized bare quantities. For instance, in flat space-time one of the simplest possibilities is to use a cutoff on the three-momentum of the modes $\Lambda_P$. However, it has been argued \cite{Akhmedov,Ossola} that the maximum value of the three-momentum is not a Lorentz invariant quantity and therefore, the regularized bare contributions break the Lorentz symmetry of Minkowski space-time. Indeed, in the case of a real minimally coupled scalar field, the regularized bare quantities read \begin{eqnarray} \langle 0\vert T^{\mu}_{ \;\;\nu}\vert 0\rangle_{\text{bare}}=\mbox{diag}(\rho_{\text{bare}},-p_{\text{bare}},-p_{\text{bare}},-p_{\text{bare}}) \end{eqnarray} with the leading contributions \begin{eqnarray} \rho_{\text{bare}}=\frac{1}{16\pi^2}\left(\Lambda_P^4+m^2\Lambda_P^2- m^4\ln\left(\frac{\Lambda_P}{\mu}\right)\right) \end{eqnarray} \begin{eqnarray} p_{\text{bare}}=\frac{1}{16\pi^2}\left(\frac{\Lambda_P^4}{3}-\frac{m^2\Lambda_P^2}{3}+ m^4\ln\left(\frac{\Lambda_P}{\mu}\right)\right) \end{eqnarray} i.e. in $\langle 0\vert T_{\mu\nu}\vert 0\rangle_{\text{bare}}$ only the logarithmic term would be proportional to $\eta_{\mu\nu}$. This problem is avoided in other regularization schemes, such as dimensional regularization, which preserve the underlying symmetries of the theory. Dimensional regularization has been carried out in flat space-time \cite{Akhmedov} yielding a cosmological constant contribution with $p_{\text{bare}}=-\rho_{\text{bare}}$, where again for scalar fields of \mbox{mass $m$} \begin{eqnarray} \rho_{\text{bare}}&=&-\frac{m^4}{64\pi^2}\left(\frac{2}{\epsilon}+\frac{3}{2}-\gamma-\ln\left(\frac{m^2}{4\pi\mu^2}\right)\right) \end{eqnarray} with $D=4-\epsilon$ the space-time dimension, $\gamma$ the Euler-Mascheroni constant and $\mu$ the renormalization scale. In curved space-time, it can be seen that the vacuum expectation value of the energy-momentum tensor is no longer a simple cosmological constant term, but in general is a nonlocal functional of the metric tensor. The calculation of the divergent local part in dimensional regularization shows that there is a contribution that behaves as a cosmological constant together with other local and conserved tensors which depend on the curvatures. Exact results including also the finite contributions have been obtained only for conformally trivial systems \cite{Birrell}. Notice, however, that strictly speaking the problem we mentioned with the cutoff regularization would not be present in a Robertson-Walker cosmological background, since in this case Lorentz invariance is not a symmetry of the background metric. As a matter of fact, in a Robertson-Walker background there is a special frame of reference (that at rest with the CMB) which is most suitable for calculations. In this case, a three-dimensional momentum cutoff defined over the homogeneous and isotropic spatial sections may have a more satisfying interpretation, since it respects the symmetries of the background geometry. Accordingly, several recent works have focused on the possibility of using different kinds of cutoff regularizations in Robertson-Walker backgrounds. Thus in \cite{Bilic1} a cutoff scale was used in the context of supersymmetric models, and in \cite{Bilic2} a covariant cutoff scheme was proposed in general curved space-times. On the other hand, one may use a cutoff to perform the integration and consider different renormalization prescriptions according to the counterterms included. Thus for instance, in \cite{Maggiore} the vacuum energy density obtained in a flat space-time is subtracted in a similar process to the definition of the Arnowitt-Deser-Misner mass on asymptotically flat space-times. Notice that in general, different renormalization schemes may provide different renormalized expressions. On general grounds \cite{Maggiore} quantum field theory makes no prediction about the actual value of $\langle 0\vert T_{\mu \nu}\vert 0\rangle_{\text{ren}}$, just in the same way as it does not predict the physical (renormalized) value of the electron charge or mass, but these quantities can only be obtained from experimental measurements. Despite the fact that the physical value of the vacuum energy can only be determined from observations, there are, however, several conditions that from a purely phenomenological point of view (and neglecting possible fine-tuned cancellations with other contributions) a physical renormalized energy-momentum tensor should satisfy \begin{itemize} \item $\langle 0\vert T_{\mu \nu}\vert 0\rangle_{\text{ren}}$ should be covariant and conserved. Notice that in a curved space-time a covariant expectation value of the energy-momentum tensor can involve not only the metric tensor but also other tensors such as curvatures or any other object which transforms covariantly under diffeomorphisms \cite{Birrell}. On the other hand, regarding conservation, in general, if nongravitational interactions of the scalar field are taken into account, then vacuum energy could be coupled to other components and the conservation should be required for the total energy-momentum tensor. In any case, in this work we limit ourselves to the simplest noninteracting case and therefore the vacuum energy-momentum tensor should be independently conserved. \item $\rho_{\text{ren}}\lsim \rho_c$, i.e. in order to have phenomenologically viable contributions, the vacuum energy should be smaller than the dominant component of the Universe at early times. Only at late times, and if we assume vacuum energy to play a role in the dark matter or dark energy problems, its value could be comparable to the critical density $\rho_c=3H^2/8\pi G$. \end{itemize} In this work we will explore the possibility of constructing the renormalized vacuum energy momentum by means of a {\it comoving} three-momentum cutoff. Unlike previous works which focused on {\it physical} cutoff scales, the use of this kind of regularization provides covariant expressions for the regularized integrals and also guarantees that the bare energy-momentum tensor is conserved. Accordingly, we do not need to include noncovariant counterterms in order to render the final results covariant. This can easily be seen in the following example. Let us consider the cutoff regularized bare energy-momentum tensor for minimally coupled massless scalar fields in a Robertson-Walker background \cite{Parker, Fulling, Maggiore}. In this case \begin{eqnarray} \rho_{\text{bare}}&=&\frac{\Lambda_P^4}{16\pi^2}+\frac{H^2(t)\Lambda_P^2}{16\pi^2}+\Od(H^4\ln \Lambda_P) \\ p_{\text{bare}}&=&\frac{\Lambda_P^4}{48\pi^2}+c_1\frac{H^2(t)\Lambda_P^2}{16\pi^2}+\Od(H^4\ln \Lambda_P) \end{eqnarray} where $c_1=$ $-1/3$, 1, 2/3 in the de Sitter, radiation and matter eras respectively. Here $\Lambda_P$ is a constant physical momentum cutoff. Notice that indeed the use of the physical cutoff prevents the bare energy-momentum tensor from being conserved. This is clearly seen for example from the dominant quartic terms whose effective equation of state would be $p_{\text{bare}}=\frac{1}{3}\rho_{\text{bare}}$, i.e. corresponding to radiation, but, however, they do not scale with $a(t)$. As shown in \cite{Maggiore} this is not a problem, since the bare quantities are not observable and by adding appropriate (noncovariant) counterterms it would always be possible to render the renormalized energy-momentum tensor conserved, provided $\rho_{\text{ren}}=-p_{\text{ren}}$. However, if we consider instead a constant comoving cutoff $\Lambda_c$, the above results read \begin{eqnarray} \rho_{\text{bare}}&=&\frac{\Lambda_c^4}{16\pi^2a^4}+\frac{H^2(t)\Lambda_c^2}{16\pi^2a^2}+\Od(H^4\ln\Lambda_c) \label{bare1} \\ p_{\text{bare}}&=&\frac{\Lambda_c^4}{48\pi^2a^4}+c_1\frac{H^2(t)\Lambda_c^2}{16\pi^2a^2}+\Od(H^4\ln \Lambda_c) \label{bare2} \end{eqnarray} which yield a conserved bare energy-momentum tensor as expected according to our previous discussion. Indeed, notice that now the leading quartic term scales as expected according to its equation of state, i.e. as radiation, and the same is true for the rest of terms. Since each of the divergent contributions (quartic, quadratic or logarithmic) is conserved independently, it would be possible in principle to add different conserved counterterms for each of them. In the simplest possibility, the counterterms are just given by the same expressions (\ref{bare1}) and (\ref{bare2}) but in which the modes have been integrated from some constant comoving renormalization scale $\Lambda_R$ up to the ultraviolet cutoff $\Lambda_c$, i.e. just subtracting the contributions of the modes in the range $[\Lambda_R,\Lambda_c]$. Then in this case the physical interpretation of the renormalized quantities is straightforward, since only the modes in the unsubtracted range $[0,\Lambda_R]$ will contribute. Thus, we can simply write \begin{eqnarray} \rho_{\text{ren}}&=&\frac{\Lambda_R^4}{16\pi^2a^4}+\frac{H^2(t)\Lambda_R^2}{16\pi^2a^2}+\Od(H^4\ln \Lambda_R) \\ p_{\text{ren}}&=&\frac{\Lambda_R^4}{48\pi^2a^4}+c_1\frac{H^2(t)\Lambda_R^2}{16\pi^2a^2}+\Od(H^4\ln \Lambda_R)\,. \end{eqnarray} Notice that $\Lambda_R$ is understood as a limit on the frequency of the Fourier modes which actually contribute to the vacuum energy and in general can be different from the standard quantum field theory UV cutoff which sets the range of validity of the theory. Thus for instance in \cite{holo2,holo3} $\Lambda_R$ is obtained by demanding that no state in the Hilbert space can have an energy such that the corresponding Schwarzschild radius exceeds the Hubble (or the event) horizon, i.e. modes which would have collapsed in a black hole are excluded in the computation of the vacuum energy. This is a generic prediction of so called holographic \cite{holo1} but also of nonholographic \cite{Visser} entropy bounds on the number of physical quantum states for any gravitating system. These models generically predict $\Lambda_R$ much smaller than the quantum field theory cutoff, thus alleviating the cosmological constant problem. In this work, however, we will not assume any particular scenario for the determination of $\Lambda_R$, instead we will adopt a phenomenological point of view leaving it as a free parameter to be fixed by observations. When trying to extend the renormalization procedure we have just described to the case of massive fields, an additional scale $m$ appears in the problem which opens up different regimes for the vacuum energy behavior. Thus, in the case in which the comoving mass is larger than the renormalization scale, i.e. $m^2a^2> \Lambda_R^2$, we will show that the effective equation of state of vacuum energy is that of nonrelativistic matter. In order to obtain this kind of results, it will be necessary to determine the behavior of the integrals not only in the high-momenta (UV) regime, as is usually considered in the literature, but also for low momenta (IR). We will show that the dark matter behavior of vacuum energy also holds at the level of perturbations, thus opening up the quite unexpected possibility for the vacuum energy to form large scale structures. The paper is organized as follows: in Sec.\ II we introduce the basic expressions for the quantization of scalar fields in a Robertson-Walker background. In Sec.\ III we particularize to de Sitter space-times and obtain exact expressions for both massless and massive fields. In Sec.\ IV we consider asymptotic expressions in the UV limit, and in Sec.\ V the results in the IR are discussed in more detail. Section VI is devoted to the generalization to arbitrary Robertson-Walker geometries, and in Sec.\ VII we calculate the vacuum energy-momentum tensor on a perturbed Robertson-Walker background and obtain the general expression for the evolution of the density contrast of the vacuum energy. Section VIII contains the main conclusions of the work. | In this work we have explored the possibility of defining the renormalized vacuum energy-momentum tensor for massive fields in an expanding universe by means of a constant comoving momentum cutoff. Although we have illustrated this idea with scalar fields, the results would hold for any massive bosonic or fermionic degree of freedom. We have shown that this regularization procedure allows one to obtain a covariantly conserved renormalized energy-momentum tensor without the need of introducing noncovariant counterterms. The behavior of the vacuum energy is then shown to depend on the relative size of the comoving mass of field ($am$) with respect to the cutoff. For large cutoffs, the UV modes dominate and the vacuum energy has the different contributions which have already been discussed in the literature \cite{Maggiore}. In the case of low cutoffs (large masses) or late times, the IR modes dominate and the vacuum energy behaves as nonrelativistic matter. This result holds in any Robertson-Walker background and seems to be independent of the UV behavior. Moreover, vacuum energy density perturbations in this regime are shown to have a low speed of sound which implies that large scale structures could be seeded by vacuum energy fluctuations. \label{sec:conclusions} \vspace{0.5cm} \subsection | 14 | 4 | 1404.5946 |
1404 | 1404.5800_arXiv.txt | An accurate determination of the mass-loss rate of the progenitor stars to core-collapse supernovae is often limited by uncertainties pertaining to various model assumptions. It is shown that under conditions when the temperature of the circumstellar medium is set by heating due to free-free absorption, observations of the accompanying free-free optical depth allow a direct determination of the mass-loss rate from observed quantities in a rather model independent way. The temperature is determined self-consistently, which results in a characteristic time dependence of the free-free optical depth. This can be used to distinguish free-free heating from other heating mechanisms. Since the importance of free-free heating is quite model dependent, this also makes possible several consistency checks of the deduced mass-loss rate. It is argued that the free-free absorption observed in SN 1993J is consistent with heating from free-free absorption. The deduced mass-loss rate of the progenitor star is, approximately, $10^{-5} \ml$ for a wind velocity of $10$\,km\,s$^{-1}$. | The properties of the circumstellar medium into which the explosion of a core-collapse supernova expands are determined by several different effects. The density structure is mainly set by the wind of the progenitor star, while its temperature is likely to be affected by radiation coming from the supernova. The initial flash of radiation from the breakout of the shock from below the stellar surface as well as the radiation from the viscous shocks resulting from the interaction with the circumstellar medium can both contribute to the heating. Since the resulting temperature depends also on the cooling properties of the gas, a self-consistent determination of the level of ionization is important. This is a non-trivial problem, which tends to make conclusions rather model dependent. There are several ways to infer the density and temperature of the circumstellar medium. An analysis of the emission assumed to be emitted from behind the viscous shocks in the standard model \citep{che82a} can constrain its density. The external medium can also be studied directly either by the effects it has on the supernova radiation or its narrow line emission excited by this radiation \citep[e.g., SNe IIn;][]{fil97}. The X-ray emission from the shocked gas is likely dominated by bremsstrahlung and/or Comptonization of the photospheric photons. A proper modeling of this emission should then give a good estimate of the density; i.e., the mass-loss rate of the progenitor star. In common with the temperature of the circumstellar medium, the result can be rather model dependent; for example, in SN 1993J both the forward \citep{fra96} and the reverse \citep{suz93} shock have been suggested as the location for the X-ray emission leading to very different mass-loss rates. External free-free absorption is sensitive to the density and temperature of the circumstellar medium. It was recognized early on \citep{che82b} that the turn-over of the radio spectrum at low frequencies seen in several supernovae could, at least in part, be due to free-free absorption. With good enough data in the low frequency range, free-free absorption can be separated from a possible contribution from synchrotron self-absorption. Even though the circumstellar medium can normally be assumed to be fully ionized \citep[e.g.,][]{che82b}, a limiting factor for those cases where free-free absorption is apparent is the sensitivity of the deduced mass-loss rate to its temperature. Usually this is dealt with by either assuming the temperature to have a given prescribed value \citep[e.g.,][]{wei02} or by parameterizing the temperature and deduce the relevant parameters from modeling \citep{f/b98}. In either case the accuracy of the mass-loss rate deduced from observations is no better than the assumptions made regarding the temperature. This paper considers the possibility that the main heating mechanism of the circumstellar medium is free-free absorption. Observations of the resulting free-free optical depth then allows a self-consistent determination of the temperature and, hence, the density. It is argued that for supernovae expanding into a hydrogen rich circumstellar medium, free-free absorption may indeed set the temperature immediately ahead of the forward shock. In Section\,2 the heating due to free-free absorption of a synchrotron spectrum is discussed analytically using a few simplifying assumptions. The derived temperature is used in Section\,3 to calculate the resulting optical depth to free-free absorption. More exact numerical calculations are presented in Section\,4. The circumstances under which the initial temperature of the circumstellar medium is low enough for the heating by free-feee absorption to be important are discussed in Section\,5. A discussion of the results follows in Section\,6 together with a summery of the main conclusions. Unless stated otherwise, cgs-units are used throughout the paper. | \label{sect6} When the temperature of the circumstellar medium is determined by free-free absorption, observation of the free-free optical depth makes it possible to directly relate the mass-loss rate to observed quantities only. This gives a method to obtain a value of the mass-loss rate which is considerably less model dependent than those normally used. It should be noticed that the brightness temperature is often not directly observable. Although for a standard synchrotron model its value is quite insensitive even to rather large variations of source parameters, the presence of inhomogeneities, large deviations from equipartition between magnetic fields and relativistic particles and/or cooling of the latter can have non-negligible effects on the deduced mass-loss rate. The analytical expression for the mass-loss rate (equ.\,(\ref{eq:1.7})) gives a rather good estimate for moderate optical depths. Although the temperature immediately ahead of the shock is adequately described by the analytical expressions, increasing the optical depth causes the heating to be localized closer to the shock. This leads, on average, to a lower temperature in the region where most of the free-free absorption occurs. Hence, using the analytical expression for the mass-loses rate would then give a value larger than the actual one. Since the time variation of the free-free optical depth is expected to be the best way to distinguish free-free absorption from other heating mechanisms, these analytical approximations should allow to evaluate the importance of the former. They can also be used to make consistency checks of the deduced mass-loss rate. For large mass-loss rates several effects can invalidate one or more of the assumptions leading up to the results in Sections 2 and 3; for example, at some density cooling will balance free-free heating and thereby reduce the maximum temperature of the circumstellar gas ahead of the shock. Likewise, recombination may become important at distances corresponding to the initial phases of radio emission. When this occurs, reionization by radiation with a spectrum hard enough would result in a temperature larger than that possible for free-free heating, making free-free heating negligible. Also, the Comptonized radiation from behind the shock hardens with increasing density and could provide an additional heating mechanism \citep{fra96}. The mass-loss rates, where these various effects set in, are model dependent and, in particular, the shock velocity is important. A prerequisite for free-free heating to leave a distinct mark on the free-free absorption is an initial temperature not much larger than $10^5$\,K. As discussed above, this requires an ionizing spectrum that is not too hard; for example, a black body or a Wien spectrum would give too high a temperature. Hence, observations of free-free absorption can be used to constrain the spectral distribution of the radiation in the initial flash associated with the breakout of the supernova shock. It was argued in Section 5.2.1 that the free-free absorption in SN 1993J could plausibly be explained by a phase where free-free heating was important. This would imply that a significant fraction of the bremsstrahlung seed photons behind the breakout shock did not reach Compton equilibrium. The mass-loss rate of the progenitor stars to supernovae is an essential quantity not only for understanding the later evolutionary stages of massive stars but also as an input parameter for the physics governing the conditions behind the viscous shock. The non-thermal properties of the shocked gas are an important aspect particularly of the forward shock. These are not well known. The reason is not only limited observations but also that the relevant physics is only partly understood; for example, the injection problem \citep[e.g.,][]{bla94} is still not solved and the amplification of the magnetic field behind shocks cannot yet be calculated from basic physics. The determination from observations of the fractions of the thermal energy input behind the shock which go into relativistic electrons and magnetic fields could give important constraints to ongoing attempts to understand both of these processes \citep [e.g.,][]{c/s13,ell13}. Although, in principle, the energy densities of relativistic electrons and magnetic fields can be obtain from an analysis of the synchrotron emission, their fraction of the total energy density behind the shock depends on the density of the circumstellar medium, i.e., the mass-loss rate of the progenitor star. A related issue is the occurrence of non-linear shocks \citep[eg.,][]{b/e99,bla05} in which the pressure behind the shock is dominated by relativistic particles. Again, the efficiency of injecting particles into the acceleration process is an important parameter determining the characteristics of such shocks. A reliable determination of the mass-loss rate could then contribute to a better understanding of a wide range of issues. In conclusion, the main points of the present paper can be summarized as follows: 1) When the heating of the circumstellar medium is by free-free absorption, its temperature can be calculated self-consistently. As a result the density of the circumstellar medium can be obtained directly from the observed free-free optical depth in a rather model independent way. The maximum temperature is around $10^5$\,K for typical supernova parameters and occurs for optical depths of order unity. 2) It was argued that for a hydrogen rich circumstellar medium, the temperature resulting from ionization by the initial flash of radiation from the shock breakout is lower than $10^5$\,K. Hence, for such supernovae the main heating mechanism of the circumstellar medium may be free-free absorption. 3) The observed time dependence of the free-free optical depth in SN 1993J can be accounted for by heating due to free-free absorption. The resulting value of the mass-loss rate of the progenitor star is estimated to be $(0.8\,-\,1.0)\times 10^{-5}\ml$ for a wind velocity of $10$\,km\,s$^{-1}$. P.L. acknowledges support from the Swedish Research Council. \clearpage | 14 | 4 | 1404.5800 |
1404 | 1404.0939_arXiv.txt | {} {We study the dark nature of GRB\,130528A through multi-wavelength observations and conclude that the main reason for the optical darkness is local extinction inside of the host galaxy.} {Automatic observations were performed at the Burst Optical Observer and Transient Exploring System (BOOTES)-4/MET robotic telescope. We also triggered target of opportunity (ToO) observations at Observatorio de Sierra Nevada (OSN), IRAM Plateau de Bure Interferometer (PdBI) and Gran Telescopio Canarias (GTC + OSIRIS). The host galaxy photometric observations in optical to near-infrared (nIR) wavelengths were achieved through large ground-based aperture telescopes, such as 10.4m Gran Telescopio Canarias (GTC), 4.2m William Herschel Telescope (WHT), 6m Bolshoi Teleskop Alt-azimutalnyi (BTA) telescope, and 2m Liverpool Telescope (LT). Based on these observations, spectral energy distributions (SED) for the host galaxy and afterglow were constructed.} {Thanks to millimetre (mm) observations at PdBI, we confirm the presence of a mm source within the XRT error circle that faded over the course of our observations and identify the host galaxy. However, we do not find any credible optical source within early observations with BOOTES-4/MET and 1.5m OSN telescopes. Spectroscopic observation of this galaxy by GTC showed a single faint emission line that likely corresponds to [OII] 3727$\AA$ at a redshift of 1.250 $\pm$ 0.001, implying a star formation rate (SFR)($M_{\odot}$/yr) $\textgreater$ 6.18 $M_{\odot}$/yr without correcting for dust extinction. The probable line-of-sight extinction towards GRB\,130528A is revealed through analysis of the afterglow SED, resulting in a value of $A^{GRB}_{V}$ $\geq$ 0.9 at the rest frame; this is comparable to extinction levels found among other dark GRBs. The SED of the host galaxy is explained well ($\chi^{2}$/$d.o.f.$=0.564) by a luminous (M$_{B}$=-21.16), low-extinction ($A_{V}$=0, rest frame), and aged (2.6 Gyr) stellar population. We can explain this apparent contradiction in global and line-of-sight extinction if the GRB birth place happened to lie in a local dense environment. In light of having relatively small specific SFR (SSFR) $\sim$ 5.3 $M_{\odot}$/yr $(L/L^{\star})^{-1}$, this also could explain the age of the old stellar population of host galaxy.} {} | \indent Since the launch of the {\it Swift}, $\sim$ 78$\%$ (667/856 as of Apr 1, 2014) of observed Gamma-ray Bursts (GRBs)\footnote{http://swift.gsfc.nasa.gov/archive/grb$\textunderscore$table/}, were detected accurately and rapidly by the {\it Swift} X-ray telescope (XRT). Among them $\sim$ 73$\%$ (488/667) of GRBs were detected by the {\it Swift} UV/optical telescope (UVOT) or ground-based telescopes at UV/optical/IR wavelengths, but UV/optical/IR emission was not detected in 20-27\% of observed GRBs (see also \citealt{Melandri:2012aa, Greiner:2011aa}), despite deep searches during several hours by ground facilities. Events lacking UV/optical/IR emission are dubbed "dark GRBs" \citep{Groot:1998aa} with GRB 970111 being the first such case \citep{Castro-Tirado:1997aa, Gorosabel:1998aa}. Currently dark GRBs are defined as those events having no UV/optical afterglow but also a relatively low optical-to-X-ray flux ratio (see \citealt{Jakobsson:2004aa} and \citealt{Horst:2009}). Plausible causes for dark GRBs, such as observational bias, high level of extinction within the galaxy, Lyman-$\alpha$ cut-off (for high redshift bursts) and intrinsically low UV/optical fluxes are claimed, although a combination of two or three causes is likely (also discussed by \citealt{Rol:2005aa, Fynbo:2001aa}). The number of well-observed dark GRBs and their hosts is continually being increased thanks to well-targeted ground-based ToO campaigns, which enable us to gain better insight into the nature of GRBs and their environments. Moreover, future space-based missions, Ultra-Fast Flash Observatory (UFFO)-pathfinder/{\it Lomonosov}, and UFFO might be helpful to understand the dark nature of GRBs using the early optical follow-up within several seconds after GRB onset \citep{Park:2013aa, Jeong:2013aa}. Recent studies have shown that dust extinction inside of the host galaxy might be the probable cause of darkness; the GRB is generated in a denser environment compared with optically bright events (\citealt{DePasquale:2003aa, Perley:2009aa, Melandri:2012aa}). The prompt properties of dark GRBs at rest frame do not differ with optically bright events, but interestingly, the average X-ray luminosity (unabsorbed X-ray flux at rest frame) of dark bursts is slightly higher, although the observed optical flux is slightly lower (see Fig. 4 in \citealt{Melandri:2012aa}). A significant correlation between intrinsic X-ray column density and $\beta_{OX}$ has been pointed out by \citet{Campana:2012aa}, and dark GRBs ($\beta_{OX}\textless0.5$, \citealt{Jakobsson:2004aa}) have been shown to have a moderately high column density in comparison to optically bright events. Host galaxies that harbour dark GRBs are interesting as a study for unbiased samples of star-bursts galaxies in the universe related with SFR \citep{Christensen:2004aa}. Some hosts of dark GRBs trace a sub-population of massive star-burst galaxies, which differ from the main GRB host galaxy population \citep{Rossi:2012aa}. \citet{Kruhler:2011aa} report similar results, in that the hosts of the dustiest afterglows have diverse properties but are on average redder, more luminous, and massive in comparison to hosts of optically bright events (see also \citealt{Hunt:2014aa}). \citet{Perley:2013aa} also deduced similar results by investigating 23 dust obscured {\it Swift} GRBs. It suggests that their hosts are more massive, about an order of magnitude, compared with unobscured GRBs at similar redshifts. On May 28, 2013, at 16:41:23 UT, the {\it Swift} Burst Alert Telescope (BAT) triggered and located the "North pole'' GRB \citep{DElia:2013aa, Goad:2013aa}. The BAT light curve is multiple-peaked with a duration of about 84 s and exhibited a peak count rate of $\sim$ 5500 counts/s in the 15-350 keV range at $\sim$ 8 s after the trigger. The time-averaged spectrum from T$_{0}$+0.12 to 79.34 s was fitted by a power law with an exponential cutoff with a photon index 1.39 $\pm$ 0.19, E$_{cutoff}$ of 118.3 $\pm$ 79.7 keV and total fluence of 5.1 $\pm$ 0.2 $\times$ $10^{-6}$ erg/cm$^{2}$ in the 15-150 keV band \citep{DElia:2013aa, Cummings:2013aa}. The {\it Swift}/XRT began observing the field at 64.9 s after the BAT trigger and found a bright, fading uncatalogued X-ray source \citep{DElia:2013aa}. An astrometrically corrected X-ray position was reported later, RA(J2000)=$09^{h}$$18^{m}$$0.12^{s}$ and Dec(J2000)=+87\textdegree18'03.7" with an uncertainty of 1.8 arcsec (radius, 90\% confidence, \citealt{Goad:2013aa}). Initial XRT spectral analysis resulted in a column density of 3.6 $\pm$ 0.6 $\times$ $10^{21}$ cm$^{-2}$ (90 $\%$ confidence, \citealt{Melandri:2013aa}) in excess of the galactic value at 8.5 $\sigma$ (5.2 $\times$ $10^{20}$ cm$^{-2}$, \citealt{Kalberla:2005aa}), which shows a high equivalent hydrogen column density $N_{H}$ resembling GRB\,051022 \citep{Castro-Tirado:2007aa}. The {\it Swift}/UVOT started follow-up observations 75 s after the BAT trigger, however, it did not detect any credible afterglow candidate within the XRT error circle down to 21.7 mag in the white filter \citep{DElia:2013aa, Pasquale:2013aa}. This encouraged ground-based observations at several different wavelengths. The 0.4m telescope at ISON-Kitab Observatory commenced observations 20 min after the BAT trigger with no optical counterpart being reported at a 3 $\sigma$ limit $\textgreater$ 19.1 mag (unfiltered images of 30 s exposure, see \citealt{Volnova:2013aa}).\ In this paper, we discuss the reason for the dark nature of GRB\,130528A, using our dataset from the optical to mm wavelengths. The structure of our paper is as follows: in Section 2, we describe our multi-wavelength observations and data reduction. In Section 3, we discuss the observational results, which lead us to consider GRB\,130528A as a dark GRB, as well as the host galaxy properties, before summarising our conclusions in Section 4.\ | \label{Conclusions} \indent In this work, we have shown that the darkness of the long duration "dark" GRB\,130528A was likely due to the high absorption close to the GRB birth place, lying in a galaxy at $z$=1.25, which is pinpointed thanks to the mm detection by PdBI. Based on optical/nIR host galaxy observations at GTC, WHT, BTA, and LT, we infer that the GRB\,130528A occurred in a low extinction ($A_{V}$$\sim$0), aged (dominate stellar population of 2.6 Gyr), red ((R-K)$_{AB}$=1.54), and luminous (M$_{B}$=$-$21.16) host. However, this host galaxy seems different with respect to the main body of long-GRB hosts \citep{Christensen:2004aa} and is consistent with the characteristics of the dustiest hosts shown by the latest statistical studies \citep{Perley:2013aa, Rossi:2012aa}. Through mm and nIR observations by PdBI and 1.5m OSN at similar epochs, we infer the relative extinction along the line-of-sight towards the GRB\,130528A, which is $A^{GRB}_{V}$$\geq$ 0.9 mag in rest frame. We also show that this result is consistent with the expected UV/optical extinction from rest frame $N_{H, X}$. The inconsistency between the significant extinction expected from the afterglow SED model and low external extinction determined from the host galaxy SED could be reconciled if the GRB was located in a high density environment, such as a local molecular cloud. | 14 | 4 | 1404.0939 |
1404 | 1404.3016_arXiv.txt | {We present a comprehensive study of star formation toward the H~$\textsc{ii}$ region S155. Star-formation activities therein were investigated based on multi-wavelength data from optical to the far-infrared. The surface density distribution of selected 2MASS sources toward S155 indicates the existence of a compact cluster, which is spatially consistent with the position of the exciting source of the H~$\textsc{ii}$ region, HD 217086. A sample of more than 200 excessive emission sources in the infrared were selected based on their 2MASS color indices. The spatial distribution of the sample sources reveals the existence of three young sub-clusters in this region, among which, sub-cluster A is spatially coincident with the bright rim of the H~$\textsc{ii}$ region. In addition, photometric data from the WISE survey were used to identify and classify young stellar objects (YSOs). To further explore the evolutionary stages of the candidate YSOs, we fit the spectral energy distribution (SEDs) of 44 sources, which led to the identification of 14 Class I, 27 Class II, and 3 Class III YSOs. The spatial distribution of the classified YSOs at different evolutionary stages presents a spatio-temporal gradient, which is consistent with a scenario of sequential star formation. On the other hand, Herschel PACS observations toward the interface between S155 and the ambient molecular cloud disclose an arc-shaped dust layer, the origin of which could be attributed to the UV dissipation from the early type stars e.g. HD 217061 in S155. Four dusty cores were revealed by the Herschel data, which hints for new generations of star formation. | % \label{sect:intro} Cepheus (Cep) OB3 is a very young association at a distance of about 800~pc from the Sun \citep{1993A&A...273..619M}. It covers a region from $22^h46^m00^s$ to $23^h10^m00^s$ in right ascension and from $+61^\circ$ to $+64^\circ$ in declination. It is mainly composed of two subgroups: the older, Cep OB3a, the largest projected dimension of which is about 17~pc, and the younger, Cep OB3b, more compact and closer to Cep molecular cloud \citep{2003MNRAS.341..805P}. Cep OB3 association has always been considered to be a very good example of large-region sequential star formation according with the model of \cite{1977ApJ...214..725E}, where supernova remnants and stellar winds of an older stellar cluster compress the ambient clouds and trigger the formation of a second generation of stars \citep{1979ApJ...233..163S}. The interface between Cep OB3b and the Cep molecular cloud is clearly delineated by the optically bright H~$\textsc{ii}$ region Sharpless 155 (S155, see Figure~\ref{HIST}), where neutral material is ionized and heated by the radiation of the O7 star HD~217086 and the illumination star, HD~217061 \citep{1986PASP...98.1294L}. Both of them belong to the youngest generation of the Cep OB3b association \citep{1981A&A....98..295P}. The photodissociation region (PDR) at S155 is favorably oriented to reveal the progression of star formation. Near-infrared studies \citep{1993A&A...273..619M,1995A&A...303..881T},CO \citep{1992A&A...265..733M},far-infrared, and radio continuum \citep{1978A&A....69..199F,1995A&A...303..881T} have revealed a few young stellar objects (YSOs) embedded in the Cep cloud behind the PDR. Sources with high extinction have been detected on the edge of the Cep molecular cloud. They maybe represent a third generation of star formation triggered by the expansion of the H~$\textsc{ii}$ region. This scenario of triggered star formation has been recently strengthened by \cite{2006ApJS..163..306G, 2009ApJ...699.1454G} with the Chandra X-ray surveys and Spitzer archived data. \begin{figure}[h!!!] \centering \includegraphics[width=10cm, angle=0]{ms1665fig1.eps} \begin{minipage}[]{100mm} \caption{H$\alpha$ narrow band image covering $30'~\times~30'$ of the S155 and its nearby region. Cep B, the hottest component of the Cep molecular cloud, is located in the center of the field. Cep OB3b, the younger subgroup of Cep OB3 association, lies to the northwest. The interface between the molecular cloud and Cep OB3b is delineated by the H~$\textsc{ii}$ region, S155. And the exiting stars HD~217086 and the illumination star HD~217061 are labeled. North is up; east is to the left.} \label{HIST} \end{minipage} \end{figure} In this paper, we present and discuss the scenario of sequential and triggered star formation in S155 and its nearby region based on 2MASS, WISE and the Herschel PACS data. Surface density distribution of the 2MASS PSC sources presents the existence of compact clusters of pre-main sequence stars (PMS). The WISE photometric data help to remove contaminants and fit spectral energy distributions (SEDs), and the Herschel PACS data present cold dusty cores which hints for new generations of star formation. We present in Section~2 optical imaging of S155 as well as details of the retrieval of archival 2MASS and WISE data. In Section~3, we discuss the spatial distribution of the sub-clusters toward S155. SED classification of the sample sources follows in Section~4. The results achieved are discussed in Section~5 and summarized in Section~6. | \subsection{Sequential and triggered star formation around S155} \begin{figure}% \centering \includegraphics[width=10cm, angle=0]{ms1665fig5.eps} \begin{minipage}[]{100mm} \caption{Distribution of YSOs classified based on SEDs. CLASS I, II, and III sources are indicated with red circles, green boxes, and magenta diamonds, respectively. The yellow asterisks indicate HD~217086 (upper) and HD~217061. Cyan dashed circles present the three subclusters marked in Figure~\ref{DMA}. Magenta circle is the location of the dense core in Cep B molecular. The Herschel PACS image region is outlined in yellow.} \label{YSOD} \end{minipage} \end{figure} In this work, we provide new additional evidence to support a scenario of sequential and triggered star formation in S155. Figure~\ref{YSOD} presents the H$\alpha$ image of S155, on which the sample sources classified based on SEDs are overlaid with different symbols. The spatial distribution of the classified sources reveals a dramatic spatiotemporal gradient: younger stars (Class I sources) are clustered in the H~$\textsc{ii}$ region S155, while older stars (Class II and Class III sources) are dispersed in the other side of the primary ionizing star HD~217086. Of the considered locations of three subclusters in Figure~\ref{DMA}, region A is indeed younger and more compact than the other two. Furthermore, most of the identified CLASS I and CLASS II sources are located along the edge of the molecular cloud. All these characters are consistent with a triggered nature of star and cluster formation in this region. \subsection{New generation star formation} \begin{figure}% \centering \includegraphics[width=14cm, angle=0]{ms1665fig6.eps} \begin{minipage}[]{140mm} \caption{Left: Color composite image of S155 and its nearby region in Herschel PACS 160 $\mu m$ (red), 70 $\mu m$ (green) and WISE W3 12 $\mu m$ (blue). Right: DSS 2 red band image of target region. Green contours in both two images are generated from the Herschel PACS image in 160 $\mu m$ band. } \label{PACS} \end{minipage} \end{figure} To further investigate the interstellar materials within the molecular cloud, Herschel PACS \citep{2010A&A...518L...2P} images of a region outlined in Figure~\ref{YSOD} were employed. The left panel of Figure~\ref{PACS} presents the composite image of this target region, which was compiled with the PACS 160 $\mu m$ (red), 70 $\mu m$ (green) and WISE W3 (blue) imaging data. It is evident that the dark edge of the molecular cloud in the DSS-2 red band image (left panel in Figure~\ref{PACS}) is bright in emission in the far-IR. This indicates the existence of large amount cold dust and star formation activity. The overlaid contours generated based on the Herschel PACS image indicate the presence of four far-IR cores. Among those bright cores, core ``a" is spatially consistent with the location of dense core in Cep B molecular cloud. Behind this dense core, an arc-shaped bright layer surround it and face to HD~217061. Its origin could be attributed to the compression from the feedback of HD~217061 to the molecular cloud. Based on distribution of them and other three cores, we infer that new generations of star formation is going on in the edge of molecular cloud, the morphology of the bright part is both effected by the illumination star HD~217061 and dense core. Based on these evidences, the scenario of the sequential and triggered star formation in the whole S155/Cep OB3b region is clear. Due to the influence of Cep OB3a, the first generation of the OB stars were born in Cep OB 3b, which contains HD~217086 and HD~217061. Then the wind originating from these stars compressed the surrounding cloud to trigger the second generation of stars (region A, B, and C marked in Figure~\ref{DMA}). On the east of Cep OB3b, a bright arc of nebulosity was produced for the existence of Cep molecular cloud, and defined the interface between the S155 H~$\textsc{ii}$ region and the Cep B molecular cloud \citep{2003MNRAS.341..805P}. As the surface of the cloud is being eroded, primarily by the illumination star HD~217061, the cloud edge moves eastward across the observer's field of view, with the third generation stars emerging from the obscuring molecular cloud (bright cores presented in Figure~\ref{PACS}). | 14 | 4 | 1404.3016 |
1404 | 1404.4636_arXiv.txt | Cosmological constraints from X-ray and microwave observations of galaxy clusters are subjected to systematic uncertainties. Non-thermal pressure support due to internal gas motions in galaxy clusters is one of the major sources of astrophysical uncertainties. Using a mass-limited sample of galaxy clusters from a high-resolution hydrodynamical cosmological simulation, we characterize the non-thermal pressure fraction profile and study its dependence on redshift, mass, and mass accretion rate. We find that the non-thermal pressure fraction profile is universal across redshift when galaxy cluster radii are defined with respect to the mean matter density of the universe instead of the commonly used critical density. We also find that the non-thermal pressure is predominantly radial, and the gas velocity anisotropy profile exhibits strong universality when galaxy cluster radii are defined with respect to the mean matter density of the universe. However, we find that the non-thermal pressure fraction is strongly dependent on the mass accretion rate of the galaxy cluster. We provide fitting formulae for the universal non-thermal pressure fraction and velocity anisotropy profiles of gas in galaxy clusters, which should be useful in modeling astrophysical uncertainties pertinent to using galaxy clusters as cosmological probes. | Clusters of galaxies are the largest gravitationally bound objects in the universe and therefore trace the growth of large scale structure. In recent years, X-ray and microwave observations have enabled detailed studies of the structure and evolution of galaxy clusters and significantly improved the use of these systems as powerful cosmological probes \citep[][for a review]{Allen2011}. However, current cluster-based cosmological constraints are limited by systematic uncertainties associated with cluster astrophysics. Controlling these astrophysical uncertainties is therefore critical for exploiting the full statistical power of ongoing and upcoming cluster surveys, such as \emph{Planck}\footnote{\url{http://www.rssd.esa.int/index.php?project=planck}} and \emph{eROSITA}\footnote{\url{http://www.mpe.mpg.de/eROSITA}}. One of the main challenges in using clusters as cosmological probes lies in the accurate determination of their masses. Cluster mass estimates from X-ray and Sunyaev-Zel'dovich (SZ) observations are based on the assumption that cluster gas is in hydrostatic equilibrium with their gravitational potential, but there have been inconsistencies between the hydrostatic mass and the mass estimated from gravitational lensing \citep[e.g.,][]{Zhang2010, Mahdavi2013, vonderLinden2014, Applegate2014}. Hydrodynamical simulations suggest that this hydrostatic mass bias arises from non-thermal pressure support in clusters that is not accounted for in current X-ray and SZ cluster mass measurements \citep[e.g.,][]{Evrard1996, Rasia2006, Nagai2007b, Piffaretti2008}. Simulations also suggest that accounting for the non-thermal pressure support can recover the cluster mass to within a few percent \citep[e.g.,][]{Rasia2004, Lau2009, Nelson2012, Nelson2013}. To date, it has been widely assumed that the bias in hydrostatic mass is constant with redshift and mass, but it is unclear whether this assumption is valid. For upcoming cluster surveys, which will detect clusters out to $z\approx 1.5$, it is necessary to characterize the mass and redshift dependence of the mass bias and its impact on cosmological inferences. Non-thermal pressure can also affects the interpretation of the angular power spectrum of the thermal SZ signal, originated from the inverse Compton scattering of the CMB photons off hot electrons in galaxy clusters. The amplitude of the angular power spectrum of the thermal SZ signal ($C_\ell$) is very sensitive to the amplitude of matter density fluctuations ($\sigma_8$) as $C_\ell \propto \sigma_8\,^{7-8}$ \citep{Komatsu_Seljak2002}. Non-thermal pressure is one of the main astrophysical uncertainties since most of the thermal SZ signal comes from integrated thermal pressure from the hot gas in the intracluster and intragroup medium at large radii, where the level of non-thermal pressure is comparable to that of thermal pressure, and where the energy injection from stars and active galactic nuclei are expected to be subdominant. The inclusion of non-thermal pressure support can change the amplitude of the thermal SZ power spectrum by as much as $60\%$ \citep{Shaw2010,Battaglia2010,Trac2011b}, significantly affecting its constraint on $\sigma_8$. Since the thermal SZ angular power spectrum gets contributions from galaxy groups and clusters in a wide range of redshifts and mass, a proper understanding of the mass and redshift dependence of the non-thermal pressure support is critical for using the SZ power spectrum and its high-order moment counterparts \citep{Bhattacharya2012,Hill2013} as cosmological probes. The upcoming {\em ASTRO-H} mission, equipped with high-resolution X-ray spectrometer, will measure internal gas motions in galaxy clusters from doppler broadening of emission lines \citep{Takahashi2010}. However, due to its limited sensitivity, the {\em ASTRO-H} measurements of the non-thermal pressure will be limited to only the inner regions of nearby massive clusters, and it will be difficult to extend these measurements to the outer regions or high-redshift clusters where the effects of non-thermal pressure are expected to be more significant. In the absence of observational constraints, hydrodynamical cosmological simulations can serve as guides for characterizing the effects of non-thermal pressure, particularly at large cluster radii and at high redshifts. In this paper we build upon previous works \citep{Shaw2010,Battaglia2012a} by examining the non-thermal pressure fraction for a mass-limited sample of highly resolved massive galaxy clusters in a wide range of mass, redshifts and dynamical states. We show that the mean non-thermal pressure fraction as well as the gas velocity anisotropy profiles exhibit remarkable universality with redshift and mass, when the cluster mass is defined with respect to the mean mass density of the universe, instead of the critical density. We also find that these profiles show cluster-to-cluster scatter which depends primarily on the mass accretion rate of the clusters, which only affects the normalization of the profiles. We present fitting formulae for these universal profiles. These formulae should useful for characterizing the effects of non-thermal pressure on the hydrostatic mass bias, incorporating their effects in semi-analytic models of thermal SZ power spectrum, and calibrating analytical models of the non-thermal pressure profiles of clusters \citep[e.g.,][]{Shi2014}. The paper is organized as follows. In Section~\ref{sec:theory} we give an overview of the different mass definitions and describe our dynamical state proxy; in Section~\ref{sec:data} we describe our simulations of galaxy cluster formation; in Section~\ref{sec:results} we present our findings; and finally we offer our conclusions and discussions in Section~\ref{sec:summary}. | \label{sec:summary} In this work we presented the redshift and mass independent non-thermal pressure fraction profile using a mass-limited, cosmologically representative sample of 65 massive galaxy clusters from a high resolution hydrodynamical cosmological simulation. This result is relevant in accounting for the systematic effects of non-thermal pressure on X-ray and microwave measurements of galaxy clusters and cosmological inferences based on these measurements. We found that the mean non-thermal pressure fraction profile exhibits remarkable universality in redshift and mass when we define the size of cluster halos using the mean matter density of the universe, instead of the critical density. However, we also showed that there is strong dependence in the non-thermal pressure fraction profile on the halo's mass accretion rate: clusters that are rapidly accreting have an overall higher non-thermal pressure fraction. As such, the mass accretion rate is a major source of systematic scatter in the mean non-thermal pressure fraction profile. A robust and quantitative proxy for measuring mass accretion rate is therefore needed to account for this effect, especially with the upcoming multi-wavelength cluster surveys where statistical errors will be considerably smaller than systematic uncertainties arising from our ignorance of cluster astrophysics. We note that the current method of characterizing the mass accretion rate using the fractional mass increase between $z=0$ and $z=0.5$ is by no means unique, and can only be applied to $z=0$ clusters. Future work should focus on developing quantitative measures of the mass accretion rate of halos that can be applied to halos across a wide range of redshifts, and relate these measures to observable proxies of the dynamical states of clusters. We found no systematic mass dependence in the universal non-thermal pressure fraction profile. But given that our sample contains only massive clusters, the independence in mass should be checked with sample of lower mass halos. Since slowly accreting halos have smaller non-thermal pressure fraction, we expect that lower mass groups and galaxies, which should experience less physical mass accretion than high mass clusters, to have lower non-thermal pressure fraction profile. However, we note that smaller mass halos are more susceptible to non-gravitational physics (such as gas cooling and energy injections from stars and active galactic nuclei) which can influence the net accretion rate into and within the halos in a non-trivial way. We found that the gas velocity is predominantly radial, with the velocity anisotropy parameter increasing from $ \approx 0.1$ to $ \approx 0.6 $ from $ 0.2 r_{200m} $ to $r_{200m}$. Moreover, we found that the velocity anisotropy profile is also universal across redshift when halos are defined using the mean matter density, indicating that gas velocity anisotropy is also a self-similar quantity. This result can be useful since the velocity anisotropy cannot be easily measured in observations, as we can only measure line-of-sight velocities from Doppler width measurements, e.g., with the upcoming {\em ASTRO-H} in the near future. Measurements of gas motions tangential to the line-of-sight are possible with resonant scattering but difficult \citep[e.g.,][]{Zhuravleva2011}. We provided fitting formulae for the universal non-thermal pressure fraction and gas velocity anisotropy profiles that work remarkably well within $r_{200m}$ and out to redshift $z=1.5$. One application of our fitting formulas is the recovery of total mass of relaxed clusters by accounting for the hydrostatic mass bias. The effect of velocity anisotropy should be included in the mass recovery, since the formalism for the full mass recovery depends on the relative contribution of the radial and tangential components of the non-thermal pressure \citep{Rasia2004,Lau2009}. We note that while non-thermal pressure motions due to random gas motions are not the only contribution to the hydrostatic mass bias, the other mass terms due to coherent gas rotation and radial gas acceleration contribute typically only a few percent to the total mass bias, and as such are subdominant to the non-thermal pressure due to gas motions \citep{Suto2013,Lau2013}. Another application of the fitting formula is the assessment of systematic uncertainties in the thermal SZ power spectrum due to non-thermal pressure. The universal, redshift independent profile provided here should make the implementation of non-thermal pressure support in the modeling of the thermal SZ power spectrum robust and straightforward. While our current simulation does not include radiative cooling, star formation or energy feedback from stars and/or active galactic nuclei, we have examined the effect of these additional physics on the non-thermal pressure fraction and gas velocity anisotropy in group and cluster size halos taken from \citet{Nagai2007a} and found no systematic dependence on gas physics in the radial range of $0.1 \lesssim r/r_{200m} \lesssim 1.5$. We note, however, that our simulation does not model plasma effects which can amplify gas turbulence and provide extra non-thermal pressure support \citep[e.g.,][]{Parrish2012}. Physical viscosity, on the other hand, can decrease the level of gas turbulence which lowers the non-thermal pressure support. The results presented in this paper based on hydrodynamical simulations serve as baseline for further studies of these effects. Magnetic fields and cosmic rays can also provide additional non-thermal pressure \citep[e.g.,][]{Lagana2010}. However, their contributions are expected to be small. The typical magnetic field strength of $\lesssim 10 \mu\mathrm{G}$ in the ICM corresponds to magnetic pressure fraction of $\lesssim 1\%$. Similarly, the ratio of the cosmic ray pressure to total pressure is constrained to $\lesssim 1\%$, set by the $\gamma$-ray observations of {\em Fermi}-LAT \citep{Fermi2013}. It is important to note, however, that the constraints on the contribution from cosmic rays assume that the cosmic ray distribution follows that of the thermal ICM and, therefore, a flattened distribution of cosmic rays could result in an increased contribution to the ICM energy \citep[e.g.,][]{Zandanel2014} The upcoming {\em ASTRO-H} mission will measure gas motions in galaxy clusters and should provide observational constraints on the level of the non-thermal pressure fraction in these systems. However, the observational constraints will be limited to inner regions ($\lesssim r_{2500c}\approx 0.2\,r_{200m}$) of nearby massive clusters, due to the lack of sensitivities in low-density regions in cluster outskirts. Extending these measurements to the outskirts or high-redshift clusters must await the next generation of X-ray missions, such as \emph{SMART-X}\footnote{\url{http://smart-x.cfa.harvard.edu/}} and/or \emph{Athena+}\footnote{\url{http://athena2.irap.omp.eu/}}. Alternatively, kinematic SZ effect can probe internal gas motions of electrons in galaxy clusters \citep{Inogamov2003,Nagai2003}. Since the SZ signal is independent of redshift and linearly proportional to gas density (unlike X-ray emission which is proportional to gas density squared), measurements of the kSZ effect with high-resolution, multifrequency radio telescopes, such as CCAT\footnote{\url{http://www.ccatobservatory.org}}, might enable characterization of the non-thermal pressure in the outer regions of high-redshift clusters. Previous works have used the definition of cluster mass normalized with respect to the critical density of the universe. In this work, we argue that an alternative definition based on the mean mass density of the universe is a preferred choice for the non-thermal pressure profile as well as velocity anisotropy of gas in clusters. It would be interesting to check whether other gas properties exhibit similar universality when the cluster profiles are normalized with respect to the mean mass density. We will investigate these issues in our next paper and explore their implications for understanding the evolution cluster gas structure and their application to cosmology. | 14 | 4 | 1404.4636 |
1404 | 1404.3961_arXiv.txt | We investigate the regular or chaotic nature of orbits of stars moving in the meridional plane $(R,z)$ of an axially symmetric galactic model with a flat disk and a central, non spherical and massive nucleus. In particular, we study the influence of the flattening parameter of the central nucleus on the nature of orbits, by computing in each case the percentage of chaotic orbits, as well as the percentages of orbits of the main regular families. In an attempt to maximize the accuracy of our results upon distinguishing between regular and chaotic motion, we use both the Fast Lyapunov Indicator (FLI) and the Smaller ALingment Index (SALI) methods to extensive samples of orbits obtained by integrating numerically the equations of motion as well as the variational equations. Moreover, a technique which is based mainly on the field of spectral dynamics that utilizes the Fourier transform of the time series of each coordinate is used for identifying the various families of regular orbits and also to recognize the secondary resonances that bifurcate from them. Varying the value of the flattening parameter, we study three different cases: (i) the case where we have a prolate nucleus (ii) the case where the central nucleus is spherical and (iii) the case where an oblate massive nucleus is present. Furthermore, we present some additional findings regarding the reliability of short time (fast) chaos indicators, as well as a new method to define the threshold between chaos and regularity for both FLI and SALI, by using them simultaneously. Comparison with early related work is also made. | \label{intro} Knowing the dynamical properties and the overall orbital structure of galaxies is an issue of paramount importance. Therefore, scientists in an attempt to explore and interpret their structure, they usually build and apply galactic dynamical models, which in most cases are mathematical expressions giving either the potential or the mass density of the galaxy, as a function of the radius $R$ from the center. The reader can find a variety of interesting models, describing motion in galaxies in [\citealp{BT08}]. Moreover, potential density pairs for galaxies were also presented by [\citealp{VL05}]. Over the last years, several types of galactic models have been proposed in an attempt to model the orbital properties in axially symmetric systems. A simple yet realistic axisymmetric logarithmic potential was introduced in [\citealp{Bin81}] for the description of galactic haloes at which the mass density drops like $R^{-2}$ [\citealp{E93}]. However, the most well-known model for cold dark matter (CDM) haloes is the flattened cuspy NFW model [\citealp{NFW96},\citealp{NFW97}], where the density at large radii falls like $R^{-1}$ . This model being self-consistent has a major advantage and that's why it is mainly used for conducting $N$-body simulations. In order to obtain the mass profiles of galaxies, we have to use dynamical models describing the main properties of the galaxies. These models can be generated by deploying two main techniques: (i) using superposition of libraries of orbits (e.g., [\citealp{G03},\citealp{TSB04},\citealp{C06}]) or (ii) using distributions functions (e.g., [\citealp{DBVZ96},\citealp{GJSB98},\citealp{KSGB00}]). In the literature there are also other more specialized dynamical models combining kinematic and photometric data. For instance, axially symmetric Schwarzschild models were used by [\citealp{B06}], while [\citealp{H08}] used Jeans models in order to fit observational data in the X-ray potential introduced by [\citealp{HBG06}]. Furthermore, axisymmetric Schwarzschild models were also used by [\citealp{SG10}] to fit data derived from the Hubble Space Telescope (HST). Over the last years, Schwarzschild's superposition method [\citealp{S79}] has been heavily utilized by several researchers (e.g., [\citealp{RZCMC97},\citealp{G03},\citealp{TSB04},\citealp{VME04},\citealp{KCEMd05},\citealp{TSB05}]) in order to model dark matter distributions in elliptical galaxies therefore, we deem it is necessary to recall and describe briefly in a few words the basic points of this interesting method. Initially, $N$ closed cells define the configuration space, while $K$ orbits extracted from a given mass distribution construct the phase space. Then, integrating numerically the equations of motion, we calculate the amount of time spent by each particular orbit in every cell. Thus, the mass of each cell is directly proportional to the total sum of the stay times of orbits in every cell. Using this technique, we manage to compute the unknown weights of the orbits, assuming they are not negative. Spherical analytical models describing the motion of stars in galaxies were studied by (e.g., [\citealp{D12},\citealp{RDZ05},\citealp{Z96}]). Moreover, interesting axially symmetric galactic models were presented by [\citealp{CZMR99}]. Recently, [\citealp{Z11}] used data derived from rotation curves of real galaxies, in order to construct a new axially symmetric model describing star motion in both elliptical and disk galaxy systems. Of particular interest, are the so-called composite galactic dynamical models. In those models the potential has several terms each one describing a distinct component of the stellar system. Such a dynamical model with four components, that is a disk, a nucleus, a bulge and a dark halo was studied by [\citealp{C97}]. A new composite mass model describing motion in axially symmetric galaxies with dark matter was recently presented and studied by [\citealp{C12}]. Composite axially symmetric galaxy models describing the orbital motion in our galaxy were also studied by [\citealp{Bin12}]. In these models, the gravitational potential is generated by three superposed disks: one representing the gas layer, one the thin disk and one representing the thick disk. In a previous work [\citealp{ZCar13a}], we introduced a new dynamical model describing three-dimensional motion in non axially symmetric galaxies. This model covers a wide range of galaxies from a disk system to an elliptical galaxy by suitably choosing the dynamical parameters. It was found, that the parameter which describes and controls the deviation from axially symmetry is indeed very influential both in the disk and the elliptical galaxy models. In the same vein, we proposed in [\citealp{CZ13},\citealp{ZCar13b}] two analytical models describing the main body of a disk or an elliptical galaxy which contains dark matter. In the first model [\citealp{CZ13}] for the main body of the galaxy we used a mass potential, while in the second model [\citealp{ZCar13b}] it was described by a logarithmic potential. The fractional portion of the dark matter in the main body of the galaxy is regulated by a parameter and our numerical calculations suggested that in both models this parameter plays a key role to the overall orbital structure of the system. Therefore, taking into account all the above there is no doubt, that modelling galaxies is an issue of great importance. On this basis, it seems of particular interest to build an analytical axially symmetric dynamical model describing the motion of stars in disk galaxies with non spherical and massive nuclei and also explore, how the deviation from axially symmetry of the central nucleus, being prolate or oblate, affects the regular or chaotic character of orbits as well as the behavior of the different families of orbits. Similar research preformed in [\citealp{HN90},\citealp{HPN93},\citealp{Z12a}], where the effects of a central, spherical mass component in a galaxy were investigated. The present article is organized as follows: In Section \ref{galmod} we present in detail the structure and the properties of our gravitational galactic model. In Section \ref{compmeth} we describe the computational methods we used in order to determine the character of orbits. In the following Section, we investigate how the flattening parameter of the central non spherical nucleus influences the character of the orbits. The next Section is devoted to some additional findings of our investigation regarding the reliability of chaos indicators. Our paper ends with Section \ref{disc}, where the discussion and the conclusions of this research are presented. | \label{disc} In the present paper, we used an analytic, axially symmetric galactic gravitational model which embraces the general features of a disk galaxy with an additional central, non spherical and dense nucleus. In order to simplify our study, we chose to work in the meridional plane $(R,z)$, thus reducing three-dimensional motion to two-dimensional. Our aim was to investigate how influential is the flattening parameter $\beta$ which controls the shape of the central nucleus, on the level of chaos and also on the distribution of regular families in our disk galaxy model. Our extensive numerical results suggest, that the level of chaos as well as the different families of regular orbits are indeed very dependent on the shape (prolate, spherical or oblate) of the central galactic nucleus. A disk galaxy with a non spherical nucleus is undoubtedly a very complex entity and, therefore, we need to assume some necessary simplifications and assumptions in order to be able to study mathematically the orbital behavior of such a complicated stellar system. For this purpose, our model is intentionally simple and contrived, in order to give us the ability to study all the different aspects regarding the kinematics and dynamics of the model. Nevertheless, contrived models can provide an insight into more realistic stellar systems, which unfortunately are very difficult to be studied, if we take into account all the astrophysical aspects. Self-consistent models on the other hand, are mainly used when conducting $N$-body simulations. However, this application is entirely out of the scope of the present research. Once again, we have to point out that the simplicity of our model is necessary; otherwise it would be extremely difficult, or even impossible, to apply the extensive and detailed dynamical study presented in this study. Similar gravitational models with the same limitations and assumptions were used successfully several times in the past in order to investigate the orbital structure in much more complicated galactic systems (e.g., [\citealp{Z12b},\citealp{Z13a}]). Since a distribution function of the galaxy model was not available so as to use it for extracting the different samples of orbits, we had to follow an alternative path. So, for determining the regular or chaotic nature of motion in our models, we chose, for each set of values of the flattening parameter, a dense grid of initial conditions in the $(R,\dot{R})$ phase plane, regularly distributed in the area allowed by the value of the orbital energy $E$. Each orbit was integrated numerically for a time period of $10^4$ time units (10 billion yr), which corresponds to a time span of the order of hundreds of orbital periods but of the order of one Hubble time. The particular choice of the total integration time was made in order to eliminate sticky orbits (classifying them correctly as chaotic orbits) with a stickiness at least of the order of one Hubble time. Then, we made a step further, in an attempt to distribute all regular orbits into different families. Therefore, once an orbit has been characterized as regular, we then further classified it using a frequency analysis method. This method calculates the Fourier transform of the coordinates and velocities of an orbit, identifies its peaks, extracts the corresponding frequencies and then searches for the fundamental frequencies and their possible resonances. In this work, we revealed the influence of the flattening parameter $\beta$ of the central non spherical nucleus on the level of chaos and also on the distribution of the regular families among its orbits in disk galaxy models with non spherical nuclei. The main results of our research can be summarized as follows: \begin{enumerate} \item In our galaxy models several types of regular orbits exist, while there is also an extended chaotic domain separating the areas of regularity. In particular, most types of regular orbits, such as the box, 1:1, 2:1, 3:2, 4:3, 6:5, higher resonant and chaotic orbits are always present when $\beta$ varies. The 2:3 resonant family, on the other hand, disappears when the flattening parameter obtains high values $(\beta > 0.5)$. Here we must clarify, that by the term ``higher resonant orbits" we refer to resonant orbits with a rational quotient of frequencies made from integers $> 5$, which of course do not belong to the main families. \item There is a strong correlation between the percentages of most types of orbits and the value of the flattening parameter. Almost throughout the values of $\beta$ chaotic motion is the dominant type of motion; only when $0.3 \leq \beta \leq 0.7$ regular motion prevails being the box orbits the most populated family. Generally, the percentages of box and 2:1 resonant orbits decrease, while the rates of the 1:1 and 4:3 resonant orbits exhibit a constant growth with increasing $\beta$. The portion of 3:2 resonant orbits decreases sharply for small values of $\beta$ $(\beta < 0.7)$, while this tendency is reversed at higher values of the flattening parameter $(\beta \geq 0.7)$. The 2:3 resonant family is stable only when $\beta < 0.4$, while for larger values of $\beta$ it becomes unstable and finally ceases to exist. The rates of the 6:5 and higher resonant orbits on the other hand, are almost unperturbed by the shifting of the value of $\beta$. Summarizing, our numerical calculations indicate that the flattening parameter of the central non spherical nucleus affects more or less almost all types of orbits in disk galaxy models. \item In disk galaxy models with non spherical nuclei, there are stable as well as unstable periodic orbits. We found, that the 2:1, 1:1, 3:2 and 4:3 periodic orbits remain stable throughout the entire range of the values of $\beta$. On the contrary, the 2:3 and 6:5 families of periodic orbits contain not only stable but also a considerable amount of unstable periodic orbits. Therefore, we may conclude that the flattening parameter $\beta$ affects substantially the stability of the regular families of orbits, hinting at a deep interplay between chaos and proportion of regular families. \end{enumerate} Over the last years, several dynamical indicators for distinguishing between ordered and chaotic motion have been developed. The vast majority of these indicators is based on the evolution of sets of deviation vectors in order to characterize an orbit and most of them claim to be equally reliable and fast. Therefore, based on this assumption we applied both the FLI and SALI indicators using a relatively short integration time of only $10^3$ time units, in order to save computation time. However, after performing a few longer integrations using a time interval of $10^4$ time units, we realized that a non-negligible number of orbits was in fact misclassified. What happened was that both chaos indicators failed to identify the true chaotic nature of sticky orbits due to the short available integration time. Thus, we may conclude that the so called ``fast" indicators of chaos cannot reliably identify chaos when the orbits are numerically integrated for short time intervals. They may be computationally faster than the traditional mLCN method, but they cannot overcome the intrinsic difficulty of disentangle sticky orbits form regular ones. As an aside, we found that, by combining two chaos indicators; the FLI and the SALI algorithms in our case, we can define for both methods reliable thresholds, thus separating more accurately chaotic from regular motion. However, the particular thresholds are valid only in our galaxy model. The bottom line of our research is that in every dynamical system one should initially perform thorough statistical tests in order to define the best thresholds of the chaotic indicators and also use sufficient time of numerical integration, thus minimizing as possible the amount of misclassified orbits. We consider the results of the present research as an initial effort and also a promising step in the task of exploring the orbital structure of disk galaxies with non spherical nuclei. Taking into account that our outcomes are encouraging, it is in our future plans to modify properly our dynamical model in order to expand our investigation into three dimensions, thus unveiling how the flattening parameter influences the nature of the three-dimensional orbits. Also, of particular interest would be to obtain the entire network of periodic orbits, revealing the evolution of the periodic points as well as their stability when varying all the available parameters of our model. | 14 | 4 | 1404.3961 |
1404 | 1404.4770_arXiv.txt | Starting from the Oppenheimer-Snyder model, we know how in classical general relativity the gravitational collapse of matter form a black hole with a central spacetime singularity. It is widely believed that the singularity must be removed by quantum gravity effects. Some static quantum-inspired singularity-free black hole solutions have been proposed in the literature, but when one considers simple examples of gravitational collapse the classical singularity is replaced by a bounce, after which the collapsing matter expands for ever. We may expect 3 possible explanations: $i)$ the static regular black hole solutions are not physical, in the sense that they cannot be realized in Nature, $ii)$ the final product of the collapse is not unique, but it depends on the initial conditions, or $iii)$ boundary effects play an important role and our simple models miss important physics. In the latter case, after proper adjustment, the bouncing solution would approach the static one. We argue that the ``correct answer" may be related to the appearance of a ghost state in de~Sitter spacetimes with super Planckian mass. Our black holes have indeed a de~Sitter core and the ghost would make these configurations unstable. Therefore we believe that these black hole static solutions represent the transient phase of a gravitational collapse, but never survive as asymptotic states. | In classical general relativity, under the main assumptions of the validity of the strong energy condition and of the existence of global hyperbolicity, the collapse of matter inevitable produces a singularity of the spacetime~\cite{sing}. At a singularity, predictability is lost and standard physics breaks down. According to the weak cosmic censorship conjecture, spacetime singularities formed from collapse must be hidden behind an event horizon and the final product of the collapse must be a black hole~\cite{wccc}. In 4-dimensional general relativity, the only uncharged black hole solution is the Kerr metric~\cite{hair}, which reduces to the Schwarzschild solution in the spherically symmetric case. The Oppenheimer-Snyder model is the simplest fully analytic example of gravitational collapse, describing the contraction of a homogeneous spherically symmetric cloud of dust~\cite{os}. It clearly shows how the collapse produces a spacetime singularity and the final product is a Schwarzschild black hole. In analogy with the appearance of divergent quantities in other classical theories, it is widely believed that spacetime singularities are a symptom of the limitations of classical general relativity, to be removed by quantum gravity effects. While we do not have yet any robust and reliable theory of quantum gravity, the resolution of spacetime singularities has been investigated in many quantum gravity inspired models. Very different approaches have studied corrections to the Schwarzschild/Kerr solution, finding black hole metrics in which the curvature invariants are always finite~\cite{regular}\footnote{We note that it may also be possible that the quantum corrections that smooth out the singularity may be intrinsically-quantum and not reducible to the metric form. In such a case, the metric description would simply break down.}. In the same spirit, one can study the modifications to the Oppenheimer-Snyder solution and to other models of collapse. In this case, the singularity is replaced by a bounce, after which the cloud starts expanding~\cite{bounce}. It is therefore disappointing that the quantum-gravity corrected model of collapse does not reproduce to the quantum-gravity corrected black hole solution. In this paper, we want to investigate this apparent contradictory result. First, we determine both the quantum-gravity corrected static black hole metric and the quantum-gravity corrected homogeneous collapse solution within the same theoretical framework, since the ones reported in the literature come from different models. We find that the problem indeed exists. Second, we try to figure out the possible reason. One possibility is that the static regular black hole spacetimes are {\it ad hoc} solutions, but they cannot be created in a collapse and therefore they are physically irrelevant. The collapse always produces an object that bounces. Another possible explanation is that the final product of the collapse depends on the initial conditions. The collapse of a homogeneous cloud creates an object that bounces, while with other initial conditions (not known at present) the final product is a static regular black hole. Lastly, it is possible that the simple homogeneous collapse oversimplifies the model, ingoing and outgoing energy fluxes between the interior and the exterior solutions are important, and, after proper readjustment that seems to be difficult to have under control within an analytic approach, the collapsing model approaches the static regular black hole solution. Our quantum-gravity inspired theories are unitary, super-renormalizable or finite at quantum level, and there are no extra degrees of freedom at perturbative level around flat spacetime. This should rule out the possibility that the explanation of our puzzle is due to the fact that these models may not be consistent descriptions of quantum gravity. However, these theories display a ghost state in de~Sitter spacetime when the cosmological constant exceeds the square of the Planck mass. This fact may be responsible for our finding and answers the question in the title of this paper. Our black holes have indeed a de~Sitter core with an effective cosmological constant larger than the square of the Planck mass when the black hole mass exceeds the Planck mass. The presence of a ghost makes the solutions unstable and therefore they cannot be the final product of the gravitational collapse. The content of the paper is as follows. In the next section, we briefly review the classical homogeneous and spherically symmetric collapse model. In Section~\ref{s-3}, we derive the spherically symmetric black hole solutions in a super-renormalizable and asymptotically-free theory of gravity with the family of form factors proposed by Krasnikov~\cite{ff-k} and Tomboulis~\cite{ff-t}. In Section~\ref{s-4}, we study the spherically symmetric homogeneous collapse in the same models. Summary and conclusions are in Section~\ref{s-5}. | } In the present paper, we have studied both the static black hole solution and the homogeneous spherically symmetric collapse of a cloud of matter in a super-renormalizable and asymptotically free theory of gravity. The spacetime singularity predicted in classical general relativity is removed in both the cases. In the literature there were so far some scattered results in different theoretical frameworks. Here we have studied this issue in more details within the Krasnikov and Tomboulis models. Static and spherically symmetric singularity free black hole solutions have been obtained. At the origin, the effective energy density is always finite and positive, independently of the exact expression of the form factor $V(z)$. In other words, these black holes have a de~Sitter core in their interior, where the effective cosmological constant is of order $\kappa^2 M \Lambda$, $\kappa^2 = 32\pi G_{\rm N}$, $M$ is the black hole mass, and $\Lambda$ is the energy scale of the theory which is naturally to expect to be close to the Planck mass. The singularity of the spacetime is therefore avoided due to the repulsive behavior of the gravitational force. For a large family of form factors, the effective energy density can be negative in some regions, which eventually provides the possibility of having {\it multi-horizon black holes}. In the homogeneous and spherically symmetric collapse of a cloud of matter, the formation of the singularity is always replaced by a bounce. Far from the bounce, the collapse follows the classical solution, while it departs from it at high densities. Strictly speaking, asymptotic freedom is sufficient to remove the singularity, but the presence of a bounce requires also a repulsive character for gravitational field in the high energy regime. In conclusion, we have provided some convincing examples that show how the final products of the quantum-gravity corrected collapse solutions are not the quantum-gravity corrected Schwarzschild black hole metrics. This is not the result that one would expect {\it a priori}. There may be 3 natural explanations. \begin{enumerate} \item Static regular black holes cannot be created in any physical process. In this case, even if they are solution of a theory, they are much less interesting than their classical counterparts that can be created in a collapse. \item The final product of the gravitational collapse is not unique. The collapse of a homogeneous and spherically symmetric cloud of matter does not produce a static regular black hole, but the collapsing matter bounces and then expands. With different initial conditions, not known at the moment, static regular black holes may form. \item The simple example of a homogeneous cloud of matter oversimplifies the picture and misses important physics. As discussed in Section~\ref{s-2}, in the classical dust case we have a homogeneous interior and a Schwarzschild exterior without ingoing or outgoing flux through any spherical shell of comoving radial coordinate $r$. However, that is not true in general, and the exterior spacetime is a generalized Vaidya solutions with ingoing or outgoing flux of energy. This means that the homogeneous solution is not stable and must evolve to an inhomogeneous model. While the bounce can still occur, after it the collapsing matter may not expand forever. The boundary effects are important and, after proper readjustment that can unlikely be described without a numerical strategy, the collapse approaches the static black hole solution. \end{enumerate} The possibility 1 excludes the possibilities 2 and 3, but the latter may also coexist. Here we have focused on the asymptotically free gravity theory with the Lagrangian given in Eq.~(\ref{eq-theory}), and we have shown that the issue indeed exists. The theoretical model is not sick, and therefore we cannot attribute the problem to the fact that we are considering a non-consistent quantum theory. However, it is easy to compute the propagator for this class of theories around de Sitter spacetime background and to show the presence of a ghost when the cosmological constant exceeds the square of the Planck mass (in preparation). This fact may explain the fact that our static black holes are not the final product of the gravitational collapse. These black holes have indeed a de~Sitter core in which the effective cosmological constant is $\kappa^2 M \Lambda$. If the black hole mass $M$ exceeds the Planck mass, there is a ghost and the black hole is unstable. Therefore the solutions here presented cannot be the final product, but only an intermediate phase of the gravitational collapse. \begin{widetext} | 14 | 4 | 1404.4770 |
1404 | 1404.1680_arXiv.txt | BICEP2's detection on the primordial B-mode of CMB polarization suggests that inflation occurred around GUT scale, with the tensor-to-scalar ratio $r\simeq0.2$. Inspired by this discosvery, we study the topological inflation which was driven by a double/single/no well potential. We show that with proper choice of parameters, all these three types of topological inflationary models could be consistent with the constraints from current observations. | Inflationary paradigm \cite{guth1980} has become a leading scenario of the early universe. It provides a very convincing solution to the flatness problem, horizon problem, and monopole problem in standard hot big bang cosmology. It is also believed that the quantum fluctuation during inflation seeds the large scale structure and CMB anisotropies nowadays. Inflation is successful but, nonetheless, also encounters some questioning on its validity \cite{Brandenberger:2012uj}. One of the conceptual problems is the fine-tuning. Inflation was introduced to eliminate the fine-tuning condition for the initial data set of cosmology, i.e. the so called horizon problem and flatness problem. However, inflation itself requires fine-tuning on the initial conditon, which renders the fine-tuning problem returns in a different guise. In the context of topological inflation \cite{Linde:1994hy}\cite{Vilenkin:1994pv}, such fine-tuning could be alleviated. Topological inflation is a wild class of models where the inflaton field is forced to stay near a local maximum of potential for topological reasons. Generally, a topological defect forms during the phase transition with spontaneous symmetry breaking. Its existence is related to the topology of the boundary of space, the topology of the set of vacua, and the existence of a nontrivial map from the boundary of space to the set of vacua. During the early universe, if the size of the soliton greater than the Hubble radius, inflation occures at the core of such a topological defect \cite{Linde:1994hy}\cite{Vilenkin:1994pv}. The recent BICEP \cite{Ade:2014gua}\cite{Ade:2014xna} measurement of primordial B mode in the polarization of cosmic microwaves background suggests that inflation occured at the energy scale of $10^{16}$ GeV, with the tensor-to-scalar ratio $r\simeq0.2$. This discovery definitively affects our understanding of early universe, see the following up research after BICEP2\cite{paperflood}. Lots of models would be ruled out due to the discovery of primordial B-mode. In this paper we check examples of the topological inflation by using recent BCEP and established cosmological results. The rest of the paper is organized as follows: at section II, we will check the consistency with experiment on the well-known double-well potential model; at section III, we will check the case with single-well model, and at section IV, we will check the model without any well. We conclude and summarize our results at the final section. | In this paper, we check several topological inflationary models. We first classify the topological inflation models into three catagories, double-well potential, single-well potential, and no-well potential inflation. In the case of double-well potential, we took the Higgs type of potential and the axion-like potential as examples. To be consistent with the observational constraints of red spectral tilt and large tensor-to-scalar ratio, we found that inflation of our Hubble volume should happen near the edge of solitons. Then we check second type of topological inflation, with only one single well. We took a potential motivated from extra-dimensional compactification as an example. With proper choice of parameters, such a model could be consistent with observations. For the 3rd type of topological inflation, without a well in the potential, we also found that this model could be consistent with observations. ~~~~~~~~~~~~~ | 14 | 4 | 1404.1680 |
1404 | 1404.7773_arXiv.txt | We propose a new field theory mechanism for generating an effective trans-Planckian decay constant from sub-Planckian ones. Using the minimal two axions and a hierarchy between two axion decay constants is sufficient for realizing inflation through non-perturbative effects only and with minimal tuning. The inflationary motion is kept entirely within a sub-Planckian domain. % We outline possible strategies of embedding the model in a string theory setup. | The recent breathtaking progress involving precision cosmological observations, in particular of the CMB \cite{Hinshaw:2012aka, Ade:2014xna}, provides rather strong evidence for a very early phase of slow-roll inflation driven by a scalar potential $V(\phi)$. A very common mechanism to protect the flatness of the scalar potential against radiative corrections is to invoke some symmetry, most straightforwardly a shift symmetry $\phi \rightarrow \phi+const.$. Radiative stability then requires that the potential itself constitutes the 'order parameter' of the breaking of the shift symmetry. Hence if the order parameter vanishes, the potential vanishes and the symmetry is exact. Then by turning on the order parameter, one can control the potential and its possible corrections, rendering the inflationary model technically natural. An elegant suggestion along these lines is "natural inflation" \cite{Freese:1990rb}, where the inflaton is a pseudo Nambu-Goldstone boson, and the potential is simply $V=\Lambda^4(1-\cos(\phi/f))$, where $f$ is the axion decay constant. Here, there is still a residual shift symmetry of $\phi \rightarrow \phi+2\pi f$. For successful inflation one needs $f \gtrsim M_{\rm P}$, and in light of the recent BICEP2 results \cite{Ade:2014xna}, the axion decay constant has actually to be as large as $f\sim 10 M_{\rm P}$ to be in accord with a tensor to scalar ratio of $r \sim \mathcal O (0.1)$. $M_{\rm P}=2.4 \times 10^{18} \text{\ GeV}$ is the reduced Planck mass. The predictions of natural inflation for such large decay constants are rather similar to those of a free massive scalar field, $V=\frac{1}{2}m^2\phi^2$. Such a large axion decay constant is challenging from the effective field theory point of view, and demands a UV completion to make sense of. Specifically, we are interested in embedding such a scenario in string theory, where generically $f\ll M_{\rm P}$ exacerbating the challenge. This is because in Planck units, for all known cases $f\propto1/\mathcal{V}^m$ with $m>0$, where $\cal V$ is the volume of the compactified dimensions and for a controlled analysis ${\cal V} \gg 1$, \cite{Baumann:2014nda}. Scenarios providing some UV completions at various levels of rigour have been proposed in \cite{ArkaniHamed:2003wu, McAllister:2008hb, Kim:2004rp, Berg:2009tg}. With an eye on string theory, two mechanisms stick out \cite{Kim:2004rp, Berg:2009tg}. In the Kim-Nilles-Peloso mechanism (KNP) \cite{Kim:2004rp}, an effective $f_{eff}\gg M_{\rm P}$ is achieved by aligning two axion decay constants that are originally sub-Planckian, $f_i\ll M_{\rm P}$. This requires a precise cancellation between parameters to the level of $0.1-1\%$. Recently \cite{Choi:2014rja,Higaki:2014pja} have suggested generalizations of the alignment mechanism to more than two axions, partially relieving the tuning required in the original model, while~\cite{Kallosh:2014vja} presented a very minimal embedding of single-axion and KNP 2-axion inflation into supergravity, see also \cite{Kallosh:2007cc}. In Dante's Inferno (DI) \cite{Berg:2009tg}, a generalization of the axion monodromy was proposed. The main idea was considering two canonically normalized fields/axions with $V=W(r)+ \Lambda_2^4(1-\cos(r/f_r-\theta/f_{\theta}))$. $W(r)$ is some monomial in $r$, generalizing the axion monodromy construction. A hierarchy between the decay constants $f_r \ll f_{\theta} \ll M_{\rm P}$ and the energy scale $\Lambda_2^4 \gg W(r_{in})$ allows one to integrate out a heavy mode, mostly $r$, thus giving rise to effectively single field chaotic inflation dynamics $V=W_{eff}(\phi_{eff})$. Thus, the fundamental axion decay constants are sub-Planckian and the entire inflationary dynamics are contained in a small region of field space of the fundamental fields $r,\theta$ with diameter $d_r\simeq f_r/f_{\theta}\Delta \phi_{eff} \ll M_{\rm P}$. Thus one avoids the need for "functional fine tuning" one generally encounters in the case of "large field models", $\Delta \phi \gg M_{\rm P}$, while keeping all the predictions of such models intact. In this note, we combine the best features of both KNP and DI -- namely, we generate a parametrically super-Planckian effective axion decay constant from fields with sub-Planckian periodicity using only non-perturbative effects, while replacing the tuned alignment of KNP with a simple hierarchy similar to that of DI. The main tool in DI is the integrating out of the mixed cosine term with $f_r\ll f_{\theta}$. In our case however, $W(r)$ is another axion term of the form $\Lambda _1^4 \left(1-\cos\left[\frac{r}{f_{r_1}}\right]\right)$, which by itself still has a residual shift symmetry. Actually $\Lambda_1,\Lambda_2$ can have arbitrary relative magnitude. The virtue is that first, $f_r\ll f_{\theta}<M_{\rm P}$ suffices and there is no need for an additional hierarchy between the summands in the potential. The motion of the two axions is then kept entirely within a sub-Planckian domain. Second, as in DI and contrary to KNP, there is no fine-tuned alignment in the axion decay constants. Third, such an additional axionic term supplemented by no requirements on the $\Lambda$'s is expected to be much easier to embed in a full string derived scenario. | Our discussion so far proceeded along the lines of 4D effective field theory. However, a model of natural inflation generating large-field directions with sub-Planckian decay constants and mild tuning requirements should ultimately be embedded into string theory. Therefore, we now shortly discuss the ingredients which type IIB string theory with its well understood avenues for moduli stabilization, a pre-requisite for successful string inflation, supplies for axion inflation~\cite{Baumann:2014nda}. For the sake of concreteness, we will assume compactification of type IIB on a Calabi-Yau orientifold with 3-form flux, which supersymmetrically stabilizes the complex structure moduli and the axio-dilaton $\tau$ at a high mass scale, see ~\cite{Baumann:2014nda} and references therein. Axionic inflaton candidates arise from the RR 4-form and 2-form gauge potentials $C_4$ and $C_2$ respectively. $C_4$ provides $h^{1,1}_+$ axions as partners of the K\"ahler moduli $T_i = vol(\Sigma_i)+i\int_{\Sigma_i}C_4$. Here, $\Sigma_i$ are the $h^{1,1}_+$ 4-cycles surviving the orientifold projection. $C_2$ generates 2-form axions partnering with NSNS $B_2$ in $h^{1,1}_-$ orientifold-odd chiral fields $G_a=\int_{S^2_a}C_2-\tau \int_{S^2_a}B_2$. Here, $S^2_i$ denote the 2-cycles Poincare-dual to the $\Sigma_i$, while only the $a=1\ldots h^{1,1}_-$ orientifold-odd combinations $S^2_a$ lead to $G_a$ axion multiplets. We now sketch two simple toy setups leading to an axion potential of the type of eq.~\eqref{eq:Vrtheta}. First, let us consider a simple model with three K\"abler moduli $T_i$ and their $C_4$-axion partners. We stabilize these moduli using non-perturbative effects from D7-branes or Euclidean D3-branes. Assuming for simplicity a 'swiss cheese' structure for the Calabi-Yau manifold, the effective action is governed by a K\"ahler and superpotential. \bea K &=& -2\,\ln\left[\left(T_L+\bar T_L\right)^{3/2}\hspace{-1.5ex}-\left(T_r+\bar T_r\right)^{3/2}\hspace{-1.5ex}-\left(T_\theta+\bar T_\theta\right)^{3/2}\right]\nonumber\\ && \\ W\hspace{-1ex} &=& \hspace{-1ex}W_0\hspace*{-0.2ex}+\hspace*{-0.2ex}A_L e^{-\frac{2\pi}{N_L}T_L}\hspace*{-0.2ex}+\hspace*{-0.2ex}A_1 e^{-\frac{2\pi}{N_{r_1}}T_r}\hspace*{-0.2ex}+\hspace*{-0.2ex}A_2 e^{-2\pi \big(\frac{T_r}{N_{r_2}}+\frac{T_\theta}{N_{\theta_2}}\big)} \nonumber \eea Here $W_0$ is the vev of the flux superpotential after stabilization of the complex structure moduli and the axio-dilaton. The F-term scalar potential provides KKLT-type minima for the moduli, while generating an axion potential for $r={\rm Im}\, T_r$ and $\theta={\rm Im}\, T_\theta$ of the kind of eq.~\eqref{eq:Vrtheta} after uplifting the KKLT minimum to approximately zero vacuum energy. A moderate hierarchy $N_L > N_r>1$ provides for stabilizing at moderately large volume ${\rm Re}\, T_L > {\rm Re}\, T_r>{\rm Re}\, T_\theta\sim {\cal O}(1)$. Alternatively, we may use a combination of $\alpha'$- and string-loop corrections to stabilize all or part of the real parts of the K\"ahler moduli~\cite{Baumann:2014nda}, while the perturbative nature of these corrections guarantees preservation of the $C_4$ shift symmetry. A complete discussion of the tuning of the parameters and stability requires the inclusion of moduli stabilization and the canonical normalization effects originating from a non trivial metric in field space. For the moment we focus only on the level of potential tuning that is achievable only at the level of W, postponing a full discussion for \cite{Ben-Dayan:2014}. Choosing microscopic parameter values $N_L=30$ (corresponding to an $E_8$ D7-brane stack), $N_{r_1}=N_{\theta_2}=10$, $N_{r_2}=2$, $W_0\sim 0.01$, $A_L\sim1$, $A_1\sim0.01$, and $A_2\sim 10$, we see that the KKLT mechanism stabilizes the moduli at ${\rm Re}\, T_L\sim 25$~, ${\rm Re}\, T_r \sim 10$ , ${\rm Re}\, T_\theta \sim 2$. This leads via the exponential terms in $W$ to $\Lambda_1^4\propto W_0 A_1 \exp(-2\pi/N_{r_1} {\rm Re}\,T_r)\sim 10^{-5}$ and $\Lambda_2^4\propto W_0 A_2 \exp(-2\pi {\rm Re}\,(T_r/N_{r_2}+T_\theta/N_{\theta_2}))\sim 10^{-6}$, while providing for right hierarchy of the effective decay constants $f_{r_2}/f_{r_1}= N_{r_2}/N_{r_1} = 5$ and also $f_{\theta_2}/f_{r_2}=N_{\theta_2}/N_{r_2}=5 $. Since ${\rm Re}\, T_L\sim 25$ implies a Calabi-Yau volume of ${\cal V}\sim 10^2\ldots 10^3$, the F-term scalar potential along the inflaton direction has a scale $\sim e^K\Lambda_2^4\sim 10^{-10}$ which is in the right range to satisfy COBE normalization of the inflationary curvature perturbations. The actual field range of the inflaton-axion potential will depend on the canonical normalization of the $\theta$ axion as $f_{eff}= 50 f^{kin}_{\theta} M_{\rm P}$ and so provided $f^{kin}_{\theta}$ is not exceedingly small, $f^{kin}_{\theta} \ge 1/50$, trans-Planckian field ranges are attainable. An alternative setting can arise from utilizing the 2-form RR-axions. A simple setup involving LVS volume stabilization, utilizing two D5-brane stacks and an Euclidean D3-brane (ED3) looks like \be \begin{split} K &= -2\,\ln\left[\left(T_L+\bar T_L\right)^{3/2} \right.\\ & \left. -\left(T_s+\bar T_s+\sum_{a=r,\theta}c_a (G_a+\bar G_a)^2\right)^{3/2}-\hat\xi\right] \end{split}\nonumber \ee \vspace{-5ex} \bea &&\\ &&\nonumber\\ W&= &W_0+A_s e^{-2\pi T_s}+A_1 e^{-\frac{2\pi}{N_{r_1}}G_r}+A_2 e^{-2\pi \big(\frac{G_r}{N_{r_2}}+\frac{G_\theta}{N_{\theta_2}}\big)}\nonumber \eea The first ED3 in $T_s$ fixes $T_s$ and the overall volume via $T_L$ by its interplay with $\alpha'^3$-correction parametrized by $\hat\xi\sim \chi(CY_3)$. Then the D5-brane stacks provide a scalar potential similar to eq.~\eqref{eq:Vrtheta} for the axions given by ${\rm Im}\,G_a=\int_{S^2_a}C_2$, while KKLT fixing the $B_2$-components of the $G_a$. We note that non-perturbative contributions to the K\"ahler potential arising from ED1 instantons can also generate the scalar potential for the $G_a$-axions~\cite{McAllister:2008hb}. In all cases, a crucial topological requirement for a string construction to reproduce an axion potential with a structure like eq.~\eqref{eq:Vrtheta} seems to be tied with the engineering of a partially ample divisor depending on a linear combination of $T_r$ and $T_\theta$. Summarizing, we have shown that a combination of two cosine potentials for two axions with a simple hierarchy of sub-Planckian decay constants can provide for successful large-field natural inflation with minimal tuning. This setup has the right bottom-up properties for potentially successful embedding into string theory construction, for which we discussed several possible avenues and which will be discussed in detail in \cite{Ben-Dayan:2014}. | 14 | 4 | 1404.7773 |
1404 | 1404.5589_arXiv.txt | We analyze the anisotropic two dimensional galaxy correlation function (2DCF) of the CMASS galaxy samples from the Sloan Digital Sky Survey Data Release 9 (DR9) of the Baryon Oscillation Spectroscopic Survey (BOSS) data. Modeling the 2DCF fully including nonlinear effects and redshift space distortions (RSD) in the scale range of 30 to 120 $h^{-1}$Mpc, we find $H(0.57)r_s(z_d)/c=0.0444 \pm 0.0019$, $D_A(0.57)/r_s(z_d)=9.01 \pm 0.23$, and $f_g(0.57)\sigma_8(0.57)=0.474 \pm 0.075$, where $r_s(z_d)$ is the sound horizon at the drag epoch computed using a simple integral, and $f_g(z)$ is the growth rate at redshift $z$, and $\sigma_8(z)$ represents the matter power spectrum normalization on $8\,h^{-1}$Mpc scale at $z$. We find that the scales larger than 120 $h^{-1}$Mpc are dominated by noise in the 2DCF analysis, and that the inclusion of scales 30-40 $h^{-1}$Mpc significantly tightens the RSD measurement. Our measurements are consistent with previous results using the same data, but have significantly better precision since we are using all the information from the 2DCF in the scale range of 30 to 120 $h^{-1}$Mpc. Our measurements have been marginalized over sufficiently wide priors for the relevant parameters; they can be combined with other data to probe dark energy and gravity. | \label{sec:intro} Galaxy clustering (GC) is one of the most powerful probes in our continuing quest to illuminate the mystery of cosmic acceleration \citep{Riess98,Perl99}, and differentiate between its two possibles causes: an unknown energy component in the Universe (i.e., dark energy), or modification of general relativity (i.e., modified gravity).\footnote{For recent reviews, see \cite{Ratra08,Frieman08,Caldwell09,Uzan10,Wang10,Li11,Weinberg12}.} This is because galaxy clustering enables the measurement of cosmic expansion history \citep{Blake03,Seo03}, as well as the growth history of cosmic large scale structure \citep{Guzzo08,Wang08}. At present, our largest GC data set comes from the Baryon Oscillation Spectroscopic Survey (BOSS) [part of the Sloan Digital Sky Survey (SDSS) III], which will obtain galaxy redshifts over 10,000 square degrees up to a redshift of 0.7 upon completion in 2014 \footnote{http://www.sdss3.org/surveys/boss.php}. The Euclid space mission, scheduled for launch in 2020, will obtain galaxy redshifts over 15,000 square degrees over a wide redshift range up to a redshift of two \footnote{http://www.euclid-ec.org/}\citep{RB}. The SDSS Data Release 9 (DR9) provides us with the first public data set for galaxy clustering from BOSS. In this paper, we build on methods first presented in \cite{CW12}, \cite{CW13}, \cite{WCH13}, and \cite{Hemantha13}, and present an independent new analysis of the DR9 BOSS galaxy clustering data. The main differences between this analysis and previous work using the same data are: (1) We utilize all the available information (not just the multipoles) in the anisotropic two dimensional galaxy correlation function (2DCF) of the CMASS galaxy samples of DR9 BOSS data, and obtain model-independent constraints on the cosmic expansion rate $H(z)$, the angular-diameter distance $D_A(z)$, and the normalized growth rate $f_g(z)\sigma_8(z)$ \citep{Song09} (with $f_g(z)$ denoting the growth rate at redshift $z$, and $\sigma_8(z)$ denoting the matter power spectrum normalization on $8\,h^{-1}$Mpc scale at $z$). (2) We marginalize over sufficiently wide priors for $\Omega_m h^2$, $\Omega_b h^2$, $n_s$, $P_0$, as well as parameters used to model nonlinear effects and RSD; thus our results can be combined with other data to probe dark energy and gravity. We present our method in Section~\ref{sec:method}, our results in Section~\ref{sec:results}, and summarize and conclude in Section~\ref{sec:conclusion}. | \label{sec:conclusion} We have analyzed the anisotropic two dimensional galaxy correlation function (2DCF) of the CMASS galaxy samples from the Sloan Digital Sky Survey Data Release 9 (DR9) of the Baryon Oscillation Spectroscopic Survey (BOSS) data, and derived robust constraints on $H(0.57)r_s(z_d)/c$, $D_A(0.57)/r_s(z_d)$, and $f_g(0.57)\sigma_8(0.57)$ (see Table \ref{table:means} and Table \ref{table:covmat}). While consistent with previous results using the same data, our results have significantly better precision since we are using all the information from the 2DCF in the scale range of interest. Since our measurements have been marginalized over sufficiently wide priors for the relevant parameters; they can be combined with other data to probe dark energy and gravity. We found that the data beyond the scale of 120 $h^{-1}$Mpc are dominated by noise (see Table \ref{table:chi2}). On the other hand, the inclusion of data below the scale of 40 $h^{-1}$Mpc is important for constraining the redshift-space distortion parameter, and hence of the growth rate (see Fig.\ref{fig:params_pdf}). We have chosen the scale range of 30 to 120 $h^{-1}$Mpc (the quasilinear and linear scales at $z=0.57$) in obtaining our fiducial results. We do not use the scale range below 30$\,h^{-1}$Mpc, where our current model is not expected to fit well as we have not included modeling for the mixing of nonlinearity and RSD on the smallest scales. The more advanced modeling that would apply to clustering on smaller scales cannot be validated using the BOSS DR9 mocks, as these were produced using a second-order Lagrangian perturbation theory (2LPT) method, and were calibrated to reproduce the clustering measurements between 30 and 80$\,h^{-1}$Mpc \citep{Manera13}. Fig.1 shows that our model fits the data and the mocks well in the scale range used (indicated by the gray band), and for transverse separations greater than 10 $\,h^{-1}$Mpc for the mocks. We carried out MCMC runs with and without making the transverse cut at $\sigma\geq 10 \,h^{-1}$Mpc, and found that they give very similar results. This may be due to the fact that the cut would only remove a relatively small number of data points (our bin size is 10$\,h^{-1}$Mpc x 10$\,h^{-1}$Mpc). Note that the results from the BOSS DR9 CMASS north and south samples have significantly smaller measurement uncertainties compared to the expectation based on the distribution of the results from the mocks (compare Fig.\ref{fig:params_pdf} and Fig.\ref{fig:meanxhxd}). This may be due to the fact that the measured 2DCF appears less noisy that those measured from the mocks (see Fig.\ref{fig:xi2d}), which reflects a statistical property of the data. \cite{Linder14} presented another independent analysis of DR9 BOSS data, using the method from \cite{Song14}, which is a similar approach with a different theoretical model. The main difference in methodology is that \cite{Linder14} effectively fixed the shape of $P(k)$, while we marginalize over the shape of $P(k)$ by marginalizing over $\Omega_m h^2$, $\Omega_b h^2$, and $n_s$. Our results are broadly similar to that of \cite{Linder14}, with the main difference being that \cite{Linder14} measured $H(0.57)$, $D_A(0.57)$, and $G_{\Theta}$ with either WMAP9 or Planck priors, while our measurements are independent of the CMB priors. Our measurements of $H(0.57)$ and $D_A(0.57)$ are consistent with the expected values from WMAP9 \citep{Bennett13} at 68\% confidence level. \cite{Spergel13} showed that Planck results \citep{PlanckXVI} may be sensitive to systematic effects; they found that the difference between Planck and WMAP 9 results are significantly reduced once the Planck data are cleaned in a consistent and systematic manner. The latest BOSS data (DR11) seem to give much more stringent results than DR9 (see \cite{Anderson13,Chuang13,Samushia13,Sanchez13}). It will be interesting to apply our method to BOSS DR11 data, once they are publicly available. As sufficiently large mock catalogues become available, we will be able to further validate our methodology for application to the Euclid GC data. | 14 | 4 | 1404.5589 |
1404 | 1404.0824_arXiv.txt | {It is well-known that stars with giant planets are on average more metal-rich than stars without giant planets, whereas stars with detected low-mass planets do not need to be metal-rich.} {With the aim of studying the weak boundary that separates giant planets and brown dwarfs (BDs) and their formation mechanism, we analyze the spectra of a sample of stars with already confirmed BD companions both by radial velocity and astrometry.} {We employ standard and automatic tools to perform an EW-based analysis and to derive chemical abundances from CORALIE spectra of stars with BD companions. } {We compare these abundances with those of stars without detected planets and with low-mass and giant-mass planets. We find that stars with BDs do not have metallicities and chemical abundances similar to those of giant-planet hosts but they resemble the composition of stars with low-mass planets. The distribution of mean abundances of $\alpha$-elements and iron peak elements of stars with BDs exhibit a peak at about solar abundance whereas for stars with low-mass and high-mass planets the [X$_\alpha$/H] and [X$_{\rm Fe}$/H] peak abundances remain at $\sim -0.1$~dex and $\sim +0.15$~dex, respectively. We display these element abundances for stars with low-mass and high-mass planets, and BDs versus the minimum mass, $m_C \sin i$, of the most-massive substellar companion in each system, and we find a maximum in $\alpha$-element as well as Fe-peak abundances at $m_C \sin i \sim 1.35\pm 0.20$ jupiter masses.} {We discuss the implication of these results in the context of the formation scenario of BDs in comparison with that of giant planets.} | The most extended convention place the mass range of brown dwarfs (BDs) at $ 13 - 80 \, M_{J}$ (being $M_J$ the mass of Jupiter), having enough mass to burn deuterium but not for hydrogen fusion~\citep{bur97}, i.e. in between the heaviest giant planets and the lightest stars. BDs above $\sim 65 \, M_J$ are thought to fuse lithium and therefore the detection of the \ion{Li}{I}~$\lambda$~6708~{\AA} could be used to identify BDs, this is the so-called ``Lithium Test''~\citep{reb92}. BDs were predicted by \citet{kum62} and \citet{hay63}, but they were not empirically confirmed until 1995, when the first {\rm field} brown dwarf was detected \citep[\textbf{Teide 1},][]{reb95}. This occurs the same year as the discovery of the first extra-solar planet~\citep{may95}. The first BD companion to a M-dwarf star was also discovered that year~\citep[\textbf{GJ 229B},][]{nak95}. During the following two decades high-precision radial velocity (RV) surveys have shown that close BDs around solar-type stars are rare~\citep[][and references therein]{gre06}. Thus, at orbital separations of less than 10 AU, the frequency BD companions remains below 1~\%~\citep{mar00}, whereas it is $\sim 7$~\% for giant planets~\citep{udr07,may11} and $\sim 13$~\% for stellar binaries~\citep{hal03}. The so-called "Brown dwarf desert" may be interpreted as the gap between the largest-mass objects that can be formed in protoplanetary discs, and the smallest-mass clumps that can collapse and/or fragment in the vicinity of a protostar~\citep{mag14}. The mass function, $dN/dm_C \propto m_C^\alpha$, of close planetary and stellar companions drops away ($\alpha \sim -1$) towards the BD mass range~\citep{gre06}. On the other hand, the mass function of isolated substellar objects is roughly flat or even with linear increase ($\alpha\sim 0$) down to $\sim 20$~$M_J$~\citep{cha02,kir12}. This may point to a different formation scenario for close BD companions and BDs in the field and clusters. \citet{sah11} presented the discovery of nine BD companions from a sample of 33 solar-type stars that exhibit RV variations caused by a companion in the mass range $m_C \sin i \sim 13-80$~$M_J$. They used Hipparcos astrometric data~\citep{per97} to confidently discard some of the BD candidates. Including literature data, these authors quoted 23 remaining potential BD candidates. From CORALIE planet-search sample, they obtain an upper limit of 0.6\% for the frequency of BD companions around Sun-like stars. Recently, \citet{mag14} have collected all the BD candidates available in the literature including those in \citet{sah11}, some from the SDSS-III MARVELS survey~\citep{gej08} and some other RV surveys~\citep[e.g.][]{mar00}. The metallicity of stars with BD companions have been briefly discussed in \citep{sah11}. They note that the sample is still too small to claim any possible metallicity distribution of stars hosting BDs. \citet{mag14} extended the sample to roughly 65 stars with BD candidates, including dwarfs and giants, and stated that the mean metallicity of their sample is $\langle$[Fe/H]$\rangle$~$=-0.04$ ($\sigma=0.28$), i.e. remarkably lower than that of stars with giant planets ($\langle$[Fe/H]$\rangle$~$=+0.08$, \citealp{sou08,sou11}). On the other hand, stars with only detected ``small'' planets (hereafter ``small'' planet refers to a low-mass planet, including Super-Earths and Neptune-like planets, with $m_C \sin i < 30 M_\oplus$, whereas ``giant'' planet refers to high-mass planets, including Saturn-like and Jupiter-like planets, with $30 M_\oplus < m_C \sin i < 13 M_J$, see Section~\ref{sec3}) do not seem to require high metal content to form planets within planetary discs~\citep{sou08,sou11,adi12b}. \citet{sou11} study a sample of 107 stars with planets (97 giant and 10 small planets) and found an average metallicity of stars with small planets at about $\langle$[Fe/H]$\rangle$~$=-0.11$, very similar to that of stars without detected planets~\citep{sou08}. Currently, there are two well-established theories for giant planet formation: core-accretion scenario~\citet{pol96} and disc gravitational instability~\citep{bos97}. The core-accretion model is more sensitive to the fraction of solids in a disc than is the disc-instability model. The formation of BDs has been also extensively studied. Two main mechanism have been proposed: molecular cloud fragmentation~\citep{pad04}, and disc fragmentation~\citep{sta09}. The latter mechanism, which requires a small fraction of Sun-like stars should host a massive extended disc, is able to explain most of the known BDs which may either remain bound to the primary star, or be ejected into the field~\citep{sta09}. In this paper, we present a uniform spectroscopic analysis for a sample of stars with BD companions from \citet{sah11} and we compare the results with those of a sample of stars with known giant and small planets from previous works~\citep{adi12b}. The aim of this work is to provide some information that could be useful to distinguish among the different and possible formation mechanisms of BD companions. \begin{table*} \caption[]{Stellar parameters of the CORALIE sample} \label{tpar} \centering \begin{tabular}{lcccccc} \noalign{\smallskip} \noalign{\smallskip} \noalign{\smallskip} \hline\hline \noalign{\smallskip} Star & $ T_{\rm eff}$ & $ \log g$ & $ \xi_t$ & $\rm [Fe/H]$ & $ M_2 \sin i$ & References \\ & $\rm [K]$ & $\rm [dex]$ & $\rm [cm/s]$ & $\rm [dex]$ & $ [M_J]$ \\ \hline \noalign{\smallskip} HD4747 & $5316\pm 50$ & $4.48\pm 0.10$ & $0.79\pm 0.10$ & $-0.21\pm 0.05$ & $46.1$ & 2\\ HD52756 & $5216\pm 65$ & $4.47\pm 0.11$ & $1.11\pm 0.13$ & $0.13\pm 0.04$ & 59.3 & 1\\ HD74014 & $5662\pm 55$ & $4.39\pm 0.08$ & $1.10\pm 0.07$ & $0.26\pm 0.04$ & 49.0 & 1\\ HD89707 & $6047\pm 42$ & $4.52\pm 0.05$ & $0.99\pm 0.06$ & $-0.33\pm 0.03$ & 53.6 & 1\\ HD167665 & $6224\pm 39$ & $4.44\pm 0.04$ & $1.18\pm 0.05$ & $-0.05\pm 0.03$ & 50.6 & 1\\ HD189310 & $5188\pm 50$ & $4.49\pm 0.09$ & $0.94\pm 0.10$ & $-0.01 \pm 0.03$ & 25.6 & 1 \\ HD211847 & $5715\pm 24$ & $4.49\pm 0.05$ & $1.05\pm 0.03$ & $-0.08\pm 0.02$ & 19.2 & 1 \\ \noalign{\smallskip} \hline \noalign{\smallskip} HD3277$^a$ & $5539\pm 49$ & $4.36\pm 0.06$ & $0.91\pm 0.07$ & $-0.06\pm 0.04$ & 64.7 & 1\\ HD17289$^a$ & $5924\pm 32$ & $4.37\pm 0.04$ & $1.15\pm 0.04$ & $-0.11\pm 0.03$ & 48.9 & 1\\ HD30501$^a$ & $5223\pm 27$ & $4.56\pm 0.08$ & $1.18\pm 0.04$ & $-0.06\pm 0.02$ & 62.3 & 1\\ HD43848$^a$ & $5334\pm 92$ & $4.56\pm 0.15$ & $1.35\pm 0.17$ & $0.22\pm 0.06$ & 24.5 & 1\\ HD53680$^a$ & $5167\pm 94$ & $5.37^b\pm 0.29$ & $2.08\pm 0.31$ & $-0.29\pm 0.04$ & 54.7 & 1\\ HD154697$^a$ & $5648\pm 45$ & $4.42\pm 0.05$ & $1.04\pm 0.06$ & $0.13\pm 0.04$ & 71.1 & 1\\ HD164427A$^a$& $6003\pm 27$ & $4.35\pm 0.03$ & $1.19\pm 0.03$ & $0.19\pm 0.02$ & 48.0 & 1\\ HIP103019$^a$& $4913\pm 115$& $4.45\pm 0.28$ & $0.54^c\pm 0.10$ & $-0.30\pm 0.06$ & 52.5 & 1\\ \noalign{\smallskip} \hline \noalign{\smallskip} HD74842$^d$ & $5517\pm 38$ & $4.50\pm 0.06$ & $1.01\pm 0.06$ & $-0.08\pm 0.03$ & -- & 3 \\ HD94340$^d$ & $5902\pm 26$ & $4.19\pm 0.03$ & $1.30\pm 0.03$ & $0.11\pm 0.02$ & -- & 3 \\ HD112863$^d$ & $5342\pm 36$ & $4.57\pm 0.07$ & $1.08\pm 0.07$ & $-0.11\pm 0.03$ & -- & 3\\ HD206505$^d$ & $5392\pm 44$ & $4.46\pm 0.07$ & $1.02\pm 0.07$ & $0.11\pm 0.03$ & -- & 3\\ \noalign{\smallskip} \hline \noalign{\smallskip} \noalign{\smallskip} \end{tabular} \tablebib{(1) \citet{sah11}; (2) \citet{san05}; (3) This work.} \tablefoot{\tablefoottext{a}{These eight stars have companion minimum masses, $m_C \sin i$, in the BD range determined from spectroscopic RV measurements, but are discarded in \citet{sah11}, from their Hipparcos astrometry.}\\ \tablefoottext{b}{The surface gravity of the star HD~53680 is unusually for its derived effective temperature. A significantly lower $T_{\rm eff}$ value (probably $ < 4500$~K) is expected from its weak and narrow $H\alpha$ profile (see Fig.~\ref{fspec} and Section~\ref{secabu}).}\\ \tablefoottext{c}{The microturbulence of HIP~103019 was calculated following the expression presented in \citet{adi12c}.}\\ \tablefoottext{d}{These four stars, as a comparison sample, are also from the CORALIE sample but they do not have detected BD companions} } \end{table*} | } We have analyzed a subsample of stars with candidate BD companions from the CORALIE radial velocity survey. We derive chemical abundances of several elements including $\alpha$-elements and Fe-peak elements. A comparison with the chemical abundances of stars with giant planets shows that BD-host stars seem to behave differently. In particular, we compute the abundance histograms [X$_\alpha$/H] and [X$_{\rm Fe}$/H], revealing a mean abundance at about solar for the BD-host sample whereas for stars without planets (NP) and with small planets (SP) remains at $-0.1$~dex, and for stars with giant planets (GP) at roughly$+0.10$~dex. The cumulative histograms of [X$_\alpha$/H] and [X$_{\rm Fe}$/H] abundances exhibit the same situation, with the stars without planets and with small planets going together, similarly to the stars with BDs. However, the stars with giant planets reach a later saturation at [X/H]~$\sim 0.3$~dex. A Kosmogorov-Smirnov (K-S) test does not show a statisticallly significant difference between the cumulative distribution of SP, NP and BD samples, but clearly separates the GP and BD samples. Finally, we depict the [X$_\alpha$/H] and [X$_{\rm Fe}$/H] abundances versus the minimum mass of the most-massive substellar companion, $m_C \sin i$, and we find a peak of these element abundances for a companion mass $m_C \sin i \sim 1.3-1.4\, M_J$, with the abundances growing with the companion mass from small planets to Jupiter-like planets and after decresing towards massive BD companions. A 3-step model also provides a similar description of the data with no statistically significant difference with the parabolic model. Recently, \citet{sah11} and \citet{mag14} have suggested that the formation mechanism may be different for BD companion below and above 42~$M_J$. We find that BDs below this mass tend to have higher abundances than those above this mass, which may support this conclusion and BDs with $m_C \sin i < 42$~$M_J$ may form by disk instability-fragmentation whereas high-mass BD may form as stars by cloud fragmentation. | 14 | 4 | 1404.0824 |
1404 | 1404.1543_arXiv.txt | A compact object moving on a quasicircular orbit about a Schwarzschild black hole gradually spirals inward due to the dissipative action of its gravitational self-force. But in addition to driving the inspiral, the self-force has a conservative piece. Within a second-order self-force formalism, I derive a second-order generalization of Detweiler's redshift variable, which provides a gauge-invariant measure of conservative effects on quasicircular orbits. I sketch a frequency-domain numerical scheme for calculating this quantity. Once this scheme has been implemented, its results may be used to determine high-order terms in post-Newtonian theory and parameters in effective-one-body theory. | The gravitational self-force program was initiated with the goal of modeling extreme-mass-ratio inspirals (EMRIs)~\cite{Mino-Sasaki-Tanaka:97}, astrophysical systems in which stellar-mass compact objects spiral into far more massive black holes in galactic nuclei. An EMRI evolves primarily due to dissipation: the object emits gravitational waves that carry away energy (or equivalently, the self-force does negative work), causing the orbit to shrink until the object plunges into the black hole. However, in the years since the program began, the \emph{conservative} effects of the self-force have also proven to be a fecund area of study. These conservative effects must be accounted for to obtain accurate long-term models of inspirals~\cite{Pound-Poisson-Nickel:05,Pound-Poisson:08,Hinderer-Flanagan:08}, and their influence on long-term orbital evolution has recently been calculated concretely for the first time~\cite{Warburton-etal:12}. Besides its long-term effect on inspirals, the conservative piece of the self-force also tells us about short-term effects~\cite{Barack-Sago:07,Detweiler:08,Barack-Sago:09,Barack-Sago:10,Barack-Sago:11,Shah-etal:12}. The most obvious example might be a correction to the standard relativistic precession of an eccentric orbit. But conservative effects arise even in the case of quasicircular orbits (i.e., orbits that would be precisely circular in the absence of dissipation). For example, the radial force alters the frequency of an orbit at a given orbital radius. Because quantities such as (coordinate) azimuthal angle and radius---and the gravitational self-force itself---are gauge dependent~\cite{Barack-Ori:01}, effects such as precession and frequency shifts at a given coordinate radius are as well. Hence, a primary goal when calculating self-force effects is to identify some gauge-invariant characterization of them. For example, orbital precession can be written in an invariant form in the circular limit~\cite{Barack-Sago:11}. A shift in frequency is invariant if the radius is physically identifiable; for example, one can consider the shift in frequency of the innermost stable circular orbit (ISCO)~\cite{Barack-Sago:09,Favata:11,LeTiec-etal:12b,Isoyama-etal:14}. For quasicircular orbits away from a special orbital radius, the principal invariant quantity of interest has been Detweiler's redshift variable, the inverse of the time component of a certain normalized four-velocity, which for later purposes I will denote by $\btilde u^t$~\cite{Detweiler:08}. The construction of this quantity is based on the fact that the orbit, which is accelerated by the self-force when considered to move in the background metric of the large black hole, is a geodesic when considered to move in a certain \emph{effective} metric, a certain smooth piece of the full, physical metric of the binary~\cite{Detweiler-Whiting:03,Pound:10a,Harte:12}. $\btilde u^t$ describes the ratio of proper time of an inertial observer at infinity to proper time along the orbit as measured in that effective metric. Its inverse, $1/\btilde u^t$, is the redshift experienced in the effective metric by a photon emitted to infinity in a direction perpendicular to the orbital plane. It can also be heuristically interpreted as the orbital energy as measured in a frame that co-rotates with the orbit. Because these interpretations of $\btilde u^t$ refer to quantities in the effective metric, rather than the binary's physical metric, their physical meaning is somewhat hazy. Nevertheless, defined strictly as the ratio of two measures of time, the quantity $\btilde u^t$ is invariant. Furthermore, it can be used to find other physical effects, such as the ISCO shift in Schwarzschild~\cite{LeTiec-etal:12b} and Kerr~\cite{Isoyama-etal:14}. Invariant conservative quantities such as these are important beyond their role in characterizing the physics of extreme-mass-ratio binaries. They have been the point of comparison between self-force calculations performed in different gauges~\cite{Sago-Barack-Detweiler:08,Dolan:13}. More notably, in efforts originally led by Detweiler, Blanchet, and collaborators~\cite{Detweiler:08,Blanchet-etal:10a,Blanchet-etal:10b}, they have allowed for comparisons with entirely distinct models such as full numerical relativity and post-Newtonian (PN) theory~\cite{LeTiec-etal:11,Favata:11,LeTiec-etal:12b,LeTiec-etal:13,Shah-etal:13}. Since self-force calculations offer the only highly accurate model in the domain of extreme mass ratios and highly relativistic fields, they can also do better than compare: they set benchmarks for numerical relativity, and they have been used to determine high-order parameters~\cite{Blanchet-etal:10b,Favata:11,Shah-etal:13, Damour:09, Barack-Damour-Sago:10,Barausse-etal:11,Akcay-etal:12,Bini-Damour:13} in PN theory and the effective-one-body theory (EOB) introduced in Refs.~\cite{Buonanno-Damour:99,Damour-etal:00}. Furthermore, study of these conservative effects has provided strong evidence that the domain of validity of the self-force formalism can be made much larger than one would naively expect, pushing it toward modeling binaries of comparable-mass objects~\cite{LeTiec-etal:11,LeTiec-etal:12b,LeTiec-etal:13}. Until recently, all of this work had been limited to linear order in the binary's mass ratio. Although some analyses had been performed at second order~\cite{Rosenthal:06a,Rosenthal:06b, Pound:10a, Detweiler:12}, they did not provide a practical means of concretely calculating second-order effects. However, with the recent development of complete second-order self-force formalisms~\cite{Pound:12a,Gralla:12,Pound:12b}, there is now no substantial obstacle to performing such concrete calculations. Proceeding to second order offers several exciting prospects: highly accurate calculations of effects on intermediate-mass-ratio and even comparable-mass binaries; stronger benchmarks for numerical relativity; and further improvements of the accuracy of PN and EOB models. The purpose of this paper is to take the first step toward realizing those goals. Restricting my attention to the simplest case, that of quasicircular orbits in Schwarzschild, I derive a gauge-invariant formula for a second-order generalization of Detweiler's redshift variable. I then outline how that quantity can be calculated numerically in the frequency domain. \subsection{Plan of this paper} Due to the nonlinear nature of the problem, defining and extracting conservative dynamics from a dissipating system at second order is more delicate than it was in the linearized problem. At first order, the time-symmetric part of the retarded solution was equal to the half-retarded-plus-half-advanced solution, and the force in the half-retarded-plus-half-advanced solution was equal to the conservative piece of the force in the retarded solution. At second order, neither of these statements is true. To avoid attachment to any particular definition of the conservative dynamics, I begin in Sec.~\ref{preview} with a preview of the main results, which hold for most, if not all, specifications of the conservative-dissipative split. Without making a precise choice of that split, I sketch the derivation of a general formula for the second-order $\btilde u^t$. Sections~\ref{SC} and \ref{GW} then describe a particular definition of the conservative dynamics, eventually recovering the result for $\btilde u^t$. In Sec.~\ref{SC} I offer a description in the self-consistent self-force formalism~\cite{Pound:10a, Pound:12a, Pound:12b, Pound:13a, Pound:14a, Pound-Miller:14}, a picture of the system in which the metric perturbation is a functional of the self-accelerated orbit. After a review of the formalism, I construct a precisely circular orbit that is a geodesic of a certain time-symmetrized effective metric constructed from the retarded field, and I derive a gauge-invariant formula for the second-order $\btilde u^t$ on that orbit. The self-consistent formalism is not ideal for numerical calculations of conservative dynamics, for reasons described below, and so in Sec.~\ref{GW} I transition to a Gralla-Wald picture, in which the perturbed motion is described as a small deviation from a reference orbit that is a geodesic of the background spacetime~\cite{Gralla-Wald:08,Gralla:12}. Although this description of the motion is not ideal for describing dissipative changes in the orbit, which grow large with time, it \emph{is} ideal for calculations of conservative dynamics, because in the absence of dissipation, deviations from the reference orbit remain small. Beginning from the self-consistent results of Sec.~\ref{SC}, I derive an expression for the second-order redshift variable in the Gralla-Wald picture. Section~\ref{gauge_GW} shows the gauge invariance of the result. In Sec.~\ref{variants} I briefly discuss alternative definitions of the conservative dynamics. The formula for $\btilde u^t$ holds true with these definitions, but some difficulties arise in interpreting that formula and enforcing its gauge invariance. I conclude in Sec.~\ref{scheme} by describing a numerical scheme for calculating $\btilde u^t$ in the frequency domain in the Gralla-Wald picture. The scheme is an extension of one recently devised by Warburton and Wardell for the scalar self-force problem~\cite{Warburton-Wardell:14}. Its technical details will be provided in a future paper~\cite{Warburton-etal:14}. Appendix~\ref{dissipation} complements the body of the paper with a treatment of quasicircular orbits in the Gralla-Wald picture, relying less on the self-consistent picture. I work in geometric units with $G=c=1$, and I use the metric signature $-+++$. All indices are raised and lowered with a background metric $g_{\mu\nu}$, both a semicolon and $\nabla$ denote the covariant derivative compatible with $g_{\mu\nu}$, and coordinate expressions always refer to Schwarzschild coordinates $\{t,r,\theta,\phi\}$ on the background manifold. | \label{scheme} The main result of this paper is Eq.~\eqref{Utilde_GW_prev}, which is an extension of Detweiler's redshift invariant $\btilde u^t\equiv\btilde U$ to second order. This formula describes the ratio between intervals of Schwarzschild coordinate time and proper time on a precisely circular orbit $\hat z^\mu$ that is accelerated only by a conservative piece of the self-force; the proper time is measured in a certain effective metric in which $\hat z^\mu$ is a geodesic. However, the formula is written in terms of quantities evaluated not on $\hat z^\mu$, but on a nearby circular orbit $z_0^\mu$, of the same orbital frequency, that is a geodesic of the background metric. This result utilizes the Gralla-Wald picture of perturbed motion, in which the perturbed orbit $\hat z^\mu$ is described as a deviation from a background geodesic $z_0^\mu$. Before arriving at that picture, my analysis began in a self-consistent picture, in which the orbit sourcing the metric perturbations is self-consistently accelerated by those perturbations. In that picture, I derived a formula for $\btilde U$, given by Eq.~\eqref{Utilde_SC}, in which all quantities were evaluated on the accelerated orbit. At the beginning of Sec.~\ref{GW_formalism}, I described why a self-consistent numerical scheme to calculate this quantity $\btilde U$ is not ideal: it requires one to know the orbit $\hat z^\mu$ in advance; in other words, one must determine the correct initial data for a circular orbit through second order in perturbation theory. This challenge does not arise when one works in the Gralla-Wald picture, because the background geodesic may be freely prescribed, making the Gralla-Wald picture ideal for a concrete numerical calculation of $\btilde U$. Indeed, over the course of my analysis, I have described most of the key ingredients for such a calculation. Putting those ingredients together, we arrive at the following scheme: \begin{enumerate} \item Choose a circular geodesic of the background metric. This amounts to choosing an orbital radius $r_0$. \item Assume decompositions \begin{align} h^n_{\mu\nu} &= \sum_{i\ell m}h_{ni\ell m}e^{-im\Omega t}Y^{i\ell m}_{\mu\nu},\\ h^{\res n}_{\mu\nu} &= \sum_{i\ell m}h^\res_{ni\ell m}e^{-im\Omega t}Y^{i\ell m}_{\mu\nu} \end{align} of the retarded and residual fields, with the frequency given by Eq.~\eqref{Omega0_prev}. \item Solve the separated version of the first-order field equation~\eqref{h1_GW} [or~\eqref{h1_GW_point}] to obtain (i) the radial functions $h_{1i\ell m}(r)$ at all points $r\neq r_0$, and (ii) the regular field $h^{\R1}_{\mu\nu}$ and its derivatives $h^{\R1}_{\mu\nu,\rho}$ on $z_0^\mu$. Transform these results to the asymptotically flat gauge using the gauge vector $\xi_1^\mu$, given in Eq.~\eqref{to-flat}. \item With the (transformed) numerical values of $h^{\R1}_{\mu\nu}$ and $h^{\R1}_{\mu\nu,r}$, calculate (i) the first-order radial force, using Eq.~\eqref{F1}, (ii) the first-order conservative shift in orbital radius, $\hat r_1$, using Eq.~\eqref{r1}, and (iii) the tensor $\delta m_{\mu\nu}$, using Eq.~\eqref{dm_GW}. \item Construct and evaluate the radial functions $S^{\rm eff}_{2i\ell m}(r)$ in the source $S^{2\rm eff}_{\mu\nu}=\sum_{i\ell m}S^{\rm eff}_{2i\ell m}e^{-im\Omega t}Y^{i\ell m}_{\mu\nu}$ for the second-order field equation. This involves \begin{enumerate} \item rewriting Eq.~\eqref{h2_GW} to account for the transformation generated by $\xi_1^\mu$, \item using the coupling formula~\eqref{coupling} to calculate the radial functions in the decomposition of $\delta^2 R_{\mu\nu}[h^1,h^1]$ from the radial functions $h_{1i\ell m}(r)$, \item constructing a puncture of the form $h^{\P2}_{\mu\nu}=\sum_{i\ell m}h^\P_{2i\ell m}e^{-im\Omega t}Y^{i\ell m}_{\mu\nu}$, which can be done by decomposing the expansion of the singular field given schematically by Eq.~\eqref{hS2_GW_schematic} and explicitly by Eq.~(144) in Ref.~\cite{Pound-Miller:14}; as input, this puncture uses the numerical values of $\hat r_1$, $\delta m_{\mu\nu}$, and $h^{\R1}_{\mu\nu}$ on $z_0^\mu$ (and potentially the derivatives of $h^{\R1}_{\mu\nu}$, depending how many orders in $|x^\alpha-z_0^\mu|$ are used in the puncture). The puncture, which was found in the Lorenz gauge, must be tweaked to account for the transformation generated by $\xi_1^\mu$. \end{enumerate} \item Solve for the radial functions $h_{2i\ell m}$ and $h^\res_{2i\ell m}$ in the separated version of the second-order field equation. \item Find a gauge vector $\xi_2^\mu$ that brings $h^2_{\mu\nu}$ to an asymptotically flat (still helically symmetric) form, and apply the resulting transformation to $h^{\R2}_{\mu\nu}$. The only necessary output from the result is $h^{\R2}_{u_0u_0}$. \item Combine $h^{\R1}_{u_0u_0}$, $F^r_1$, and $h^{\R2}_{u_0u_0}$ in Eq.~\eqref{Utilde_GWv2} to calculate the redshift variable $\btilde U$. \end{enumerate} The technical details of this scheme, particularly those involved in steps 5 and 6, will be presented in a future paper~\cite{Warburton-etal:14}. A comparison of the numerically calculated $\btilde U$ to its value in PN theory will be the first test of the second-order self-force formalism. Assuming that test is passed, second-order results can begin to inform high-order PN theory and EOB. And although I have focused on a means of calculating $\btilde U$ and nothing else, the general formalism I have presented, and the same type of numerical scheme, can be used to calculate any other conservative effects that may occur on circular orbits. Most significantly, it should be straightforward to generalize the techniques of Ref.~\cite{Isoyama-etal:14} to derive a formula for the second-order shift in the frequency of the ISCO. | 14 | 4 | 1404.1543 |
1404 | 1404.6964_arXiv.txt | Using direct numerical simulations of three-dimensional hydromagnetic turbulence, either with helical or non-helical forcing, we show that the ratio of kinetic-to-magnetic energy dissipation always increases with the magnetic Prandtl number, i.e., the ratio of kinematic viscosity to magnetic diffusivity. This dependence can always be approximated by a power law, but the exponent is not the same in all cases. For non-helical turbulence, the exponent is around 1/3, while for helical turbulence it is between 0.6 and 2/3. In the statistically steady state, the rate of the energy conversion from kinetic into magnetic by the dynamo must be equal to the Joule dissipation rate. We emphasize that for both small-scale and large-scale dynamos, the efficiency of energy conversion depends sensitively on the magnetic Prandtl number, and thus on the microphysical dissipation process. To understand this behavior, we also study shell models of turbulence and one-dimensional passive and active scalar models. We conclude that the magnetic Prandtl number dependence is qualitatively best reproduced in the one-dimensional model as a result of dissipation via localized Alfv\'en kinks. | One of the central paradigms of hydrodynamic turbulence is the equivalence of large-scale energy injection and small-scale dissipation into heat through viscosity---regardless of how small its value. This is believed also to apply under conditions of astrophysically large Reynolds numbers, when the microphysical viscosity becomes very small compared with the product of the physical scales and velocities of the system. Dramatic examples are quasars, whose luminosities are equal to that of a hundred galaxies and this emission is caused just by the dissipation of turbulence, even though the microphysical viscosity is extremely small. The detailed physical processes are not well understood, but it is now generally believed that they also involve magnetic fields \citep{SS73,BH98}. Indeed, magnetic fields provide an additional important pathway for dissipating turbulent energy through Joule heating. The heating rates for both viscous and Joule dissipation are proportional to the microphysical values of viscosity $\nu$ and magnetic diffusivity $\eta$, respectively. The ratio of these coefficients is the magnetic Prandtl number, $\Pm=\nu/\eta$. As these coefficients are decreasing, the velocity and magnetic field gradients sharpen just enough so that the heating rates remain independent of these coefficients. For the magnetic case of Joule heating, the independence of the magnetic Reynolds number was demonstrated by \cite{GN96} and \cite{Hendrix} in connection with the coronal heating problem. Over a range of magnetic Reynolds numbers, the approximate constancy of Joule dissipation has also been seen in turbulent dynamo simulations \citep{CHMB11}. While this picture is appealing and seemingly well confirmed, at least in special cases such as for fixed values of $\Pm$, questions have arisen in those cases when the magnetic and fluid Reynolds numbers are changed in such a way that their ratio changes. Hydromagnetic turbulence simulations exhibiting dynamo action have shown that the values of energy dissipation are then no longer constant, and that their ratio scales with $\Pm$ \citep{Min07,B09,B11,B11an}. Given that all of the energy that is eventually dissipated comes from the forcing in the momentum equation, a change in the dissipation ratio can only be a consequence of a change in the conversion of kinetic to magnetic energy through the dynamo process. Therefore, the dynamo process would be intimately linked to Joule dissipation and one must therefore be concerned that it is also linked to the physical or even numerical nature of energy dissipation. This would be surprising, because dynamo action has frequently been modeled in many astrophysical turbulence simulations by focusing on the so-called ideal equations with numerical dissipation only where no $\Pm$ can be defined. Examples in the context of local accretion disk dynamo simulations can be found in the papers by \cite{BNST95}, \cite{HGB96}, and \cite{SHGB96}. This leads to an ignorance that is potentially dangerous if such simulations are employed to make predictions concerning energy deposition in accretion disks \citep[see discussion by][]{BKL97}. There is some concern that the numerical results of \cite{B09,B11} may not yet be in the asymptotic regime and that the $\Pm$ dependence might disappear at sufficiently large values of $\Rey$. However, two arguments against this possibility have now emerged. First, there are analytic results in two-dimensional magnetohydrodynamics (MHD) by \cite{TYB13} that demonstrate the boundedness of the mean-squared current density and mean-squared vorticity in the limits of large and small values of $\Pm$, respectively. In fact, \cite{TYB13} also produce numerical scalings similar to the results of \cite{B11,B11an}. Second, MHD shell models of turbulence by \cite{PS10} for $\Pm>1$ show a similar $\Pm$ dependence, which is remarkable because those models can be extended to much larger values of $\Rm$ than what is currently possible with DNS. Thus, there is now mounting evidence for a genuine dependence of the macroscopic properties of MHD turbulence on $\Pm$. Another such dependence has been discussed for some time in connection with non-helical turbulence exhibiting small-scale dynamo action in the {\em kinematic} regime. Note, however, that this no longer applies in the non-kinematic regime \citep{B11}. For a kinematic small-scale dynamo dynamo, the magnetic energy spectra grow in an approximately shape-invariant fashion with an approximate $k^{3/2}$ spectrum at small wavenumbers. This spectrum was first predicted by \cite{Kaz68} in the case of a smooth flow. This case corresponds to an idealized representation of turbulence at large values of $\Pm$ \citep{Scheko02}, but this spectrum is apparently also found at small values of $\Pm$ near unity \citep[see Figure~4 of][]{HBD04}. Depending on the value of $\Pm$, the magnetic energy spectrum peaks at wavenumbers either within the inertial range of the turbulence or in the viscous subrange. This has implications for the critical magnetic Reynolds number for the onset of dynamo action \citep{RK97}. As explained by \cite{BC04}, the velocity field is rough in the inertial range. This interpretation has been successfully applied when clarifying the reason for an apparent divergence \citep{Scheko05} of the critical Reynolds number above which dynamo action is possible \citep{Isk07,Scheko07}. There has been a similar debate regarding the onset of the magneto-rotational instability in local simulations of accretion disks \citep{FP07,FPLH07}, where the instability was found not to be excited for small values of $\Pm$. However, these examples are restricted to the physics of small-scale magnetic fields only. If one allows large-scale fields to develop, e.g., by relaxing the restriction to closed or periodic boundary conditions, this $\Pm$ dependence disappears \citep{KK11}. In the following, we will be concerned with the fully dynamic case where kinetic and magnetic energies are comparable. The purpose of the present paper is to illuminate the problem of the $\Pm$ dependence of the dissipation ratio through a combination of different approaches to MHD turbulence ranging from direct numerical simulations (DNS) of the MHD equations in three dimensions and shell models of turbulence capturing aspects of the spectral cascade, to a simple one-dimensional model of MHD \citep[cf.][]{Tho68,Pou93,BNP14}. This leads us to suggest that the $\Pm$ dependence found in turbulent dynamo simulations is caused by the dominant influence of dissipative structures on the turbulent cascade at larger scales. These dissipative structures can be thought of as local Alfv\'en kinks whose width is determined by the algebraic mean of kinematic viscosity and magnetic diffusivity. | In the present work, he have extended earlier findings of a $\Pm$ dependence of the kinetic-to-magnetic energy dissipation ratio, $\epsK/\epsM$, to the regime of small-scale and large-scale dynamos for $\Pm>1$ and at higher resolution than what was previously possible \citep{B11an}. In most cases, our results confirm earlier results that for large-scale dynamos, the ratio $\epsK/\epsM$ is proportionate to $\Pm^{0.6}$. Furthermore, we have shown that a similar scaling with $\Pm$ can be obtained for a simple one-dimensional Alfv\'en kink, where ram pressure locally balances magnetic pressure. Interestingly, in these cases kinetic energy dissipation is accomplished mainly by the irrotational part of the flow rather than the solenoidal part as in the turbulence simulations presented here. We note in this connection that the kinetic energy dissipation, which is proportional to $\bra{2\SSSS^2}=\bra{(\nab\times\uu)^2}+\bra{{4\over3}(\nab\cdot\uu)^2}$, has similar contributions from vortical and irrotational parts. We have also shown that for fixed values of $\Pm$, the ratio $\epsK/\epsM$ is not strongly dependent on the presence of rotation, provided the magnetic Reynolds number is not too close to the marginal value for the onset of dynamo action. In the simulations with $\Co\neq0$ presented here, the runs were often not very long and therefore the error bars large, but the number of similar results support our conclusions that $\epsK/\epsM$ is roughly independent of $\Co$. For many astrophysical systems, the microscopic energy dissipation mechanism is not of Spitzer type, as assumed here. It is not obvious how this would affect our results. Nevertheless, it is clear that conclusions based on the kinetic-to-magnetic energy ratio itself do not have much bearing on the energy {\em dissipation} ratio. This became clear some time ago in connection with local accretion disk simulations driven by the magneto-rotational instability, where magnetic energy strongly dominates over kinetic. However, as it turned out, most energy is dissipated viscously rather than resistively \citep{BNST95}. Unfortunately, the question of energy dissipation is not routinely examined in astrophysical fluid dynamics, nor is it always easy to determine energy dissipation rates, because many astrophysical fluid codes ignore explicit dissipation and rely entirely on numerical prescriptions needed to dissipate energy when and where needed. Our present work highlights once again that this can be a questionable procedure, because it means that even non-dissipative aspects, such as the strength of the dynamo which is characterized by $\bra{\uu\cdot(\JJ\times\BB)}$, are then ill-determined. The reason why this has not been noted earlier is that most previous work assumed $\Pm$ to be of the order of unity. An exception is the work of \cite{B09}, where dynamo simulations for values of $\Pm$ as small as $10^{-3}$ were considered. One reason why such extreme values of $\Pm$ have been possible is the fact that at very small values of $\Pm$, most of the energy is dissipated resistivity, and there is not much kinetic energy left at the end of the turbulent kinetic energy cascade. As a consequence, it is then possible to decrease the value of $\nu$ further and still dissipate the remaining kinetic energy, which implies that the nominal value of the fluid Reynolds number can become much larger than what is usually possible when there is no additional resistive dissipation. However, one may wonder how a large-scale dynamo can depend on $\Pm$. We expect that this is only possible if most of the energy transfer comes ultimately from small scales. It is also noteworthy that there is now some evidence for the non-universal behavior of the scaling of the kinetic-to-magnetic energy dissipation ratio with $\Pm$. Although some of the earlier results with slightly different exponents could be explained by inaccuracies and other physical effects, there are now examples such as one-dimensional simulations and the passive scalar analogy that display different exponents which cannot easily be explained through artifacts. Also, the result that for large enough magnetic Reynolds numbers the dissipation ratio scales differently in the presence of helicity ($q\approx0.7$) than without ($q\approx1/3$) is surprising. It would therefore be interesting to revisit the viscous-to-magnetic dissipation ratios over a broader range of circumstances. | 14 | 4 | 1404.6964 |
1404 | 1404.0773_arXiv.txt | We present a model-independent determination of the curvature parameter $\Omega_k$ by using the Hubble parameter $H(z)$ and angular diameter distance $D_A(z)$ from the recent baryon acoustic oscillation (BAO) measurements. Each $H(z)$ and $D_A(z)$ pair from a BAO measurement can constrain a curvature parameter. The accuracy of the curvature measurement improves with increased redshift of $H(z)$ and $D_A(z)$ data. By using the $H(z)$ and $D_A(z)$ pair derived from BAO Lyman $\alpha$ forest measurement at $z=2.36$, the $\Omega_k$ is confined to be -0.05$\pm$0.06, which is consistent with the curvature $-0.037^{+0.044}_{-0.042}$ constrained by the nine-year WMAP data only. Considering future BAO meausurements, at least one order of magnitude improvement of this curvature measurement could be expected. | The strong degeneracy between the curvature of the universe and the dark energy equation of state causes difficulties for constraining the two parameters simultaneously. The curvature is commonly left out in a dark energy analysis, or conversely, a dark energy constant is assumed in a determination of the curvature. However, a simple flatness assumption may result in erroneously reconstructing the dark energy equation of state even if the true curvature is very small \citep{Clarkson2007}, and a cosmological constant assumption may arise confusions between a dynamical dark energy non-flat model and the flat $\Lambda$CDM model \citep{Virey2008}. In \citet{Clarkson2007}, when arguing the defects of a zero curvature assumption, a direct curvature determination by combining measurements of the Hubble parameter $H(z)$ and the comoving angular diameter distance $D(z)$ was proposed: \begin{equation} \Omega_k=\frac{[H(z)D'(z)]^2-c^2}{[H_0D(z)]^2} \label{eq:curv} \end{equation} where $'$ denotes derivative with respect to redshift $z$. This formula benefits from the Baryon Acoustic Oscillation (BAO) measurements which can provide $H(z)$ and $D_A(z)$ simultaneously at the same redshift. Here $D_A(z)$ is the angular diameter distance, which is correlated to the comoving angular diameter distance by $D(z)=(1+z)D_A(z)$. Since the derivation of $H(z)$ and $D_A(z)$ pairs from BAO measurements are purely geometrical, Eq.(\ref{eq:curv}) can be evaluated without any assumption of dynamic evolution of universe , therefore breaks the degeneracy between curvature and dark energy equation of state. Several works have already derived the $H(z)$ and $D_A(z)$ pairs from the data of WiggleZ Dark Energy Survey at $z=0.44, 0.6, 0.73$ \citep{Blake2012}, and the third generation Sloan Digital Sky Survey (SDSS-III) at $z=0.35$ \citep{Chuang2012, Hemantha2013, Xu2013} and $z=0.57$ \citep{Reid2012, Kazin2013, Chuang2013, Anderson2014, Samushia2013}. With the quasar-Lyman $\alpha$ forest in SDSS-III, the measurement of $H(z)$ and $D_A(z)$ has extended to high redshift such as $z=2.36$ \citep{Font-Ribera2013}. These data can afford us to directly determine the curvature parameter via Eq.(\ref{eq:curv}). The remaining issue is to estimate the $D'(z)$ reasonably. \citet{Mignone2008} has applied a novel method to take the derivative of the luminosity distance $D_L(a)$ with respect to the scale factor in their model-independent reconstruction of Hubble parameter. They decomposed the observables into a suitable basis functions, then recombined the derivatives of the basis functions to yield the $D'_L(a)$. The basis system was whereafter optimized by \citet{Maturi2009} to be capable to describe cosmologies independently of their background physics and improve the quality of the estimation of $D'_L(a)$. This method is independent to any cosmology model and can be employed by us to estimate the $D'(z)$. By combining the data and method described above, we can determine the curvature parameter in a model-independent manner. This approach is different from previous works employing smoothing procedures in redshift bins or reconstruction of both Hubble parameter and comoving angular diameter distance \citep[e.g.][]{Mortsell2011}. The property of Eq.(\ref{eq:curv}) has determined that the error on the measured curvature parameter decreases as the redshift increases, thus we can benefit from the BAO Lyman $\alpha$ forest measurement which can provide $H(z)$ and $D_A(z)$ pair at high redshift. The structure of this paper is as follows. In Section \ref{sec:method}, we review the essential parts of the model-independent method. The description of data and application of the method are shown in Section \ref{sec:application}. The discussions are presented in Section \ref{sec:discussion} and the conclusions are drawn in Section \ref{sec:conclusion}. | \label{sec:conclusion} Based on the work of \citet{Clarkson2007}, \citet{Mignone2008}, \citet{Maturi2009} and \citet{Benitez2013}, we present a model-independent method to determine the curvature parameter. The $H(z)$ and $D_A(z)$ pairs involved in this method are derived by BAO measurements which only depend on the space-time geometry, thus can afford us to measure the curvature without any assumptions of the dynamic evolution of the universe. The luminosity distances $D_L(z)$ from Union2.1 SN Ia compilation are included to have a better constrain on estimation of the derivative of comoving angular diameter distance with respect to redshift. The curvature parameters measured in this work are in agreement of a flat universe within error limits. The feature of Eq.(\ref{eq:curv}) leads to the fact that the accuracy of the curvature measurement improves with increasing redshift of $H$ and $D_A$ and will reach a limit primarily determined by the data quality. In this work, the errors of curvature measurements at low redshift are nearly of order unit, while the curvature measurement at a high redshift $z=2.36$ has derived a much better constrain $\Omega_k=-0.05\pm0.06$, which is consistent with the nine year WMAP-only results. We use the density parameters from \citet{Planck2013} and theoretical BAO cosmic variance forecast from \citet{Weinberg2012} to generate a small synthetic sample to test the curvature measurement. At least one order of magnitude improvement of this curvature measurement could be expected. | 14 | 4 | 1404.0773 |
1404 | 1404.2295_arXiv.txt | {We present spatially resolved Atacama Large Millimeter/submillimeter Array (ALMA) [C{\sc ii}] observations of the $z=$\,4.7555 submillimetre galaxy, ALESS\,73.1. Our 0\farcs5 {\sc fwhm} map resolves the [C{\sc ii}] emitting gas which is centred close to the active galactic nucleus (AGN). The gas kinematics are dominated by rotation but with high turbulence, $v_{\rm rot}/\sigma_{\rm int}\sim$\,3.1, and a Toomre $Q$ parameter $<$1 throughout the disk. By fitting three independent thin rotating disk models to our data, we derive a total dynamical mass of 3$\pm$2\,$\times$\,10$^{10}$\,$M_\odot$. This is close to the molecular gas mass derived from previous CO(2-1) observations, and implies a CO to H$_2$ conversion factor $\alpha_{\rm CO}$$<$2.3\,M$_{\odot}$(K\,km\,s$^{-1}$\,pc$^2$)$^{-1}$. The mass budget also constrains the stellar mass to $<$3.1$\times$\,10$^{10}$\,$M_\odot$, and entails a gas fraction of $f_{\rm gas}\gtrsim$\,0.4. The diameter of the dust continuum emission is $<$2\,kpc, while the star-formation rate is as high as 1000\,M$_{\odot}$yr$^{-1}$. Combined with our stellar mass constraint, this implies an extreme specific star formation rate $>$80\,Gyr$^{-1}$, especially since there are no clear indications of recent merger activity. Finally, our high signal-to-noise [C{\sc ii}] measurement revises the observed [N{\sc ii}]/[C{\sc ii}] ratio, which suggests a close to solar metallicity, unless the [C{\sc ii}] flux contains significant contributions from H{\sc ii} regions. Our observations suggest that ALESS73.1 is a nascent galaxy undergoing its first major burst of star formation, embedded within an unstable but metal-rich gas disk. } | The [C{\sc ii}]\,$\lambda$157.74\,$\mu$m line is a powerful alternative line to $^{12}$CO for studying the interstellar medium in high-redshift galaxies \citep[e.g. review by][]{carilli13b}. The [C{\sc ii}] line arises predominantly from photodissociation regions (PDRs) associated with star-forming regions; other contributions come from diffuse H{\sc i} clouds, low-density warm gas, or denser H{\sc ii} regions \citep[e.g.][]{madden97}, and possibly from shock enhancement \citep[e.g.][]{appleton13}. In the most active systems, [C{\sc ii}] is the dominant cooling line, representing $\sim $\,0.1--1\% of the total luminosity \citep[e.g.][]{stacey91}. This luminosity means that [C{\sc ii}] has significant promise as a route for determining redshifts of even the most obscured systems \citep{swinbank12b,weiss13}. Until recently, [C{\sc ii}] has remained relatively unexplored in the local Universe as its rest-frame wavelength requires balloon-borne or space-based observations. However, {\it Herschel}/PACS observations have now begun to provide spatially resolved [C{\sc ii}] maps at scales of 0.1–-1\,kpc in nearby galaxies \citep[e.g.][]{beirao12,parkin13}. These observations show significant variations in the line and continuum ratios involving [C{\sc ii}] due to a range of physical processes including changes in the ionisation mechanism, gradients in metallicity or radiation field strengths -- hinting at the potential diagnostic power of this line. Ironically, [C{\sc ii}] observations from the ground are easier at $z>$\,1 as the line is redshifted into the submillimetre atmospheric windows. Over the past decade, [C{\sc ii}] detections have been reported in an increasing number of galaxies at $z=$\,1--2 \citep{hailey10,stacey10,ferkinhoff13}, as well as more distant $z>$\,2--6 systems \citep{maiolino05,maiolino09,iono06,wagg10,ivison10,debreuck11,cox11,swinbank12b,venemans12,riechers13,wang13a,rawle13,neri14}. The first of these high-redshift [C{\sc ii}] detections were made in powerful quasars. These observations seemed to confirm the trend seen in local galaxies, where the most luminous far-infrared sources ($L_{\rm FIR} >$\,10$^{11}$\,L$_\odot$) have a ratio of [C{\sc ii}] to far-infrared (FIR) luminosity $L_{\rm [C{II}]}$\,/\,$L_{\rm FIR}$ that is lower by about an order of magnitude \citep[e.g.][]{luhman98,dios-santos13}. However, subsequent observations of a larger sample of powerful far-infrared sources, less-dominated by powerful active galactic nuclei (AGNs), revealed that the many high-redshift sources show [C{\sc ii}] lines with similar $L_{\rm [C{II}]}/L_{\rm FIR}$ ratios to those of nearby normal galaxies \citep{stacey10,carilli13b}. By comparing the $^{12}$CO, [C{\sc ii}] and far-infrared luminosities in a sample of $z$\,=\,1--2 galaxies, \citet{stacey10} showed that star-formation dominated systems have similar $L_{\rm [C{II}]}$\,/\,$L_{\rm FIR}$ to local (lower-luminosity) normal galaxies, while AGN dominated systems have lower ratios, as seen in local ultra-luminous infra-red galaxies (ULIRGs). In terms of PDR models \citep[e.g.][]{kaufman99}, both classes are interpreted as having kpc-scale emitting regions, but the AGN-dominated sources appear to have an order of magnitude more intense far-UV radiation fields. Luminous, high-redshift star-forming galaxies (submillimetre galaxies; SMGs) rather than quasar hosts are ideal targets to study the ISM of distant, luminous galaxies free from the influence of AGN. Although some SMGs contain luminous AGNs, it is clear from deep X-ray studies that in $\sim$\,85\% of SMGs, the AGN does not dominate the bolometric luminosity \citep{alexander05,georgantopoulos11}. Indeed for the less luminous SMGs the X-ray emission potentially originates from star-forming processes rather than an AGN \citep[e.g.][]{wang13b}. In this paper, we present new ALMA observations which spatially resolve the [C{\sc ii}] emission around an SMG at $z=$\,4.76 in the Extended {\it Chandra} Deep Field South (ECDFS): ALESS\,73.1 (also known as LESS\,J033229.4$-$275619 or XID\,403). This galaxy was originally identified as a compact, high-redshift AGN \citep{vanzella06,fontanot07} and also a faint X-ray source from the {\it Chandra} observations of ECDFS \citep{gilli11} and was then detected as the most likely counterpart of a luminous submillimetre source in the LABOCA survey of ECDFS by \citet{weiss09}. Its properties, including both $^{12}$CO, [C{\sc ii}] and [N{\sc ii}] gas emission, were studied in a series of papers \citep{coppin09,coppin10,biggs11,wardlow11,debreuck11,nagao12,gilli14}. Subsequent higher-resolution ALMA continuum observations by \citet{hodge13} provide an unambiguous identification of the $z$\,=\,4.76 source as a luminous SMG. Our new ALMA observations map the spatial distribution and kinematics of the [C{\sc ii}] and rest-frame far-infrared emission within this system on $\sim $\,kpc scales, providing new insights into the structure of the most vigorous starbursts seen in the SMG population. Throughout the paper, we assume $H_0=$\,73\,km\,s$^{-1}$\,Mpc$^{-1}$, $\Omega_m=$\,0.27, and $\Omega_{\Lambda}=$\,0.73, indicating a scale size of 6.4\,kpc/\arcsec at $z=$\,4.76. | Using ALMA, we have spatially resolved the [C{\sc ii}]\,158\,$\mu$m emission in the $z=$\,4.7555 SMG ALESS\,73.1. The high SNR data cube shows that the [C{\sc ii}] emitting gas extends twice as far out as the dust continuum and exhibits with clear kinematical signatures of rotation. We demonstrate that these kinematical signatures are well-described by a rotating disk with a disk size $\sim$\,2.4\,kpc and a maximum deprojected rotation velocity of $v_{\rm rot}$=\,120\,$\pm$\,10\,km\,s$^{-1}$. The disk is highly turbulent with a $v_{\rm rot}/\sigma_v\sim$\,3.1, and a Toomre $Q$ parameter $<$1 throughout the disk, implying it is unstable. Using this model we constrain the dynamical mass of this galaxy to be 3$\pm$2\,$\times $\,10$^{10}$\,M$_{\odot}$, which is close to the M(H$_2$) derived from CO(2-1) \citep{coppin10}, and requires $\alpha_{\rm CO}$$<$2.3\,(K\,km\,s$^{-1}$\,pc$^2$)$^{-1}$. Combined with the atomic mass M$_a$=4.7$\pm$0.5$\times$\,10$^{9}$\,M$_{\odot}$, our dynamical mass constrains the stellar mass to $<$3.1$\times$\,10$^{10}$\,M$_{\odot}$. Such low stellar mass is remarkable for an isolated galaxy with a SFR=1000\,M$_{\odot}$yr$^{-1}$, and suggests we are observing its first major burst of star formation. Interestingly, our revised integrated [N{\sc ii}]\,205\,$\mu$m/[C{\sc ii}]\,158\,$\mu$m ratio suggest that the gas already has close to solar metallicity. However, one should keep in mind that [C{\sc ii}] may have significant contributions from non-PDR gas, which may have an impact on the reliability of [N{\sc ii}]/[C{\sc ii}] as metallicity tracer and of [C{\sc ii}] as a tracer of the star-forming gas \citep{delooze11}. Spatially resolved observations of pure H$_2$ tracers such as the $J_{\rm upper}$$\leq$2 CO lines or the [CI] lines \citep[e.g.][]{papadopoulos04} would be needed to provide a more reliable determination of both the metallicity and the full extent of the star-forming gas reservoir in ALESS73.1. The ALMA Cycle 0 observations presented here, while still limited in spatial resolution but not in SNR, illustrate the great potential of ALMA to extend dynamical analysis tools out to the epoch when galaxies had their first major burst of star-formation. Such observations of atomic (or molecular) lines can be the only way to probe the dynamics of even the highest redshift galaxies, which can be obscured or barely resolved at optical/near-IR wavelengths. The final ALMA array will increase its spatial resolution by an order of magnitude, allowing us to regularly probe the scales of star-forming clouds, which have thus far only been seen in studies of strongly lensed galaxies \citep[e.g.][]{swinbank10}. | 14 | 4 | 1404.2295 |
1404 | 1404.5360_arXiv.txt | {The majority of binary stars do not eclipse. Current searches for transiting circumbinary planets concentrate on eclipsing binaries, and are therefore restricted to a small fraction of potential hosts. We investigate the concept of finding planets transiting non-eclipsing binaries, whose geometry would require mutually inclined planes. Using an N-body code we explore how the number and sequence of transits vary as functions of observing time and orbital parameters. The concept is then generalised thanks to a suite of simulated circumbinary systems. Binaries are constructed from radial-velocity surveys of the solar neighbourhood. They are then populated with orbiting gas giants, drawn from a range of distributions. The binary population is shown to be compatible with the {\it Kepler} eclipsing binary catalogue, indicating that the properties of binaries may be as universal as the initial mass function. These synthetic systems produce transiting circumbinary planets occurring on both eclipsing and non-eclipsing binaries. Simulated planets transiting eclipsing binaries are compared with published {\it Kepler} detections. We obtain 1) that planets transiting non-eclipsing binaries probably exist in the {\it Kepler} data, 2) that observational biases alone cannot account for the observed over-density of circumbinary planets near the stability limit, implying a physical pile-up, and 3) that the distributions of gas giants orbiting single and binary stars are likely different. Estimating the frequency of circumbinary planets is degenerate with the spread in mutual inclination. Only a minimum occurrence rate can be produced, which we find to be compatible with 9\%. Searching for inclined circumbinary planets may significantly increase the population of known objects and will test our conclusions. Their existence, or absence, will reveal the true occurrence rate and help develop circumbinary planet formation theories. | We started this paper as an enquiry into whether any circumbinary planet could be caught transiting a non-eclipsing system. After studying and describing how the dynamics and how various physical and orbital parameters affect the probability of transit, we constructed synthetic populations of circumbinary systems. By simulating the orbits over 4 years and checking for transits, we reveal that {\it Kepler} could have caught such planets. We urge a change in the protocols behind the search for circumbinary planets. Efforts should not just focus on eclipsing binaries since most binaries do not eclipse. We also find that applying a quasi-periodic transit signal criterion to find and confirm these planets severely restricts the number of objects that can be found, and biases them towards coplanarity. Our simulations allow us to affirm that the binary mass and period distributions are similar in the solar neighbourhood and within in the {\it Kepler} field. This indicates the formation of binaries might be a universal process, probably linked to the initial mass function (e.g. \citealt{Salpeter:1955fj,Kroupa:2001qy,Chabrier:2003fk,Bate:2012rt}). We also find that it is likely that circumbinary planets are rare for binaries with periods $<$ 5 days lending further support for a dynamical origin for the closest of binaries \citep{Mazeh:1979eu,Fabrycky:2007pd,Tokovinin:2006la}. Comparing the existing detections with the output of our simulations, we remark that the occurrence rate of circumbinary gas giants may be close to that of single stars. Current models of gas giant formation (e.g. \citealt{Pollack:1996uq,Boss:2000fj,Helled:2013fj}) produce planets far from their star. To a first order it would seem that whether the central object is a singleton or a close pair does not have a large impact on planet formation efficiency. Inclined orbits are frequently found in single star systems and have highlighted the important role dynamical interactions have in shaping exoplanetary systems. A similar formation rate would suggest similar mutual interactions happening in circumbinary systems. This further supports our claim that there should be a number of planets transiting non-eclipsing binaries waiting to be discovered within the {\it Kepler} timeseries. The location of the current detections reveals that after formation, circumbinary gas giants have a migration history that is different from single star systems, with planet likely piling-up at orbits near their binary's stability limit. It remains to be seen whether disc-driven migration could place planets on such particular orbits without pushing them onto an unstable orbit, or whether a different mechanism, maybe specific to binaries, would be at work. | 14 | 4 | 1404.5360 |
|
1404 | 1404.5967_arXiv.txt | We have been using the 0.76-m Katzman Automatic Imaging Telescope (KAIT) at Lick Observatory to optically monitor a sample of 157 blazars that are bright in gamma rays, being detected with high significance ($\ge 10\sigma$) in one year by the Large Area Telescope (LAT) on the {\it Fermi Gamma-ray Space Telescope}. We attempt to observe each source on a 3-day cadence with KAIT, subject to weather and seasonal visibility. The gamma-ray coverage is essentially continuous. KAIT observations extend over much of the 5-year {\it Fermi} mission for several objects, and most have $>100$ optical measurements spanning the last three years. These blazars (flat-spectrum radio quasars and BL~Lac objects) exhibit a wide range of flaring behavior. Using the discrete correlation function (DCF), here we search for temporal relationships between optical and gamma-ray light curves in the 40 brightest sources in hopes of placing constraints on blazar acceleration and emission zones. We find strong optical--gamma-ray correlation in many of these sources at time delays of $\sim 1$ to $\sim 10$ days, ranging between $-40$ and +30 days. A stacked average DCF of the 40 sources verifies this correlation trend, with a peak above 99\% significance indicating a characteristic time delay consistent with 0 days. These findings strongly support the widely accepted leptonic models of blazar emission. However, we also find examples of apparently uncorrelated flares (optical flares with no gamma-ray counterpart and gamma-ray flares with no optical counterpart) that challenge simple, one-zone models of blazar emission. Moreover, we find that flat-spectrum radio quasars tend to have gamma rays leading the optical, while intermediate and high synchrotron peak blazars with the most significant peaks have smaller lags/leads. It is clear that long-term monitoring at high cadence is necessary to reveal the underlying physical correlation. | Blazars make up a class of radio-loud active galactic nuclei (AGNs) that have a relativistic jet pointing very nearly along Earth's line of sight. These sources are generally extremely bright and highly variable from radio to gamma-ray wavebands \citep[e.g.,][]{bk79,up95}. The spectral energy distributions (SEDs) of blazars are characterized by two dominant peaks, one near radio to ultraviolet wavelengths and the other at higher, X-ray/gamma-ray energies. Optical to ultraviolet emission in blazars is widely accepted to be caused by synchrotron emission from electrons in the jet. Higher energy, hard-X-ray--GeV--TeV emission is attributed to inverse-Compton scattering (ICS) of seed photons by the synchrotron-emitting electrons (the ones responsible for the lower-energy emission), or the alternative hadronic processes based in jet proton interactions \citep[e.g.,][]{jon74,kon81,mb92}. In the favored leptonic models of blazar emission, synchrotron radiation and ICS both occur along the jet and derive from the same population of electrons, yielding a strong correlation between low- and high-energy wavebands. \citep[e.g.,][]{sik94}. Observed flares derive from events, commonly modeled as propagating shocks (or collisions of shocks), that occur in the jet at subparsec to parsec distances from the central engine and accelerate the jet electrons to high energies \citep[e.g.,][]{spa01}. While synchrotron photons are emitted near the shock front in the jet, the origin of the seed photons for ICS is not clear. These seed photons could be produced in the synchrotron-emitting jet itself (synchrotron self-Compton [SSC]) or from an external source (external Compton [EC]) such as the accretion disk, broad-line region (BLR), or dusty infrared torus (hot-dust region [HDR]) \citep[e.g.,][]{jon74,sik94}. Multi-wavelength correlation studies of blazars can thus help to place constraints on the dominant mechanisms driving variability and identify the relationship between emission zones. For example, the leptonic models predict a strong correlation between synchrotron-produced optical and ICS-produced gamma-ray emission. Lags or leads of high significance between flares in these wavebands may help place constraints on the location of the ICS seed photons relative to the synchrotron-emitting shock in the jet and discern between the SSC and EC processes. Alternatively, observations of a flare in one waveband with no correlated flare in the other might suggest multiple zones of emission or support hadronic models of blazar emission. With the advent and success of the {\it Fermi Gamma-ray Space Telescope} and its primary scientific instrument the Large Area Telescope ({\it Fermi}/LAT), multi-wavelength studies have been extended into this MeV--GeV energy range and these goals are being realized. For example, \citet{fur14} and \citet{max14} both present fascinating investigations of radio--gamma-ray correlations in blazars utilizing the discrete correlation function (DCF) -- the former using cm to sub-mm data from the F-GAMMA monitoring project and the latter using 15~GHz data from the Owens Valley 40-m telescope. In this study, we use the DCF to investigate correlations between optical and gamma-ray light curves of blazars. Optical data were collected with the robotic 0.76-m Katzman Automatic Imaging Telescope (KAIT) at Lick Observatory, which has been monitoring sources detected by LAT for much of the {\it Fermi} mission. Here we present results from computing the DCFs between optical and gamma-ray light curves in the 40 brightest sources out of the 157 monitored blazars. A future paper will report the results for the other sources. This paper is organized as follows. In \S \ref{obs} we describe data collection and production of the light curves. Section \ref{lags} and \S \ref{stacks} present the results and interpretation for DCFs of individual sources and for stacked DCFs of subsets of sources, respectively. We conclude in \S \ref{disc} with a brief discussion of our findings. | \label{disc} We have been monitoring 157 gamma-ray-bright sources detected by {\it Fermi}/LAT with KAIT at Lick Observatory, and here present a study of optical--gamma-ray correlations in 40 sources selected based on {\it Fermi}/LAT detection significance. Overall, optical and gamma-ray emission were found to be highly correlated in these sources, at time delays of roughly days. An average DCF for all 40 sources was found to have a peak significance above 99\%, confirming the strength in correlation between the two wavebands. Such strong correlations support the leptonic models of ICS gamma-ray emission, in which seed photons are upscattered by relativistic jet electrons responsible for synchrotron optical emission. Whether the seed photons are dominated by the synchrotron radiation produced by these electrons (SSC) or by external radiation (EC) is difficult to discern based on lags and correlation strengths of these sources. However, we find that the well-measured FSRQs tend to have positive lags (gamma rays leading the optical) while the best-measured BL~Lacs show no clear trend toward lag or lead. This supports models with EC being dominant in FSRQs and SSC dominant in BL~Lacs. Stacked DCFs of LSP, ISP, and HSP BL~Lacs are consistent with increasing SSC dominance as synchrotron peak energy increases; ISP and HSP BL~Lacs are found to have average DCF peak lags closer to 0 days than LSP BL~Lacs. However, a larger sample is required to make definitive claims. We plan on performing a similar study with {\it Fermi}/LAT light curves for the full set of 157 blazars being monitored in order to verify these findings based on the 40 brightest sources. Recently, optical--gamma-ray correlations in blazars have been investigated through modulation indices (rather than DCFs and lags between wavebands) by \citet{hov14}. With a very large sample size, this study found that HSP BL~Lacs were most strongly and tightly correlated, supporting the notion that SSC becomes more prevalent in ISP and HSP sources while EC is more dominant in LSP sources. Based on the 40 sources in our study, we also find a stronger average correlation in BL~Lacs (but narrower average peak for FSRQs, likely owing to the high variability of FSRQs in our sample). Observationally, this trend is somewhat surprising, as the strongest correlations in individual sources have been found for FSRQs \citep[e.g.,][]{hay12}. That BL~Lacs are on average more strongly correlated than FSRQs will need further testing, although our findings and those of \citet{hov14} support this claim. We have shown that strongly flaring, well-measured FSRQs tend to show gamma-ray leads, supporting the conclusions of other variability studies. However, the situation for the BL~Lacs is evidently more complex. Multi-year, multi-wavelength monitoring at high cadence is clearly needed to probe the mechanisms driving variability in these sources and possible connections to the central engines. With further KAIT coverage and the continued success of {\it Fermi}/LAT, we can start to break down this complexity and understand these objects at their most fundamental level. | 14 | 4 | 1404.5967 |
1404 | 1404.0403_arXiv.txt | We search for variations in the disk of Centaurus~A of the emission from atomic fine structure lines using \emph{Herschel} PACS and SPIRE spectroscopy. In particular we observe the [C~\textsc{ii}] (158~$\mu$m), [N~\textsc{ii}](122 and 205~$\mu$m), [O~\textsc{i}](63 and 145~$\mu$m) and [O~\textsc{iii}](88~$\mu$m) lines, which all play an important role in cooling the gas in photo-ionized and photodissociation regions. We determine that the ([C~\textsc{ii}]+[O~\textsc{i}]$_{63}$)/$F_{\mathrm{TIR}}$ line ratio, a proxy for the heating efficiency of the gas, shows no significant radial trend across the observed region, in contrast to observations of other nearby galaxies. We determine that 10--20\% of the observed [C\,\textsc{ii}] emission originates in ionized gas. Comparison between our observations and a PDR model shows that the strength of the far-ultraviolet radiation field, $G_{0}$, varies between 10$^{1.75}$ and 10$^{2.75}$ and the hydrogen nucleus density varies between 10$^{2.75}$ and 10$^{3.75}$~cm$^{-3}$, with no significant radial trend in either property. In the context of the emission line properties of the grand-design spiral galaxy M51 and the elliptical galaxy NGC~4125, the gas in Cen~A appears more characteristic of that in typical disk galaxies rather than elliptical galaxies. | Nearby galaxies are excellent laboratories in which to study the properties of the cold interstellar medium (ISM), as the current capabilities of infrared and submillimeter observatories allow us to study them on sub-kiloparsec (kpc) scales. In particular, we can investigate the origin of key far-infrared atomic fine-structure lines on these physical scales using the \emph{Herschel Space Observatory} \citep{2010A&A...518L...1P}. Centaurus~A (Cen~A; NGC~5128), located only $3.8 \pm 0.1$~Mpc away \citep{2010PASA...27..457H}, is resolved at scales of a few hundred parsecs, thus giving us the opportunity to search for variations within the interstellar gas throughout the galaxy. Cen~A (13$^{\mathrm{h}}$25$^{\mathrm{m}}$27.6$^{\mathrm{s}}$, $-43^{\circ}01\arcmin09\arcsec$) has an unusual morphology, as it is a giant elliptical that appears to have swallowed a smaller disk galaxy and estimates put this merger around 380~Myr ago \citep{1980ApJ...241..969T}. The disk provides a prominent dust lane through the center, and shows a strong warp, giving it an `S' like shape at infrared wavelengths \citep{2002ApJ...565..131L, 2006ApJ...645.1092Q, 2008A&A...490...77W, 2012MNRAS.422.2291P}. Cen~A is the closest galaxy with an active galactic nucleus (AGN) and associated radio jets extending approximately 4$^{\circ}$ in either direction \citep[e.g.][]{1997A&AS..121...11C, 1998A&ARv...8..237I}. It is also rich in gas, both atomic (H~\textsc{i}) and molecular (H$_{2}$) hydrogen \citep{2008A&A...485L...5M,2010A&A...515A..67S}, as well as carbon monoxide (CO), as observed in various rotational transitions \citep{1987ApJ...322L..73P,1990ApJ...363..451E,1992ApJ...391..121Q,1993A&A...270L..13R, 2012MNRAS.422.2291P}. For a detailed summary of the physical properties of the galaxy see \citet{1998A&ARv...8..237I} and \citet{2010PASA...27..463M}. Recently, \citet{2012MNRAS.422.2291P} presented new photometric observations at 70, 160, 250, 350 and 500~$\mu$m using the Photodetector Array Camera and Spectrometer \citep[PACS;][]{2010A&A...518L...2P} and the Spectral and Photometric Imaging Receiver \citep[SPIRE;][]{2010A&A...518L...3G} on \emph{Herschel}. Through dust spectral energy distribution (SED) modelling they found a radially decreasing trend in dust temperature from about 30 to 20~K. Then they combined the resulting dust map with a gas map, created with CO($J=3-2$) observations from the James Clerk Maxwell Telescope (JCMT) and an H~\textsc{i} map \citep{2010A&A...515A..67S}, to produce a gas-to-dust mass ratio map. This ratio also shows a radial trend from 275 near the center of the galaxy, decreasing to Galactic values of roughly 100 in the outer disk. The high ratio in the center is attributed to local effects on the ISM from the AGN. Here, we extend the investigation of the disk of Cen~A by combining the \emph{Herschel} PACS photometry with new PACS spectroscopic observations of important atomic fine structure lines to characterize the neutral and ionized gas. Fine structure lines such as [C~\textsc{ii}](158~$\mu$m), [N~\textsc{ii}](122 and 205~$\mu$m), [O~\textsc{i}](63 and 145~$\mu$m) and [O\,\textsc{iii}](88~$\mu$m) (hereafter [C~\textsc{ii}], [N~\textsc{ii}]$_{122}$, [N~\textsc{ii}]$_{205}$, [O~\textsc{i}]$_{63}$, [O~\textsc{i}]$_{145}$ and [O\,\textsc{iii}], respectively) play a crucial role in the thermal balance of the gas in the ISM. These lines provide a means of gas cooling by de-excitation via photon emission, rather than collisional de-excitation, which does not result in photon emission and thus inhibits gas cooling. The [C~\textsc{ii}] line is a tracer of both neutral and ionized gas as C$^{+}$ is produced by far-ultraviolet (FUV) photons with energy greater than 11.26~eV, and it is one of the dominant coolants among the aforementioned lines with a luminosity of roughly 0.1--1~\% that of the far-infrared (FIR) luminosity in typical star-forming galaxies \citep[e.g.][]{1985ApJ...289..803S, 1993ApJ...404..219S, 2001ApJ...561..766M, 2011ApJ...728L...7G, parkin_2013}. The two [O~\textsc{i}] lines trace neutral gas, while the [N~\textsc{ii}] and [O~\textsc{iii}] lines trace ionized gas. A commonly used diagnostic of the heating efficiency of the gas is the ([C~\textsc{ii}]+[O~\textsc{i}]$_{63}$)/$F_{\mathrm{TIR}}$ (or sometimes [C~\textsc{ii}]/$F_{\mathrm{FIR}}$) line ratio, which represents the relative contributions of the FUV flux to the heating of gas versus dust, assuming [C~\textsc{ii}] and [O~\textsc{i}]$_{63}$ are the main coolants \citep{1985ApJ...291..722T}. Observations show that as infrared color increases (thus increasing dust temperature), the heating efficiency decreases because the dust grains and polycyclic aromatic hydrocarbons (PAHs) that provide free electrons for gas heating via the photoelectric effect have become too positively charged to free electrons efficiently \citep{2001ApJ...561..766M, 2008ApJS..178..280B, 2011ApJ...728L...7G, 2012ApJ...747...81C, 2012A&A...544A..55B, 2012A&A...548A..91L, 2013A&A...549A.118C, parkin_2013}. To determine the physical properties of the gas we need to compare ratios of our observed fine structure lines to those predicted by a PDR model. There are a number of models which explore the characteristics of PDRs such as \citet{1986ApJS...62..109V,1988ApJ...334..771V}, \citet{1989ApJ...338..197S, 1995ApJS...99..565S}, \citet{1997ApJ...482..298L}, \citet{2000A&A...358..682S}, \citet{2006ApJS..164..506L} and \citet{2006A&A...451..917R}, but one of the most commonly used models was first developed by \citet{1985ApJ...291..722T}, consisting of a plane-parallel, semi-infinite slab PDR. The gas is characterized by two free parameters, the hydrogen nucleus density, $n$, and the strength of the FUV radiation field, $G_0$, normalized to the Habing Field, $1.6 \times 10^{-3}$~erg~cm$^{-2}$~s$^{-1}$ \citep{1968BAN....19..421H}. This model has now been updated by \citet{1990ApJ...358..116W}, \cite{1991ApJ...377..192H}, and \citet{1999ApJ...527..795K,2006ApJ...644..283K}. Investigations of PDRs and cooling lines in Cen~A have previously been carried out by \citet{2000A&A...355..885U} and \citet{2001A&A...375..566N} using the Long Wavelength (LWS) spectrometer on the \emph{Infrared Space Observatory} (ISO). \citet{2000A&A...355..885U} observed Cen~A at four pointings along the dust lane and found $G_{0} \sim 10^{2}$ and $n \sim 10^{3}$~cm$^{-3}$. Using the same observations, \citet{2001A&A...375..566N} find $G_{0} = 10^{2.7}$ and $n \sim 10^{3.1}$~cm$^{-3}$. In samples of normal star-forming galaxies, as well as samples including starburst, AGN, and star-forming galaxies such as those of \citet{2001ApJ...561..766M} and \citet{2001A&A...375..566N}, respectively, global values for $G_{0}$ range from 10$^{2}$ to 10$^{4.5}$ and $n$ ranges between 10$^{2}$ and 10$^{4.5}$~cm$^{-3}$. In this paper, we look at the PDR characteristics of Cen~A on smaller scales (roughly 260~pc at the 14$\arcsec$ resolution of the JCMT) in search of radial variations. The paper is organized as follows. We describe our data processing for the spectroscopic observations in Section~\ref{Herschel_obs}, and discuss the general morphology of the various lines in Section~\ref{results}. In Section~\ref{pdrs} we compare our observations to theoretical models and discuss their implications. We compare the gas characteristics of Cen~A with M51 in Section~\ref{compare_m51} and summarize this work in Section~\ref{conclusions}. | We have presented new spectroscopic observations of the unusual elliptical galaxy Centaurus~A from the \emph{Herschel} PACS instrument. These observations focus on important atomic cooling lines originating from both neutral ([C~\textsc{ii}](158~$\mu$m), [O~\textsc{i}](63 and 145~$\mu$m)) and ionized gas ([N~\textsc{ii}](122 and 205~$\mu$m) and [O~\textsc{iii}](88~$\mu$m)) covering a radial strip on the eastern side of the nucleus of the galaxy (or a central aperture for the [N~\textsc{ii}](205~$\mu$m) line). These lines show very similar morphologies, except the two [O~\textsc{i}] lines that peak toward the center of the galaxy. We find that the heating efficiency in the disk, represented by the ([C~\textsc{ii}]+[O~\textsc{i}]$_{63}$)/$F_{\mathrm{TIR}}$ line ratio, ranges from $4 \times 10^{-3}$ to $8 \times 10^{-3}$, consistent with values determined in galaxies on global scales, as well as on resolved scales in other individual galaxies. However, we do not observe a significant decrease in the heating efficiency with increasing dust temperature, as represented by the 70~$\mu$m/160~$\mu$m color, nor do we observe a suppression in the heating efficiency in the vicinity of the nucleus. We also find that the heating efficiency is slightly higher in Cen~A than the grand-design spiral galaxy, M51, suggesting the dust grains and PAHs in Cen~A are more neutral in PDRs than in M51. Furthermore, the line ratio [O~\textsc{iii}]/[N~\textsc{ii}]$_{122}$ reveals that the youngest stars are of a slightly earlier stellar type than those in M51, thus producing a harder radiation field in the disk of Cen~A. However, there is a possibility that the AGN is partially contributing to the observed emission, resulting in an earlier stellar type classification than is actually present. A comparison between a PDR model and our observations reveals that the strength of the FUV radiation field incident on the PDR surfaces ranges from $\sim 10^{1.75}$--10$^{2.75}$ and the hydrogen gas density ranges from $\sim 10^{2.75}$--$10^{3.75}$~cm$^{-3}$, in agreement with typical values in other star forming galaxies, including M82, which has a central starburst. However, the conditions (PDRs) producing the fine structure lines in Cen~A are distinctly different from the elliptical galaxy NGC~4125, where the gas may be completely ionized. Contrary to M51, we do not see a significant radial trend in either $n$ or $G_{0}$. Furthermore, while the results from the PDR modelling for Cen~A agree with those for the arm and interarm regions in M51, the central region of M51 shows higher values for $n$ and $G_{0}$. Observations of the nucleus of Cen~A in the important fine structure lines may reveal a similar trend; however, we point out that in the central region of M51 up to 70\% of the [C~\textsc{ii}] emission originates in diffuse ionized gas while in Cen~A this fraction is only 10--20\%, thus this may also explain the differences between the two galaxies. We conclude that the disk of Cen~A exhibits properties in its PDRs that are similar to other normal disk galaxies, despite its unusual morphological characteristics. | 14 | 4 | 1404.0403 |
1404 | 1404.5821_arXiv.txt | It is possible that black holes hide a core of Planckian density, sustained by quantum-gravitational pressure. As a black hole evaporates, the core remembers the initial mass and the final explosion occurs at macroscopic scale. We investigate possible phenomenological consequences of this idea. Under several rough assumptions, we estimate that up to several short gamma-ray bursts per day, around $10$ MeV, with isotropic distribution, can be expected coming from a region of a few hundred light years around us. | Recently, a new possible consequence of quantum gravity has been suggested \cite{Rovelli2014}. The idea is grounded in a robust result of loop cosmology \cite{Ashtekar2006}: when matter reaches Planck density, quantum gravity generates pressure sufficient to counterbalance weight. For a black hole, this implies that matter's collapse can be stopped before the central singularity is formed: the event horizon is replaced by a ``trapping'' horizon \cite{Ashtekar:2005cj} which resembles the standard horizon locally, but from which matter can eventually bounce out. Because of the huge time dilation inside the gravitational potential well of the star, the bounce is seen in extreme slow motion from the outside, appearing as a nearly stationary black hole. The core, called ``Planck star", retains memory of the initial collapsed mass $m_i$ (because there is no reason for the metric of the core to be fully determined by the area of the external evaporating horizon) and the final exploding objects depends on $m_i$ and is much larger than Planckian \cite{Rovelli2014}. The process is illustrated by the conformal diagram of Fig. \ref{ps3}. In particular, primordial black holes exploding today may produce a distinctive signal. The observability of a quantum gravitational phenomenon is made possible by the amplification due to the large ratio of the black hole lifetime (Hubble time $t_H$) over the Planck time \cite{Amelino:13}. If this scenario is realised in nature, can the final explosion of a primordial Planck star be observed? This is the question we investigate here. \begin{figure} \centerline{\includegraphics[width=3.5cm]{PlanckStar.pdf}} \caption{Penrose diagram of a collapsing star. The dotted line is the external boundary of the star. The shaded area is the region where quantum gravity plays an important role. The dark line represents the two trapping horizons: the external evaporating one, and the internal expanding one. The lowest light-line is where the horizon of the black hole would be without evaporation. $P$ is where the explosion happens. The thin arrows indicate the Hawking radiation. The thick arrow is the signal studied in this paper. } \label{ps3} \end{figure} | We have shown that the detection of individual explosions of Planck stars is not impossible and we have established the main spectral characteristic of the signal. Quantum gravity might show up in the tens of MeV range. We have estimated the order of magnitudes for the expected frequency of events: in some cases, it might not be small. Several approximations about the dynamics of the evaporation can be improved. The details of the explosion remain to be investigated. The shape of the diffuse integrated signal, and more specifically its potential specific signature allowing to distinguish it from standard primordial black holes, requires a full numerical analysis. It could also be interesting to investigate the emission of charged articles, in particular positrons and antiprotons (some interesting threshold effets could be expected). As well known, the much smaller horizon can be compensated by the large galactic confinement effect. | 14 | 4 | 1404.5821 |
1404 | 1404.7147_arXiv.txt | In this paper, we study the formation and dynamical evolution of black hole-black hole (BH-BH) binaries in young star clusters (YSCs), by means of N-body simulations. The simulations include metallicity-dependent recipes for stellar evolution and stellar winds, and have been run for three different metallicities ($Z = 0.01, 0.1\text{ and 1 Z}_\odot$). Following recent theoretical models of wind mass-loss and core-collapse supernovae, we assume that the mass of the stellar remnants depends on the metallicity of the progenitor stars. We find that BH-BH binaries form efficiently because of dynamical exchanges: in our simulations, we find about 10 times more BH-BH binaries than double neutron star binaries. The simulated BH-BH binaries form earlier in metal-poor YSCs, which host more massive black holes (BHs) than in metal-rich YSCs. The simulated BH-BH binaries have very large chirp masses (up to 80 M$_\odot$), because the BH mass is assumed to depend on metallicity, and because BHs can grow in mass due to the merger with stars. The simulated BH-BH binaries span a wide range of orbital periods ($10^{-3}-10^7$ yr), and only a small fraction of them (0.3 per cent) is expected to merge within a Hubble time. We discuss the estimated merger rate from our simulations and the implications for Advanced VIRGO and LIGO. | \label{sec:intro} Most stars are expected to form in young star clusters (YSCs, \protect\citealt{carpenter2000}; \protect\citealt{ladalada2003}; \protect\citealt{porras2003}). Like globular clusters (GCs), the densest YSCs are collisional systems: their two-body relaxation timescale is shorter than their lifetime, and they undergo intense dynamical evolution. On the other hand, YSCs are considerably different from GCs: the former have generally lower mass ($<10^{5}$ M$_\odot{}$) and smaller size (half-mass radius $r_{\rm hm}\lesssim{}1$ pc) than the latter (see e.g. \citealt{pz2010}, for a recent review). This explains why the central relaxation time of YSCs is $\sim{}10-50$ Myr, orders of magnitude shorter than that of GCs (e.g. \citealt{pz2004}). YSCs populate the disc of late-type galaxies, while GCs are sphe\-ri\-cal\-ly distributed in the host-galaxy halo. Finally, GCs are old ($\gtrsim{}12$ Gyr) and long-lived systems, whereas YSCs are young and short lived: most of them dissolve in the disc of the host galaxy in $\le{}10^8$ yr (e.g. \citealt{k2011}). Thus, the stellar content of dissolved YSCs is expected to build up a considerable fraction of the field population of the host galaxy. This must be taken into account when mo\-del\-ling the evolution of binary stellar systems in the galactic field: a large fraction of these binaries likely formed in YSCs, and then evolved through intense dynamical interactions, before being ejected into the field after the disruption of the parent YSC. This scenario is important for the study of stellar black hole (BH) binaries. In \citet[][hereafter Paper I]{mapelli2012}, we studied the formation and the dynamical evolution of accreting BH binaries in YSCs. We found that dynamical interactions in YSCs have a significant impact on the expected population of X-ray sources powered by BHs. In the current paper, we study the formation and the dynamical evolution of black hole-black hole (BH-BH) binaries in YSCs. For the sake of completeness, we will compare the evolution of BH-BH binaries with that of neutron star-neutron star (NS-NS) binaries and with that of binaries composed of a BH and a neutron star (NS) in YSCs. BH-BH, NS-NS and NS-BH binaries are among the most promising sources of gravitational waves (GWs) detectable by ground-based detectors (e.g. \citealt{peters1964}; \citealt{abra1994}). Understanding the demographics of such double compact object binaries (DCOBs) is particularly important in light of the forthcoming second-generation ground-based GW detectors, Advanced LIGO and VIRGO \citep{harry2010, acernese2009, accadia2012}. The dynamics of YSCs can influence the formation and evolution of BH-BH binaries in three different ways: (i) dynamical friction causes the BHs (which are more massive than most stars) to sink to the denser YSC core, where they have a higher probability to interact with other BHs (e.g. \citealp{sigurdsson1996}); (ii) three-body encounters (i.e. close encounters between a binary and a single star) change the binary orbital properties: if the binary is hard (i.e. if its binding energy is higher than the average kinetic energy of a star in the cluster\footnote{A binary can be classified as hard if its binding energy is higher than the average kinetic energy of stars in the cluster, that is \begin{equation} \frac{G\,{}m_1\,{}m_2}{2\,{}a}\gtrsim \frac{1}{2}\langle m\rangle\sigma^2, \end{equation} where $G$ is the gravitational constant, $m_1$ and $m_2$ are the mass of the primary member and the mass of the secondary member of the binary, respectively, while $\langle m\rangle$ and $\sigma$ are the average mass and velocity dispersion of a star in the star cluster.}), three-body encounters tend to shrink the binary semi-major axis \citep{heggie1975}; (iii) dynamical exchanges (i.e. three-body interactions in which one of the members of the binary is replaced by the single star) enhance the formation of BH-BH binaries. In fact, the probability for a single star with mass $m_3$ to replace a binary member is higher if $m_3\ge{}m_1$ or $m_3\ge{}m_2$ (where $m_1$ and $m_2$ are the masses of the former binary members, see \citealt{hills1989} and \citealt{hills1992}). As BHs are more massive than most stars, they efficiently acquire companions through dynamical exchanges. Previous studies investigated the formation and evolution of DCOBs either in GCs, via Monte Carlo codes (e.g. \citealt{oleary2006}; \citealt{sadowski2008}; \citealt{downing2010}; \citealt{downing2011}; \citealt{clausen2012}), or in the field, using population synthesis simulations of isolated binaries (e.g. \citealt{b2002}; \citealt{voss2003}; \citealt{pfahl2005}; \citealt{dewi2006}; \citealt{b2007}; \citealt{b2010a}; \citealt{dominik2012}). Our study provides a new perspective on this subject: we study the formation of BH-BH binaries in YSCs, by using direct N-body simulations coupled with up-to-date stellar and binary evolution recipes. The paper is organized as follows. In Section \ref{sec:MethodsAndSimulations}, we briefly describe our simulations. In Section \ref{sec:results}, we present our results. Section \ref{sec:Discussion} is devoted to discuss the results and to compare them with previous work. Our conclusions are presented in Section \ref{sec:Conclusions}. \section[]{Methods and simulations} \label{sec:MethodsAndSimulations} \begin{table} \begin{center} \caption{Summary of initial YSC properties} \begin{tabular}{ll} \hline Parameter & Value \\ \hline $W_0$ & 5\\ $N_\ast$ & 5500\\ $r_{\rm c}$ (pc) & 0.4 \\ $c \equiv \log_{10}(r_{\rm t}/r_{\rm c})$ & 1.03\\ IMF & Kroupa (2001) \\ $m_{\rm min}$ (M$_\odot$) & 0.1 \\ $m_{\rm max}$ (M$_\odot$) & 150 \\ $Z$ (Z$_{\rm \odot}$) & 0.01, 0.1, 1\\ $t_{\rm max}$ (Myr) & $100$\\ $f_{\rm PB}$ & 0.1 \vspace{0.1cm}\\ \hline \end{tabular} \label{tab:SCSummary} \begin{flushleft} \footnotesize{$W_0$: central dimensionless potential in the \citet{king1966} model; $N_{\ast}$: number of stars per YSC; $r_{\rm c}$: initial core radius; $c\equiv{}\log{}_{10}{(r_{\rm t}/r_{\rm c})}$: concentration ($r_{\rm t}$ is the initial tidal radius); IMF: initial mass function; $m_{\rm min}$ and $m_{\rm max}$: minimum and maximum simulated stellar mass, respectively; $Z$: metallicity of the YSC (in our simulations, we assume Z$_\odot{}= 0.019$); $t_{\rm max}$: duration of each simulation (in Myr); $f_{\rm PB}$: fraction of PBs, defined as the number of PBs in each YSC divided by the number of `centres of mass' (CMs) in the YSC. In each simulated YSC, there are initially 5000 CMs, among which 500 are designated as `binaries' and 4500 are `single stars' (see \citealt{downing2010} for a description of this formalism). Thus, 1000 stars per YSC are initially in binaries.} \end{flushleft} \end{center} \end{table} The simulations analysed in this paper adopt the same technique as described in paper~I. In particular, we used a modified version of the {\sc starlab} public software environment (see \citealt{pz2001}). Our upgraded version of {\sc starlab} includes (i) analytic formulae for stellar evolution as a function of mass and metallicity \citep{hurley2000}, (ii) metallicity-dependent stellar winds for main sequence \citep{vink2001} and evolved stars \citep{vink2006}, and (iii) the possibility that massive BHs form by direct collapse, i.e. with a weak or no supernova (SN) explosion (e.g. \citealt{fryer1999}; \citealt{fek2001}; \citealt{mapelli2009}; \citealt{b2010b}; \citealt{fryer2012}). According to these recipes, if the final mass of the progenitor star (i.e. the mass before the collapse), is $>40$ M$_\odot{}$, we assume that the SN fails and that the star collapses quiet\-ly to a BH. As the final mass of a massive star is higher at low metallicity, because of the weaker stellar winds, BH masses are allowed to be higher at low metallicity. In particular, the BH mass depends on the metallicity and on the zero age main sequence (ZAMS) mass of the progenitor as described in Fig. 1 of paper~I. In this scenario, BHs with mass up to $\sim{}80$ M$_\odot{}$ ($\sim{}40$ M$_\odot{}$) can form if the metallicity of the progenitor is $Z \sim{} 0.01\text{ Z}_\odot$ ($Z\sim{} 0.1\text{ Z}_\odot$). The ma\-xi\-mum BH mass at $Z \sim{}\text{ Z}_\odot$ is $23$ M$_\odot{}$. This is higher than assumed in previous studies (e.g. \citealt{b2010b}), but is still consistent with the observations, given the large uncertainties (e.g. \citealt{ozel2010}). NSs and BHs that form from a SN explosion receive a natal kick in a random direction. The natal kick of NSs is chosen randomly from the distribution $P(u)=(4/\pi{})\,{}(1+u^2)^{-2}$, where $u=v/\tilde{v}$, $v$ is the modulus of the velocity vector of the NS and $\tilde{v}=600$ km s$^{-1}$ \citep{hartman1997, pz2001}. The natal kick of BHs is drawn from the same distribution, but is normalized by a factor $f_{\rm kick}=(m_{\rm NS}/m_{\rm BH})^{1/2}$ (where $m_{\rm BH}$ is the BH mass and $m_{\rm NS}=1.3\,{}{\rm M}_\odot{}$ is the typical NS mass). Instead, BHs that form from quiet collapse are assumed to receive no natal kick (see \citealt{fryer2012}). Furthermore, {\sc starlab} includes recipes for binary evolution, such as mass transfer (via wind accretion and via Roche lobe overflow), tidal circularization, magnetic braking, and also orbital decay and circularization by GW emission (see \citealt{pz1996}; \citealt{pz2001}). We doubled the simulation sample with respect to paper~I: we have 600 N-body realizations of YSCs (1/3 of them with solar metallicity, 1/3 with metallicity $Z=0.1\text{ Z}_\odot$, and the remaining 1/3 with $Z=0.01\text{ Z}_\odot$). Half of the simulations were already presented in paper~I, whereas the remaining are new simulations. The simulated YSCs are initially modelled with 5000 centres of mass (single stars or binaries), following a King profile with central dimensionless potential $W_0=5$. The core density at the beginning of the simulation is $\rho_\mathrm{C} \sim 2\times 10^3\msun pc^{-3}$. We chose a primordial binary fraction of $f_{\mathrm{PB}} = 0.1$ so the total number of stars is $N_\ast{} = 5500$. The total mass of a single YSC is $M_{\mathrm{TOT}}\sim 3-4\times 10^3\msun$. The single stars and the primary stars ($m_1$) of the binaries follow a Kroupa initial mass function \citep[IMF, ][]{kroupa2001} with minimum and maximum mass equal to 0.1 and 150$\msun$, respectively. The masses of the secondaries ($m_2$) are generated according to a uniform distribution between $0.1m_1$ and $m_1$. The initial semi-major axis $a$ of the binaries are drawn from a log-uniform distribution $f(a)\propto 1/a$ between $R_\odot$ and $10^5R_\odot$, for consistency with the observation of binaries in the Solar neighbourhood \citep{kraicheva1978, duquennoy1991}. Values of $a$ leading to a periastron separation smaller than the sum of the radii of the two stars in the binary were discarded. We randomly select the initial eccentricity from a thermal distribution $f(e) = 2\,{}e$ in the range [0, 1] \citep{heggie1975}. The central relaxation timescale is \citep{pz2004} $t_{\rm rlx} \sim 10 \myr \,{} (r_{\rm hm}/0.8\pc)^{3/2}(M_{\rm TOT}/3500\msun)^{1/2}$ where $r_{\rm hm}$ is the half-mass radius of the YSC ($\sim 0.8-0.9\pc$ in our simulations). The core collapse timescale \citep{pz2002} is $t_{\rm cc}\sim 2\myr(t_{\rm rlx}/10\myr)$. A summary of the properties of the simulated YSCs is shown in Table~\ref{tab:SCSummary}. These were chosen to match the properties of the most common YSCs in our Galaxy. Each YSC was simulated for 100 Myr: at later times the YSCs are expected to be disrupted by the galactic tidal field (e.g. \citealt{sv2010}; \citealt{goddard2010}; \citealt{gieles2011}). We do not use recipes for the galactic tidal field but they will be included in future work. The structural evolution of our simulated YSCs is described in a companion paper (\citealt{mapelli2013}). From Fig.~4 of \cite{mapelli2013}, it is apparent that the half-mass radius of the YSCs at 100 Myr is $\sim{}3$ times the initial value. The average fraction of stars that are still bound to the YSC at 100 Myr is $0.85-0.9$. Thus, the simulated YSCs are expanding but most of them have not evaporated by the end of the simulation. This means that our results likely overestimate the number of dynamical exchanges and three-body encounters in the late stages of YSC life. We do not expect that this severely affects our predictions for the merger rate of BH-BH binaries, since the most intense dynamical activity of the YSCs occurs during (and immediately after) the core collapse (i.e. at $t\gtrsim{}3$ Myr), because of the dramatic increase in the core density (by a factor of $\ge{}10$). In fact, most of the BH-BH binaries form in the first $\sim{}3-40$ Myr (see the discussion in Section~\ref{sec:DBHpopulation}), and the BH-BH systems that are expected to merge in less than a Hubble time (and that are not disrupted before the end of the simulation, see Section~\ref{sec:CoalescenceTimescale}) form at $4-7$ Myr. In a forthcoming paper, we will add different models for the galactic tidal field, and we will be able to quantify their impact on the BH-BH binary population. | \label{sec:Conclusions} We studied the impact of metallicity and dynamics on the formation and evolution of DCOBs. To this purpose, we have run 600 N-body realizations of YSCs chosen to match the properties of the most common YSCs in our Galaxy. We simulated YSCs, because most stars form in YSCs. Thus, we cannot study the formation and evolution of DCOBs without accounting for the fact that most of them originate in YSCs. For our simulations, we used an upgraded version of the public code {\sc starlab}, which includes recipes for metallicity-dependent stellar evolution and winds, and which allows stars with final mass larger than $40\, M_\odot$ to directly collapse to a BH. Direct collapse leads to the formation of massive stellar BHs ($\geq 25\,M_\odot$) at low metallicity. We found that, while the number of NSs is about four times larger than the number of BHs, the number of BH-BH binaries is about ten times higher than the number of NS-NS binaries. The reason is that dynamical interactions enhance the formation of BH-BH binaries with respect to NS-NS binaries. Heavier BHs sink to the centre of the YSC, where they are more likely to interact with other BHs: BHs can acquire companions through three-body exchanges. Since the probability of a dynamical exchange is higher when the single star is more massive than one of the members of the binary and since BHs are among the most massive objects in a YSC, exchanges favour the formation of BH-BH binaries. BH-BH binaries form earlier at low metallicity, because BHs are more massive in metal-poor YSCs. Furthermore, BH-BH binaries formed at low metallicity are more stable: they live longer than BH-BH binaries in metal-rich YSCs. The simulated BH-BH binaries have very large chirp masses ($5-70$ M$_\odot$), because of the direct collapse at low metallicity and because mergers between stars and BHs are allowed. % BH-BH binaries span a wide range in periods ($10^{-3}-10^7$ yr). In contrast, most NS-NS binaries have periods $<1$ yr. As a consequence, the coalescence timescale is generally longer for BH-BH binaries than for NS-NS binaries. The minimum coalescence timescale for BH-BH binaries and NS-NS binaries is $t_{\rm GW}\sim 0.1$ Gyr and $t_{\rm GW}\sim 10^{-5}$ Gyr, respectively. Only 7 BH-BH binaries are expected to merge within a Hubble time. Moreover, no BH-BH binaries merge during our simulations, while 11 NS-NS binaries do. From our simulations, we can estimate the merger rate of DCOBs in the local Universe. We find a merger rate $R_{\rm BH-BH}\le{}3.5\times{}10^{-3} \,{}{\rm Mpc}^{-3}\,{}{\rm Myr}^{-1}$, $R_{\rm NS-BH}<10^{-4}\,{}{\rm Mpc}^{-3}\,{}{\rm Myr}^{-1}$ and $R_{\rm NS-NS}\sim{}0.03-0.15 \,{}{\rm Mpc}^{-3}\,{}{\rm Myr}^{-1}$ for BH-BH, NS-BH and NS-NS binaries, respectively. The merger rate of NS-NS binaries is fairly consistent with the estimates based on both the observed Galactic NS-NS binaries (\citealt{kalogera2004}) and the observed rate of short gamma-ray bursts (\citealt{coward2012, siellez2014}). The merger rate of BH-BH binaries is consistent with recent Monte Carlo simulations of dense star clusters (e.g. \citealt{oleary2006}; \citealt{downing2010}). The merger rate of NS-BH binaries is quite low with respect to previous estimates based on population synthesis codes (e.g. \citealt{oshaughnessy2008}). This can be explained with the fact that the formation of NS-BH binaries is less favoured by dynamical exchanges than the formation of BH-BH binaries. Our merger rates are still affected by a number of assumptions that will be improved in forthcoming studies. First, in our study we assume that the lifetime of the simulated YSCs is 100 Myr, but we do not take into account the presence of a realistic galactic tidal field. Second, we explore only a limited portion of the parameter space. In forthcoming studies, we will consider YSCs with different concentration, half-mass radius, total mass and binary fraction. Our simulated YSCs are expected to dissolve in the galactic disc in $\sim 100$ Myr, that is much shorter than the coalescence timescale of all BH-BH binaries and of some NS-NS binaries. The DCOBs that form within the simulated YSCs are ejected in the field (due to three-body interactions or because of the disruption of the parent YSC). Once in the field, the DCOBs will not undergo more dynamical interactions and will continue their evolution in isolation, until they merge. Thus, the mergers of (most) our simulated DCOBs are expected to take place in the field. Accounting for the fact that most DCOBs form in YSCs and evolve through dynamical interactions is a crucial step towards obtaining a realistic description of the demographics % of DCOBs, in light of the forthcoming Advanced LIGO and VIRGO scientific runs. | 14 | 4 | 1404.7147 |
1404 | 1404.2281_arXiv.txt | Upcoming large imaging surveys will allow detailed studies of the structure and morphology of galaxies aimed at addressing how galaxies form and evolve. Computational approaches are needed to characterize their morphologies over large samples. We introduce an automatic method to quantify the outer structure of galaxies. The key to our approach is the division of a galaxy image into two sections delineated by the isophote which encloses half the total brightness of the galaxy. We call the central section the inner half-flux region (IHR) and the outer section the outer half-flux region (OHR). From this division, we derive two parameters: $A_{\rm o}$, which measures the asymmetry of the OHR, and $D_{\rm o}$, which measures the deviation of the intensity weighted centroid of the OHR from that of the IHR relative to the effective radius. We derive the two parameters from $HST$/ACS $z_{850}$-band images for a sample of 764 galaxies with $z_{850}<22$\,mag and $0.35<z<0.9$ selected from GEMS and GOODS-South surveys. We show that the sample galaxies having strong asymmetric structures, in particular tidal tails, are well-separated from those with regular morphologies in the $A_{\rm o}$-$D_{\rm o}$ space. Meanwhile, the widely used {\it CAS} and Gini-$M_{20}$ methods turn out to be insensitive to such morphological features. We stress that the $A_{\rm o}$-$D_{\rm o}$ method is an efficient way to select galaxies with significant asymmetric features like tidal tails and study galaxy mergers in the dynamical phase traced by these delicate features. | Major mergers between galaxies of comparable mass are expected to occur frequently in hierarchical models of galaxy formation and evolution \citep[e.g.,][]{1978MNRAS.183..341W,1993MNRAS.262..627L}. Galaxy merging may be a crucial process that regulates galaxy mass assembly, galaxy morphology reshaping, growth of supermassive black holes, and enhancement of star formation \citep[e.g.,][]{1992ARA&A..30..705B,1996ARA&A..34..749S,2005Natur.435..629S,2008ApJS..175..356H,2010ApJ...724..915H,2009ApJ...697.1369B,2014arXiv1403.2783C}. Measuring the galaxy merger rate over cosmic time is thus a central task in determining the importance of the merging process relative to that of other physical processes (e.g., feedback and gas accretion) to driving galaxy evolution. Much effort has been made to measure galaxy merger rate. Interacting or merging galaxies are rare ($\sim$2\%) in the local universe \citep{1985ARA&A..23..147A,1997ApJ...475...29P,2004ApJ...603L..73X,2008ApJ...685..235P,2009ApJ...695.1559D}, but they become more numerous at higher redshifts. However, the measurements of the merger rate are inconsistent with each other and are still under debate. While strong evolution characterized by $(1 + z)^{3-6}$ was often reported \citep{2000MNRAS.311..565L,2002ApJ...565..208P,2003AJ....126.1183C,2005MNRAS.357..903C,2007ApJS..172..329K,2007ApJS..172..320K,2009MNRAS.394.1956C,2009ApJ...697.1971J,2010ApJ...713..330X,2011ApJ...742..103L}, mild evolution following $\sim (1+z)^{0.5}$ or even no evolution was obtained by other studies \citep{2000ApJ...532L...1C,2004ApJ...601L.123B,2008ApJ...681..232L,2010ApJ...719..844R,2012ApJ...744...85M}. The controversy is likely caused by large uncertainties in current observational techniques adopted for merger identification (see \citealt{2008MNRAS.391.1137L} for more details). Disturbed morphology is mostly used as the probe of a merger. The violent tidal forces between merging galaxies can destroy galaxy structures and produce tidal features. For instance, extended tidal tails can be created when the mergers involve a disk galaxy \citep{1972ApJ...178..623T,1972MNRAS.157..309W,1992Natur.360..715B,2004IAUS..217..390M}. The characteristics of the tidal tails in turn disclose key properties of the parent galaxies such as kinematics, mass ratio, and orbital parameters \citep[][]{2013ASPC..477...47D,2013LNP...861..327D}. A long tidal tail is usually seen as evidence for a merger between disk galaxies \citep[e.g.,][]{2007ApJ...663..734E,2010ApJ...709.1067B}. Resolving specific features from mergers helps to provide information on the frequency of mergers, a better understanding of the merger time scale, and a complete census of various types of mergers over cosmic time. It further delivers insights on evolutionary pathways for different galaxy populations. This will be possible with upcoming deep imaging surveys over large areas \citep[e.g., Euclid,][]{2013LRR....16....6A}. Computational approaches are keenly needed to detect the specific features tracing given types of mergers. Non-parametric methods $CAS$ \citep{2000ApJ...529..886C, 2003ApJS..147....1C} and Gini-$M_{20}$ \citep{2004AJ....128..163L} are widely used for merger selection. $CAS$ selects mergers mainly according to their morphological asymmetry, but fails to pick up those with weaker asymmetry in morphology (e.g., double-nucleus). The Gini coefficient and $M_{20}$ parameters measure the relative distribution of pixel fluxes and spatial light concentration of a galaxy, respectively. Mergers and regular galaxies are globally separated in the Gini-$M_{20}$ space. This method favors to select mergers that are in their first pass or the final stage \citep{2008MNRAS.391.1137L,2010MNRAS.404..575L,2010MNRAS.404..590L}. Neither $CAS$ nor Gini-$M_{20}$ provides a complete selection for major mergers \citep{2007ApJS..172..329K,2007ApJS..172..406S,2009ApJ...697.1971J,2010ApJ...721...98K}. This is in part because the parameters adopted in the two methods are flux weighted. These parameters are largely determined by the light distribution of the bright section of a galaxy, and are insensitive to the tidal features with lower surface brightness in the outskirts of the galaxy. In this paper, we present a new approach to quantifying the structure of the outskirts of a galaxy, aimed at searching for tidal tails. Two parameters are introduced to accomplish this. In Section~\ref{sec:sec2} we describe how to measure the two parameters. In Section~\ref{sec:sec3}, we verify our method using a visually classified sample of galaxies. Finally, we compare our method with $CAS$ and Gini-$M_{20}$ in Section~\ref{sec:sec4}. Throughout this paper, we assume $H_0=70$\,km\,s$^{-1}$\,Mpc$^{-1}$, $\Omega_{\rm \Lambda}=0.7$ and $\Omega_{\rm m}=0.3$. | \label{sec:sec6} We develop a new automatic method to quantify the structure in the outskirts of galaxies, aiming at probing delicate features like tidal tails. Using the isophote which encloses half the total light of a galaxy, the division of the galaxy image into two sections (the IHR and OHR) is the key to our method. Two parameters are introduced in the method: $A_{\rm o}$, which measures the asymmetry of the OHR, and $D_{\rm o}$, which measures the deviation of the intensity weighted centroids of the OHR from that of the IHR relative to the effective radius. The galaxies with stronger disturbance in morphology are expected to have higher $A_{\rm o}$ and $D_{\rm o}$. Moreover, the two parameters are designed to be less affected by the central high surface brightness section of galaxies, and thus sensitive to low surface brightness features in the OHR. A sample of 764 galaxies with $\log (M/{\rm M}_\odot)>3\times 10^{10}$ and $0.35<z<0.9$ selected from the GEMS and GOODS-S surveys is used to verify our method. For a comparison, we visually classify morphologies for the sample using $HST$ $z_{850}$-band images, following the usual classification scheme given in the literature. The $z_{850}$ band corresponds to the rest-frame optical over the redshift range examined here. Our investigation shows that all sample galaxies fall on a sequence in the $A_{\rm o}$-$D_{\rm o}$ space. The position along the sequence is in general correlated with the degree of morphological disturbance. Galaxies with more disturbed morphologies have higher $A_{\rm o}$ and $D_{\rm o}$ in a statistical sense. The merging galaxies with tidal tails are well separated from regular galaxies (spheroids and disks) along the sequence. The regular galaxies are mostly with $D_{\rm o}<0.5$ and $A_{\rm o}<0.6$, following a relation described by ${\rm log}\,A_{\rm o}=0.6\,{\rm log}\,D_{\rm o}$. The galaxies with tidal tails are mostly with $A_{\rm o}>$0.5 and $D_{\rm o}$ ranging from 0.3 to 1.4. The criterion ${\rm log}\,A_{\rm o} > -1.6\,{\rm log}\,D_{\rm o}-1.1$ is able to select all galaxies with tidal tails and most major mergers (without apparent tidal tails). The advantage of this selection is that major mergers with highly asymmetric morphologies are nearly complete and about 87\% of galaxies with regular morphologies (spheroids and disks) are excluded at the same time. The left 13\% of regular galaxies tend to have higher $A_{\rm o}$ and $D_{\rm o}$ contributed by odd spiral arms, strong dust lanes, warped disks, or contamination from neighboring sources. Low surface brightness galaxies suffer more from the contamination by surrounding sources or background noise, leaving $A_{\rm o}$ and $D_{\rm o}$ highly uncertain. Given that nearly 63\% of the major mergers (including those with tidal tails) can be selected by a single cut in the $A_{\rm o}$-$D_{\rm o}$ space, out method can be used for a relatively complete search for major mergers from large scale imaging surveys. Compared with $CAS$ and Gini-$M_{20}$, our $A_{\rm o}$-$D_{\rm o}$ method is able to provide a better separation between mergers and regular galaxies. In particular, our method is unique in probing extended delicate features. In Gini-$M_{20}$, galaxies with tidal tails mix together with regular galaxies. And $CAS$ is also insensitive to galaxies of this kind. We point out that our $A_{\rm o}$ is in a better position than $A$ in $CAS$ for probing asymmetric structures of galaxies. Next-generation deep imaging surveys carried out by the Large Synoptic Survey Telescope (LSST) and Euclid will provide high-quality multi-band imaging data over large areas of sky, allowing for detailed studies of the structure and morphology of galaxies to address how galaxies form and evolve. Automatic approaches like our $A_{\rm o}$-$D_{\rm o}$ method for morphological analysis are essential in the era of big data. | 14 | 4 | 1404.2281 |
1404 | 1404.4372_arXiv.txt | For there to be a successful measurement of the $21\,\textrm{cm}$ Epoch of Reionization (EoR) power spectrum, it is crucial that strong foreground contaminants be robustly suppressed. These foregrounds come from a variety of sources (such as Galactic synchrotron emission and extragalactic point sources), but almost all share the property of being spectrally smooth, and when viewed through the chromatic response of an interferometer, occupy a signature ``wedge" region in cylindrical $k_\perp k_\parallel$ Fourier space. The complement of the foreground wedge is termed the ``EoR window", and is expected to be mostly foreground-free, allowing clean measurements of the power spectrum. This paper is a sequel to a previous paper that established a rigorous mathematical framework for describing the foreground wedge and the EoR window. Here, we use our framework to explore statistical methods by which the EoR window can be enlarged, thereby increasing the sensitivity of a power spectrum measurement. We adapt the Feldman-Kaiser-Peacock approximation (commonly used in galaxy surveys) for $21\,\textrm{cm}$ cosmology, and also compare the optimal quadratic estimator to simpler estimators that ignore covariances between different Fourier modes. The optimal quadratic estimator is found to suppress foregrounds by an extra factor of $\sim 10^5$ in power at the peripheries of the EoR window, boosting the detection of the cosmological signal from $12\sigma$ to $50\sigma$ at the midpoint of reionization in our fiducial models. If numerical issues can be finessed, decorrelation techniques allow the EoR window to be further enlarged, enabling measurements to be made deep within the foreground wedge. These techniques do not assume that foreground are Gaussian-distributed, and we additionally prove that a final round of foreground subtraction can be performed after decorrelation in a way that is guaranteed to have no cosmological signal loss. | By mapping the intensity of the redshifted hyperfine transition of hydrogen in three dimensions, $21\,\textrm{cm}$ cosmology has the potential to survey a larger volume of our observable Universe than any other cosmological probe to date \cite{Furlanetto2006,Morales2010,Pritchard2012,AviBook}. Efforts aimed at lower redshifts ($0 < z \lesssim 4$, depending on the experiment) aim to use neutral hydrogen as a tracer for large scale structure and are expected to be incisive probes of dark energy and its time evolution \cite{Pober2013a,Ansari2012,Battye2012,Shaw2014a,SaiyadAli2013,Chen2012}. Interferometer arrays such as the Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER \cite{Parsons2010,Parsons2013}), the Murchison Widefield Array (MWA \cite{Tingay2013,Bowman2013}), the Low Frequency Array (LOFAR \cite{Yatawatta2013}), and the Giant Metrewave Radio Telescope Epoch of Reionization experiment (GMRT-EoR \cite{Paciga2013}) are currently targeting higher redshifts ($6 \lesssim z \lesssim 13$, again depending on the experiment). These experiments open up a previously unexplored period in our Universe's history---the Epoch of Reionization (EoR)---during which the first luminous objects ionized the intergalactic medium (IGM). Future instruments such as the Hydrogen Epoch of Reionization Array (HERA \cite{Pober2014}) and the Square Kilometer Array (SKA \cite{Mellema2013}) will further push the redshift and sensitivity frontiers, probing an even broader range of redshifts with greater sensitivity. This will enable not only detailed studies of the properties of the first objects and their effect on the IGM, but also of more exotic physics such as dark matter annihilation \cite{Valdes2013}, and may eventually even lead to constraints on fundamental parameters such as the neutrino mass \cite{McQuinn2006,Mao2008} and non-Gaussianity \cite{Mao2013}. For $21\,\textrm{cm}$ cosmology to become a reality, however, it will be necessary to deal with foreground systematics. The cosmological signal that experiments seek to detect is faint (favored to be roughly a few mK in brightness temperature with most theoretical models \cite{Lidz2007,Barkana2009,Zahn2011}), whereas sources of foreground radio emission such as Galactic synchrotron radiation are bright (known empirically to be on the order of a few hundred Kelvin at frequencies relevant to EoR experiments \cite{deOliveiraCosta2008}). A systematic way to subtract or evade these foregrounds is therefore crucial. Proposals for foreground mitigation can be roughly split into two categories: foreground subtraction and foreground avoidance. Foreground subtraction schemes typically propose to model the foregrounds before subtracting them off directly from the data. Different proposals require modeling the foregrounds to different levels of detail. Some rely only on the fact that the foregrounds are expected to be spectrally smooth compared to the cosmological signal \cite{Wang2006,Gleser2008,Liu2009a,Bowman2009,Harker2009,Liu2009b,Petrovic2011,Cho2012,Liu2012,Parsons2012b}. Others also take advantage of the angular dependence of foregrounds \cite{Paciga2011,Liu2011,Dillon2013,Masui2013,Dillon2014}, or leverage their inherent non-Gaussianity \cite{Chapman2012,Chapman2013}. If modeling inaccuracies can be minimized and accidental cosmological signal losses (if any) are correctly accounted for, foreground subtraction techniques in principle allow extremely high signal-to-noise measurements. As an alternative to foreground subtraction, one may instead opt for a more conservative approach of foreground avoidance. Foreground avoidance strategies have been developed primarily for measurements of the $21\,\textrm{cm}$ power spectrum, which will be the focus of this paper. In a power spectrum measurement, one essentially takes a three-dimensional survey volume and performs spatial Fourier transforms over all three spatial axes to give a set of Fourier amplitudes labeled by three wavenumbers: $k_x$ and $k_y$ for the angular directions, and $k_\parallel$ for the line-of-sight direction. The data are then squared and appropriately binned. Now, recall that because $21\,\textrm{cm}$ surveys map our Universe using a spectral line, there is a direct correspondence between the observation frequency and the line-of-sight distance. Foreground emission (being spectrally smooth \cite{Oh2003}) is therefore expected to contaminate only the lowest $k_\parallel$ modes, unlike the cosmological signal, which is typically spread throughout Fourier space. It should therefore be possible to pursue a strategy of foreground avoidance, where power spectrum measurements are only made at higher $k_\parallel$. \begin{figure}[!ht] \centering \includegraphics[width=.49\textwidth]{simpleEstBias.pdf} \caption{Residual bias (which is expected to contain only foregrounds) for a basic power spectrum estimator, reproduced from Paper I. The foregrounds strongly contaminate a wedge region, but fall sharply beyond the wedge.} \label{fig:basicEstBias} \end{figure} Unfortunately, recent work has shown that it may be overly simplistic to assume that foregrounds occupy only the lowest $k_\parallel$ modes. In Figure \ref{fig:basicEstBias} we show a numerical computation from a preceding companion paper (Ref. \cite{Liu2014a}, henceforth ``Paper I"), where we plot the expected power spectrum contamination from foregrounds as a function of cylindrical Fourier wavenumbers $k_\parallel$ and $k_\perp \equiv \sqrt{k_x^2 + k_y^2}$. At low $k_\perp$, we see that our previous expectations are met, with the bright foregrounds contaminating only the first few $k_\parallel$ bins. At high $k_\perp$, however, the foregrounds extend to higher $k_\parallel$, forming a characteristic ``wedge". Through detailed simulations, theoretical work, and observations, it is now understood that the wedge arises from the fundamentally chromatic nature of interferometry \cite{Datta2010,Vedantham2012,Parsons2012b,Morales2012,Trott2012,Thyagarajan2013,Hazelton2013,Pober2013b,Dillon2014}. Since interferometric fringe patterns depend on the observation frequency, the spatial wavenumber $k_\perp$ is coupled to the frequency/line-of-sight wavenumber $k_\parallel$. This coupling is more pronounced at higher $k_\perp$, which tend to be probed by the baselines of an interferometer array that are longer, and are thus known to be more chromatic. The result is a leakage of foregrounds from low to high $k_\parallel$ that is more pronounced at high $k_\perp$, i.e., the wedge. Previous work has shown that while the existence of the wedge means that more of the Fourier plane is contaminated with foregrounds than one might have naively expected, this contamination is limited, in the sense that there are theoretical and observational reasons for a sharp drop-off in foreground power beyond the wedge. Foreground avoidance is therefore still a viable foreground mitigation strategy, as long as one is careful to only include power spectrum measurements outside the wedge, in a region colloquially known as the ``EoR window". In Paper I, we extended and unified previously disparate aspects of the existing literature in a mathematical framework of the wedge and the EoR window. Importantly, our framework was fully covariant, allowing errors and error correlations to be properly captured, whether they arose from instrumental effects or foreground contamination. In this paper, we make use of our mathematical framework to examine ways in which the EoR window may be enlarged using statistical methods. In other words, we consider ways in which the foreground wedge can be reduced without directly modeling and subtracting foreground models from the data, thus preserving the conservative spirit of foreground avoidance. If successful, an enlargement of the EoR window can result in higher significance measurements of the EoR power spectrum, since thermal noise is typically independent of $k_\parallel$, while the cosmological signal increases in strength towards low $k_\parallel$. The ability to push into the wedge can be the difference between a non-detection and a significant detection with current-generation experiments, and much-improved astrophysical constraints with next-generation experiments \cite{Pober2014}. We will find that minimum-variance power spectrum estimators can reduce foregrounds at the edge of the wedge by a factor of up to $10^5$ in power (i.e., in temperature-squared units). Pushing beyond a simple application of the minimum-variance power spectrum estimator, the error statistics computed using the framework presented in Paper I can be used to push deeper into the wedge. In Paper I, we described the wedge as a scattering of foregrounds from low $k_\parallel$ regions to higher $k_\parallel$. The form of this scattering is computable in a foreground-independent manner using the formalism of Paper I. Since this scattering is a well-defined linear operation that acts on the power spectrum, it can in principle be undone using decorrelation techniques. Decorrelation allows foregrounds to be more readily identified and removed in a final post-processing step following power spectrum estimation. We prove that such a strategy does not require assumptions of foreground Gaussianity, is immune to possible modeling inaccuracies of the subtracted foregrounds, and does not suffer from any formal signal loss. The last two features, in particular, stand in contrast to methods that directly subtract foregrounds from the input data \cite{Wang2006,Liu2009a,Bowman2009,Harker2009,Liu2009b,Liu2012}. With decorrelation and a subsequent foreground removal (a combination that we dub ``foreground isolation"), one may potentially allow work deep within the wedge, although numerical issues must be dealt with. The rest of this paper is organized as follows. In Section \ref{sec:PaperI} we establish notation and summarize the results of Paper I. These results form a basic picture of the wedge and the EoR window that serve as a reference; our goal is to improve upon this basic picture. Section \ref{sec:Direct} comments briefly on the interplay between foreground subtraction and foreground avoidance. In Section \ref{sec:Enlarging}, we first examine the possibility of enlarging the EoR window using the computationally cheap class of separable power spectrum estimators before discussing the more computationally expensive non-separable estimators, which include the optimal minimum-variance estimator. The computationally expensive estimators are explored numerically, using exactly the same setup as we used in Paper I, from the foreground model and the fiducial instrument down to algorithmic details such as binning. Finally, we examine the foreground isolation approach in Section \ref{sec:Decorr}, before ending with some concluding remarks in Section \ref{sec:Conclusions}. | \label{sec:Conclusions} This paper is a direct continuation of Paper I \cite{Liu2014a}, where a rigorous framework was established for describing the foreground wedge and its complement, the EoR window. In this paper, we made use of our framework to examine statistical methods for enlarging the EoR window, with an eye towards enabling high significance measurements of the power spectrum deep inside the foreground wedge. In Paper I we examined a basic noise-weighted estimator of the power spectrum. In the limit of a very finely discretized Fourier plane, we showed that this is equivalent to a separable estimator where the visibilities are gridded with a primary beam kernel, and then squared and binned. In Section \ref{sec:FKP} of the present paper we considered a more general class of separable estimators, and searched for a more optimal way to weight our data by adapting the FKP approximation from galaxy surveys. Assuming that the power spectrum is a slowly varying function and that one is working on small scales, the FKP approximation can be shown to be optimal (even when compared to the more general class of non-separable estimators). It is therefore a useful reference for comparing with our basic prescription. Making such a comparison reveals that the basic prescription is optimal only if the thermal noise is large compared to the sky signal. Such an assumption is clearly violated as one moves from higher $k_\parallel$ to lower $k_\parallel$ in an attempt to work within the wedge. This can be rectified by weighting the data using FKP weights instead of just instrumental noise. However, as one pushes to the lowest $k_\parallel$, the assumptions underlying the FKP approximation itself (such as the assumption that one is working on small length scales) break down. While the FKP approximation may be a useful approximation that is relatively computationally cheap, a viable prescription for working within the wedge will involve more complicated non-separable estimators. In Section \ref{sec:BetterEst}, we considered the larger class of non-separable estimators. Performing a numerical analysis of what is a provably optimal estimator, we find that the optimal estimator's window functions are naturally shifted away from the deepest depths of the wedge. However, the optimal estimator is able to reduce the foreground biases and errors by up to factors of $10^5$ in power at the edge of the wedge, thus enlarging the EoR window slightly. In our fiducial models, this boosts the detection significance of the cosmological signal from $12\sigma$ to $50\sigma$ around the midpoint of reionization, although this is of course an array-dependent statement. With a fully covariant framework (and thus the ability to compute window functions), one can trade ``horizontal error bars" for ``vertical error bars" in a power spectrum measurement. By reducing the horizontal error bars (i.e., by narrowing the window functions), one can reduce the leakage of foregrounds across the Fourier plane, which was what caused the foreground wedge in the first place. In Section \ref{sec:Decorr}, we proposed a foreground isolation scheme where the window functions are first fully deconvolved to delta functions in order to isolate the foregrounds as much as possible. This is followed by a zeroing out of modes that still contain strong foreground contamination, before a final resmoothing (or rebinning) of the $k_\perp k_\parallel$ plane to reduce the vertical error bars, which were inadvertently magnified by the window function deconvolution. While future work is required to tame expected numerical issues, early indications suggest that this scheme may allow measurements to be made within the wedge. Crucially, our proposed method has no formal signal loss associated with it, and does not assume that the sky signals are Gaussian. Importantly, we note that the techniques developed in this paper are widely applicable to cosmological $21\,\textrm{cm}$ surveys at all redshifts, not just those that seek to study reionization. Our conclusions rely only on the assumptions that one uses an interferometer to map the intensity of a spectral line, and that the foregrounds are spectrally smooth to some degree. Indeed, techniques similar to the ones we explore in Paper I and the present paper have been applied to forecasts for lower-redshift $21\,\textrm{cm}$ surveys targeting baryon acoustic oscillation measurements \cite{Shaw2014a,Shaw2014b}. In battling the twin challenges of sensitivity and foreground systematics, $21\,\textrm{cm}$ power spectrum measurements are in a somewhat unfortunate situation, with thermal noise large where foregrounds are weak and vice versa. To increase the significance of future measurements, one must therefore either reduce the thermal noise or the influence of foregrounds in the final power spectrum. These approaches are of course not mutually exclusive, and next-generation instruments such as the recently-proposed HERA \cite{Pober2014} and the SKA will achieve the former, while in this paper we have proposed various methods for achieving the latter. The work presented here suggests that it may indeed be possible to enlarge the EoR window, and further progress on this front will be a crucial step in fully realizing the great promise of $21\,\textrm{cm}$ cosmology. | 14 | 4 | 1404.4372 |
1404 | 1404.6141_arXiv.txt | {\noindent \normalsize We consider the Higgs portal $Z_2$ scalar model as the minimal extension of the Standard Model (SM) to incorporate the dark matter. We analyze this model by using the two-loop renormalization group equations. We find that the dark matter mass is bounded to be lighter than 1000\,GeV within the framework that we have proposed earlier, where the Higgs inflation occurs above the SM cutoff $\Lambda$, thanks to the fact that the Higgs potential becomes much smaller than its typical value in the SM: $V\ll\Lambda^4$. We can further fix the dark matter mass to be $400\GeV< m_\text{DM}<470\GeV$ if we impose that the cutoff is at the string scale $\Lambda\sim10^{17}\GeV$ and that the Higgs potential becomes flat around $\Lambda$, as is required by the multiple point principle or by the Higgs inflation at the critical point. This prediction is testable by the dark matter detection experiments in the near future. In this framework, the dark matter and top quark masses are strongly correlated, which is also testable. } \normalsize \newpage | Recent discovery of the Higgs boson~\cite{Aad:2012tfa,Chatrchyan:2012ufa} determines all the parameters % of the Standard Model (SM) except for the neutrino sector. Since we have seen nothing beyond the SM at the Large Hadron Collider so far, it becomes more important to consider a scenario where SM is not much altered up to a very high scale such as the string (Planck) scale, around $10^{17}$ ($10^{18}$) GeV. If we extrapolate the obtained SM parameters toward this scale assuming no new physics, we find a curious situation that both the Higgs self coupling $\lambda$ and its beta function $\beta_\lambda$ become very small~\cite{Holthausen:2011aa,Bezrukov:2012sa,Degrassi:2012ry,Alekhin:2012py,Masina:2012tz,Hamada:2012bp,Jegerlehner:2013cta,Buttazzo:2013uya}, as well as the bare Higgs mass $m_B^2$~\cite{Hamada:2012bp,Jegerlehner:2013cta,Jegerlehner:2013nna,Hamada:2013cta,Bian:2013xra,Jones:2013aua}; see also Ref.~\cite{Alsarhi:1991ji} for the earlier two-loop computation of $m_B^2$. This fact may give us a hint for a deeper understanding of the Planck scale physics, and is very interesting. So far, there are several proposals of the physics behind this fact: the multiple point principle (MPP)~\cite{Froggatt:1995rt,Froggatt:2001pa,Nielsen:2012pu}, the asymptotic safety~\cite{Shaposhnikov:2009pv}, the scale invariance~\cite{Meissner:2007xv,Aoki:2012xs,Khoze:2014xha,Kobakhidze:2014afa}, the maximum entropy principle~\cite{Kawai:2011qb,Kawai:2013wwa,Hamada:2014ofa,Kawana:2014vra,Hamada:2014xra}, the hidden duality and symmetry~\cite{Kawamura:2013kua,Kawamura:2013xwa}, etc. There are also bottom-up approaches to extend the SM to realize such a structure at high scales~\cite{Meissner:2006zh,Foot:2007iy,Iso:2009ss,Iso:2009nw,Iso:2012jn,Haba:2013lga,Hashimoto:2014ela,Chankowski:2014fva,Kawana:2014zxa,Kawana:2015tka}. The flat potential, namely the vanishing quartic coupling around the string scale, is interesting not only theoretically but also phenomenologically. Recently, the authors have pointed out the possibility that this flat potential can be used for the cosmic inflation~\cite{Hamada:2013mya}. More concrete model can be found in Refs.~\cite{Hamada:2014iga,Bezrukov:2014bra}, where the inflation scale is sufficiently large to explain the recently observed B-mode polarization, i.e.\ the large tensor-to-scalar ratio, by the BICEP2 experiment~\cite{Ade:2014xna}. See also Refs.~\cite{Kamada:2013bia,Jegerlehner:2014mua,Burgess:2014lza,Lee:2014spa,Gong:2014cqa,Okada:2014lxa,Fairbairn:2014nxa,DiBari:2014oja,Oda:2014rpa,Cheng:2014bta,Enqvist:2014tta,Enqvist:2014bua,Feng:2014naa,Bamba:2014mua,Ren:2014sya,Bartrum:2013fia,Bastero-Gil:2014jsa,Bastero-Gil:2014oga,Hosotani:1985at,Chakravarty:2013eqa}. However, it is certain that we need to extend the SM since it does not contain a dark matter (DM). It is probable that Nature chooses minimal extension among many candidate models since it has not shown us any symptom of new physics at the Large Hadron Collider so far. One of the most minimal models is the gauge singlet scalar model with the $Z_2$ symmetry~\cite{Silveira:1985rk,McDonald:1993ex,Burgess:2000yq,Davoudiasl:2004be,Patt:2006fw,Grzadkowski:2009mj,Drozd:2011aa,Haba:2013lga}. This model is well studied so that the relation between the mass of the DM and its coupling to the Higgs is constrained to yield the correct thermal abundance of the DM; the bounds from the collider and (in)direct detection experiments are also examined; see Ref.~\cite{Cline:2013gha} for the latest analysis. In this paper, we study the modification of the running of the SM parameters in this model. Particularly, we examine the running of the Higgs quartic coupling to check its consistency with the Higgs inflation above the SM cutoff~\cite{Hamada:2013mya}.\footnote{ \magenta{One may think of the possibility of using this singlet dark matter as the inflaton. However, its quartic coupling does not become small in the minimal model since it does not have a Yukawa coupling. Therefore we do not consider the possibility of using the scalar dark matter as the inflaton. It may be interesting to pursue such a possibility in the model where the Higgs portal scalar has a Yukawa coupling to extra fermion; see e.g.\ Ref.~\cite{Ko:2014eia} and references therein.} } We show that the DM mass must be smaller than 1000\,GeV in order for the SM Higgs potential to be smaller than the inflation energy $10^{65}\,\text{GeV}^4$ all the way up to the string scale $\sim10^{17}$\,GeV. It is interesting that the allowed region is testable in future direct detection experiments~\cite{Cline:2013gha}. We further get the DM mass $400\GeV< m_\text{DM}<470\GeV$ if we impose the flatness of the Higgs potential $\lambda\simeq\beta_\lambda\simeq0$ around the string scale $10^{17}\GeV$, as is expected from the MPP or is required in the Higgs inflation at the critical point~\cite{Hamada:2013mya,Bezrukov:2014bra}. This paper is organized as follows: In Section~\ref{model}, we review the $Z_2$ scalar model and its allowed region of the parameter space. In Section~\ref{constraint}, we briefly explain the flat potential Higgs inflation, and its constraint on the parameter space. We will see that the DM mass is strongly constrained. In Section~\ref{summary}, we conclude this paper. | \label{summary} We have obtained the constraints on the DM mass $m_\text{DM}<1000\GeV$ and on the top quark mass $171\GeV< M_t< 174\GeV$ in the Higgs portal $Z_2$ singlet model, imposing the condition to achieve the Higgs inflation above the cutoff~\cite{Hamada:2013mya}. We can further fix the DM mass to be $400\GeV< m_\text{DM}<470\GeV$ if we impose the flatness of the potential around the string scale $10^{17}\GeV$, $\lambda\sim\beta_\lambda\sim0$, as is required by the multiple point principle or by the Higgs inflation at the critical point. Both of these regions are testable in the near future by the direct and indirect DM detection experiments and by the precision measurement of the top quark pole mass. We emphasize that the idea of the Higgs inflation above cutoff uses the fact the Higgs quartic coupling and its beta function become very close to zero around the string scale $10^{17}\GeV$. Therefore, if the relation between the DM and top masses is confirmed, it suggests that the cutoff of the SM is around $10^{17}\GeV$.\footnote{ See e.g.\ Ref.~\cite{Mizoguchi:2014gva,Hamada:2014hpa,Hamada:2014eia} for an attempt along this line. } This framework does not predict a particular value of the spectral index $n_s$, but gives the tensor-to-scalar ratio $r> 10^{-3}$. This prediction is consistent to the B-mode polarization detection by the BICEP2 experiment. It would be interesting to construct a model that makes the Higgs potential above the cutoff to be flat in field theory and in string theory~\cite{Hamada:2015ria}. \subsection*{Note added} While this paper was in preparation, there appeared Ref.~\cite{Haba:2014zda} with similar subject. The result is in qualitative agreement with ours. Afterwards, there also appeared a related work~\cite{Channuie:2014kda}. \subsection*{Acknowledgement} We thank Seong Chan Park for useful discussions and Yukinari Sumino for helpful comment. This work is in part supported by the Grant-in-Aid for Scientific Research Nos.~22540277 (HK), 23104009, 20244028, and 23740192 (KO). The work of Y. H. is supported by a Grant-in-Aid for Japan Society for the Promotion of Science (JSPS) Fellows No.25$\cdot$1107. \appendix | 14 | 4 | 1404.6141 |
1404 | 1404.3880_arXiv.txt | The QCD axion solving the strong CP problem may originate from antisymmetric tensor gauge fields in compactified string theory, with a decay constant around the GUT scale. Such possibility appears to be ruled out now by the detection of tensor modes by BICEP2 and the PLANCK constraints on isocurvature density perturbations. A more interesting and still viable possibility is that the string theoretic QCD axion is charged under an anomalous U$(1)_A$ gauge symmetry. In such case, the axion decay constant can be much lower than the GUT scale if moduli are stabilized near the point of vanishing Fayet-Illiopoulos term, and U$(1)_A$-charged matter fields get a vacuum value $v\sim (m_{\rm SUSY}M_{Pl}^n)^{1/(n+1)}$ $(n\geq 0)$ induced by a tachyonic SUSY breaking mass $m_{\rm SUSY}$. We examine the symmetry breaking pattern of such models during the inflationary epoch with $H_I\simeq 10^{14}$~GeV, and identify the range of the QCD axion decay constant, as well as the corresponding relic axion abundance, consistent with known cosmological constraints. In addition to the case that the PQ symmetry is restored during inflation, i.e. $v(t_I) =0$, there are other viable scenarios, including that the PQ symmetry is broken during inflation with $v(t_I) \sim (4\pi H_IM_{Pl}^n)^{1/(n+1)}\sim 10^{16}$--$10^{17}$~GeV due to the Hubble-induced $D$-term $D_A\sim 8\pi^2 H_I^2$, while $v(t_0)\sim (m_{\rm SUSY}M_{Pl}^n)^{1/(n+1)}\sim 10^{9}$--$5\times 10^{13}$~GeV in the present universe, where $v(t_0)$ above $10^{12}$~GeV requires a fine-tuning of the axion misalignment angle. We also discuss the implications of our results for the size of SUSY breaking soft masses. | \label{sec:1} The strong CP problem~\cite{axion-review} of the Standard Model of particle physics is about the question why the strong CP violating parameter $\bar\theta =\theta_{\rm QCD}+\arg(y_uy_d)$ is smaller than $10^{-10}$, while the weak CP violating Kobayashi-Maskawa phase originating from the same quark Yukawa couplings $y_{u,d}$ is of order unity. Presently the most compelling solution to this problem is to introduce a non-linearly realized anomalous global U$(1)$ symmetry, the Peccei-Quinn (PQ) symmetry~\cite{Peccei:1977hh}, which predicts a pseudo-Goldstone boson, the QCD axion, whose vacuum expectation value (VEV) can be identified as $\bar\theta$~\cite{old-axion-papers,KSVZ,DFSZ}. Yet, there still remain some questions. One question is, what is the origin of the PQ symmetry? The PQ symmetry is required to be explicitly broken by the QCD anomaly, while being protected well from other forms of explicit breaking. In view of that global symmetry is not respected in general by UV physics at scales where quantum gravity becomes important~\cite{global-symmetry-gravity}, the existence of such global symmetry at low energy scales may require a specific form of UV completion of the model~\cite{UV-PQ-symmetry}. Another question is about the mechanism to determine the axion decay constant $f_a$, which determines most of the phenomenological consequences of the QCD axion, including the cosmological ones. It has been known for many years that string theory provides an attractive theoretical framework to address these questions~\cite{Witten:1984dg}. String theory includes a variety of higher-dimensional antisymmetric tensor gauge fields, whose zero modes behave like axions in the 4-dimensional effective theory. The shift symmetries associated with these axion-like fields are valid in perturbation theory~\cite{axion-string-theory,Ibanze-Uranga}. It is then conceivable that a certain combination of the shift symmetries is broken dominantly by the QCD anomaly, and therefore can be identified as the PQ symmetry solving the strong CP problem. As for the decay constant, if the compactification scale is comparable to the Planck scale, the decay constants of such stringy axions are estimated to be~\cite{Choi:1985bz,Svrcek:2006yi,axion-models-in-string}, \bea \label{axion_scale1} f_a \,\sim\, {g^2M_{Pl}}/{8\pi^2}, \eea where the factor $8\pi^2$ comes from the convention for the axion decay constant, and $M_{Pl} \simeq 2.4\times 10^{18}$~GeV is the reduced Planck scale. Although it is subject to severe cosmological constraints~\cite{axion-cosmology1,works-on-axion-iso,axion-cosmology2}, such QCD axion arising from antisymmetric tensor gauge fields in compactified string theory has been considered to be a viable possibility for many years. An interesting generalization of this scheme, involving an anomalous U$(1)_A$ gauge symmetry with a nonzero U$(1)_A$-SU$(3)_c$-SU$(3)_c$ anomaly cancelled by the 4-dimensional Green-Schwarz (GS) mechanism~\cite{Green:1984sg}, has been discussed before for the purpose of having an intermediate scale QCD axion even when the compactification scale is comparable to the Planck scale~\cite{Barr:1985hk,Svrcek:2006yi,Choi:2011xt}. It is based on the compactification models in which moduli are stabilized at the point of vanishing U$(1)_A$ Fayet-Illiopoulos (FI) term $\xi_{\rm FI}=0$ in the supersymmetric limit, when all U$(1)_A$-charged matter fields $\phi$ are set to zero. Such supersymmetric solutions are known to exist in many of the Type II string theory with $D$-branes~\cite{vanishing-FI,Ibanze-Uranga}, as well as in the heterotic string theory with U$(1)$ gauge bundles~\cite{Blumenhagen:2005ga,Anderson:2009nt}. In the limit of $\xi_{\rm FI}=\phi=0$, the U$(1)_A$ gauge boson obtains a superheavy mass $M_A \sim M_{Pl}/8\pi^2$ by absorbing the stringy axion $\theta_{\rm st}$ implementing the GS anomaly cancellation mechanism, while leaving an unbroken perturbative global U$(1)$ symmetry, which corresponds the global part of U$(1)_A$ without the transformation of $\theta_{\rm st}$. By construction, this perturbative global U$(1)$ symmetry has nonzero U$(1)$-SU$(3)_c$-SU$(3)_c$ anomaly, and therefore can be identified as the PQ symmetry solving the strong CP problem. To satisfy the astrophysical constraints on the QCD axion, this PQ symmetry should be spontaneously broken at a scale higher than $10^{9}$~GeV~\cite{axion-review}. For this, some U$(1)_A$-charged matter field $\phi$ should have a tachyonic supersymmetry (SUSY) breaking scalar mass $m_{\rm SUSY}$, destabilizing the supersymmetric solution $\xi_{\rm FI}=\phi=0$. The matter scalar field $\phi$ then takes a vacuum value $\langle \phi\rangle > 10^9$~GeV by an interplay between the tachyonic SUSY breaking mass term and a supersymmetric higher order term which schematically takes the form $|\phi|^{2n+4}/M_{Pl}^{2n}$ with $n\geq 0$ if the cutoff-scale of the model is assumed to be comparable to the Planck scale~\cite{fa-susy}. This scheme to determine $\langle \phi\rangle$ leads to an appealing connection between the axion scale and the SUSY breaking scale as \bea\label{axion_scale2} f_a \,\simeq \,\langle \phi\rangle \,\sim\, (m_{\rm SUSY} M_{Pl}^n)^{1/(n+1)} \quad (n\geq 0), \eea which makes it possible that a wide range of the QCD axion decay constant much lower than the Planck scale is obtained within the framework of string theory. The recent detection of tensor modes in the cosmic microwave background (CMB) by BICEP2~\cite{Ade:2014xna} has important implications for axion cosmology~\cite{axion-after-bicep2}, particularly for the string theoretic QCD axion. First of all, the BICEP2 results imply that the inflation energy scale is about $10^{16}$~GeV. This suggests that the string compactification scale is higher than $10^{16}$~GeV, and therefore the estimate (\ref{axion_scale1}) of the decay constants of stringy axion-like fields is at least qualitatively correct. For the expansion rate $H_I \sim 10^{14}$~GeV, if the PQ symmetry were spontaneously broken during inflation, the corresponding QCD axion is severely constrained by the PLANCK constraints on isocurvature density perturbations and non-Gaussianity~\cite{Ade:2013uln}.\footnote{ It is in principle possible that the axion under the consideration obtains a heavy mass $m_a(t_I) \gtrsim H_I$ during inflation, so is free from the isocurvature and non-Gaussianity constraints~\cite{Jeong:2013xta,Higaki:2014ooa}. However, it is not likely to be realized in our theoretical framework, as $m_a$ is protected by both the shift symmetry broken only by non-perturbative effects and the softly broken SUSY during inflation with $H_I \ll M_{Pl}$. } As we will see, this rules out the simple possibility that the QCD axion corresponds to a combination of the zero modes of antisymmetric tensor fields in compactified string theory, having a decay constant $f_a\sim g^2M_{Pl}/8\pi^2$. On the other hand, in the presence of an anomalous U$(1)_A$ gauge symmetry with vanishing FI term, under which the QCD axion is charged, the model can have rich symmetry breaking patterns during inflation, while giving a present axion decay constant much lower than $g^2M_{Pl}/8\pi^2$. This may make it possible that the model allows a variety of different cosmologically viable scenarios. In this paper, we examine the symmetry breaking pattern of the string theoretic QCD axion models involving an anomalous U$(1)_A$ gauge symmetry during the inflationary epoch with $H_I\simeq 10^{14}$~GeV. We identify the allowed range of the axion decay constant in such models, as well as the corresponding relic axion abundance, being consistent with known cosmological constraints, within a general framework in which the axion scale during inflation can be different from the axion scale in the present universe. We note first that if the PQ symmetry were broken during inflation, the cosmological constraints can be satisfied {\it only} when the axion scale during inflation is much higher than the present axion scale. The most natural setup to realize this possibility is to generate the axion scale through SUSY breaking effects. We show that indeed the string theoretic QCD axion models with anomalous U$(1)_A$ gauge symmetry provides such setup. If the modulus-axion superfield implementing the GS mechanism is {\it not} sequestered from the SUSY breaking by the inflaton sector, which would be the case in generic situations, U$(1)_A$-charged matter fields develop a large expectation value during inflation, \bea \langle \phi(t_I)\rangle \sim (\sqrt{8\pi^2} H_I M_{Pl}^n)^{1/(n+1)}, \eea due to the tachyonic SUSY breaking scalar mass induced dominantly by the $U(1)_A$ $D$-term: \bea m^2_\phi(t_I) \simeq q_\phi g^2_A D_A(t_I) \sim -8\pi^2 H_I^2, \nonumber \eea while \bea \langle \phi(t_0)\rangle \sim (m_{\rm SUSY}M_{Pl}^n)^{1/(n+1)}, \nonumber \eea for the SUSY breaking scalar mass $m_{\rm SUSY}$ in the present universe. Then the QCD axion during inflation has a much higher decay constant than the present value, and even is a different degree of freedom. As we will see, this makes it possible that a certain parameter space of the model is consistent with the constraints on isocurvature perturbations and non-Gaussianity, as summarized in Fig.~\ref{fig:axion} in section \ref{sec:3}. The allowed range of the present axion decay constant for reasonable choice of model parameters is given by \bea 10^{9} \,\, {\rm GeV} \,\lesssim\, f_a(t_0) \,\lesssim\, 5\times 10^{13} \,\, {\rm GeV}, \eea where $f(t_0)\gtrsim 10^{12}$~GeV requires a fine-tuning of the axion misalignment angle as $\theta_0\lesssim {\cal O}(10^{-1})$. If we assume $\theta_0={\cal O}(1)$, the allowed range is reduced to $f_a(t_0)\simeq 10^9$--$10^{11}$~GeV, with the axion dark matter making up roughly $0.1$--$10$~\% of the total dark matter energy density. On the other hand, if the modulus-axion superfield for the GS mechanism is sequestered from the SUSY breaking by the inflaton sector, so that the soft scalar masses during inflation are not dominated by the U$(1)_A$ $D$-term contribution, it is possible that \bea \langle \phi(t_I)\rangle =0, \eea so the PQ symmetry is restored during inflation, while again \bea \langle \phi(t_0)\rangle \sim (m_{\rm SUSY}M_{Pl}^n)^{1/(n+1)}, \nonumber \eea in the present universe. In this case, the model is free from the isocurvature and non-Gaussianity constraints, however required to have the axion domain-wall number $N_{\rm DW}=1$, which is a non-trivial constraint on the model building. Furthermore, if one adopts the recent simulation for the axion production by axionic strings and domain walls~\cite{Hiramatsu:2012gg}, only the following narrow window of the axion decay constant \bea 10^9~{\rm GeV} \,\lesssim\, f_a(t_0)\, \lesssim\, (\mbox{a few})\times 10^{10}~{\rm GeV} \eea is allowed by the astrophysical and cosmological constraints, where the relic axions can account for the total dark matter energy density when $f_a(t_0)$ saturates the upper bound. Our results have an intriguing implication for the size of SUSY breaking soft masses in the present universe. Regardless of whether the PQ symmetry is broken or not during inflation, the cosmologically allowed parameter region for a natural axion misalignment angle $\theta_0={\cal O}(1)$ points to two possibilities:\footnote{ The possibility of the axion scale SUSY was noticed also in Ref.~\cite{Hall:2014vga} recently.} \bea &i)& \mbox{Axion scale SUSY:}\quad m_{\rm SUSY}\,\sim\, f_a(t_0) \,\sim\, 10^9-10^{11}~{\rm GeV}, \nonumber \\ &ii)& \mbox{Low scale SUSY:}\quad m_{\rm SUSY}\,\sim\, f_a^2(t_0)/M_{Pl} \,\sim \,10^3-10^4~{\rm GeV}. \eea The results for the case of broken PQ symmetry during inflation suggest also that the axion isocurvature density perturbations have an amplitude close to the present observational bound. The organization of this paper is as follows. In section \ref{sec:2}, we review the relevant features of the string theoretic QCD axion. In section \ref{sec:3}, we examine the cosmological constraints on the QCD axion, while taking into account that the axion decay constant during inflation can be much higher than the present value. Although we consider here a specific type of string motivated models, it should be noted that our results apply to generic supersymmetric axion models in which the PQ breaking scale is generated by SUSY breaking effects. In section \ref{sec:fa}, we present a simple 4-dimensional supergravity (SUGRA) model involving both the inflaton sector and the U$(1)_A$ sector, and examine possible symmetry breaking patterns during inflation. | \label{sec:5} In this paper, we have examined the cosmological constraints on string theoretic QCD axion in the light of the recent PLANCK and BICEP2 results. We were focusing on models with anomalous U$(1)_A$ gauge symmetry, which admit a supersymmetric solution with vanishing Fayet-Illiopoulos (FI) term $\xi_{\rm FI}=0$, as such models can be realized in many of the known compactified string theories, while being consistent with all the known cosmological constraints for a certain range of model parameters. If the QCD axion is charged under U$(1)_A$, the axion decay constant is determined essentially by the vacuum expectation values of U$(1)_A$ charged matter fields $\phi$. To have a phenomenologically viable axion scale, the supersymmetric solution $\xi_{\rm FI}=\phi=0$ should be destabilized by a tachyonic SUSY breaking mass of $\phi$, which would result in an intriguing connection between the axion scale and the SUSY breaking soft masses in the present universe: $f_a(t_0) \sim (m_{\rm SUSY}M_{Pl}^n)^{1/(n+1)}$ ($n\geq 0$). We note that such models can have rich symmetry breaking patterns during inflation, and therefore allow a certain range of the model parameters compatible with strong cosmological constraints. If the modulus-axion superfield implementing the Green-Schwarz (GS) anomaly cancellation mechanism is {\it not} sequestered from the SUSY breaking by the inflaton sector, the U$(1)_A$-charged matter fields develop a large expectation value $\langle \phi(t_I)\rangle\sim (\sqrt{8\pi^2} H_I M_{Pl}^n)^{1/(n+1)}$ during inflation, due to the tachyonic soft scalar mass $m_\phi^2\sim -8\pi^2 H_I^2$ induced by the U$(1)_A$ $D$-term. This makes it possible that the model is free from the axion domain wall problem, while satisfying the severe constraints on isocurvature density perturbations for the axion scale and relic abundance depicted in Fig.~\ref{fig:axion}. If one allows a fine-tuning of the classical axion misalignment angle $\theta_0$, then the axion scale in the range $10^9 \, {\rm GeV} < f_a(t_0) < 5\times 10^{13}$~GeV is cosmologically viable for a reasonable choice of the model parameters. On the other hand, for $\theta_0={\cal O}(1)$, the allowed range is reduced to $10^9 \, {\rm GeV} < f_a(t_0) < 10^{11}$~GeV, with the relic axions composing up to $0.1$--$10$~\% of the total dark matter energy density. On the other hand, if the dilaton-axion superfield for the GS mechanism is sequestered from the SUSY breaking by the inflaton sector, it is possible that the PQ symmetry is restored during inflation with $\langle\phi(t_I)\rangle =0$. Such scenario is obviously free from the isocurvature constraint, but is subject to the domain-wall constraint $N_{\rm DW}=1$. Furthermore, if one adopts the recent numerical simulation for the axion production by the annihilations of axionic stings and domain walls for the case of $N_{\rm DW}=1$, one finds that only a narrow range of the axion decay constant, $10^9 \, {\rm GeV} < f_a(t_0) < (\mbox{a few})\times 10^{10}$~GeV, is allowed. | 14 | 4 | 1404.3880 |
1404 | 1404.2004_arXiv.txt | In recent years, wide-field sky surveys providing deep multi-band imaging have presented a new path for indirectly characterizing the progenitor populations of core-collapse supernovae (SN): systematic light curve studies. We assemble a set of \NIIPtotalF\ $grizy$-band Type~IIP SN light~curves from {\PS}, obtained over a constant survey program of 4~years and classified using both spectroscopy and machine learning-based photometric techniques. We develop and apply a new Bayesian model for the full multi-band evolution of each light curve in the sample. We find no evidence of a sub-population of fast-declining explosions (historically referred to as ``Type~IIL'' SNe). However, we identify a highly significant relation between the plateau phase decay rate and peak luminosity among our SNe~IIP. These results argue in favor of a single parameter, likely determined by initial stellar mass, predominantly controlling the explosions of red supergiants. This relation could also be applied for supernova cosmology, offering a standardizable candle good to an intrinsic scatter of $\lesssim0.2$~mag. We compare each light curve to physical models from hydrodynamic simulations to estimate progenitor initial masses and other properties of the \PS\ Type~IIP SN sample. We show that correction of systematic discrepancies between modeled and observed SN~IIP light curve properties and an expanded grid of progenitor properties, are needed to enable robust progenitor inferences from multi-band light curve samples of this kind. This work will serve as a pathfinder for photometric studies of core-collapse SNe to be conducted through future wide field transient searches. \smallskip | \label{sec:intro} Core-collapse supernovae (SNe) mark the explosive deaths of massive stars. Several independent lines of evidence including explosion modeling \citep{Nadyozhin03,Maguire12,Jerkstrand13,Takats13}, progenitor star photometry \citep{Li07,Smartt09MNRAS,Walmswell12}, rate statistics \citep{Smith11}, and theory \citep{Heger03,Ekstrom12} combine to suggest a lower main sequence initial mass ($M_{in}$) limit for achieving core collapse of $M_{in}\gtrsim8-12~\rm{M}_\odot$. Red supergiant progenitor stars in this mass range are known to produce Type~IIP (hydrogen rich) SN explosions, the most common form of core-collapse SN. The upper mass limit for SNe~IIP progenitors is more uncertain, with stars of $M_{in}\gtrsim16-30~\rm{M}_\odot$ realizing significant mass loss depending on their mass, metallicity, rotation rate, binarity, and other properties; and even more massive stars ending their lives through more exotic explosion mechanisms. These mass limits for CC-SN progenitor stars have profound implications throughout stellar and galactic astrophysics and cosmology, including as an input to and constraint on models of stellar evolution for massive stars \citep{Groh13,Meynet13}, chemical evolution \citep{Timmes95,Nomoto06,Nomoto13}, supernova feedback in the interstellar medium and galaxy formation \citep{Leitherer92,Stilp13}, and astrobiological planetary sterilization rates \citep{Clark77,Lineweaver04}. The electromagnetic signatures of these core-collapse explosions are diverse, depending sensitively on the properties of both the core and the outer envelope of the progenitor star at the time of explosion. Supernovae with hydrogen features detected in their optical spectra are referred to as Type~II SNe, with a variety of subtypes defined by more specific spectroscopic and/or photometric criteria \citep[see e.g.][]{Filippenko97,Li11}. The most common subclass, Type~IIP, are typified by broad ($\sim10,000~\kms$) hydrogen Balmer P-Cygni spectroscopic features, fast rise times of a few days and optical light curves dominated by a long lived, $\sim100$~day ``plateau'' phase of roughly constant luminosity. The plateau phase is understood to arise from hydrogen recombination in the ejecta, with cooling temperature balancing the expansion of the blastwave to essentially equilibrate the $R$-band luminosity \citep[see e.g.][]{Kasen09}. The Type~IIL sub-class is historically designated based on spectroscopic properties similar to SNe~IIP, but faster, ``linearly'' declining optical light curves rather than a long lived plateau. Type IIb supernovae are classified spectroscopically based on the disappearance of H features and the prominence of He absorptions. Type~IIb light curves feature slow rise times and rapid decline rates (in each case, a few weeks) typical of Type~I (H deficient) SNe. The most extreme subclass, Type~IIn, are identified by intermediate width ($\sim10^3~\kms$) H emission features reflecting interaction of supernova ejecta with circumstellar material, and contributions from this interaction can power these explosions to reach extreme luminosities at peak. The optical evolution of Type~IIP SNe has been explored in light curve studies by a number of authors, including \cite{Patat94,Chieffi03,Hamuy03,Nadyozhin03,Bersten09,Li11,Arcavi12,Anderson14phot,Faran14}. The relationship between these observables and the properties of SN progenitor stars has been explored in theoretical parameter studies by \cite{Arnett80,Litvinova85,Young04,Kasen09,Dessart13}, and others. Combining a uniform analysis of a statistical population of Type~IIP supernova light curves with consistent physical models for inferring the properties of their stellar progenitors represents a path forward for characterizing the progenitor population. Here we describe an analysis of a statistical sample of SN~IIP light curve properties, performed using observations from the Panoramic Survey Telescope \& Rapid Response System 1 survey (\PS, abbreviated PS1). This represents the first such population analysis of SN~IIP light curves based on a homogeneously-collected and multi-band photometric sample from a wide field optical survey. In Section~\ref{sec:obs} we describe the PS1 optical observations and follow-up optical spectroscopy program used to construct the light curve sample. We have developed a novel Bayesian methodology for self-consistently modeling the full population of light curves in the sample and obtaining robust measurements of physically-meaningful light curve parameters (Section~\ref{sec:model}). We discuss the population wide distributions of these parameters and compare them to previous observational studies (Section~\ref{sec:res}). By comparison to theoretical light curve models, we recover estimates of the progenitor properties of the objects in our sample, and discuss the limitations of the available models in Section~\ref{sec:prog}. We summarize and conclude in Section~\ref{sec:conc}. In a companion paper, \cite{Sanders14Unsup}, we apply the PS1 SN~II data presented here as a test case for a hierarchical Bayesian light curve fitting methodology which enables simultaneous modeling of full populations of transient light curves. | \label{sec:conc} We have assembled and studied the full sample of Type~IIP SN light curves from the \PS\ Medium Deep Survey, totaling \NphotTot\ photometric data points (\NphotTotDet\ robust transient detections) in $grizy$ filters for \NIItotal\ individual SNe (\NIIPtotalF\ SNe~IIP). We have developed a Bayesian light curve fitting methodology for SNe~II based on a physically-motivated 5-component segmentation of the SN~IIP light curve (Section~\ref{ssec:mod}). We present an implementation of our SN~IIP model for use with the Hamiltonian Monte Carlo library \textit{Stan} in Appendix~\ref{ap:stan}. We have interpreted our light curve modeling in terms of the hydrodynamic Type~IIP SN progenitor model grid of \cite{Kasen09}. The primary conclusions of this work are as follows: \begin{itemize} \item We present photometric $K$-corrections and SN~IIP light curve templates in the $grizy$ bands (Sections~\ref{ssec:Kcor} and \ref{sec:res:stack}). Our templates are based on \stackNtemptotalALL\ individual photometric detections for \stackNacceptr\ individual SNe~IIP from $-15$ to $+114$ days from peak magnitude. \item Consistent with theoretical expectations, our SN~IIP sample spans a diverse range of light curve parameters: a factor of $\sim20$ in plateau phase decay rate (Figure~\ref{fig:betakde}), $\sim2$ orders of magnitude in ejected $^{56}$Ni (Figure~\ref{fig:MNidist}), a factor of $\sim2$ in plateau duration (Figure~\ref{fig:tpfdist}), and $\gtrsim4$~mag in absolute magnitude (Figure~\ref{fig:mpeakdist}). This evidence stands in contrast to recent suggestions by \cite{Arcavi12} and \cite{Poznanski13} that the SN~IIP plateau duration distribution, a critical observational parameter tied to progenitor initial mass, is tightly distributed (Section~\ref{sec:res:tp}). \item Addressing a longstanding debate in the literature, we have searched for the existence of a fast declining ``SN~IIL'' sub-population in the decline rate distribution of our SN~IIP sample (Section~\ref{sec:res:IIL}). We find no evidence for a discontinuity in this distribution for any photometric band, questioning the existence of a discrete SN~IIL sub-population. \item We identify a highly significant statistical correlation between the peak magnitude and plateau phase decline rate of SNe~IIP (Section~\ref{sec:res:pcor}). Together with the previous results, this supports the interpretation of core-collapse among hydrogen-rich red supergiants as a predominantly single parameter family of explosions, whose observational behavior is determined primarily by the explosion energy and likely set by the initial mass of the progenitor star. This represents an independent discovery and confirmation of results recently reported in \cite{Anderson14phot}. \item Through the largest systematic comparison to date of SN~IIP lightcurves to hydrodynamic progenitor models, we have derived mass, radius, and explosion energy estimates for the objects in our sample (Section~\ref{sec:prog:mass}). However, we find that the available theoretical model grids are insufficient to cover the full range of observed variation in SN~IIP light curve properties. We point to the need for additional hydrodynamic modeling to produce updated and expanded self-consistent model grids, particularly in the low luminosity regime. \item Though our progenitor inferences are based on hydrodynamic light curve models, which are known to produce systematically higher masses than direct progenitor detection searches, we do not find evidence for an absence of high-mass SN~IIP progenitors (Section~\ref{sec:prog:RSGprob}). We point to future direct progenitor detections of luminous SNe~IIP as having the potential to ease the discrepancy between the maximum SN~IIP progenitor mass identified by various theoretical and observational methods, known as the Red Supergiant Problem. \end{itemize} In a companion paper, \cite{Sanders14Unsup}, we discuss and demonstrate a hierarchical expansion of the model presented here to provide a general framework for the analysis of supernova light curve populations in the coming era of next generation wide field transient searches. We advocate continued investment in statistical and computational tools in the future as a means to compensate for the relative decline anticipated in the availability of detailed spectroscopic and other follow-up information on individual transients. | 14 | 4 | 1404.2004 |
1404 | 1404.2718_arXiv.txt | More than about twenty central stars of planetary nebulae (CSPN) have been observed spectropolarimetrically, yet no clear, unambiguous signal of the presence of a magnetic field in these objects has been found. We perform a statistical (Bayesian) analysis of all the available spectropolarimetric observations of CSPN to constrain the magnetic fields on these objects. Assuming that the stellar field is dipolar and that the dipole axis of the objects are oriented randomly (isotropically), we find that the dipole magnetic field strength is smaller than 400~G with 95\% probability using all available observations. The analysis introduced allows integration of future observations to further constrain the parameters of the distribution, and it is general, so that it can be easily applied to other classes of magnetic objects. We propose several ways to improve the upper limits found here. | The detection of magnetic fields in the CSPN has been a subject of considerable interest recently. The presence of magnetic fields on CSPN could shed some light on the magnetic field of planetary nebulae (PNe) themselves, and hence on the role of magnetic fields on the shaping of PNe \citep[][]{ChevalierLuo94, Tweedy+95, Guille99, Blackman+01a, Blackman+01, BalickFrank02, Soker04, Soker06, Vlemmings+06, Sabin+07}. Yet, magnetic fields on CSPN have proved elusive and so far, no clear, unambiguous spectropolarimetric detection of a magnetic field in a CSPN has been possible \citep{Leone+11, Bagnulo+12, Jordan+12}. Spectropolarimetry of CSPN is challenging because they are intrinsically faint and must be observed at relatively low spectral resolutions, which leads to cancellations attenuating the, already weak, polarimetric signals. Additionally, CSPN present a relatively low number of spectral lines, which hampers {\em line addition} techniques that exploit the collective contribution of hundreds (or even thousands) of spectral lines to increase the signal-to-noise ratio \citep{Semel96, Donati+97, Martinez+08}. Here we follow a different approach. We aim at constraining the magnetic field on CSPN statistically, combining the overall information of all available observations to constrain the magnetism of CSPN \citep[in a way similar, but more general, to the analysis of magnetic fields in RR Lyrae of][]{kolenberg_bagnulo09}. A common procedure would be combining the inferred values of the field strengths (obtained for example, from least-squares fitting) in a histogram. However, this is unsuitable because on the one hand, noise introduces large uncertainties and degeneracies in the determination of the field that are not properly propagated when carrying out a histogram; and on the other, the magnetic field is not a directly measurable quantity, it is {\em inferred} from observations. Consequently, a robust inference of the distribution of magnetic fields in CSPN is better done within the Bayesian formalism \citep[see][2011 for a similar approach]{Bovy+11}. In fact, we will follow a hierarchical Bayesian approach similar to that recently follower by \cite{Hogg+10} to estimate the distribution of eccentricities in the orbits of binary stars and exoplanets; but unlike them, here, we carry out the full hierarchical Bayesian analysis. | An important property of ${\cal L}_b$ is its ability to concentrate for large $N_\mathrm{obs}$. Consider, for example, an ensemble of objects with similar spectra that are observed with identical uncertainties $\sigma_V$ (hence, they have similar $C_1$); they only differ in their magnetic field strength (i.e., $\hat{B}_{\parallel i}$). Then, the maximum of ${\cal L}_b$ (or $\log{\cal L}_b$) in equation~(\ref{eq08}) will lie at \begin{equation} \begin{array}{ll} b_{\rm ML}=0 & \mbox{if } \langle \hat{B}^2\rangle < \frac{1}{2C_1} \\ b_{\rm ML}=\frac{\sqrt{2C_1 \langle \hat{B}^2\rangle}-1}{2C_1} & \mbox{if } \langle \hat{B}^2\rangle \geq \frac{1}{2C_1}, \end{array} \end{equation} where $\langle \hat{B}^2\rangle = \sum_i B_{\parallel_i}^2/N_\mathrm{obs}$. In the first case, the observations are inadequate (too noisy, and therefore, $C_1$ too large), for the estimated $\hat{B}_i$ to be informative. ${\cal L}_b$ is relatively flat near $b=0$ and when multiplied by the Jeffreys prior, the posterior clearly diverges towards smaller values, always reaching its maximum a-posteriori (MAP) value at the cut-off, $b_\mathrm{MAP}=b_{\rm min}$, which is not very helpful. An illustration of this situation is given by one of the dotted lines in figure~\ref{fig:posterior_b_newmeasurements}, which corresponds to an incomplete subset of just four observed objects from table~\ref{tab:table}. The two other dotted lines correspond to different subsets with the same number of objects. In those other cases, ${\cal L}_b$ has a maximum at some non-zero value $b_{\rm ML}$, which is noticeable also in the posterior $p(b|{D_i})$. But they are notably wider (spanning several hundreds of gauss) than the likelihood obtained from the full set of observed objects (gray solid line). In fact, it can be shown that for large values of $N_{\rm obj}$, the width of ${\cal L}_b$ converges to 0 as $N_{\rm obj}^{-1/2}$. Therefore, ${\cal L}_b$ becomes more and more informative on the value of $b$ as we accumulate observations ($N_\mathrm{obs}\rightarrow\infty$), even if the individual observations are too noisy to get a clear detection (cf. solid gray line in Figure~\ref{fig:posterior_b_newmeasurements}). In a sense, this is a generalization of {\em multiline addition techniques} in which the collective contribution of many individual spectral lines from an object is used to increase the signal-to-noise ratio of the polarization pattern \citep{Semel96, Donati+97, Martinez+08}. Here, the collective contribution of many different objects contribute to constrain the statistical distribution of fields. \begin{figure} \includegraphics[width=\columnwidth]{posterior_b_newmeasurements.pdf} \caption{Illustration of how adding two new objects with clear magnetic field detections of 200~G, 1000~G, or 1500~G, would lead to a rapid change of the posterior (blue lines). By contrast, if had observed just four objects out of the total sample, the posterior would be far less informative (dotted lines for three random realizations of four elements, superposed), than the complete sample to date (solid grey line).} \label{fig:posterior_b_newmeasurements} \end{figure} It is also interesting to see how a few {\em better} observations may affect the estimates. For example, consider that we observed two objects with well-defined $\hat{B}_\parallel$, but with a much better precision than up to now (say, $\sigma_V$ is a factor 100 better), i.e., in case we had a clear detection for some (perhaps, different) object. Figure~\ref{fig:posterior_b_newmeasurements} shows how $p(b|\{D_i\})$ change from the original (solid grey line) for three different values of $\hat{B}_\parallel$. Likewise, we also display in dotted grey line what happens if we only take into account 4 of the available observations. This demonstrates that, although there is not a single detection of magnetic fields, adding more objects produces a collapse of the posterior. We have introduced two major simplifications in the method which are not essential. The first one regards noise estimation. We have assumed that the variance of the observed quantities ($\sigma_V$ and $\sigma_{I'}$) was known for the derivation the likelihood functions (see Appendix), and that they are independent of wavelength. Their actual values have been independently estimated from the intensity fluctuations in the continuum windows between spectral lines. Estimating the unknown variance of a set of measurements is a fundamental problem in Bayesian theory which can be done independently (like here) or consistently within the Bayesian analysis itself by assigning (e.g., non-informative, Jeffreys) priors to $\sigma_V$ and $\sigma_{I'}$, and marginalizing these parameters. We have not pursued this more general approach here to keep our main argument simple. Secondly, the approximation in equation~(\ref{eq03}) has allowed the analytical derivation of equation~(\ref{eq08}). This approximation is accurate beyond the strict limits stated above. When the more general equation~(\ref{eq02}) is required, the integrals in equation~(\ref{eq08}) have to be performed numerically using Markov Chain Monte Carlo methods or alike, depending on the dimensionality of the problem. An important characteristic of the analysis presented is that it naturally allows integration of new data to improve the magnetic field estimates. We have already shown how things change when the data of \cite{Jordan+12} is added to the observations of \cite{Leone+14}. From the analysis of all the available observations so far we have obtained the upper-limit of 400 G. Our analysis here suggests several ways in which such estimates can be improved. As shown above, the mere addition of new observations helps constraining the magnetic field distribution, even when no clear detection in the individual objects is possible. The constraints on the global distribution can be even stronger when either the new observations have a better (lower) noise level, or if clear detection on individual objects is achieved. The analysis presented in this paper is not limited to any particular spectral range, provided that the weak-field approximation holds. Observations at different spectral windows can be straightforwardly included in the analysis after computing their corresponding $C_{1}$, $\hat{B}_\parallel$, and $\sigma_V$ values (although in some cases it might be advisable to consider the general expression for the likelihood (Eq.~(\ref{eq02})). Given that the amplitude of the Zeeman Stokes $V$ scales with $\lambda_0$ \citep[see, e.g.,][]{landi_landolfi04}, spectropolarimetry of the Paschen and Brackett series should be favoured. The joint analysis of linear and circular polarization would impose stronger constrains on the magnetic field distribution under the, very likely, assumption of isotropic distribution of fields for the observed objects. The Zeeman effect generates linear polarization patterns which are usually smaller than those of circular polarization and that are, in the weak-field approximation, proportional to the square of the transversal component $B_\perp^2$ of the magnetic field to the LOS \citep[e.g.,][]{Landi92, L4, Martinez+12}. However, we understand that the detection of linear polarization is extremely improbable, given that no reliable detection of circular polarization has been achieved so far. Additionally, magnetic alignment of dust grains creates linear polarization in the continuum from which we may infer the presence of a magnetic field \citep[e.g.,][]{DavisGreenstein51, Lazarian07}. The information thus obtained is not quantitative and cannot be directly included in our formalism. Yet, it may provide important general and symmetry constraints and bounds that could be implemented within the Bayesian methodology. Finally, it is clear that the approach presented here can be applied to other sets of objects (e.g., white dwarfs, \ldots) once they can be assumed to belong to the same magnetic class, i.e., they are all characterized by the same statistical distribution of fields. | 14 | 4 | 1404.2718 |
1404 | 1404.5624_arXiv.txt | Detailed studies of the stellar populations of intermediate-redshift galaxies can shed light onto the processes responsible for the growth of the massive galaxy population in the last 8 billion years. We here take a step toward this goal by means of deep, multi-object rest-frame optical spectroscopy, performed with IMACS on the Magellan telescope, of a sample of $\sim$70 galaxies in the E-CDFS with redshift $0.65\leq z\leq0.75$, apparent $R>22.7$ $\rm mag_{Vega}$ and stellar mass $>10^{10}M_\odot$. We measure velocity dispersion and stellar absorption features for individual sources. We interpret them by means of a large Monte Carlo library of star formation histories, following the Bayesian approach adopted for previous low redshift studies and derive constraints on the stellar mass, mean stellar age and stellar metallicity of these galaxies. We characterize for the first time the relations between stellar age and stellar mass and between stellar metallicity and stellar mass at $z\sim0.7$ for the galaxy population as a whole and for quiescent and star-forming galaxies separately. These relations of increasing age and metallicity with galaxy mass for the galaxy population as a whole have a similar shape as the $z\sim0.1$ analog derived for SDSS galaxies, but are shifted by $-0.28$~dex in age and by $-0.13$~dex in metallicity, at odds with simple passive evolution. Considering $z=0.7$ quiescent galaxies alone we find that no additional star formation and chemical enrichment are required for them to evolve into the present-day quiescent population. However, other observations require that the quiescent population grows from $z=0.7$ to the present-day. This could be supplied by the quenching of a fraction of $z=0.7$ $M_\star>10^{11}M_\odot$ star-forming galaxies with metallicities already comparable to those of quiescent galaxies, thus leading to the observed increase of the scatter in age without affecting the metallicity distribution. However rapid quenching of the entire population of massive star-forming galaxies at $z=0.7$ would be inconsistent with the age/metallicity--mass relations for the population as a whole and with the metallicity distribution of star-forming galaxies only, which are on average 0.12 dex less metal-rich than their local counterparts. This indicates chemical enrichment until the present in at least a fraction of the $z=0.7$ star-forming galaxies in our sample. | \label{sec:intro} Multi-wavelength and spectroscopic surveys at high redshift have revealed significant evolution from $z\sim1-2$ down to the present-day in the massive galaxy population. In particular, the star formation rate (SFR) density of the Universe, dominated at all epochs by blue galaxies with stellar mass in the range $10^{10}-10^{11}M_\odot$ \citep{Panter07,xzz07}, has declined by a factor of $\sim10$ in the last 8 billion years in a way that is almost independent of galaxy mass \citep[e.g.][]{Hopkins06,smolcic09,karim11,cucciati12}. This is accompanied by the evolution of the galaxy stellar mass function indicating that $\sim50$\% of the current stellar mass density was already in place by $z\sim1$ \citep[e.g.][]{muzzin13}. The massive galaxy population may keep on evolving in number density at $z<1$, albeit at a slower rate than lower-mass galaxies \citep{moustakas13}. Several studies have shown that the growth of the population as a whole hides a different evolution of the quiescent and star-forming galaxy populations. The number density of massive quiescent galaxies grows by $\sim0.2-0.5$~dex since $z\sim1$, while that of star-forming galaxies remains constant or even declines \citep{muzzin13,moustakas13,Ilbert13,Ilbert10,Brammer11,bell07,faber07,borch06,cimatti06}. The massive end of the stellar mass function becomes increasingly dominated by quiescent galaxies at lower redshifts \citep{muzzin13,pozzetti10,bell07,bundy06}. By the present day, quiescent galaxies contain more than half of the mass and metals in stars \citep{bell03,Baldry04,Gallazzi08} and dominate at stellar masses above $3\times10^{10}M_\odot$. The physical properties of galaxy stellar populations, such as mean age and metallicity, give us insight into their past history of star formation. In the local Universe the light-weighted ages and metallicities (stellar and gaseous) of both star-forming and quiescent galaxies have been shown to correlate to first order with galaxy mass \citep[e.g.][]{gallazzi05,panter08,Tremonti04,mateus06}, with environment playing a stronger role in less massive galaxies \citep[e.g.][]{bernardi09,Thomas10,pasquali10,pasquali12,Cooper08,Cooper10}. In particular quiescent, elliptical galaxies follow tight relations, such as the color-magnitude relation and the relation between absorption index strengths and velocity dispersion, originating from the increase of their light-weighted age, stellar metallicity and element abundance ratio with galaxy mass \citep[e.g.][]{trager2000,kuntschner01,Thomas05,nelan05,gallazzi06,graves09a}. This indicates that the stars in present-day more massive ellipticals have reached a higher degree of chemical enrichment and have formed earlier and on shorter timescales than less massive galaxies. The small intrinsic scatter in these observational relations is primarily driven by variation in light-weighted age and, to a smaller extent, stellar metallicity \citep[e.g.][]{gallazzi06,graves09b}. Tracing the evolution with redshift of galaxy stellar population properties in relation to galaxy mass and star formation activity puts additional constraints to the mechanisms leading to the suppression of star formation and the ensuing build-up of the present-day quiescent massive galaxy population. The chemical properties of the gas in massive star-forming galaxies have been traced up to $z\sim3$ through emission line analysis \citep[][]{Erb06,cowie08,Lamareille09,Mannucci10,moustakas11}. These studies have indicated a significant evolution in gas-phase metallicity with redshift, which is however tied to the evolution in SFR such that star-forming galaxies appear to follow a non-evolving relation between their mass, gas-phase metallicity and SFR \citep{Mannucci10,LaraLopez10}. On the contrary, stellar population studies are observationally more challenging as they require deep spectroscopy in order to trace the stellar continuum and the strength of key absorption features chiefly sensitive to age and metallicity. Few works have pushed metallicity analysis to $z\sim2$ based on rest-frame UV absorption features, which trace the {\it youngest} stellar populations \citep{Rix04,Halliday08,Sommariva12}. Studies of the evolution of the {\it bulk} of stellar populations in galaxies, which require rest-frame optical diagnostics \citep[e.g.][]{worthey94,wo97}, are so far limited to relatively few deep spectroscopic works at intermediate redshifts. These studies target red-sequence, quiescent galaxies with weak or no emission lines, and the majority analyze cluster galaxies at $z\lesssim 1$ \citep{Jorgensen05,Kelson06,SB09,Jorgensen13}, with only few works addressing the field population \citep{Schiavon06,fritz09,ziegler05,ferreras09}. Purely passive evolution of the quiescent galaxy population has been put into question in the work of \cite{Schiavon06} who analyze the co-added spectra of red-sequence field galaxies at $z=0.8-1$ from the DEEP2 survey \citep{davis03}. From comparison with SDSS stacked red-sequence galaxy spectra from \cite{eisenstein03} they find that the evolution in the $H\delta$~absorption index is slower than predicted by passive evolution of a Simple Stellar Population (SSP). The observed evolution could instead be described by a series of continuous star formation models that get quenched at successive epochs \citep{harker06}. Such evolution is consistent with the modest evolution in the scatter of the color-magnitude relation of quiescent galaxies from $z\sim1$ to the present-day \citep{ruhland09}. \cite{SB09} analyze cluster and group red-sequence galaxies at $z=0.45-0.75$ in the EDisCS survey \citep{Ediscs} by means of their co-added spectra in three bins of redshift and two bins of velocity dispersion. They find that the most massive galaxies ($\rm \sigma_V>175$km/s) are consistent with high formation redshifts and subsequent passive evolution, while lower-mass galaxies require an extended star formation at low level without inducing metal enrichment. They argue that the observed evolution in index--velocity dispersion relations is consistent with a scenario in which 40\% of $\sigma_V<175$km/s galaxies enter the red-sequence between $z=0.75$ and $z=0.45$. Comparison between field and cluster studies suggests that the mass scale at which simple passive evolution does not apply is different in different environments, being lower in clusters. These studies however, based on co-added galaxy spectra, cannot distinguish between an ongoing (low-level) star formation in galaxies that are on the red sequence already at high/intermediate redshift and the continuous addition at lower redshifts of quenched blue galaxies. \cite{Jorgensen13} recently published a very thorough analysis, with good spectral quality for individual galaxies for a total sample of $\sim130$~cluster early-type galaxies at intermediate redshifts (in particular they study three clusters at $z=0.54, 0.83, 0.89$). The evolution of the Fundamental Plane is consistent with passive evolution after a mass-dependent formation redshift. However such formation redshifts are rather low ($z_{form}=1.95$ for $\rm \sigma_V=225km/s$) and inconsistent with the absorption index strengths. Moreover the metallicity and the element abundance ratio of at least two of the studied clusters differ from that of other clusters both at intermediate and low redshift, implying chemical enrichment in cluster galaxies and cluster-to-cluster variations. In this work we aim at quantifying the evolution of the stellar populations of massive galaxies at $z\lesssim1$ in relation to global galaxy properties such as stellar mass and star formation activity. As an added value over previous works we do not target only quiescent, early-type galaxies but instead we consider galaxies more massive than $3\times10^{10}M_\odot$ without any pre-selection on their star formation activity. The goal is to compare the stellar population properties of the massive galaxy population as a whole and of quiescent galaxies alone to those of the corresponding present-day populations, and explore whether the intermediate-redshift star-forming galaxies can supply the necessary population for the observed evolution. By targeting a more representative {\it field} galaxy population this work is also complementary to most previous studies focused on cluster or group galaxies toward a more comprehensive view of galaxy evolution as a function of environment. We select a sample of bright galaxies from the \combo~survey \citep{wolf03,wolf04} with stellar mass $>10^{10}M_\odot$ and redshift $0.65<z<0.75$. We observe a final sample of 77 galaxies with the Inamori Magellan Areal Camera and Spectrograph (IMACS) on the 6.5 m Magellan telescope at the Las Campanas Observatory gathering multi-object deep medium-resolution spectroscopy covering the rest-frame optical range from the 4000\AA-break up to the red Mg and Fe absorption features. In order to resolve the dispersion in galaxy properties and gain insight into {\it individual} galaxy evolution (as opposed to evolution of the {\it overall population} through the addition of quenched galaxies), we work with individual galaxies rather than co-added spectra. This sample is directly compared with local samples of massive galaxies, extracted from the SDSS with comparable spectral quality. We perform a consistent analysis of the $z=0.7$ galaxies and of the SDSS samples thus minimizing systematic uncertainties in the inferred evolution due to different diagnostics and analysis techniques. Specifically, we analyze an optimally-selected set of stellar absorption features with distinct sensitivity to age and metallicity. Building on our work on SDSS \citep{gallazzi05}, these are interpreted with a large Monte Carlo library of star formation histories (SFH) applied to the \cite{bc03} simple stellar population (SSP) models and adopting a Bayesian statistical approach in order to derive full probability density functions of stellar mass, light-weighted mean age and stellar metallicity. The sample selection is described in Sec.~\ref{sec:data}, along with the spectroscopic observations and the extraction of redshift, velocity dispersion, emission and absorption lines. The method to interpret absorption features in terms of physical properties of the galaxy stellar populations, already developed and applied to SDSS data, is outlined in Sec.~\ref{sec:physparam_method} and the resulting mass, age and metallicity estimates are described in Sec.~\ref{sec:physparam_result}. Stellar ages and metallicities are related to galaxy stellar mass and compared to the corresponding scaling relations for $z=0.1$ SDSS galaxies in Sec.~\ref{sec:results} for the entire population. In Sec.~\ref{sec:relations_ssfr} we characterize the sample in terms of the galaxy star formation activity and discuss how this affects the location of galaxies in the stellar population relations and their evolution to $z=0.1$. We discuss our findings in Sec.~\ref{sec:discussion} and summarize them in Sec.~\ref{sec:conclusion}. Throughout the paper we adopt a $\Lambda$CDM cosmology with $\rm \Omega_m=0.3$, $\rm \Omega_\Lambda=0.7$ and $\rm H_0=70~km~s^{-1}~Mpc^{-1}$, and we assume a \cite{chabrier03} IMF. | \label{sec:conclusion} We have gathered medium-resolution, rest-frame optical spectroscopic data with IMACS on Magellan for a magnitude- and mass-selected sample of $\sim70$ galaxies at $z\sim0.7$. The quality of the data allows reliable measurements of stellar velocity dispersion and of both age- and metallicity-sensitive absorption features in about 85\% of the sample (for the remaining fraction only age-sensitive absorption features and more uncertain velocity dispersion measures are available). We apply a Bayesian statistical approach, originally developed for the analysis of low-redshift SDSS galaxies, to interpret the strength of a set of absorption features in terms of stellar metallicity, light-weighted age and stellar mass by means of comparison with a comprehensive library of SFHs and metallicities, based on the \cite{bc03} SPS models. We adopt the same prior distribution of models as used for SDSS spectra in order to minimize the impact of systematic effects on the inferred evolution between $z=0.7$ and $z=0$. Stellar masses and light-weighted ages are constrained to better than 0.2~dex and to 0.11~dex and 0.13~dex on average respectively, while the average uncertainty on stellar metallicity is 0.3~dex for galaxies with at least one of \mgtwofe~and \mgfep~(86\% of the sample). Our $z=0.7$ sample, which includes both quiescent and star-forming galaxies, span a range in stellar mass from about $3\times10^{10}$ to $5\times10^{11}M_\odot$ corresponding to the massive end of the SDSS distribution, a range in light-weighted age from 600~Myr to 6~Gyr and a range in metallicity similar to the SDSS distribution from about 20\% solar to $2\times Z_\odot$. We explore the distribution of $z=0.7$ massive galaxies in stellar metallicity and light-weighted age as a function of stellar mass. We find that the population as a whole follows stellar metallicity--stellar mass and stellar age--stellar mass relations qualitatively similar to the local relations with both age and metallicity increasing with mass and showing a flattening of the trend above $10^{11}M_\odot$. The parameters describing the {\it shape} of the relations are consistent within the uncertainties with those fitted to low-redshift galaxies, with only a tentative evidence for an increase by 0.3~dex in the characteristic mass (where the relation starts to flatten) of the age--mass relation with respect to the local value. The zero-point and the shape of the $z=0.7$ relations are however inconsistent with pure passive evolution of the population as a whole: {\it i)} the age--mass relation at $z=0.7$ is shifted by only $-0.28$~dex ($\sim4$Gyr, i.e. less than the time elapsed between $z=0.7$ and $z=0.1$) from the local relation and is too shallow with respect to the passively-evolved $z=0.1$ relation, implying a mass-dependent evolution in age that is slower than a purely passive evolution; {\it ii)} the median metallicity at $10^{11.5}M_\odot$ is lower by 0.13~dex than in the local sample. These results indicate that at least a fraction of $z=0.7$ massive ($>3\times10^{10}M_\odot$) galaxies have to experience some level of star formation and increase their stellar metallicity in the last 5~Gyr. We considered more complex scenarios than pure passive evolution by adopting the average SFHs for four different stellar masses estimated by \cite{behroozi13} including galaxies with any star formation activity. The mass-dependent relative age offset in the mass--age relation that arises from these SFHs in the time lapse between $z=0.7$ and $z=0.1$ is consistent with the observed one. However we note that these SFHs result in a systematic absolute age offset between the predicted and observed light-weighted ages at both redshifts. By differentiating galaxies on the basis of their star formation activity we show that the location of $z=0.7$ galaxies in the age/metallicity versus mass plane depends on the galaxy specific SFR. Quiescent galaxies are preferentially located at higher masses, with 72\% of them having a mass larger than $10^{11}M_\odot$, light-weighted ages typically between $\sim3$Gyr and $\sim6$Gyr, and stellar metallicities around solar. Star-forming galaxies have a more uniform distribution in stellar mass, from $\sim10^{10}$ to $3\times10^{11}M_\odot$, they are located on average at younger ages by 2.2~Gyr and lower stellar metallicities by 0.15~dex than quiescent galaxies, with a larger dispersion in both parameters. Quiescent galaxies at $z=0.7$ have metallicities consistent with those of local quiescent galaxies, thus not requiring an additional metal enrichment toward $z=0$ in accord with what expected from passive evolution. They are on average $\sim3$Gyr younger than the present-day population of $M_\star>10^{10}M_\odot$ galaxies. Their passively evolved ages are also consistent with the {\it range} of ages of present-day quiescent galaxies. However, our analysis also shows that, if evolved passively, $z=0.7$ quiescent galaxies would evolve in a present-day population with smaller scatter and higher average age than observed in massive present-day galaxies, contributing only to the oldest portion of the present-day populations. There is thus the need of an additional evolutionary path in order to populate the younger portion of present-day quiescent galaxies without significantly altering the metallicity distribution. Studies of the redshift evolution of the number and mass density of quiescent and star-forming galaxies show that the population of star-forming galaxies has remained constant or has even declined since $z<1$ until the present \citep{moustakas13,Brammer11,Ilbert10,Ilbert13} with the largest decrease affecting the more actively star-forming galaxies \citep{Ilbert10}. Suppression of star formation thus contributes to the build-up of the massive quiescent galaxy population. Newly-quenched, larger galaxies can also in part explain the redshift evolution of the zero-point of the mass-size relation of quiescent galaxies \citep[e.g.][]{vdW09,carollo13,krogager13,poggianti13}. We show that massive star-forming galaxies at $z=0.7$ are on average $\sim5$Gyr younger than local quiescent galaxies, i.e. close to the expected offset in the hypothesis of passive evolution. The most metal-rich $z=0.7$ star-forming galaxies, which have metallicities comparable to local quiescent galaxies, have the right physical parameter values to supply the necessary population for the build-up of the red-sequence at masses $>10^{11}M_\odot$. These comprise about 40\% of the star-forming galaxies in our sample at these masses. However, passive evolution of the {\it whole} population of massive star-forming galaxies is ruled out by the age/metallicity--mass relation for the population as a whole and by the metallicity distribution of star-forming galaxies only. Indeed $z=0.7$ star-forming galaxies are offset by $-0.12\pm0.05$ dex with respect to equally massive local star-forming galaxies, and show a tail of galaxies metal-poorer than the lower percentile of the local distribution. This suggests that even at masses $>10^{11}M_\odot$ a sizable fraction of galaxies at $z=0.7$ must experience chemical enrichment since then. This work shows that the combined analysis of the stellar populations in both quiescent and star-forming galaxies at intermediate redshifts provides important constraints to the evolution of the massive galaxy population, complementary to those obtained from the evolution of the mass and number density of galaxy populations. Multi-object spectrographs in the red-optical and near-IR on current large telescopes, such as M2FS on Magellan, GMOS on Gemini, KMOS on VLT, MOSFIRE on Keck, and next generation telescopes, such as E-ELT and TMT, will allow to compile more statistically significant and complete galaxy samples, extend to lower stellar masses and to redshift $z\sim2$. These will be crucial to build a complete and coherent picture of the evolution of galaxy populations. \\ | 14 | 4 | 1404.5624 |
1404 | 1404.0976_arXiv.txt | Parsec-scale VLBA images of BL Lac at 15 GHz show that the jet contains a permanent quasi-stationary emission feature 0.26 mas (0.34 pc projected) from the core, along with numerous moving features. In projection, the tracks of the moving features cluster around an axis at position angle -166.6\deg~ that connects the core with the standing feature. The moving features appear to emanate from the standing feature in a manner strikingly similar to the results of numerical 2-D relativistic magneto-hydrodynamic (RMHD) simulations in which moving shocks are generated at a recollimation shock. Because of this, and the close analogy to the jet feature HST-1 in M\,87, we identify the standing feature in BL Lac as a recollimation shock. We assume that the magnetic field dominates the dynamics in the jet, and that the field is predominantly toroidal. From this we suggest that the moving features are compressions established by slow and fast mode magneto-acoustic MHD waves. We illustrate the situation with a simple model in which the slowest moving feature is a slow-mode wave, and the fastest feature is a fast-mode wave. In the model the beam has Lorentz factor $\rm \Gamma_{beam}^{gal}\approx 3.5$ in the frame of the host galaxy, and the fast mode wave has Lorentz factor $\rm \Gamma_{Fwave}^{beam}\approx 1.6$ in the frame of the beam. This gives a maximum apparent speed for the moving features, $\rm \beta_{app}=v_{app}/c= 10$. In this model the Lorentz factor of the pattern in the galaxy frame is approximately 3 times larger than that of the beam itself. | \label{sec:intro} BL Lacertae objects are a class of active galactic nucleus (AGN) that contain a relativistic narrow outflow (a jet) aimed close to the line-of-sight (LOS). This produces the characteristic features seen at radio wavelengths: high brightness temperature, rapid variability, and high polarization. Many of the BL Lacs are gamma-ray emitters. In high resolution radio images, some show a sharply bent or kinked jet that changes on time scales as short as a year or less. In some cases bright features, or components, in the jet move downstream at nearly the speed of light, $c$, giving them a proper motion $\mu$ with an apparent speed $\beta_{app} > 1$ (in units of $c$) in the coordinate frame of the galaxy. It is these rapid changes in the jet of the eponymous BL Lacertae itself that we investigate in this series of papers. In the current paper we consider the kinematics of the components, and suggest that the quasi-stationary component is a recollimation shock (RCS), that the moving components emanate from the RCS, and that the moving components are magneto-acoustic waves. In the next paper (Paper II, in prep.) we show that the jet supports transverse waves as well, and suggest that they are Alfv\'en waves. We need to distinguish between the pattern speed of a component and the speed of the beam itself; i.e., the bulk speed of the plasma. It is the latter that, through its Doppler factor, provides a relativistic boost to the flux density, and it is the former that gives the apparent motion. These speeds do not have to be the same, but it often is assumed that they are (e.g. Lister et al. 2009). In \S\ref{move_comp_mhd} we suggest that in BL Lac the moving components correspond to MHD waves traveling longitudinally in a helical magnetic field, and thus that the pattern and beam speeds are not the same. We will need a value for $\theta$, the angle between the jet axis and the LOS, and to choose one we have investigated values based on statistics, and others based on observations of BL Lac as interpreted with synchrotron-emitting models of the core. The first statistical method is based on the maximum observed apparent speed, $\beta_{app}=10.0$ (\citealt*{Lis13}, hereafter \citetalias{Lis13}), which gives an upper limit $\theta < 11.4\deg$. However, a source selected on the basis of its beamed emission is highly unlikely to have $\theta$ near its extreme upper limit, because the flux density is strongly deboosted there. Roughly half of the sources in a beamed flux density-limited sample will have $\rm\Gamma \sim \beta_{app}$ and $\theta \sim 1/\Gamma$, while the most probable value of $\theta$ is $\sim 1/2\Gamma$ \citep{LM97, Coh07}. Also, Pushkarev et al. (2009, 2012) showed that the probability density function for $\theta$ for a subset of MOJAVE sources that were detected with the Fermi LAT has a peak near $2\deg$ and a median of $3\deg$. BL Lac is in this group of gamma-ray emitters. These studies suggest that $\theta$ is probably on the order of $3\deg$. On the other hand, \citet{Hov09} have derived a value of $\theta=7.3\deg$ for BL Lac from the variability Doppler factor technique, and \cite{J05} (hereafter \citetalias{J05}) have derived $\theta=7.7\deg \pm 1.9\deg$ using a light-travel time argument. These are remarkably close. Thus measurements and synchrotron theory give $\theta \sim 7.5\deg$, while probability arguments suggest $\theta \sim 3\deg$. Further observations that affect $\theta$ are of the position angle (PA) of the jet, which for BL Lac is variable and changes by up to $20\deg$ on time scales of 5 years (\citetalias{J05}, \citetalias{Lis13}). When this is deprojected it means that $\theta$ itself changes by a few degrees. \citet{CAM13} have studied these changes with a precession model, and find that $\theta$ changes by about $\rm 4\deg~to~5\deg$, apparently without crossing the LOS. In this paper, when necessary, we will assume $\theta \approx 6\deg$, and that the foreshortening is a factor of 10. High-resolution observations at millimeter wavelengths show that, on a scale of 0.2 mas, the PA of the inner jet of BL Lac is variable \citepalias{J05}. These PA variations led to a suggestion by \citet[hereafter S03]{Sti03} that the PA swings periodically, with a period of $2.3 \pm 0.3$ years. This time scale was verified by \citet{MD05} (hereafter MD05) who also said that the period was not unique, and that a period of 13.1 years would fit as well. The \citet{CAM13} study yielded a precession period of 12.1 yr. In this paper we will show that on time scales of 1-12 years the PA is variable but not periodic. The PA variations form an important part of our story, as they appear to be connected to the excitation of waves on the ridge line (Paper II). Observational studies \citep{GPC00, LH05} have shown that the jets of BL Lac sources can be highly polarized, and that they have a bimodal distribution of electric vector position angle (EVPA) relative to the jet axis. In most cases the EVPA is longitudinal; i.e. roughly parallel to the axis, but in a small fraction of the cases it is transverse. Longitudinal EVPA is often interpreted as arising from an optically thin jet with a predominantly transverse magnetic field; although \citet{LPG05} have emphasized that this is not necessarily the case. For a relativistic beam the ray path in the beam frame is perpendicular to the axis when $\theta=\theta_{crit}\equiv\sin^{-1}(1/\Gamma)$ and in this case, when the field is helical with a high pitch angle and the jet is unresolved, the EVPA is longitudinal. However, the EVPA will vary as $\theta$ moves away from $\theta_{crit}$. Transverse EVPA will be seen only for small $\theta$ \citep{LPG05}. If the jet is resolved, then for a helical field there should be a transverse gradient of rotation measure (RM) \citep{Bla93}. \citet{GMC04} tested this by measuring the RM in four BL Lacs, and they found indications of transverse gradients as expected for a helical magnetic field. However, this result is controversial as \citet{TZ10}, using stricter criteria, did not detect a gradient of RM in four objects, including two of those studied by \citet{GMC04}. This has been further studied by \citet{Hov12} with extensive simulations of noise and other errors. They find a significant transverse gradient in four sources, of which two, 3C 273 \citep{Asa02, ZT05} and 3C 454.3 \citep{Zam13}, have the signature expected for a helical field. The evidence for a helical magnetic field in BL Lac comes from the high polarization and from the longitudinal EVPA. \citet{OG09a} have shown that its EVPA, corrected for rotation measure, remains longitudinal around a bend, and that at 7.9 GHz the polarization rises above $30\%$. Since the maximum polarization that can be attained by synchrotron radiation is 71\% in a uniform magnetic field, then in BL Lac the field must be well-ordered, at least in those parts of the jet where the polarization is high. From these studies, and because we can reasonably infer the existence of a helical field in 3C\,273 and 3C\,454.3, we assume that in the jet frame of BL Lac the magnetic field basically has a helical shape, and that the pitch angle is not small. The plan of this paper is as follows. In \S\ref{sec:obs} we discuss the various bright features (components) in the jet (core, quasi-stationary, moving) that are tracked by the MOJAVE program. In \S\ref{sec:cpt7} we consider the quasi-stationary component near the core and why it is likely that it is a recollimation shock. In \ref{sec:other_AGN} we extend this discussion to several other sources. In \S\ref{move_comp_mhd} we discuss the physical nature of the moving components in terms of fast and slow magneto-acoustic waves. \S\ref{sec:discussion} contains a discussion of our results, and conclusions are in \S\ref{sec:conclusions}. BL Lac is nearby for a blazar ($z=0.0686$) and our linear resolution is high (1 mas corresponds to 1.29 pc in the galaxy). This provides a great advantage to our study. The second great advantage we have is that BL Lac varies rapidly, and phenomena including PA variation and wave motion can be captured in a few years. | \label{sec:conclusions} The set of 110 images of BL Lac, observed with the VLBA at 15 GHz between 1999.2 and 2013.0, provides a remarkable view of the jet of this exceptional AGN. The jet has a strong quasi-stationary component (C7) at $r\approx 0.26$ mas from the core. Fast superluminal components appear to emanate from C7, in a manner strikingly similar to the ejection of fast shocks from the RCS that is seen in 2D RMHD numerical simulations of jets that have a dominant, helical magnetic field. Furthermore, C7 is analogous to the component HST-1 in M\,87, which has been called an RCS. We therefore identify C7 as an RCS in the BL Lac jet. A simple model is employed, one that uses the observed slowest and fastest moving components, with the assumption that they are manifestations of slow and fast magneto-acoustic waves propagating downstream on the relativistic beam. The model assumes that $\theta=6\deg$ and that the beam speed is constant. The result of fitting the model to the data is that the Lorentz factor for the beam is $\rm \Gamma_{beam}^{gal}\approx 3.5$, and that the fast magneto-acoustic wave has a speed relative to the beam of $\rm \beta_{Fwave}^{beam}\approx 0.79$. This is mildly relativistic, with $\rm \Gamma_{Fwave}^{beam}\approx 1.6$. These give the observed pattern speed $\rm \beta_{app} = 10$. In the model, the Lorentz factor of the observed pattern is approximately 3 times larger than the Lorentz factor of the beam. This difference is in the correct sense to help alleviate difficulties in the BL Lac -- FR\,I unification; but it is in the wrong sense to reduce the difficulties seen in explaining very high brightness temperatures. | 14 | 4 | 1404.0976 |
1404 | 1404.0692_arXiv.txt | We study the dependence of the electromagnetic luminosity---produced by interactions of force-free magnetospheres---on dipole inclinations in binary neutron star systems. We show that this interaction extracts kinetic energy from the system and powers a Poynting flux with a strong dependence on the dipole orientations. This dependence can be linked to the reconnection and redistribution of magnetic field as the stars interact. Although the details of the Poynting luminosity are very much dependent on the orientation, all the cases considered here nevertheless radiate a large Poynting flux. This robust emission suggests that the pre-merger stage of binary neutron star systems can yield interesting electromagnetic counterparts to gravitational wave events. | Binary neutron stars are one of the primary sources of detectable gravitational radiation expected in the next generation of gravitational wave interferometers LIGO/VIRGO/KAGRA~\cite{Abbott:2007kv,2011CQGra..28k4002A,Somiya:2011np}. Moreover, these systems are also among the strongest candidates for observable neutrino production and energetic electromagnetic output in stellar mass systems, and thus they represent exciting possibilities for upcoming multimessenger astronomy (e.g.~\cite{Andersson:2013mrx,Kelley:2012tc,Metzger:2011bv}). Through the combined efforts of the numerical relativity and astrophysics communities, considerable knowledge has been gained about the expected characteristics of the gravitational waves produced in binary neutron star mergers. Bearing in mind that a thorough exploration of the physical parameter space is still not at hand, several issues have been largely addressed. For instance, much work has studied the dependence of gravitational waves on total mass, mass ratio, and, to some extent, the equation of state (see e.g.~\cite{Shibata:2005ss,Shibata:2003ga,2008PhRvD..78h4033B,Read:2009yp}). Recently, simulations within full general relativity have also begun providing important clues into the dependence on neutron star magnetization~\cite{2008PhRvL.100s1101A,Liu:2008xy,2011PhRvD..83d4014G,2013PhRvL.111f1105P,Lehner:2011aa,2013PhRvD..88d3011P} and cooling~\cite{Sekiguchi:2011zd,Sekiguchi:2011mc,2014arXiv1403.3680N}. In addition to the dynamics and gravitational wave production, the exploration of possible electromagnetic counterparts that complement gravitational wave observations is particularly intriguing. Recently we demonstrated that the interaction between the magnetospheres of each neutron star in a binary can radiate considerable electromagnetic energy~\cite{2013PhRvL.111f1105P,2013PhRvD..88d3011P}. This work used a novel resistive Magneto-HydroDynamics (MHD) approach to describe the magnetic field within the disparate regimes inside and outside each star. Within the star, the approach adopted the ideal MHD limit while the force-free approximation described the magnetospheres. This work started with each star having an initial dipole field either aligned or anti-aligned with the orbital angular momentum and found a powerful Poynting luminosity produced as the stars orbited. Such a large luminosity provides the tantalizing possibility of powering electromagnetic counterparts to gravitational waves from the system. The Poynting flux for equally magnetized stars with either aligned or anti-aligned dipole moments was found to be collimated along the polar region. In contrast, when one star was unmagnetized or barely magnetized with respect to the other, the Poynting flux was mainly directed around the equatorial region. Naturally, generic systems are not expected to have such a preferred alignment of dipole magnetic moments, and thus the study of different scenarios is important. We address this question here by considering misaligned dipoles in binary neutron star mergers. According to the standard formation channel, a binary neutron star system is formed from a primordial binary through a sequence of complex processes \cite{lrr-2012-8,Lorimer:2008se,Kalogera:2006uj,1991PhR...203....1B}. The first of these processes is a supernova explosion of the more massive star once it evolves off the main sequence and through its giant phase. The remnant of such an explosion becomes the first NS of the binary, generally more massive than the second NS and with a potential recoil. Subsequently, the secondary star then evolves off the main sequence and, ultimately, explodes as a supernova becoming the second NS. The discovery of strongly relativistic, binary pulsars provides strong support for the formation channel described above. Any kicks provided by the supernovae are important not only in determining whether the binary survives, but also in determining the properties of the resulting binary. In particular, kicks can tilt the orbital plane of the binary and misalign the individual spins of the NSs \cite{Kalogera:1999tq}. Furthermore, it has been empirically argued~\cite{2008MNRAS.387.1755W,2010MNRAS.402.1317Y} that the angle between the magnetic and spin axes of NSs may not be random but instead correlated to each other. The orientations of the magnetic moments in generic binaries are therefore plausibly arbitrary. In this work, we consider different orientations of the stellar magnetic dipoles and compute the resulting Poynting flux characteristics as the stars coalesce\footnote{Tilted magnetic fields have also been considered in black hole-neutron star binaries to asses their role in inducing toroidal magnetic configurations in the resulting accretion disk~\cite{Etienne:2012te}.}. In addition to a strong flux of electromagnetic energy produced due to magnetosphere interactions, our results indicate that one can bracket the expected luminosities from general configurations. Our simulations focus primarily on the last orbits before the merger in which the dynamics are most rapid and violent and simplified analytic models are not applicable. Additional insight comes from modeling the behavior of a magnetized star moving within the field of a distant star, modeled here as a constant external field. While such an approach is only valid when the stars are well separated, it serves to generalize well-known results with the unipolar inductor. This work is organized as follows, in Sec.~\ref{section:model} we present theoretical arguments and estimates for the possible electromagnetic luminosity induced by the system. Sec.~\ref{section:methods} summarizes briefly the evolution equations describing the magnetized neutron stars, as well as our numerical setup. Our results are presented in Sec.~\ref{section:results}, followed by conclusions in Sec.~\ref{section:discussion}. | \label{section:discussion} We study the interaction of magnetospheres in binary systems in two different magnetization regimes. The first corresponds to a strongly magnetized primary with a weakly magnetized companion at large separations. We extend the analytic estimates for binaries with a single magnetized star, obtained with the unipolar induction model~\cite{2001MNRAS.322..695H,Piro:2012rq,Lai:2012qe}, to cases where both stars are magnetized. We confirm the validity of this extension by studying a magnetized star boosted with respect to an external magnetic field. This scenario is a reasonable approximation to the dynamics of these binaries at large separations. In the second regime, we explore magnetosphere interactions in the final orbits prior to merger. We employ numerical simulations, solving the general relativistic resistive magnetohydrodynamics equations to capture the complex dynamics of the binary and its magnetosphere. By comparing our results with previous work~\cite{2013PhRvL.111f1105P,2013PhRvD..88d3011P}, we show that magnetospheric interaction extracts kinetic energy from the system and powers a strong Poynting flux for different orientations of the stellar magnetic dipoles. Indeed, the electromagnetic luminosity for all configurations is sizable, giving strong hope for the observation of electromagnetic counterparts to gravitational wave events sourced during the late orbiting stages. In particular, our results show that during these stages, the luminosities present an approximately cyclic temporal oscillation tied to the magnetic field and orbital dynamics. The luminosities for these misaligned configurations (and possibly for generic ones as these represent rather contrasting configurations) are roughly within the range defined by the previously studied aligned $U/u$ and $U/D$ cases, as shown in Fig.~\ref{fig:lums}. As discussed in detail in~\cite{2013PhRvD..88d3011P}, the energy radiated during the coalescence of these binary systems can give rise to several promising emission channels. Indeed, the field configuration and dynamics obtained have features clearly tied to models for non-thermal components in pulsars and related systems. As our studies indicate, the resulting Poynting flux is not strongly collimated---and thus could induce isotropic emissions---and its complex time dependence is intimately tied to the field configurations in the stars. The basic premises for non-thermal components in pulsars are present in binaries such as studied here and can contribute to the spectra. In particular, standard estimates for synchrotron self-absorption indicate synchrotron radiation could be observed from radio to gamma rays~\cite{1979rpa..book.....R} and bear imprints of the oscillations observed in the luminosities. Further, these BNSs may power an expanding electron-positron wind with a thermal spectra that could be observable in X-ray by ISS-Lobster at distances $10^{0-2}(B/10^{11}G)$ Mpc, depending on the particular configuration of the magnetic moments. \begin{figure} \includegraphics[width=0.8\columnwidth]{./0-90_xi_12} \\ \includegraphics[width=0.8\columnwidth]{./90-90_xi_13} \caption{Current sheets in the $P/U$ (upper panel) and \textit{P/-P} (lower panel) cases, roughly $1.5 {\rm ms}$ before merger. The current sheets associated with each star appear on the plane perpendicular to the magnetic dipole crossing roughly through the star itself. Consequently, the current sheets in the $P/U$ case appear both along and orthogonal to the orbital plane, while in the \textit{P/-P} case current sheets occur only in planes perpendicular to the orbital plane.} \label{fig:currentSheets} \end{figure} \begin{figure} \includegraphics[width=0.9\columnwidth]{./0-90_UP_Bpolarity--08} \caption{Polarity of the $B_z$ component (red positive, blue negative) for the $P/U$ case, displayed slightly below the orbital plane ($z=-7.5 {\rm km}$), roughly $3 {\rm ms}$ before merger. The ``striped'' pattern displays a spiral structure that persists during the evolution and rotates with the binary, alternating the polarity at any particular point approximately once per orbit. Similar patterns and dynamics are present for the corresponding components of the magnetic field in the other two orthogonal coordinate planes (i.e. \textit{x-z} and \textit{y-z}). } \label{fig:UP-polarity} \end{figure} The structure of the magnetic field lines for the misaligned cases --except the $P/u$ case-- clearly cycles through repeated configurations involving both stars (reconnections-stretching-deflection), indicating that a simple model of ``electric circuits,'' with currents flowing along the magnetic field lines, might still be useful for these systems. However, it should be stressed that these are transitory circuits because they are created and destroyed twice per orbit. Indeed, the maxima in electromagnetic luminosity correlate with the reconnection events that produce a very tight connection via magnetic flux between the stars. For the $P/P$ case in particular, the luminosity peaks occur when the dipoles roughly align (i.e. fall along a line) and such an aligned configuration naturally produces a very compact, tight field configuration. As evident in Fig.~\ref{fig:lums}, the maxima in the $P/P$ case are more luminous for those brief moments than any of the other cases. As in the case of isolated pulsars and aligned dipole configurations in binary systems, current sheets\footnote{Current sheets have been linked to different emission channels for energetic electromagnetic signals in which synchrotron or inverse Compton scattering may produce gamma-rays~\cite{2011SSRv..160...45U}.} also arise in the misaligned cases. However, the character of these current sheets is quite different, being much more dynamical and temporal, with an appearance that is recurrent with the orbital period and orbiting with a lag of roughly a quarter orbit with respect to the stars. Examination of the current sheets, such as shown in Fig.~\ref{fig:currentSheets}, suggests that in the neighborhood of each star, one finds current sheets forming in the plane orthogonal to its dipole field and roughly bisecting the star itself. For the $P/U$ case shown in the top panel, current sheets about the star on the left form in a vertical plane whereas the star on the right forms current sheets within the orbital plane. In the \textit{P/-P} case (bottom panel), both dipoles lie in the orbital plane and current sheets form in two vertical planes that rotate with the stars. The results of the aligned cases of Ref.~\cite{2013PhRvL.111f1105P} in which the dipoles are aligned vertically are consistent with this suggestion; the current sheets in those cases generally arose in the orbital plane which is the plane perpendicular to each dipole (see Fig.~1 of Ref.~\cite{2013PhRvL.111f1105P}). Finally, it is interesting to mention that certain features common to both aligned and oblique rotators~\cite{Spitkovsky:2006np} clearly arise in the $P/U$ case. We observe an alternating polarity in the induced magnetic field configurations, see Fig.~\ref{fig:UP-polarity}. As discussed in~\cite{2011ApJ...741...39S}, this behavior may cause strong particle acceleration and generate intense radiation via synchrotron. The phenomenology discussed here, together with results presented in~\cite{2013PhRvL.111f1105P,2013PhRvD..88d3011P}, explicitly argue that magnetospheric interaction in binary neutron star systems can produce a strong electromagnetic output prior to merger, regardless of the magnetic moments configurations. Identifying pre-merger counterparts is important for concurrent detection because the GW frequency of the binary will increase at merger out of the sensitivity band of advanced GW detectors. \vspace{0.5cm} \noindent{\bf{\em Acknowledgments:}} It is a pleasure to thank A. Broderick and C. Thompson, and our long time collaborators M. Anderson, E. Hirschmann, D. Neilsen and P. Motl for useful discussions about this subject. This work was supported by the NSF under grants PHY-0969827~(LIU) PHY-1308621~(LIU), NASA's ATP program through grant NNX13AH01G, NSERC through a Discovery Grant (to LL) and CIFAR (to LL). C.P acknowledges support by the Jeffrey L.~Bishop Fellowship. Research at Perimeter Institute is supported through Industry Canada and by the Province of Ontario through the Ministry of Research \& Innovation. Computations were performed on the gpc supercomputer at the SciNet HPC Consortium. SciNet is funded by: the Canada Foundation for Innovation under the auspices of Compute Canada; the Government of Ontario; Ontario Research Fund - Research Excellence; and the University of Toronto. | 14 | 4 | 1404.0692 |
1404 | 1404.3691_arXiv.txt | { Turbulence is ubiquitous in the insterstellar medium and plays a major role in several processes such as the formation of dense structures and stars, the stability of molecular clouds, the amplification of magnetic fields, and the re-acceleration and diffusion of cosmic rays. Despite its importance, interstellar turbulence, alike turbulence in general, is far from being fully understood. In this review we present the basics of turbulence physics, focusing on the statistics of its structure and energy cascade. We explore the physics of compressible and incompressible turbulent flows, as well as magnetized cases. The most relevant observational techniques that provide quantitative insights of interstellar turbulence are also presented. We also discuss the main difficulties in developing a three-dimensional view of interstellar turbulence from these observations. Finally, we briefly present what could be the the main sources of turbulence in the interstellar medium. | Turbulence is characterized by chaotic motions in a fluid \citep{rempel04, he05, chian06, chian07, chian10} that lead to diffusion of matter and dissipation of kinetic energy. It is to be stressed that not all chaotic motions in a fluid may be called ``turbulent". Because of its chaotic nature turbulence can only be studied and modelled in terms of statistical quantities. Long-term deterministic local properties of a turbulent fluid are unpredictable. For nearly incompressible and unmagnetized fluids, the temporal evolution of the fluid velocity field is given by the Navier-Stokes equation: \begin{equation} \frac{\partial {\bf u}({\bf x},t)}{\partial t} + {\bf u}({\bf x},t) \cdot {\bf \nabla u}({\bf x},t) = - \frac{{\bf \nabla}p({\bf x},t)}{\rho({\bf x},t)}+\nu \nabla^2 {\bf u}({\bf x},t)+{\bf F}({\bf x},t), \label{eq1} \end{equation} \noindent where ${\bf u}({\bf x},t)$ represents the velocity field, $p$ the pressure, $\nu$ the kinematic viscosity, and ${\bf F}$ an external force normalized by the local density. $\rho$ is the gas mass density and is set constant in the incompressible case (with ${\bf \nabla \cdot u}=0$). Even in this simplified mathematical description the fluid dynamics is not a trivial solution. Equation~\ref{eq1} is non-linear, as seen from the advective term in the left hand side, and non-local - in the sense that the local properties of the fluid are related to all the other regions -, through the pressure term. The incompressibility condition results in an infinite sound speed, and in an instantaneous propagation of any perturbation in the fluid. \citet{burg39} modeled the time evolution of the simplified version of the Navier-Stokes equation by considering $\nabla p = 0$. This equation has exact solutions, which may sound interesting, but it results in non-universal ``turbulence". Eventhough Burgers turbulence models have gained increasing interest due to their ability to describe the statistics of shock induced structures, and many other applications \cite[see review by][]{bec07}. In the full Navier-Stokes equation, perturbations in ${\bf u}({\bf x},t)$ are expected to have their distribution changed due to non-linear terms. These instabilities may drive local vorticity and result in the fragmentation of large amplitude eddies into smaller ones, creating a turbulent pattern. As imagined by \citet{ric22}, {\it big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls, and so on to viscosity}. This statement represents one of the first conceptual descriptions of the energy cascade in turbulent flows. The shear drives unstable motions at large scales, which are broken and fragmented into smaller vortices, down to the smallest scales where they are damped, e.g. due to viscosity. In an incompressible viscous fluid this damping scale is that at which the timescale for viscous damping is of the order of the turnover dynamical time. At that scale, the eddy kinetic energy is transferred to internal energy due to viscosity. Turbulence is naturally developed over larger range of scales if viscosity is small, i.e. with large Reynolds number ($Re = UL/\nu \gg 1$), being the characteristic velocity $U$ injected at a lengthscale $L$. \citet[hereafter K41]{kol41} realized that it would be possible to solve the Navier-Stokes equation for a turbulent flow if ${\bf u}({\bf x},t)$ is considered a stochastic distribution. One of the key assumptions in the K41 theory is that the energy transfer rate $\epsilon$ should be constant at all scale. It is defined as $\epsilon \simeq \delta u_l^2/\tau_l$, where $\delta u_l$ is the velocity fluctuation amplitude at lengthscale $l$, and $\tau_l = \tau_{\rm eddy} = l/\delta u_l$ its dynamical timescale\footnote{Note that we distinguish $\tau_l$ and $\tau_{\rm eddy}$ here, since $\tau_l$ represents the timescale for energy transfer at scale $l$, while $\tau_{\rm eddy}$ is the eddy turnover timescale. In the K41 theory both timescales are the same, but this is not true for other cases, e.g. as in some magnetized cases}. Therefore, one obtains: \begin{equation} \delta u_l \simeq (\epsilon l)^\frac{1}{3}. \label{eq2} \end{equation} Equation~\ref{eq2} means that turbulence can be modeled by scaling laws. This would be true within the so called {\it inertial range of scales}, i.e. the scales where the energy transfer rate is constant, generally between the energy injection and the viscous damping scales. The velocity power spectrum $P_u(k)$ is defined\footnote{The power spectrum is defined as the one dimensional spectrum in Fourier space while the energy spectrum, generally defined as $E_u(k) =k^2P_u(k)$ is the three-dimensional spectrum. For the sake of simplicity, we use the term {\it power spectrum} to represent the latter.} here by $\int_{k=1/l}^\infty P_u(k')dk'= \delta u_l^2$, from which we obtain the standard Kolmogorov power spectrum for the velocity field: \begin{equation} P_u(k) \propto \epsilon^{2/3} k^{-5/3}. \end{equation} In other words, it is possible to reinterpret Kolmogorov's idea in Fourier space in terms of non-linear interaction between similar wavenumbers. This theory is a result of the so-called {\it locality}, i.e. similar wavenumbers, $k=2\pi/\lambda$, of the non-linear wave-wave interaction that result in the energy cascade through smaller scales \cite{kra65a}. From the spectral form of the Navier-Stokes equation, the three-wave interactions follow the selection rule $k_3=k_1+k_2$. The extrema are found at $k_3\rightarrow0$ and $k_1=k_2$, which is the locality assumed in Kolmogorov's theory, resulting in $k_3=2k_1$. The theory also predicts the scaling laws for the moments of velocity spatial increments, known as {\it velocity structure functions}, defined as: \begin{equation} S_p(l)=\left\langle \left\{\left[ \textbf{u}\left( \textbf{r} + \textbf{l} \right) - \textbf{u} \left( \textbf{r} \right) \right] \cdot \textbf{l}/l \right\} ^p \right\rangle = C(p) \epsilon^{p/3}l^{p/3}, \end{equation} \noindent where $p$ is a positive integer representing the moment order and ${\bf l}$ is the spatial increment vector. In incompressible fluids, if the turbulence is considered {\bf \it homogeneous}, {\bf \it isotropic} and {\bf \it self-similar}, i.e. scale invariant, then: \begin{equation} S_p(l)=C(p) \epsilon^{p/3} l^{p/3} , \end{equation} \noindent where $C(p)$ was initially assumed by Kolmogorov to be constant with $p$. One of the main successes of the Kolmogorov-Obukhov turbulence theory is the explanation of the empirical determination of the diffusion coefficient by \citet{ric26}, done more than a decade before K41. The diffusion coefficient is related to the time evolution of the separation between Lagrangian points (e.g. particles dragged by the flow) in a turbulent medium. The probability distribution function $\Phi$ of pairs of points separated by a distance ${\bf r}$ may be described as: \begin{equation} \frac{\partial \Phi \left({\bf r},t\right)}{\partial t} = \frac{1}{r^2} \frac{\partial}{\partial r} r^2 K(r) \frac{\partial \Phi \left({\bf r},t\right)}{\partial r}, \label{eq6} \end{equation} \noindent where $K(r)$ represents the diffusion coefficient. It is easy to determine, from dimensional analysis, that if $\dot{r} = u(r) \propto r^{1/3}$ as in the Kolmogorov scaling, the diffusion coefficient for the inertial range will be $K(r) = k_0 \epsilon^{1/3} r^{4/3}$, the scaling proposed by \citet{ric26}. This diffusion coefficient for the inertial range substituted in Equation~\ref{eq6} then results in: \begin{equation} \Phi \left({\bf r},t\right) = \frac{A}{(k_0 t)^3\epsilon} \exp\left(-\frac{9r^{2/3}}{4k_0\epsilon^{1/3}t} \right), \end{equation} \noindent where $A$ is a normalization coefficient. The Richardson distribution is therefore non-Gaussian. Several experiments and numerical models have shown the validity of the turbulent diffusion scaling \cite{ell96, fun98, zov94, bof02}, as has also been recently used in the predictions of stochastic magnetic reconnection \footnote{this term accounts for the magnetic reconnection that is induced by turbulent motions near the current sheet - separation layer between fields with components of opposed directions -, which would then result in reconnection rates as a function of the stochastic motions of the fluid.} \cite{laz12}. This theory of turbulence has been quite successful in reproducing most of experimental data, and there is a flourishing literature with hundreds of works available e.g. \citet{arm95, lea98, bal05, koga07, bou09, chian09, che10, sah10, chian11, cha12, hur12, miranda13}, just to mention a few. Naturally, many authors criticized the fact of $C(p)$ is a constant in Kolmogorov's initial theory, given the breakdown of self-similarity at small scales and the possible non-universality of turbulence (given its ``memory" related to the energy injection). These criticisms have been later addressed in the Kolmogorov-Obukhov turbulence theory \cite{kol62, obu62}, including the effects of {\it intermittency}. Intermittency results from rare and large local fluctuations in the velocity field which break the similarity condition \cite{fri95}. One of the effects of intermittency is observed in the probability distribution function (PDF) of velocity longitudinal increments $\delta u_l = [{\bf u}({\bf r}+{\bf l})-{\bf u}({\bf r})]\cdot \hat{l}$, which shows large deviations from the Gaussian distribution at small scales, with large amplitude tails and peaked distributions at $\delta u_l \sim 0$ (see Figure~\ref{fig1}). \citet{kra91} pointed that sharp shocks could, for intance, result in more regions with smooth fluid flows and also more regions with sharp transitions in velocities, compared to the standard picture of the self-similar K41 turbulence. We would then expect non-Gaussian PDFs at both small and large scales. \begin{figure}[t] \vspace*{2mm} \begin{center} \includegraphics[width=8.3cm]{fig1.eps} \end{center} \caption{PDF of velocity increments as a function of the lag length $\left|{\bf l}\right|$, from small (top) to large scales (bottom) \cite[extracted from][]{wil10}. The non-Gaussianity is clear for velocity increments at small scales. \label{fig1}} \end{figure} Many authors attempted to theoretically determine the scalings of turbulence with intermittency. One of the most successful approaches is the multifractal description for the energy dissipation field proposed by \citet{she94}. This theory results in $S_p(l) \propto l^{\zeta(p)}$, with: \begin{equation} \zeta(p)=\frac{p}{3}(1+\frac{2}{3})+(3-D')\left[1-\left(1-\frac{2}{3(3-D')} \right)^{p/3} \right], \end{equation} \noindent where $D'$ represents the dimensionality of the dissipation structures. In the Kolmogorov-Obukhov theory, structures of highest dissipation are filamentary, better described then by $D' \sim 1$, while recent numerical simulations reveal a dominance of two dimensional intermittent structures at small scales \cite[e.g.][]{moi04,kow07a,kow07b,bol12}, what is also supported by experimental data \cite[e.g.][]{fre03, the07}. Multifractal analysis of Voyager 1 and 2 {\it in situ} data have also showed intermittent features on the magnetic turbulence at the solar wind and the termination shock \citep{macek08,macek11,macek12}. On the theoretical side, \citet{bir13} derived a statistical solution of the stochastic Navier-Stokes equation from the linear Kolmogorov-Hopf differential equation, accounting for the She-Lev\^eque intermittency corrections. His results satisfactorily reproduce the PDFs built on observations and numerical simulations of turbulent flows. Compressibility and coupling between magnetic fields and the plasma flow - both present in the dynamics of the interstellar medium (ISM) - make the description of the interstellar turbulence even more complex. \subsection{Supersonic turbulence} \label{sec1.1} Compressible plasmas are of great interest in astrophysics, and particularly in the case of interstellar turbulence. Compressibility in turbulent flows results in the formation of a hierarchy of density structures, viewed as dense cores nested in less dense regions, which are in turn embedded in low density regions and so on. Such a hierarchical structure was described by \citet{von51} as: \begin{equation} \frac{\rho_\nu}{\rho_{\nu-1}} = \left(\frac{l_\nu}{l_{\nu-1}} \right)^{-3\alpha}, \end{equation} \noindent where $\rho_\nu$ represents the average density of a structure at hierarchical level $\nu$, at a lengthscale $l$, and $\alpha$ the compressibility degree, assumed to be the same at each level. The dimensionality of the system is obtained by $D'=3-3\alpha$. Therefore, the average mass within each substructure must follow the relation $M_l \propto l^{3-3\alpha}$. The density hierarchy as described above must then be coupled to the local turbulent motions. The energy density transfer rate must now be rewritten as $\epsilon_l = \rho_l \delta u_l^3/l$ to account for the density changes at different scales \cite{lig55}. If, once again, one assumes the constancy of the energy transfer rate across scales within the inertial range \cite{fle96}, one obtains the scaling of the amplitude of the velocity fluctuations: \begin{equation} \delta u_l \propto l^{\frac{1}{3}+\alpha}, \end{equation} \noindent and the velocity power spectrum is then given by: \begin{equation} P_u(k) \propto k^{-5/3 -2\alpha}. \end{equation} Note that for stationary energy distribution solutions in compressible turbulence, $\alpha> 0$ which results in steeper velocity power spectra, compared to the standard K41 scaling. The density power spectrum, on the other hand, instead of following the velocity field as a passive scalar would do, presents a distinct power spectrum given by: \begin{equation} P_\rho(k) \propto k^{6\alpha-1}, \end{equation} \noindent i.e. for $\alpha \sim 1/6$, the power spectrum of the density field becomes flat in the inertial range. One of the most striking results of the hierarchical model for the density field in compressible turbulence is its ability to recover the standard Kolmogorov scalings for the density weighted velocity field ${\bf v} \equiv \rho^{1/3} {\bf u}$ \cite{fle96}. Numerical simulations of compressible turbulence have confirmed the scalings described above for $\alpha \simeq 0.15$ \cite{kri07, kow07b}, close to $\alpha = 1/6$ for which the density power spectrum becomes flat. The velocity power spectrum on the other hand becomes $P_u(k) \propto k^{-2}$. Remarkably, this is the exact slope obtained for Burger's turbulence, despite the different framework of that theory. \subsection{Magnetized turbulence} Magnetic fields introduce further complexity in the plasma dynamics that can be described by the magneto-hydrodynamic (MHD) equations in the fluid approximation and assuming perfect coupling between the field and the plasma: \begin{eqnarray} \frac{\partial {\bf u}}{\partial t} + {\bf u} \cdot {\bf \nabla u} = - \frac{{\bf \nabla}p}{\rho}+ \nu \nabla^2 {\bf u}+\frac{\left( {\bf \nabla \times B} \right) \times {\bf B}}{4\pi\rho}+{\bf F}, \label{eq13} \end{eqnarray} \begin{equation} \frac{\partial {\bf B}}{\partial t} = {\bf \nabla \times} \left( {\bf u}{\bf \times B} \right)+\eta \nabla^2{\bf B}, \label{eq14} \end{equation} \noindent where ${\bf B}$ is the magnetic field and $\eta$ the plasma resistivity ($\eta =0$ for ideal plasmas). Let us first consider an external uniform magnetic field $B_0$. Any perturbation in the fluid velocity field will be coupled to the magnetic field. The magnetic tension/pressure results in a decrease of the non-linear growth of perturbations, but only of those perpendicular to the magnetic field lines. This complex coupling between the flow and magnetic field makes the modelling of turbulence in magnetized plasmas an interesting task\footnote{More details on MHD turbulence may be found in \citet{bis03}}. \subsubsection{The Iroshnikov-Kraichnan model} An useful simplification to the equations above is made by considering ${\bf B}={\bf B}_0+{\bf \delta B}$, and using the Els\"{a}sser variable ${\bf z^\pm}={\bf u}\pm{\bf \delta \breve{B}}$, where $\breve{B} = B/(4\pi \rho)^{1/2}$. This has been independently derived by \citet{iro63} and \citet[]{kra65a, kra65b} (IK hereafter). From this change of variables, Eqs~\ref{eq13} and \ref{eq14} result in \cite[see][]{sch07}: \begin{equation} \frac{\partial {\bf z^\pm}}{\partial t} \mp v_A \nabla_{||}{\bf z^\pm}+{\bf z^\mp} \cdot {\bf \nabla z^\pm} = -{\bf \nabla} p + \frac{\nu + \eta}{2} \delta z^\pm + \frac{\nu - \eta}{2} \delta z^\mp +{\bf F}, \end{equation} \noindent where $v_A = B_0/\sqrt{4 \pi \rho}$ is the Alfv\'en velocity and $\nabla_{||}$ is the spatial derivative parallel to the direction of the mean magnetic field. In their model, Iroshnikov and Kraichnan proposed that incompressible magnetized turbulence results from the non-linear interactions of counter propagating waves packets. The timescale for the two wave packets to cross each other is of order of the Alfv\'en time $\tau_A \sim l_{||}/v_A$, where $l_{||}$ is the lengthscale of the wave packet parallel to the mean magnetic field. In their phenomenological description of the MHD turbulence, the interactions between the wave packets are {\bf weak}, i.e. $|{\bf z}^\pm| \ll \breve{B}_0$ or the field perturbations are much smaller than $B_0$. Notice that, superimposed to the magnetic fluctuations, the fluid is also perturbed and the dynamical timescale of a fluid ``eddy'' is $\tau_{\rm eddy} \equiv l/ \delta u_l$. The different wave modes (mechanical and magnetic perturbations) thus interact with each other. For the interaction between modes to be weak the Alfv\'en time must be much smaller than the dynamical timescale, i.e. $\tau_A \ll \tau_{\rm eddy}$. The non-linear decay of the wave packets in such weak interactions, and subsequently the turbulent cascade, can only occur after several interactions. Since interactions are random, the wave packet amplitude changes in a random walk fashion, i.e. $N = (\tau_l/\tau_A)^{1/2}$ interactions are needed for the wave packet to significantly change. At the same time, $N$ is also defined by the number of crossings in a decay timescale $N = \tau_l / \tau_{\rm eddy}$, which results in: \begin{equation} \tau_l \sim \frac{\tau_{\rm eddy}^2}{\tau_A} \sim \frac{l^2 v_A}{l_{||} \delta u_l^2}. \end{equation} Therefore, the turnover time at scale $l$ is longer by a large factor and, as expected, the non-linear cascade proceeds much more slowly. The second major assumption in the IK theory of weak turbulence is its isotropy, i.e. $l_{||} \sim l$. Substituting this scaling into the relation $\epsilon = \delta u_l^2/\tau_l$, one obtains: \begin{equation} \delta u_l \sim (\epsilon v_A)^{1/4} l^{1/4}\\ {\rm and}\\ P_u(k) \sim (\epsilon v_A)^{1/2} k^{-3/2}. \end{equation} There is evidence for an IK cascade in the solar wind and interplanetary medium \cite[e.g.][]{bam08, ng10}. However, many observations of the solar wind turbulence also suggest a more Kolmogorov-like turbulence, i.e. $\propto k^{-5/3}$ \cite[e.g. the early studies of \citeauthor{col68}, \citeyear{col68}; \citeauthor{mat82}, \citeyear{mat82}; and the more recent papers by][]{ale08, chian09, sah10, li11, chian11, koz12, hel13}. It is possible though that a mix of both cascades may occur, as pointed by e.g. \citet{sal09} and \citet{ale13}, which showed a mix of K41 and IK cascades for the magnetic and velocity field fluctuations, respectively. Moreover, most of these data also reveal the solar wind turbulence to be highly anisotropic (i.e. $\delta u_l^{||} \neq \delta u_l^{\perp}$) with respect to the local magnetic field \citep{hor08,hor12}. As pointed by \citet{gol01}, one of the main issues raised by the solar wind is {\it why is the power spectrum of this anisotropic, compressible, magnetofluid often Kolmogorov-like?} \subsubsection{The Goldreich-Sridhar model} \begin{figure*}[ht] \vspace*{2mm} \begin{center} \includegraphics[width=5cm]{fig2a.eps} \includegraphics[width=5cm]{fig2b.eps} \includegraphics[width=5cm]{fig2c.eps} \includegraphics[width=5cm]{fig2d.eps} \includegraphics[width=5cm]{fig2e.eps} \includegraphics[width=5cm]{fig2f.eps} \end{center} \caption{Spectra and second order structure function anisotropy of dispersion ($\delta v$) of the different wave modes in MHD turbulence. The Alfv\'en and slow modes present K41 power cascade and strong anisotropy of dispersion of velocity at small scales, while fast waves present IK cascade and are basically isotropic at all scales. Data from a $1024^3$ isothermal, sub-Alfv\'enic and subsonic turbulence model. \label{fig2}} \end{figure*} \citet{mar90} remarked that if, instead of an Alfv\'en time, the timescale for the waves to non-linearly interact with each other was the regular eddy turnover time, i.e. $\tau_l \simeq \tau_{\rm eddy} \sim l_{||}/\delta u_l$, one would get a K41 cascade for the magnetized turbulence. This would be true also for the case of strong turbulence, $|{\bf z}^\pm| > \breve{B}_0$. The isotropy condition was retained, which was raising a problem, most of the observational data mentioned above revealing strongly anisotropic turbulence. \citet[GS95 hereafter]{gol95} proposed a turbulent model based on anisotropic fluctuations, with strong coupling between the wave modes. Strictly speaking the GS95 model assumes a critical balance between mechanical and Alfv\'enic modes in such a way that $l_{\perp}/\delta u_l \simeq l_{||}/v_A$. Therefore: \begin{equation} l_{||} \sim v_A \epsilon^{-1/3} l_{\perp}^{2/3}\\ {\rm and}\\ P_u(k) \propto k^{-5/3}. \label{eq18} \end{equation} From Eq.~\ref{eq18}, not only the magnetized turbulence is anisotropic but it is {\it local} in the sense that the anisotropy is measured in the reference frame of the local magnetic field. Such an anisotropy is expected to occur in both the dispersion of velocity ($\delta v$) and wave vectors ${\bf k}$, though it is easier to observe velocity dispersion anisotropies from the interstellar medium, as discussed below. Therefore, statistically, a large number of eddies with local fields randomly distributed in space result in an average zero anisotropy (even at small scales). In the strong magnetized cases though, the anisotropy would be more clearly detected in experiments and observations. Several direct numerical simulations of magnetized turbulence in a quasi-incompressible regime have been performed in the past decade. Many numerical experiments reveal that MHD turbulence indeed has a large part of its energy cascade close to a K41 distribution. However, as shown by \citet{cho02a, cho03, cho02b} and \citet{kow10}, the decomposition of the different modes in MHD turbulence actually reveals that, although Alfv\'en and slow modes behave as K41 type of turbulence and are anisotropic, the fast modes are isotropic and follow IK statistics (see Figure~\ref{fig2}). Effects of imbalanced (or cross-helicity) turbulence in the cascade and statistics of the local fields have also been addressed in the past few years \citep[][and references therein]{lit07, ber08, ber10, wic11, mar13}. Imbalanced turbulence occurs when waves traveling in opposite directions along the mean magnetic field are of unequal amplitudes, i.e. carry different energy fluxes to small length scales, so that ${\bf z}_l^+/{\bf z}_l^- \neq 1$ and ${\epsilon}_l^+/{\epsilon}_l^- \neq 1$. The imbalance may arise in MHD turbulence since the interaction timescales between the waves ${\bf z}_l^+$ and ${\bf z}_l^-$ are different, and the cascade generally occurs faster for ${\bf z}_l^-$. This is understood as the number of interactions ($N$) is much larger for counter-propagating wave packets, resulting in ${\epsilon}_l^+/{\epsilon}_l^- > 1$. In such a scenario, numerical simulations show that the anisotropy is not equal for the different wave modes. Locality of scales for wave-wave interactions has also been the subject of recent studies in turbulence \citep{car06, ale07, min08, alu09, ber10}. Magnetic fields are responsible for long range interactions, from the Lorentz force acting over the whole fluid frozen to it. Therefore, different wavelengths may interact with each other non-linearly. Bi-spectra of fluctuations of density are discussed in \citet{bur09}, and the non-local interactions appear to be important in MHD and supersonic turbulence models. A similar approach is used for studying the non-local interactions of Els\"asser modes \cite{cho10}, resulting in a substantial fraction of non-local interactions in MHD turbulence. The role of the non-local interactions in the turbulent cascade is still not clear though. Turbulence in magnetized collisionless plasmas has been also studied in the past few years \cite[e.g.][and others]{hel06, sch08, bal09} in order to determine the role of collisionless plasma instabilities on the dynamics of plasma turbulence. Simulations of \citet{kow11, san13}, reveal that the statistics are still dominantly Kolmogorov-like, though strong asymmetries may also arise due to instabilities (firehose, mirror and cyclotron instabilities) are small scales. | 14 | 4 | 1404.3691 |
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1404 | 1404.3833_arXiv.txt | Neutrino-neutrino refraction can lead to non-periodic flavor oscillations in dense neutrino gases, and it has been hypothesized that some solutions are chaotic in nature. This is of particular interest in the case of neutrino emission from core-collapse supernovae where the measurement of the spectral shape for different flavors can provide crucial information about both neutrino physics and the physical conditions close to the proto-neutron star. Whether a system is chaotic or not can be assessed by the Lyapunov exponents which quantify the rate of divergence of nearby trajectories in the system. We have done a numerical case study for a simple toy model of two neutrino flavors with two momentum states traveling against each other which is known to exhibit flavor transition instabilities. We find the leading Lyapunov exponent to be positive in all cases, confirming the chaoticity of the system for both the normal and the inverted neutrino mass hierarchy. However, more Lyapunov exponents were approximately zero in the inverted hierarchy compared to the normal which has implications for the stability of the system. To investigate this, we have calculated a generalized set of normal modes, the so-called covariant Lyapunov vectors. The covariant Lyapunov vectors associated with vanishing Lyapunov exponents showed the existence of marginally stable directions in phase space for some cases. While our analysis was done for a toy model example, it should work equally well for more realistic cases of neutrinos streaming from a proto-neutron star and provide valuable insight into the nature of the flavor instability. We finally stress that our approach captures many more properties of the physical system than the linear stability analyses which have previously been performed. | 14 | 4 | 1404.3833 |
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1404 | 1404.6501_arXiv.txt | Through a previous analysis of multi-epoch astrometry from the {\it Wide-field Infrared Survey Explorer (WISE)}, I identified WISE J085510.83$-$071442.5 as a new high proper motion object. By combining astrometry from {\it WISE} and the {\it Spitzer Space Telescope}, I have measured a proper motion of $8.1\pm0.1\arcsec$~yr$^{-1}$ and a parallax of $0.454\pm0.045\arcsec$ ($2.20^{+0.24}_{-0.20}$~pc) for WISE J085510.83$-$071442.5, giving it the third highest proper motion and the fourth largest parallax of any known star or brown dwarf. It is also the coldest known brown dwarf based on its absolute magnitude at 4.5~\micron\ and its color in $[3.6]-[4.5]$. By comparing $M_{4.5}$ with the values predicted by theoretical evolutionary models, I estimate an effective temperature of 225--260~K and a mass of 3--10~$M_{\rm Jup}$ for the age range of 1--10~Gyr that encompasses most nearby stars. | The closest stars to the Sun have played a central role in studies of stellar astrophysics, as well as appealing to the imagination of the general public \citep{hen97}. Over the last century, wide-field imaging surveys have been conducted at progressively fainter magnitudes and longer wavelengths, enabling the detection of the Sun's neighbors down to the hydrogen burning limit \citep[e.g.,][]{bar16,wol19,ros26,luy79,lep05b} and into the substellar regime \citep[e.g.,][]{kir99,str99,bur04,burn10}. One of the most recent surveys was performed by the {\it Wide-field Infrared Survey Explorer} \citep[{\it WISE},][]{wri10}, which obtained mid-infrared (IR) images of the entire sky. Those data have proven to be highly effective at uncovering the coldest brown dwarfs in the vicinity of the Sun \citep{cus11,kir11}. Most of the brown dwarfs found with {\it WISE} have been selected based on their colors. However, nearby brown dwarfs also can be identified through their large proper motions, which avoids photometric selection biases \citep[e.g.,][]{dea09,she09,art10,kir10,sch10}. This method has been successfully applied to the {\it WISE} astrometry by measuring motions relative to near-IR surveys \citep{giz11,liu11,sch11,bih13} and within the multiple epochs from {\it WISE} \citep{luh13,luh14,tho13,wri14,kir14}. The latter data are especially well-suited for finding nearby objects that are too cold to be detected in near-IR surveys. In this Letter, I characterize an object of this kind from my proper motion survey in \citet{luh14}\footnote{In a subsequent study, \citet{kir14} also independently identified this high proper motion object.}, demonstrating that it is one of the Sun's closest neighbors and the coldest known brown dwarf. | WISE~0855$-$0714 has the third highest proper motion of any known object outside the solar system ($\mu=8\farcs1$~yr$^{-1}$), behind only Barnard's star \citep[][$\mu=10\farcs3$~yr$^{-1}$]{bar16} and Kapteyn's star \citep[][$\mu=8\farcs6$~yr$^{-1}$]{kap97}. The four closest systems to the Sun known prior to this study are $\alpha$ Cen AB and Proxima Cen \citep[1.338$\pm$0.002, 1.296$\pm$0.004~pc,][]{sod99,van07}, Barnard's star \citep[1.834$\pm$0.001~pc,][]{ben99}, WISE J104915.57$-$531906.1~AB \citep[2.02$\pm$0.02~pc,][]{luh13,bof14}, and Wolf 359 \citep[2.386$\pm$0.012~pc,][]{van95}. With a parallactic distance of $2.20^{+0.24}_{-0.20}$~pc, WISE~0855$-$0714 likely ranks fourth in proximity to the Sun. Among known T and Y dwarfs, WISE~0855$-$0714 is the reddest in $[3.6]-[4.5]$, a contender for the reddest in $J-[4.5]$, and the faintest in $M_{4.5}$, indicating that it is the coldest known brown dwarf (and hence a Y dwarf). When compared to the model predictions of \citet{bur03}, \citet{sau08}, and \citet{mor14}, the constraints on $J-[4.5]$ and $M_{4.5}$ imply effective temperatures of $\lesssim300$~K and 225--260~K, respectively. If it is within the age range of 1--10~Gyr that encompasses most nearby stars, then it should have a mass of 3--10~$M_{\rm Jup}$ according to the theoretical values of $M_{4.5}$. At this mass, WISE~0855$-$0714 could be either a brown dwarf or a gas giant planet that was ejected from its system. The former seems more likely given that the frequency of planetary-mass brown dwarfs is non-negligible\footnote{This is based on surveys of star-forming regions \citep[e.g.,][]{alv12}, which are young enough that planet ejection is unlikely to have occurred at a significant level.} while the frequency of ejected planets is unknown. Assuming that WISE~0855$-$0714 is a Y dwarf, the four closest known systems now consist of two M dwarfs and one member of every other spectral type from G through Y. WISE~0855$-$0714 offers an opportunity to test atmospheric models in an unexplored temperature regime. Exploiting this opportunity will require additional astrometry to refine its parallax measurement and deeper near-IR photometry to better constrain its spectral energy distribution. Spectroscopy will be necessary for detailed tests of the model atmospheres, but given the current limits on the near-IR fluxes ($J>23$), it may not be feasible until the deployment of the {\it James Webb Space Telescope}. | 14 | 4 | 1404.6501 |
1404 | 1404.1926_arXiv.txt | As a comet, asteroid or planet approaches its parent star, the orbit changes shape due to the curvature of spacetime. For comets in particular, the deviation at the pericentre may noticeably change their ephemerides and affect the dynamics of outgassing, tidal disruption or other processes which act on orbital timescales and are assumed to follow Newtonian gravity. By obtaining and analysing the unaveraged equations of motion in orbital elements due to the dominant post-Newtonian contribution (1PN), I derive a simple analytic expression for the maximum deviation in terms of only the stellar mass and eccentricity of the orbit. This relation can be used to assess the potential importance of including short-period relativistic terms in models containing comets, asteroids or planets, and help determine the level of precision needed in numerical integrations. The magnitude of the deviation in systems with Solar-like stars is typically comparable to the size of comet nuclei, and the direction of the deviation is determined by the eccentricity. I show that for eccentricities above a critical value of $\sqrt{19} - 4 \approx 0.359$, the direction is away from the star. | The November 2013 perihelion passage and disintegration of comet C/2012 S1 (ISON) \citep{knietal2013} has reinvigorated interest about the physical processes comets experience at closest approach to their parent stars. Both sublimation and tidal forces affect the orbit, ephemeris, and the prospect of the comet surviving the close encounter intact. As suggested by \cite{maqetal2012}, another potentially important effect arises from general relativity (GR), which they added into their model. That study is not alone. \cite{shayeo1994} reported that for orbits of comets and asteroids, incorporating GR can significantly improve orbital solutions. Consequently, investigators of comets such as 55P/Tempel-Tuttle have heeded this advice \citep{yeoetal1996}. Also, the update to the Marshall Space Flight Center Meteoroid Stream Model \citep{moscoo2008} featured the inclusion of GR. Linking the metrics of GR to the idea of a force in Newtonian gravity can be challenging, but is well-elucidated in the Appendix of \cite{bengal2008}. That paper also presents the Einstein-Infeld-Hoffman equation \citep{einetal1938}, which provides the corrections to the Newtonian equation of motions in a system where every object causes the curvature of spacetime. Cometary studies may assume that only the parent star causes such a perturbation because this approximation is excellent, given the many orders of difference in mass between a comet and a star. This approximation, which is used in this paper, is also suitable for asteroids orbiting stars, planets orbiting stars, and even comets which suffer close encounters with planets, such as Shoemaker-Levy 9 did with Jupiter. The curvature of spacetime due to the star will cause the comet's orbit to deviate from a perfect ellipse, parabola or hyperbola. In the bound (elliptic) case, this curvature causes the long-term (or secular) precession of the argument of pericentre, a well-known effect for the planet Mercury\footnote{When referring to the word {\it pericentre} by itself, I indicate the actual osculating closest approach distance, and not the longitude of pericentre nor argument of pericentre. Some relativity-based studies use the former as shorthand for the latter.}. The comet's osculating semimajor axis and eccentricity do not change over long timescales, but do change during a single orbit. The magnitude of the change depends on both the orbital and spin properties of the comet, which enter into the equations of motion at different orders of powers of the speed of light \citep[see equation 3.1a of][]{buoetal2013}. The leading order is independent of spin and is known as the 1PN term. Here I isolate and quantify the effect of the 1PN term on a single cometary close passage to the star. My main result, which is derived in the next section, is \begin{eqnarray} \Delta_{\rm max} &\approx& \frac{2 G M_{\star}}{c^2} \frac{\left(e^2 + 8 e - 3\right)}{\left(1 + e\right)^2} \nonumber \\ &\approx& 2.95 \ {\rm km} \left( \frac{M_{\star}}{M_{\odot}} \right) \frac{\left(e^2 + 8 e - 3\right)}{\left(1 + e\right)^2} \label{main} \end{eqnarray} \noindent{where} $e$ is the orbital eccentricity, $M_{\star}$ is the stellar mass, and $c$ is the speed of light. The quantity $\Delta$ represents the actual closest encounter distance (including relativity) minus the closest encounter distance predicted by Newtonian gravity alone. For a nearly-parabolic cometary orbit in a system with a Solar-mass star, GR would increase the Newtonian pericentre by about 4.4 km. Figure \ref{mainfig} graphically illustrates the dependence of the deviation on eccentricity and stellar mass. This result illustrates that typical deviations are a few km, which is comparable to typical sizes of cometary nuclei \citep{donrah1982}. Close-up imaging by spacecraft has helped to establish these sizes \citep[e.g.][]{keletal2013}. Also, Hubble Space Telescope Wide Field Camera 3 images suggest that the pre-disruption radius of the nucleus of ISON was no larger than 2 km \citep{keletal2014}. The remainder of this Letter includes the derivation of equation (\ref{main}) plus a description of the unaveraged 2-body 1PN problem [Section 2], a short discussion [Section 3] and a summary [Section 4]. \begin{figure} \centerline{ \psfig{figure=mainplot.eps,height=8.0cm,width=9.3cm} } \caption{ How the orbital pericentre changes when effects from general relativity are included. The solid, short-dashed, dot-dashed, and long-dashed lines correspond to stellar masses of $0.2M_{\odot}$, $1.0M_{\odot}$, $2.0M_{\odot}$, and $5.0M_{\odot}$. This plot is based on equation (\ref{main}), and illustrates how the change is comparable to comet nuclei sizes (of km) for Solar-mass stars. For highly eccentric bodies, such as observed comets originating from the Oort cloud, relativity pushes the comets away from rather than towards the star at the closest approach. } \label{mainfig} \end{figure} | Equation (\ref{main}) is applicable to any relatively small secondary, not just comets. However, for objects such as planets, the variations at the pericentre are 3-5 orders of magnitude smaller than their physical radii. For hot Jupiters, which orbit close to their stars ($a \lesssim 0.1$ au), the effect generally causes inward drift toward the star because of the planets' relatively circular orbits. In fact, as of 18 Feb 2014, only 5 out of 292 such planets\footnote{See the Exoplanets Data Explorer at exoplanets.org} have measured eccentricities greater than $e_{\rm crit}$. The applicability of Equation (\ref{main}) is not limited to the Solar System. There are tantalising hints of exocomets in systems with A stars \citep{welmon2013,kieetal2014}. Also, over 25 per cent of all white dwarfs are thought to host remnant planetary systems due to the presence of rocky atmospheric pollutants \citep{zucetal2010}. These pollutants might arise from asteroids or comets on highly eccentric orbits, which could disrupt into dusty discs \citep[e.g.][]{faretal2010} or gaseous discs \citep[e.g.][]{gaeetal2008}. Given that about half of all stars in the Galaxy are more massive than a few tenths of a $M_{\odot}$ \citep{offetal2013}, Figure \ref{mainfig} suggests that the maximum variation at pericentre is comparable to the size of a comet nucleus for most stars in the Milky Way. Nevertheless, in extrasolar systems with a single main sequence star, the importance of short-period GR terms may be limited to highly accurate numerical simulations until observational capabilities improve. | 14 | 4 | 1404.1926 |
1404 | 1404.1267_arXiv.txt | The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) project currently observes 43 pulsars using the Green Bank and Arecibo radio telescopes. In this work we use a subset of 17 pulsars timed for a span of roughly five years (2005--2010). We analyze these data using standard pulsar timing models, with the addition of time-variable dispersion measure and frequency-variable pulse shape terms. Within the timing data, we perform a search for continuous gravitational waves from individual supermassive black hole binaries in circular orbits using robust frequentist and Bayesian techniques. We find that there is no evidence for the presence of a detectable continuous gravitational wave; however, we can use these data to place the most constraining upper limits to date on the strength of such gravitational waves. Using the full 17 pulsar dataset we place a 95\% upper limit on the sky-averaged strain amplitude of $h_0\lesssim 3.8\times 10^{-14}$ at a frequency of 10 nHz. Furthermore, we place 95\% \emph{all sky} lower limits on the luminosity distance to such gravitational wave sources finding that the $d_L \gtrsim 425$ Mpc for sources at a frequency of 10 nHz and chirp mass $10^{10}{\rm M}_{\odot}$. We find that for gravitational wave sources near our best timed pulsars in the sky, the sensitivity of the pulsar timing array is increased by a factor of $\sim$4 over the sky-averaged sensitivity. Finally we place limits on the coalescence rate of the most massive supermassive black hole binaries. | The direct detection of Gravitational Waves (GWs) is a major goal of experimental physics and astrophysics. One of the most promising means of detecting GWs is through the precise timing of an array of millisecond pulsars (MSPs). The concept of a pulsar timing array (PTA) was first conceived of over two decades ago \citep{saz78,det79,hd83,r89,fb90}. Twenty years later three main PTAs are in full operation around the world: the North American Nanohertz Observatory for Gravitational waves \citep[NANOGrav;][]{jfl+09}, the Parkes Pulsar Timing Array \citep[PPTA;][]{m08}, and the European Pulsar Timing Array \citep[EPTA;][]{jsk+08}. The three PTAs collaborate to form the International Pulsar Timing Array \citep[IPTA;][]{haa+10} which will result in increased sensitivity to GWs through more data and longer time-spans than any single PTA. PTAs are most sensitive to GWs with frequencies in the nanohertz regime (i.e., $10^{-9}$ Hz -- $10^{-7}$ Hz). Potential sources of GWs in this frequency range include supermassive black hole binary systems (SMBHBs) \citep{svc08}, cosmic (super)strings \citep{Olmez:2010bi}, inflation \citep{sa79}, and a first order phase transition at the QCD scale \citep{ccd+10}. The community has thus far focused mostly on stochastic backgrounds produced by these sources; however, sufficiently nearby individual SMBHBs may produce detectable continuous waves with periods on the order of years for masses in the range $10^8 {\rm M}_{\odot}$--$10^{10}{\rm M}_{\odot}$ \citep{wl03,svv09,sv10}. Several upper limits have been placed on the strength of the stochastic background \citep{ktr94, jhs+06,vhj+11, dfg+12, src+13} and continuous waves \citep{jll+04, yhj+10} but no successful detection has yet been made. In this paper we will use current-generation frequentist \citep{esc12} and Bayesian \citep{e13} data analysis pipelines to compute upper limits on the strain amplitude of continuous GWs from SMBHBs in circular orbits. We make use of the 5-year, 17 pulsar data set obtained as part of the NANOGrav project \citep{dfg+12}. In Section \ref{sec:obs} we briefly review the radio observations and timing analysis. In Section \ref{sec:gws} we describe the signal model used to describe the continuous GWs in the PTA band. In Section \ref{sec:search} we describe, in detail, the time domain likelihood function, the noise model, and the frequentist and Bayesian search pipelines. In Section 5 we apply our search and upper limit pipelines to the NANOGrav dataset and report our findings. In section \ref{sec:conclusions} we summarize our results. In the Appendices we derive the form of the frequency evolution of SMBHBs, and give full details on the computational implementation of our Bayesian code. | \label{sec:conclusions} In this paper we have performed various searches for continuous GWs from non-spinning SMBHBs in circular orbits using both frequentist and Bayesian techniques. Specifically, we have run a fixed-noise frequentist and Bayesian pipeline, as well as a varying noise Bayesian pipeline. In the absence of any detections we have placed upper limits on the strain amplitude of continuous GWs as a function of GW frequency. We have also computed a lower limit on the distance to such SMBHBs as a function of sky location, as well as placing constraints on the differential coalescence rate of such SMBHBs. Our sky-averaged upper limits on strain amplitude as a function of frequency are a factor of $\sim 3$ times more constraining than the previously published upper limits \citep{yhj+10} and we see good agreement between all three data analysis methods. Although improving, our limits still lie well above the amplitudes of individual sources produced from several realizations of an optimistic SMBHB population. We have shown that with good estimates of the intrinsic noise we can rule out any sources with luminosity distance $<2$ Gpc and a chirp mass of $\sim 10^{10}{\rm M}_{\odot}$. Unfortunately we are not yet able to place any constraints on predictions for the coalescence rate of SMBHBs obtained from both theory and observations. Throughout the paper we have made several statements about what is needed for completely \emph{robust} data analysis techniques and what will be required from future PTAs in order to secure a \emph{confident} detection of a continuous GW. These statements can be summarized as follows: \begin{enumerate} \item Currently we have no way to confidently separate intrinsic noise in the residuals from any GW that may be present. Therefore, it is necessary to include both noise and GW parameters in any data analysis pipeline that aims to be truly robust. This is not to say that fixed-noise methods should not be used; instead we advocate a hierarchical approach where the faster fixed-noise methods are used as a first-pass and then followed up with a full GW plus noise search. Lastly, a signal with more information, such as that from an eccentric system, could help break this degeneracy between signal and noise models and will be the subject of a future paper. \item Even with simultaneous noise and GW characterization, unless we have several well timed pulsars (with very similar timing precision on all) with decent sky coverage, a \emph{confident} detection of a continuous GW is unlikely even if the signal is loud. \end{enumerate} While not as likely as a detection of a stochastic GW background, with continually improving timing precision, the addition of new pulsars to PTAs and improved data analysis techniques, prospects are good for obtaining astrophysically constraining GW limits, or possibly even a detection of a continuous GW, over the next decade. | 14 | 4 | 1404.1267 |
1404 | 1404.4990_arXiv.txt | We investigate the formation of multiple--planet systems in the presence of a hot Jupiter using extended \textit{N}--body simulations that are performed simultaneously with semi--analytic calculations. Our primary aims are to describe the planet formation process starting from planetesimals using high--resolution simulations, and to examine the dependences of the architecture of planetary systems on input parameters (e.g., disk mass, disk viscosity). We observe that protoplanets that arise from oligarchic growth and undergo type I migration stop migrating when they join a chain of resonant planets outside the orbit of a hot Jupiter. The formation of a resonant chain is almost independent of our model parameters, and is thus a robust process. At the end of our simulations, several terrestrial planets remain at around 0.1 AU. The formed planets are not equal--mass; the largest planet constitutes more than 50 percent of the total mass in the close--in region, which is also less dependent on parameters. In the previous work of this paper \citep{ogihara_etal13}, we have found a new physical mechanism of induced migration of the hot Jupiter, which is called a crowding--out. If the hot Jupiter opens up a wide gap in the disk (e.g., owing to low disk viscosity), crowding--out becomes less efficient and the hot Jupiter remains. We also discuss angular momentum transfer between the planets and disk. | \label{sec:intro} Over 900 extrasolar planets have been discovered so far; a large fraction of them are close--in giant planets (``hot Jupiters'' or HJs) which account for more than 20 percent of all exoplanets. Because HJs are considered to be gaseous planets, they are formed in protoplanetary disks during their formation era, which may affect the subsequent formation of terrestrial planets. For the origin of HJs, there are two commonly--invoked models that include type II migration (e.g., \citealt{lin_etal96}) and tidal circularization of high--eccentricity planets (e.g., \citealt{nagasawa_etal08}) based on the standard scenario of planet formation. In addition, we introduce a hybrid scenario of planet formation \citep{inutsuka09}, in which giant planets that formed through gravitational instability can survive until the accretion phase of terrestrial planets. Recent resistive magnetohydrodynamic simulations of the formation of protostars and protoplanetary disks show the formation of multiple planetary--mass objects in the massive circumstellar disks in their formation stages (\citealt{inutsuka_etal10}; \citealt{machida_etal10,machida_etal11a,machida_etal11b,machida_etal14}). Those objects tend to migrate inward rapidly in the early evolutionary phase of disks (\citealt{machida_etal11b}; \citealt{baruteau_etal11}). To determine the fates of the objects, realistic numerical simulations of long--term evolution of those systems are required, but still remains computationally infeasible (see, however, \citealt{vorobyov_basu10} for their efforts on 2D simulations without magnetic field). On the other hand, recent observations of protoplanetary disks (e.g., \citealt{andrews_etal11}) and theoretical work on the disk accretion (e.g., \citealt{suzuki_inutsuka09}; \citealt{suzuki_etal10}; \citealt{fromang_etal13}; \citealt{bai_stone13}) indicate that an inner cavity tends to be created in a relatively early phase of disk accretion stage, which eventually stops the planetary migration in the inner region of the disk. Therefore we can envision that some of gaseous planetary--mass objects formed through the gravitational fragmentation of massive disks undergo halfway migration to the inner regions and remain as HJs. This model provides a possible origin of the HJ, in addition to the commonly--invoked models. Giant planets, such as HJs, gravitationally influence the formation of terrestrial planets in several ways. To date, the formation of terrestrial planets in the presence of giant planets has been studied from several perspectives (e.g., \citealt{kortenkamp_etal01}; \citealt{levison_agnor03}; \citealt{fogg_nelson07, fogg_nelson09}). For example, \citet{raymond_etal06} performed \textit{N}--body simulations to investigate the formation of habitable planets during and after giant planet migration and found that water--rich planets can survive outside the orbit of giant planets. Giant planets can open up a ring--like gap in a protoplanetary disk (e.g., \citealt{crida_etal06}; \citealt{tanigawa_ikoma07}), outside of which a radial pressure maximum is created. \citet{ayliffe_etal12} demonstrated with SPH simulations that the inward migration of meter--sized solid bodies is efficiently halted at the pressure maximum, which may trigger gravitational collapse (see also \citealt{lyra_etal09}). \citet{kobayashi_etal12} conducted numerical simulations that include collisional fragmentation of solid bodies developed by \citet{kobayashi_etal10, kobayashi_etal11} and found that fragments produced from planetesimals are accumulated at the edge of a Jovian--opened density gap, leading to the rapid formation of Saturn's core. Several \textit{N}--body investigations have also been carried out. \citet{thommes05} considered the case in which a giant planet is located at about 5 AU and several planetary cores placed outside its orbit undergo type I inward migration. They observed that such planetary cores cease their migration by being captured into mean motion resonances (MMRs) with the giant planet. Several bodies are in 3:2 or 2:1 MMRs at the end of simulation, thus many bodies are in 1:1 commensurabilities with each other. Planetary cores are not lost via collision with the central star, which may act to enhance the growth of planets outside the orbit of the giant planet. Type I migration can also be halted if the planet is in a region of positive surface density gradient where the coorbital corotation torque acts as a planet trap \citep{masset_etal06}, which is neglected by \citet{thommes05}. \citet{morbidelli_etal08} calculated the orbital evolution of several solid planets that undergo type I migration toward the outer edge of the density gap and confirmed that the planets can survive at the planet trap. \citet{jakubik_etal12} performed \textit{N}--body investigations of protoplanets ($N$=10--30) in the presence of Jupiter and Saturn to examine the possibility of the accretion of Uranus and Neptune outside the gap opened by the giant planets. They found that more than two planets form at the planet trap, where the most massive planets are much larger than the second most massive cores. We perform \textit{N}--body simulations of the accretion of close--in terrestrial planets in the presence of an HJ. In this study, the growth of protoplanets is calculated using high--resolution simulations, and the long term evolution for about $10^9$ orbits is examined. In addition, unlike most previous \textit{N}--body simulations where all bodies that are handled in the calculation are placed in the initial setup, thus rather limiting the calculation region, we use a new, more realistic code in which the \textit{N}--body simulation is combined with a semianalytical calculation of planet formation in order to consider the migration of protoplanets from distant regions. Furthermore, we use several parameters that indicate uncertainties in the planet formation model (e.g., disk profile, type I migration rate) and vary them over wide ranges to discuss the dependences of the results on the parameters. We especially focus on the close--in region, and thus our results are suitable for comparison with observational data of exoplanets. Recent observations have discovered multiple planetary systems in such regions, and several basic properties have been revealed. For example, there is a lack of companion planets near the orbit of HJs (e.g., \citealt{steffen_etal12}). \citet{ogihara_etal13} (hereafter OIK13) investigated the formation of terrestrial planets outside the orbit of HJs assuming a relatively high--viscosity disk and found that the orbit of the HJ moves inward by being pushed by terrestrial planets that are captured in a 2:1 MMR with the HJ, which is called ``crowding--out.'' Through this mechanism, we proposed a possible origin for the lack of additional planets in HJ systems. In this paper, we also discuss the dependence of the results on disk viscosity. In the previous letter (OIK13), we proposed a new physical mechanism of crowding--out, and this paper extends OIK13 mainly in terms of the following points of view. (1) By performing high--resolution \textit{N}--body simulations of planetary accretion from planetesimals, we investigate planet formation along with the growth of protoplanets. (2) We adopt several model parameters and vary them over wide ranges in order to examine the dependences of the results on the parameters. (3) We also carry out in--depth discussions, for example, on angular momentum transfer between planets. The structure of this paper is as follows. In Section~\ref{sec:model}, we describe the numerical methods; in Section~\ref{sec:results1}, we present the results of high--resolution \textit{N}--body simulations; and in Section~\ref{sec:results2}, we show the results of \textit{N}--body simulations using model parameters varied over wide ranges. In Section~\ref{sec:torques}, we analyze the results and examine angular momentum transfer. In Section~\ref{sec:discussion}, we give a discussion of the parameter dependence of the results, and in Section~\ref{sec:observation}, we compare our results with observational properties. In Section~\ref{sec:conclusions}, we offer our conclusion. | \label{sec:conclusions} We have investigated planetary accretion in the presence of an HJ with a range of various model parameters. Through detailed \textit{N}--body calculations, we confirm the following planet formation process. \begin{enumerate} \item Embryo formation stage: the first stage after formation of planetesimals is the oligarchic growth stage. Planetesimals grow to protoplanets while keeping their mutual orbital separations $\simeq 8 r_{\rm H}$. This stage terminates when the embryo mass reached the isolation mass or if the embryos begin to migrate faster. The typical duration of this stage is $10^5~T_{\rm K} \simeq 3 \times 10^3~{\rm yr}$. \item Migration stage: the protoplanets undergo inward migration with the migration timescale $t_a$, which is determined by the embryo mass and several parameters (e.g., $f_{\rm g}$ and $C_{\rm I}$). The innermost body ceases its migration when it is trapped by the gap edge or captured in a 2:1 MMR with the HJ, whichever happens first. During this stage, embryos that formed in the outer region sequentially migrate inward before the depletion of the gas disk. They are captured in MMRs with inner planets that reside in a chain of resonant planets or undergo close encounters with the inner bodies leading to a rearrangement of orbital configurations. The innermost planet tends to be the largest body, which consists of about 50 percent of the total mass of the close--in planets. When the resonant chain is captured in a 2:1 resonance with the HJ, the HJ can be pushed inward to the vicinity of the central star, the migration speed of which depends on the conditions. This stage continues until the gas has almost decayed $(t \la 3 t_{\rm dep})$. \item Final stage: after the gas depletion, final orbital configurations are established. In some cases, as the effect of eccentricity--damping weakens, planets exhibit local orbital crossings resulting in giant impacts. Even after local orbital instability, several commensurabilities tend to remain, although in some cases all resonant relations are lost via collisions. \end{enumerate} We have also determined the dependence of our results on model parameters. Several properties of the final states can be summarized as follows. \begin{description} \item[Mass:] The typical mass of the largest planet is $\simeq 1-2~M_\oplus$. The mass ratio of the largest planet and the total mass in planets is large $(\simeq 0.4-0.8)$. Owing to the stalling of migration, solid bodies are accreted by one or a few planets, and eventually a large difference in mass between the largest planet and small planets is created. The mass also hardly depends on $C_{\rm I}$. An increase/decrease in $f_{\rm d}$ results in an increase/decrease of the embryo growth rate and mass. \item[MMR:] We find that the formation of chains of resonant planets is robust if both migration and trapping by the edge or the 2:1 resonance with the HJ are effective. The typical commensurability in the resonant chain is between the 4:3 resonance and the 9:8 resonance, which also weakly depends on the input parameters (e.g., $C_{\rm I}$ and $f_{\rm d}$). We also observe a tendency that orbital crossings after gas dissipation occur more frequently in the case of large $f_{\rm d}$. Almost no planets formed are captured in 1:1 coorbital resonances. \end{description} Through a series of simulations, our understanding of the reason for the lack of companion planets in HJ systems is improved. If $\alpha = 10^{-4}$ is assumed, it is difficult to explain the observations. Therefore, this may suggest that the disk viscosity near the HJ is high $(\alpha \simeq 10^{-2})$ and the crowding--out of the HJ by terrestrial planets is effective. This study provides several suggestions for future study. One is the fact that the results for the final orbital configuration are almost identical for small--$N$ and large--$N$ simulations. Thus, for the purpose of examining the configuration of final states, \textit{N}--body simulations can be started with relatively large protoplanets. In addition, we show capability of numerical simulations that combine an \textit{N}--body code with a semi--analytic population synthesis model. We also find the orbital velocity of planets that are located near the HJ to be altered, resulting in the transport of angular momentum through gas drag. This should be investigated in detail using high--resolution dynamical simulations in which the gas motion is also calculated by a magneto--hydrodynamical code. This study can be applied to the formation of planets outside warm/cool Jupiters, which may solve several issues regarding the formation of gaseous/icy planets in the Solar system. As stated in Sections~\ref{sec:intro} and \ref{sec:model}, it is of particular importance to resolve the gas flow around HJs and to examine the structure and evolution of the inner disk, which should be investigated in future studies. \subsection*{ACKNOWLEDGMENT} We thank the anonymous referee for useful comments. We also thank Shoichi Oshino, Eiichiro Kokubo, and Yasunori Hori for helpful discussions, and thank Jennifer M. Stone for variable comments. Numerical computations were in part conducted on the GRAPE system and general-purpose PC farm at the Center for Computational Astrophysics, CfCA, of the National Astronomical Observatory of Japan. This work is supported by a Grant-in-Aid for JSPS Fellows (23004841). | 14 | 4 | 1404.4990 |
1404 | 1404.2578_arXiv.txt | The evolution of magnetic fields in galaxies is still an open problem in astrophysics. In nearby galaxies the far-infrared-radio correlation indicates the coupling between magnetic fields and star formation. The correlation arises from the synchrotron emission of cosmic ray electrons traveling through the interstellar magnetic fields. However, with an increase of the interstellar radiation field (ISRF), inverse Compton scattering becomes the dominant energy loss mechanism of cosmic ray electrons with a typical emission frequency in the X-ray regime. The ISRF depends on the one hand on the star formation rate and becomes stronger in starburst galaxies, and on the other hand increases with redshift due to the evolution of the cosmic microwave background. With a model for the star formation rate of galaxies, the ISRF, and the cosmic ray spectrum, we can calculate the expected X-ray luminosity resulting from the inverse Compton emission. Except for galaxies with an active galactic nucleus the main additional contribution to the X-ray luminosity comes from X-ray binaries. We estimate this contribution with an analytical model as well as with an observational relation, and compare it to the pure inverse Compton luminosity. Using data from the \textit{Chandra} Deep Field Survey and far-infrared observations from ALMA we then determine upper limits for the cosmic ray energy. Assuming that the magnetic energy in a galaxy is in equipartition with the energy density of the cosmic rays, we obtain upper limits for the magnetic field strength. Our results suggest that the mean magnetic energy of young galaxies is similar to the one in local galaxies. This points toward an early generation of galactic magnetic fields, which is in agreement with current dynamo evolution models. | Observations show that magnetic fields contribute significantly to a galaxys energy budget. The current picture predicts the magnetic energy density to be roughly $0.89~\mathrm{erg~cm}^{-3}$, which is comparable to the thermal kinetic energy density with roughly $0.49~\mathrm{erg~cm}^{-3}$, and the energy density of cosmic rays to be $1.39~\mathrm{erg~cm}^{-3}$ \citep{Draine1978}. Moreover, the magnetic energy is distributed over many orders of magnitudes in physical length scales. It is thus expected that the magnetic field plays a major role in the dynamics of the whole galaxy and also on smaller scales down to individual star formation processes. \\ The structure of magnetic fields in local galaxies is known quiet well \citep{BeckEtAl1999,Beck2011}. A spiral galaxy typically shows a large-scale magnetic field, which follows the optical spiral arms and is strongest in the interarm regions. The typical coherence length is 10 kpc and the strength roughly $10^{-5}$ G. Even more important in terms of the energy density is the small-scale unordered magnetic field, which exceeds the one of the ordered field by a factor of a few. \\ The origin and evolution of galactic magnetic fields is still an active field of research with many open questions to answer \citep{KulsrudZweibel2008}. Theory predicts that unordered fields were generated already in young galaxies by a turbulent dynamo. This mechanism amplifies weak magnetic seed fields by randomly stretching, twisting, and folding the field lines in turbulent motions \citep{Kazantsev1968,BrandenburgSubramanian2005,SchoberEtAl2012.1,SchoberEtAl2012.3,BovinoEtAl2013}. Semi-analytical calculations \citep{SchoberEtAl2013} as well as numerical simulations \citep{BeckEtAl2012,LatifEtAl2013} show that the turbulent dynamo can produce a field of the order of $10^{-6}$ G within a few Myrs. The large-scale magnetic field is likely produced by a large-scale galactic dynamo, which operates on much longer timescales then the turbulent dynamo. \\ In order to test the evolution scenario of galactic fields, in addition to the analytical and numerical calculations an observational test is essential. However, the problem is that standard methods for magnetic field observations are difficult to pursue at high redshifts. Only indirect observations like the CMB bispectrum \citep{ShiraishiEtAl2012}, the non-detection of TeV blazers \citep{NeronovVovk2010} and Faraday rotation measurements \citep{HammondRobishawGaensler2012}, which detect the magnetic field strength along the line of sight, can be applied at high redshifts. \\ A very frequently used method to estimate magnetic field strengths in galaxies is synchrotron emission, which is observed in the radio band. This type of radiation is emitted by high energy cosmic ray electrons traveling through the magnetized interstellar medium (ISM). With the intensity of synchrotron emission one can calculate the energy density of cosmic rays. By assuming that cosmic rays and interstellar magnetic fields are in energy equilibrium the magnetic field strength can be computed \citep{BeckKrause2005}. \\ A further important observation was made by \cite{YunEtAl2001}, who observed a correlation between the radio flux and the far-infrared (FIR) flux. This FIR-radio correlation shows a coupling between the star formation rate (SFR), which determines the FIR flux, and the magnetic field in the ISM. A new interpretation of this correlation was suggested by \cite{SchleicherBeck2013}. They claim that the supernova rate, which is proportional to the SFR, sets the amount of turbulence in the ISM, which in turn determines the magnetic energy produced by turbulent dynamo. Due to energy conservation and additional efficiency effects a turbulent dynamo can only convert a certain fraction of turbulent kinetic energy into magnetic energy \citep{FederrathEtAl2011.2}. A coupling between the SFR (FIR flux) and the magnetic field (radio flux) can thus be assumed in local galaxies. \\ But what happens in higher redshifted galaxies? Here one needs to take into account the rapidly growing number of cosmic microwave background (CMB) photons. These can interact with the cosmic ray electrons in inverse Compton scattering, typically resulting in X-ray photons. \cite{SchleicherBeck2013} have shown that inverse Compton scattering is in fact the dominant energy loss mechanism of cosmic ray electrons at high redshifts. Thus, we expect a breakdown of the FIR-radio correlation and X-ray bright galaxies above a critical redshift. \\ We propose here a method based on the inverse Compton scattering process to gain information about cosmic rays and magnetic fields in young galaxies. With a given SFR and interstellar radiation field (ISRF) we determine the inverse Compton component of the X-ray luminosity of a redshifted star-forming galaxy. From this we calculate the energy of the cosmic ray electrons and the resulting total cosmic ray energy density. By assuming equipartition between the cosmic ray energy density and the magnetic field energy density, we are able to predict an upper limit of the field strength. \\ New instruments provide exceptionally good data of galaxies at very high redshifts. Especially the deep fields of the \textit{Chandra} satellite\footnote{http://chandra.harvard.edu/}, the extended \textit{Chandra} Deep Field-South (E-CDF-S) and the \textit{Chandra} Deep Field-North (CDF-N), include lots of information about the X-ray properties of extremely low luminosity objects. As a very important future tool we discuss also limits that will be obtained by X-ray observatory \textit{Athena+}\footnote{http://www.the-athena-x-ray-observatory.eu/}. Combination with the new FIR data from the Atacama Large Millimeter/submillimeter Array (ALMA\footnote{http://www.almaobservatory.org/}) can lead to new conclusions. The ALMA LABOCA E-CDF-S Submillimeter Survey makes a multi-wavelength analyses possible. \\ The paper is structured as follows: We present our model of young galaxies in section \ref{Galaxies}, including the SFR, the ISRF and the cosmic ray spectrum. In section \ref{Breakdown} we summarize the results of \cite{SchleicherBeck2013}, who proposed the breakdown of the FIR-radio correlation. The combination of our ISRF and the cosmic ray spectrum results in a typical inverse Compton spectrum. The derivation of the inverse Compton X-ray luminosity is given in section \ref{ExpectedIC}. We discuss additional X-ray sources in section \ref{OtherXrays}. In the last section, section \ref{Examples}, we apply our model to some exemplary galaxies, for which data from \textit{Chandra} and ALMA is available. We draw our conclusions in section \ref{Conclusions}. \newpage | \label{Conclusions} In this work we construct a model for the X-ray emission of star-forming galaxies via inverse Compton scattering as a function of redshift. We model the star formation rate (SFR) history, the evolution of the interstellar radiation field (ISRF) and the cosmic ray spectrum. The inverse Compton scattering process between high energy cosmic ray electrons and the ISRF is quantified and analyzed in terms of different properties of the galaxy. We focus on two galaxy models: a galaxy with normal star formation rate, similar to the Milky Way, and a starburst galaxy similar to M82. With a detailed description of the ISRF and the steady state cosmic ray spectrum we are able to calculate the expected inverse Compton luminosity. \\ In order to estimate the significance of the inverse Compton scattering compared to other galactic X-ray sources, we investigate the role of X-ray binaries, which are one of the main X-ray sources in nearby galaxies. We summarize an analytical model for the number of high-mass X-ray binaries (HMXB) and low-mass X-ray binaries (LMXB) by \citet{GhoshWhite2001}. For comparison we also discuss an observational correlation for X-ray binary luminosity by \citet{LehmerEtAl2010}. Furthermore, we estimate the influence of supernova remnants on the total galactic X-ray luminosity. \\ In the last part of the paper (section \ref{Examples}) we apply our model to real observations. As observational input we use M82 as a test case and two higher redshifted galaxies of the data set of \citet{WangEtAl2013}, which have not been identified as hosts of active galactic nuclei (AGNs). We compare the observed X-ray luminosity with the one resulting from our inverse Compton model. This way we can fix the free parameter in our model, namely the normalization of the cosmic ray spectrum. In the next step we calculate the total energy of cosmic rays and assume that it is in equipartition with the magnetic energy. \\ The main findings of this work are: \begin{itemize} \renewcommand{\labelitemi}{$\bullet$} \item{The spectral energy distribution $u_{\mathrm{ISRF},\nu}$ of a normal galaxy is dominated by the cosmic microwave background (CMB), while the one of a starburst galaxy is dominated by the cold infrared (IR) component at least at moderate redshifts (see figure \ref{ISRF_nu}). The strong IR component makes inverse Compton scattering in starburst galaxies more efficient (see also figures \ref{Efficiency_nuin} and \ref{L_z__z}).} \item{Our analysis of the energy loss timescales of cosmic ray electrons (see figure \ref{timescales_SFR}) has shown, that the inverse Compton scattering is not dominant in galaxies with normal star formation. At low redshifts $z$ bremsstrahlung and synchrotron emission are most important. With increasing redshift the inverse Compton timescale decreases, but even at $z=5$, bremsstrahlung is still dominating. On the other hand in starburst galaxies energy losses proceed mostly via inverse Compton scattering. These galaxies are thus in the focus of this work.} \item{The X-ray flux from pure inverse Compton scattering can be detected with \textit{Chandra} up to $z\approx1$ for starburst galaxies with $\dot{M}_\star \gtrsim 200~\mathrm{M}_\odot \mathrm{yr}^{-1}$. With the future X-ray observatory \textit{Athena+} detections up to $z\gtrsim2$ will be possible (see figure \ref{SIC_SFR}).} \item{Comparison of the expected inverse Compton luminosity with other X-ray sources shows that supernova remnants are negligible. X-ray binaries play a more important role. In our model their luminosity is a factor of 2 brighter than the inverse Compton luminosity at present day. At redshifts above roughly 2 inverse Compton luminosity becomes comparable or even dominant over the X-ray binaries (see figure \ref{LXB_z}).} \item{With our model the energy density of cosmic rays can be determined directly from the observed X-ray flux under the assumption that the flux only origins from inverse Compton scattering. The results for different redshifts are plotted in figure \ref{uCRB_S__givenSFR}.} \item{We apply our model to the two galaxies from the data set of \citet{WangEtAl2013} that have not been clearly identified as hosting an AGN. Our results for the fraction of energy going from supernovae into cosmic ray acceleration is higher then the theoretically expected value of 10 percent. This suggests that we are overestimating the inverse Compton luminosity and thus the energy of cosmic rays by a factor of up to 9 (see discussion in section \ref{TestM82}). Our results for the cosmic ray density and the equipartition field strengths are thus only upper limits. Depending on the galactic volume we find values for the magnetic field strength of roughly $10^{-4}-10^{-3}$ G for the exemplary galaxies (see table \ref{TableResults}).} \end{itemize} There are several uncertainties in our model including the modeling of the cosmic ray spectrum, the additional X-ray sources and the evolution and total size of the galaxy volume. Most of the galaxies observed at high redshift include AGNs. We try not to include the X-ray emission of these by using the uncorrected X-ray luminosities given in \citet{WangEtAl2013}. However, we still substantially overestimate the X-ray luminosity from inverse Compton scattering. It thus is essential to model the X-ray emission of galaxies in more detail in future. \\ We expect that also the available data of high redshifted galaxies will increase in the next years. For our studies especially observations of distant starburst galaxies without active galactic nuclei would be important. With X-ray data from the \textit{Chandra} deep fields the next step would be to identify infrared counterparts of X-ray galaxies, in order to determine their SFR. This is possible with the \textit{ALMA} telescope. Further the next generation of X-ray telescopes is planned and we hopefully will receive a lot of data with \textit{Athena+}. \\ With these new technologies our knowledge of the origin and evolution of galactic magnetic field hopefully will increase. This will help us to understand moreover the evolution of galaxies in total, as magnetic fields play a crucial role in many physical processes in the interstellar medium and the dynamics of the whole galaxy. | 14 | 4 | 1404.2578 |
1404 | 1404.7441_arXiv.txt | Over the years, directed surveys and incidental spectroscopy have identified 12 Wolf-Rayet (WR) stars in the SMC and 139 in the LMC, numbers which are often described as ``{\it essentially} complete." Yet, new WRs are discovered in the LMC almost yearly. We have therefore initiated a new survey of both Magellanic Clouds using the same interference-filter imaging technique previously applied to M31 and M33. We report on our first observing season, in which we have successfully surveyed $\sim15$\% of our intended area of the SMC and LMC. Spectroscopy has confirmed 9 newly found WRs in the LMC (a 6\% increase), including one of WO-type, only the third known in that galaxy and the second to be discovered recently. The other eight are WN3 stars that include an absorption component. In two, the absorption is likely from an O-type companion, but the other six are quite unusual. Five would be classified naively as ``WN3+O3~V," but such a pairing is unlikely given the rarity of O3 stars, the short duration of this phase (which is incommensurate with the evolution of a companion to a WN star), and because these stars are considerably fainter than O3~V stars. The sixth star may also fall into this category. CMFGEN modeling suggests these stars are hot, bolometrically luminous, and N-rich like other WN3 stars, but lack the strong winds that characterize WNs. Finally, we discuss two rare Of?p stars and four Of supergiants we found, and propose that the B[e] star HD~38489 may have a WN companion. \vskip -10pt | \label{Sec-intro} \vskip -10pt Wolf-Rayet (WR) stars are the evolved descendants of massive O-type stars. Mass loss during the main-sequence phase, possibly aided by episodic mass ejection during the Luminous Blue Variable (LBV) stage and/or Roche-lobe overflow in close binary systems, strips off the star's H-rich outer layers. This mass loss, plus mixing from the interior, helps to reveal enhanced He and N (the products of CNO H-burning) at the surface. Such a star is identified spectroscopically as a WN-type WR. If the star has sufficiently high mass, then additional evolution, mass loss, and mixing will lead to a WC-type WR, with enhanced C and O (the products of He-burning). Further evolution may lead to one of the very rare WO-type WRs. The spectra of WRs are characterized by broad, strong emission lines as these lines are formed in an extended, expanding atmosphere/stellar wind; if absorption is present in the spectrum, it is usually (but not always) due to a close OB companion. Reviews are provided by Maeder \& Conti (1994), Crowther (2008) and Massey (2013), among others. The relative number of WN- and WC-type WRs as a function of metallicity has long been used as a key diagnostic of massive star evolutionary models. Main-sequence mass-loss rates are larger at higher metallicities, as they are driven by radiation pressure acting on highly ionized metal ions. (The metallicity-dependence of wind-driven mass loss was first offered as an explanation for the changing WC to WN number ratio by Vanbeveren \& Conti 1980.) The conventional wisdom has long been that while single-star evolutionary models do a good job of matching the WC/WN ratio at lower metallicities (such as those found in the Magellanic Clouds), they fail at the higher metallicities characteristic of the center of M33, which has a metallicity that is approximately solar, and M31, which has a metallicity that is approximately $2\times$ solar. Examples of this are shown by Massey \& Johnson (1998), Meynet \& Maeder (2005), and most recently by Neugent et al.\ (2012a). The linchpins for such comparisons at lower metallicities are the Magellanic Clouds. They are the nearest star-forming galaxies to our own, and studies over the years have identified 139 WRs in the LMC (134 stars listed in the Breysacher et al.\ 1999 catalog [BAT99] plus 7 WRs subsequently discovered by various studies, minus 2 that have been demoted to Of-type; see Table 3 of Neugent et al.\ 2012b and references therein\footnote{Note that the reference for the discovery of [M2002] LMC 15666 as a WR star is incorrectly given in that table. Instead, the discovery should be credited to Gvaramadze et al.\ (2012), who reported the discovery of a WR star in the LMC, but did not provide any coordinates or cross-IDs in that brief conference proceeding. Brian Skiff identified the object from their images, and this is the source of the information in Neugent et al.\ (2012b) and in SIMBAD. It is the NE component of a 2\arcsec\ pair, with the companion a B0~V star.}) and 12 in the SMC (8 listed by Azzopardi \& Breysacher 1979a, plus 4 WRs subsequently discovered; see Table 1 of Massey et al.\ 2003 and references therein). For years it has been commonly accepted that these numbers are {\it essentially} complete. For instance, in their report of discovering two WRs in the LMC, Howarth \& Walborn (2012) suggested that perhaps as many as a dozen or so weak-lined WNEs (10\% of the LMC's total WR population) remained to be found, but no more. However, even before the Howarth \& Walborn (2012) paper appeared in print, Neugent et al.\ (2012b) announced the discovery of a very strong-lined WO-type WR in the LMC. Similarly, Massey \& Duffy (2001) concluded that the completeness of their survey for WRs in the SMC could not ``preclude a WR star (or two) [from] having been overlooked," a statement that proved prescient, as another SMC WN star was chanced upon within a year (Massey et al.\ 2003). These discoveries were unsettling, and forced us to examine how we came to know the WR content of the Magellanic Clouds, and what would be involved in conducting a more thorough survey, particularly in the LMC where the number of WR stars is large enough to provide robust statistics. Some of the discoveries of WRs in the Clouds came about as part of general spectroscopy, while others came about as a result of directed objective prism searches. Of the 158 ``brightest stars" in the Magellanic Clouds, 15 were classified as WR type (Feast et al.\ 1960) through various spectroscopic surveys. An objective prism survey of the LMC aimed at finding WRs by Westerlund \& Rodgers (1959) resulted in the identification of 50 WRs, 30 of which were in common with those known from the HD catalog. (See also Westerlund \& Smith 1964.) Deeper and more complete surveys for WRs in the Magellanic Clouds were carried out by Azzopardi \& Breysacher (1979a, 1979b, 1980). Their surveys employed an objective prism in combination with an interference filter that isolated the region around C~III $\lambda 4650$ and He~II $\lambda 4686$ (the two strongest optical emission lines in the spectra of WC- and WN-type WRs, respectively) in order to reduce problems with crowding and sky background that would have occurred with the use of the objective prism by itself. These studies added 4 additional WRs to the 4 that were previously known in the SMC (Breysacher \& Westerlund 1978), and 17 additional WRs to the 80 known in the LMC (Fehrenbach et al.\ 1976). It is worth noting that {\it all} of the new WRs found by Azzopardi \& Breysacher (1979a, 1979b, 1980) were of WN type. Indeed, the difficulty in identifying unbiased samples of WRs has been described by Massey \& Johnson (1998): the strongest optical line in WC stars (typically C III $\lambda4650$) is about 4$\times$ stronger (on average) than that found in WN stars (He~II $\lambda$4686). The weakest-lined WN stars have He~II $\lambda 4686$ equivalent widths of just $-$10~\AA, in contrast to the $-$50~\AA\ equivalent widths found in the weakest-lined WCs (see, e.g., Fig.~1 of Massey \& Johnson 1998). Thus, a survey for WRs has to be sufficiently sensitive to detect weak-lined WNs if it is going to be useful for comparing with the predictions of the evolutionary models. Armandroff \& Massey (1985) described a set of interference filters that has proven very effective at this task: three 50~\AA\ wide filters centered on C III $\lambda 4650$, He~II $\lambda 4686$, and neighboring continuum at $\lambda 4750$ are used to image a region with CCDs, and the brightness of objects compared. This was done by Armandroff \& Massey (1985), Massey et al.\ (1986, 1992), and Massey \& Johnson (1998) to survey small regions of Local Group galaxies beyond the Magellanic Clouds (e.g., parts of M31, M33, NGC~6822, IC~1613, IC 10, and NGC~6822) using the relatively tiny CCDs that were then available. Crowded-field photometry algorithms (i.e., PSF-fitting with {\it DAOPHOT}, Stetson 1987) were then used to find WR candidates that were significantly brighter in one of the on-band filters compared to the expected photometric errors. More recently, we have been able to take advantage of CCD cameras with much larger fields of view to survey all of M33 (Neugent \& Massey 2011) and M31 (Neugent et al.\ 2012a). These two surveys used image-subtraction techniques to search for candidates in order to avoid the many false positives that plagued the photometry method. Spectroscopic confirmation of these candidates demonstrated that we were finding WRs as weak-lined as any known, and indeed finding new Of-type stars with even smaller emission-lines fluxes, lending some confidence that these surveys were sufficiently sensitive and deep to be detecting the vast majority of the WNs. For the SMC, Massey \& Duffy (2001) undertook such a survey using a wide-area CCD on the CTIO Curtis Schmidt. It covered 9.6 deg$^2$ and spectroscopy confirmed two new WR stars (both WNs), bringing the total number of known WRs in the SMC to 11, the result of photometry of over 1.6 million stars. Still, the survey had some deficiencies: the pixel size with the instrument was 2\farcs3, reducing the precision in crowded regions. The areal coverage, while large, did not cover all of the star-forming regions of the SMC. As mentioned above, the next year saw the discovery of a 12th SMC WR (another WN) which had been overlooked in the Massey \& Duffy (2001) survey because of crowding. For the LMC, in the 20 years between the Azzopardi \& Breysacher (1979b, 1980) survey and the compilation of the BAT99 ``Fourth Catalogue," the number of WRs known grew from 97 to 134 (roughly 40\%), mostly as a result of accidental discovery through spectroscopy of stars in selected regions of the Clouds, with only 6 found as the result of new objective prism surveys for WRs (Morgan \& Good 1985, 1990). Since BAT99, the number of known LMC WRs has grown to 139 (an increase of 4\%), including two demotions of WRs to Of-type. To us, our discovery (Neugent et al.\ 2012b) of a very rare (and very strong-lined) WO-type WR in Lucke-Hodge 41, a well-studied LMC OB association (harboring, among other things, another WR star and two LBVs, including the archetype S Doradus itself), seemed a wakeup call. We are in the somewhat embarrassing position of knowing more about the WR content of M33 and M31 (at distances of $\sim$ 800 kpc) than we do about our next-door neighbors, the Magellanic Clouds (at distances of 50-60 kpc, i.e., $\sim 15 \times$ closer). The question, then, was what to do about it. We decided to survey the Magellanic Clouds for WRs using the same method that we had so successfully employed in M31 and M33, using interference-filter imaging and image-subtraction to identify WR candidates and then using spectroscopy to confirm and classify them. The task, however, is quite daunting, as one of the things that makes the Magellanic Clouds so attractive---their closeness---also results in their very large angular sizes. The need, however, is timely: Improved evolutionary models have become available from the Geneva group that actually now predict a significantly smaller WC/WN ratio ($\sim 0.1$) for the LMC than the ``observed" ratio (0.23). Is the problem with the models, or is the problem that too many WNs have been missed in past studies? At the same time, the Cambridge STARS evolutionary models continue to improve and become increasingly available (see, e.g., Eldridge et al.\ 2008), allowing comparison with models that include the effects of close binary evolution as well. And, of course, one never knows what surprises await in such new surveys, as we shall see. Here we report the results of our first observing season. Although we have only surveyed $\sim15$\% of the SMC and LMC, we have already discovered nine new WRs (all in the LMC), two interesting ``Of?p" stars, four Of-type supergiants and a new O4~V star. Of the 9 new WRs, the majority show strong early-type absorption. Are these extremely massive binaries, or are they members of a newly discovered class of massive stars? We describe the details of the new survey and follow-up spectroscopy in Section~\ref{Sec-survey}, provide our new spectral types in Section~\ref{Sec-results}, demonstrate the sensitivity of our survey in Section~\ref{Sec-completeness}, and discuss the nature of our new discoveries in Section~\ref{Sec-sum}. | \label{Sec-sum} We have described the first exciting results of our survey. Despite having covered only 15\% of the LMC and SMC, we have confirmed 9 new WR stars in the LMC (an increase of 6\%), and suggested that a well-known B[e] star, HD 38489, may be a tenth. We have also identified 2 of the rare Of?p objects, 4 previously unknown Of supergiants, and an O4 dwarf. We detected all of the known WRs in these fields (except the most crowded members of R136 in 30 Dor), as well as many previously known Of-type stars. We have argued that our survey is going both faint enough and that our detection method is sensitive to even the weakest-lined WRs. The most remarkable aspect of our find is not the quantity of new WRs, but their characteristics. First, one of the newly found WRs is a WO star, only the third to be found in the LMC. It is of WO2 type, and is located just 9\arcsec\ (2.2 pc in projected distance) from the WO4 we found two years ago (Neugent et al.\ 2012b). The other 8 newly found WRs are WN3s that also show absorption lines. Two of these WN3s appear to have normal mid-to-late O-type companions and show radial velocity variations consistent with a binary nature. However, our most remarkable find has been that of the five stars we would naively classify as ``WN3+O3~V." The presence of absorption in the spectrum of a WR star is nearly always indicative of binarity. If absorption is otherwise present, it is usually combined with P Cygni emission, such as the case for the very luminous and massive hydrogen-rich late-type WNs seen in the R136 cluster (Massey \& Hunter 1998, Crowther et al.\ 2010) and in NGC 3603 (Melena et al.\ 2008). Those are unevolved stars but which are so luminous that their winds mimic the emission found in evolved WRs. Possibly a closer analogy to our ``WN3+O3~V' objects are some of the SMC WN3 stars which show the absorption signature of an early-type O star, although none as early as O3~V (Table 1 of Massey et al.\ 2003). None of these have been shown to be binaries. However, they are all significantly more luminous than ours ($M_V\sim -3.6$ to $-5.5$) and therefore could simply be multiples viewed at unfavorable inclinations, or whose components are too widely separated to have detectable radial velocity variations. What, then, is the nature of our ``WN3+O3~V" objects? There are several reasons why these stars are unlikely to be actual WN3+O3~V pairs. First, O3~V stars are the ``rarest of the rare," as only the most luminous and massive stars start their lives in an O3~V phase. (Only stars of 50$M_\odot$ and larger obtain sufficiently high effective temperatures to be spectroscopically identified as O3 stars; see, e.g., Ekstr\"{o}m et al.\ 2012.) Thus, outside of the concentration of O3 stars in the very young and massive R136 cluster (Massey \& Hunter 1998), only about a dozen O3~V stars are known in the entire LMC (Skiff 2014). So, to have come across five O3~V stars that just all happen to be members of a binary system with WN3 stars seems rather far-fetched. A second, and perhaps more irrefutable argument, is that the absolute magnitudes of these ``WN3 + O3~V" systems are all quite faint, with $M_V=-2.3$ to $-3.0$. But, this is much fainter than an O3~V star ($M_V\sim -5.4$, Conti 1988), and in fact is even faint for a WN3 ($M_V\sim -3.8$, Hainich et al.\ 2014). Thus, there would seem to be no way that these objects can truly consist of a WN3+O3~V pair. Third, we have two observations for three of these systems, and none show the radial velocity variations we might expect to find in binaries. Finally, such a WN3+O3~V system would be very hard to understand from an evolution point of view: the O3~V component must be quite young ($<$1-2~Myr), while it would have taken several million years to have formed the WR component. With five such objects (and likely a sixth) we are forced to conclude that we have discovered a hitherto unrecognized class of WRs, stars that are under-luminous visually and whose winds are thin enough to show underlying absorption. For absorption lines to be present from the WR itself requires a different set of physical conditions in the stellar wind than is found in other WRs. Are these ``WN3+O3~V" stars even evolved objects? A preliminary effort at modeling the optical data of LMC170-2 using CMFGEN (Hillier \& Miller 1998) shows that a good match to the observed spectrum (emission {\it and} absorption) can be achieved with a model using a high effective temperature ($\sim$80,000-100,000 K) along with a strongly enhanced helium (He/H$\sim$1.0 by number) and nitrogen abundances ($\sim$10 $\times$ solar), indicative of advanced CNO processing. The models require mass-loss rates of $0.8-1.2\times 10^{-6} M_\odot$ yr$^{-1}$, corrected for clumping using a volume filling factor of 0.1. Fig.~\ref{fig:john} shows how successful the best-fitting model matches the spectrum. The high effective temperatures would imply a bolometric luminosity of $\log L/L_\odot\sim$ 5.3-5.6. These physical parameters are all in accord with what we expect for LMC WN3 stars (Hainich et al.\ 2014), except for the mass-loss rate, which is lower than what we expect for a WN3 star by a factor of 3 (see Fig.~6 of Hainich et al.\ 2014), and more similar to what we would expect from O2-3~V stars (see, e.g., Massey et al.\ 2005). However, none of these values are well determined by the optical data alone, as we lack lines arising from multiple ionization stages of the same species, severely hindering our ability to constrain the effective temperature. For instance, we detect He~II but not He~I, and we see N~V but not N~IV. We have applied for {\it HST} time to obtain the UV data needed to better determine these values, as these will provide additional ionization states (for instance, N~IV $\lambda 1718$), and key diagnostics of the stellar wind (e.g., C~IV $\lambda 1550$). The full modeling will be discussed once those data are obtained, or, if we are not successful in securing UV data, once we have additional optical data. But the preliminary modeling does show that the observed spectra {\it can} be produced by a single object, and (if our effective temperatures are correct) that the bolometric luminosities, and hence the progenitor masses, would be normal rather than small. Why the mass-loss rates are low, and how these stars evolved, remain unanswered questions for the present. Are they the hitherto unrecognized products of single star evolution, or are binary models needed to produce such objects? If the latter, then where is the spectroscopic signature of the companion? The results from our first observing season have certainly justified in our minds the effort involved in our survey. As Figs.~\ref{fig:SMC} and \ref{fig:LMC} show, we have so far concentrated on where many WRs were already known. So it is possible that that we will have a lower success rate next year in terms of finding new ones. On the other hand, we will not know until we look. Will any new ones be as equally intriguing as the ones we found this year? We look forward to more surprises. | 14 | 4 | 1404.7441 |
1404 | 1404.5391_arXiv.txt | We investigate the formation of dust in a stellar wind during the red-supergiant (RSG) phase of a very massive Population III star with the zero-age main sequence mass of 500 $M_\odot$. We show that, in a carbon-rich wind with a constant velocity, carbon grains can form with a lognormal-like size distribution, and that all of the carbon available for dust formation finally condense into dust for wide ranges of the mass-loss rate ((0.1--3)$\times 10^{-3}$ $M_\odot$ yr$^{-1}$) and wind velocity (1--100 km s$^{-1}$). We also find that the acceleration of the wind driven by newly formed dust suppresses the grain growth but still allows more than half of gas-phase carbon to be finally locked up in dust grains. These results indicate that at most 1.7 $M_\odot$ of carbon grains can form in total during the RSG phase of 500 $M_\odot$ Population III stars. Such a high dust yield could place very massive primordial stars as important sources of dust at the very early epoch of the universe if the initial mass function of Population III stars was top-heavy. We also briefly discuss a new formation scenario of carbon-rich ultra-metal-poor stars considering the feedback from very massive Population III stars. | The discoveries of huge amounts of dust grains in high-redshift quasars (Bertoldi et al.\ 2003; Priddey et al.\ 2003) have posed the fundamental problems on the origin of dust in the early universe. At such an early epoch, core-collapse supernovae (CCSNe) arising from massive stars are considered to be the most promising sources of dust (e.g., Dwek et al.\ 2007). On the other hand, the contribution from asymptotic giant branch stars evolving from intermediate-mass ($M_{\rm ZAMS} \simeq$ 3--8 $M_\odot$) stars has also been invoked to explain a large content of dust in high-redshift objects (Valiante et al.\ 2009; Dwek \& Cherchneff 2011). What stellar mass range can mainly contribute to the dust budget in the early universe strongly depends on the initial mass function (IMF) of the stars (Valiante et al.\ 2011; Gall et al.\ 2011a, 2011b). Numerical simulations of the formation of metal-free stars have shown that the IMF of the first generation of stars, so-called Population III (Pop III) stars, would be weighted towards much higher mass than those in the present universe (Bromm \& Larson 2004; Hirano et al.\ 2014). However, a characteristic mass of Pop III stars remains to be clarified, spanning from $\sim$40 $M_\odot$ (Hosokawa et al.\ 2011; Susa 2013) up to more than 300 $M_\odot$ (Omukai \& Palla 2003; Ohkubo et al.\ 2009). In particular, Pop III stars with the masses exceeding $\sim$250 $M_\odot$ emit numerous ionizing photons and finally collapse into black holes (BHs), serving as seeds of supermassive BHs. Thus, such very massive Pop III stars would have crucial impacts on the reionization of the universe and dynamical evolution of galaxies. Even though most of very massive Pop III stars are not supposed to explode as supernovae (SNe), they are likely to play an important role in the chemical enrichment of the early universe. Yoon et al.\ (2012) found that non-rotating models with $M_\mathrm{ZAMS} > 250~M_\odot$ undergo convective dredge-up of large amounts of carbon and oxygen from the helium-burning core to the hydrogen-rich envelope during the red-supergiant (RSG) phase. This may lead to enrichment of the surrounding medium with CNO elements via RSG winds. More importantly, such CNO-enriched RSG winds can serve as formation sites of dust in the early universe. In this Letter, we elaborate this new scenario of dust formation by Pop III stars, using an exemplary model with $M_{\rm ZAMS} = 500$ $M_\odot$. We show that C grains can form efficiently in the stellar wind with a constant velocity for a reasonable range of mass-loss rates and wind velocities. We also discuss the effect of the wind acceleration on dust formation. \begin{deluxetable*}{cclcccc} \tabletypesize{\scriptsize} \tablewidth{0pt} \tablecaption{Chemical Reactions for Formation of C Clusters Considered in This Paper} \tablehead{ & \colhead{key molecule} & \colhead{chemical reaction} & \colhead{$A/10^4$K} & \colhead{$B$} & \colhead{$a_0$ (\AA)} & \colhead{$\sigma$ (erg cm$^{-2}$)}} \startdata \\ (1) Model A & C & C$_{n-1}$ + C $\rightleftharpoons$ C$_{n}$ ~~~ ($n \ge 2$) & 8.3715 & 22.1509 & 1.281 & 1400 \\ \\ (2) Model B & C$_2$H & 2(C$_2$H + H) $\rightleftharpoons$ C$_{2n}$ + 2H$_2$ ~~~~~~~~~~~~~ ($n = 2$) & 8.6425 & 18.9884 & 1.614 & 1400 \\ & & C$_{2(n-1)}$ + C$_2$H + H $\rightleftharpoons$ C$_{2n}$ + H$_2$ ~~~ ($n \ge 3$) & & & \\ \enddata \tablecomments{ The key molecule is defined as the gas species whose collisional frequency is the least among the reactants. The Gibbs free energy ${\it \Delta} \mathring{g}$ for the formation of the condensate from reactants per key molecule is approximated by ${\it \Delta} \mathring{g} / k T = - A/T + B$ with the numerical values $A$ and $B$ derived by least-squares fittings of the thermodynamics data (Chase et al.\ 1985). The radius of the condensate per key molecule and the surface tension of bulk grains are $a_0$ and $\sigma$, respectively.} \end{deluxetable*} | We have investigated the formation of C grains in a mass-loss wind of a Pop III RSG with $M_{\rm ZAMS} = 500$ $M_\odot$. We find that, in a stellar wind with a constant velocity, the condensation efficiency of C grains is unity under the condition in Equation (3), and that at most 1.7 $M_\odot$ of C grains can be produced during the lifetimes of Pop III RSGs. We also find that the wind acceleration caused by newly formed dust can change the final size distribution of the dust, but still leads to the high final condensation efficiency ($f_{{\rm con}, \infty} \ga 0.5$). Such dust masses would be high enough to have an impact on the dust enrichment history in the early universe if the IMF of Pop III stars was top-heavy. Recent sophisticated simulations of the first star formation (Hirano et al.\ 2014) have suggested that the number of very massive stars (VMSs) with $M_{\rm ZAMS} \ga 250$ $M_\odot$ ($N_{\rm VMS}$) is likely to be as large as that of massive stars exploding as CCSNe ($N_{\rm CCSN}$). If this is true and if all of the VMSs lead to $X_{\rm VMS} = 3.4 \times 10^{-3}$, the contribution of the interstellar dust from VMSs is comparable with, or even higher ($N_{\rm VMS} X_{\rm VMS}/N_{\rm CCSN} X_{\rm CCSN} \ga 1$) than that from CCSNe in the case that the destruction of dust by the reverse shock is efficient ($X_{\rm CCSN} \la 1.0 \times 10^{-3}$).\footnote{ For pair-instability SNe occurring from stars with $M_{\rm ZAMS} \simeq$ 130--250 $M_\odot$, $X_{\rm PISN} \la$ 0.05 and $M_{\rm dust} / M_{\rm metal} \la$ 0.15, depending on the destruction efficiency of dust by the reverse shocks (Nozawa et al.\ 2007). We also note that pair-instability SNe might be inefficient sources of C grains (Nozawa et al.\ 2003).} Thus, very massive Pop III stars could be potentially dominant sources of dust grains at very early times of the universe. Our results also have important indications on the formation scenario of carbon-rich ultra-metal-poor (UMP) stars with [Fe/H] $< -4$, which would record the chemical imprints of Pop III stars (Beers \& Christlieb 2005). The formation of such low-mass metal-poor stars is considered to be triggered through the cooling of gas by dust ejected from Pop III SNe (Schneider et al.\ 2012a, 2012b; Chiaki et al.\ 2013). Ji et al.\ (2014) suggested that the formation of carbon-rich UMP stars relies on the cooling by fine structure lines of C and O atoms, assuming that the first SNe produced no C grain. Here we propose another possible channel for the formation of carbon-rich UMP stars. As shown in this study, very massive Pop III RSGs are efficient sources of C grains as well as CNO elements. Thus, in the gas clouds enriched by these Pop III RSGs, C grains enable the formation of low-mass stars whose chemical compositions are highly enhanced in carbon and oxygen. As the investigated 500 $M_\odot$ model undergoes mild hot-bottom burning, some nitrogen is also produced, giving rise to [N/C] = $-4.2$ to $-1.3$ depending on the assumed mass-loss history, where observations of carbon-rich UMP stars indicate [N/C] $\ge -1.7$ (Christlieb et al.\ 2002; Norris et al.\ 2007; Frebel et al.\ 2008). From our zero-metallicity model, we do not predict the presence of any heavier metals. Further observations and more quantitative theoretical studies are needed to show whether any UMP stars have formed through our scenario. | 14 | 4 | 1404.5391 |
1404 | 1404.2264_arXiv.txt | Millisecond pulsars (MSPs) are a growing class of gamma-ray emitters. Pulsed gamma-ray signals have been detected from more than 40 MSPs with the \fermi\ Large Area Telescope (LAT). The wider radio beams and more compact magnetospheres of MSPs enable studies of emission geometries over a broader range of phase space than non-recycled radio-loud gamma-ray pulsars. We have modeled the gamma-ray light curves of 40 LAT-detected MSPs using geometric emission models assuming a vacuum retarded-dipole magnetic field. We modeled the radio profiles using a single-altitude hollow-cone beam, with a core component when indicated by polarimetry; however, for MSPs with gamma-ray and radio light curve peaks occurring at nearly the same rotational phase we assume that the radio emission is co-located with the gamma rays and caustic in nature. The best-fit parameters and confidence intervals are determined using a maximum likelihood technique. We divide the light curves into three model classes, with gamma-ray peaks trailing (Class I), aligned (Class II) or leading (Class III) the radio peaks. Outer gap and slot gap (two-pole caustic) models best fit roughly equal numbers of Class I and II, while Class III are exclusively fit with pair-starved polar cap models. Distinguishing between the model classes based on typical derived parameters is difficult. We explore the evolution of magnetic inclination angle with period and spin-down power, finding possible correlations. While the presence of significant off-peak emission can often be used as a discriminator between outer gap and slot gap models, a hybrid model may be needed. | Millisecond pulsars \citep[MSPs, first discovered by][]{Backer82} are thought to be old pulsars, spun up to extremely short periods ($P \lesssim 25$ ms) via accretion from a companion \citep[e.g.,][]{Alpar82}, and are often dubbed ``recycled'' pulsars. The recycled pulsar scenario is supported by the fact that $\sim80$\% of MSPs are in binary systems and the detection of millisecond X-ray pulsations from neutron stars in low-mass X-ray binaries \citep[LMXBs, e.g.,][]{WK98,Chak05}, presumed to be the progenitors of radio MSPs. Further evidence supporting this model was provided by the discovery of a radio MSP that had shown LMXB behavior, and no pulsations, in the past \citep{Archibald09}, and is thought to be a missing link in the LMXB-to-MSP evolutionary chain. More recent observations of PSR J1824$-$2452I in the globular cluster M28 (NGC 6626) transitioning from rotation-powered radio pulsar to accretion-powered X-ray pulsar, and back, have made this interpretation even more certain \citep{Papitto13,ATEL5069}. The rotation periods of MSPs are observed to be increasing at a much slower rate than non-recycled pulsars \citep[\Pd\ typically $\sim 10^{-20}$ s s$^{-1}$ for MSPs versus $\sim 10^{-15}$ s s$^{-1}$ for non-recycled pulsars,][]{handbook}. This leads to weaker inferred surface magnetic fields ($B_{\rm surf}= (1.5 I c^{3} \dot{P} P)^{1/2}/(2\pi R_{\rm NS}^{3}) \lesssim 10^{9}$ G, for an orthogonal rotator assuming dipole spin down and with \Rns\ the neutron star radius, $c$ the speed of light in vacuum, and $I$ the neutron star moment of inertia). \citet{Lee12} have empirically defined MSPs as those pulsars satisfying: \begin{equation}\label{eqn-LeeMSPs} \frac{\dot{P}}{10^{-17}}\ \leq\ 3.23\Big(\frac{P}{100\ \rm{ms}}\Big)^{-2.34}. \end{equation} The light-cylinder radii of MSPs (cylindrical radius where co-rotation with the neutron star requires moving at the speed of light, $R_{\rm LC} = c/\Omega$ with $\Omega = 2\pi/P$) are on the order of tens to hundreds of kilometers as opposed to many thousands of kilometers in non-recycled pulsars. The radio beams and polar cap sizes of MSPs are also very broad, making them detectable over a larger range of viewing geometries than non-recycled pulsars. Therefore, MSPs provide excellent opportunities to study the global pulsar magnetosphere in detail through analysis of pulse profiles at different wavelengths. Using timing solutions from radio observatories around the world \citep{Smith08}, MSPs have been established as a class of high-energy (HE, $\geq$0.1 GeV) emitters \citep[e.g.,][]{MSPpop,1PC,J0034,Guillemot12} via observations with the Large Area Telescope \citep[LAT,][]{Atwood09}, the main instrument on the \emph{Fermi Gamma-ray Space Telescope}. Additionally, steady point-source emission has been detected from the vicinity of more than a dozen globular clusters \citep{47Tuc,Kong10,GCpop,Tam11,2FGL} consistent with emission from the combination of many MSPs. HE pulsations have been detected from two extremely luminous MSPs in globular clusters \citep{Freire11,wuM28A,JohnsonB1821}. The population of known radio MSPs in the Galactic field\footnote{Those not in globular clusters.} has been increased by $\sim$50\% through follow-up searches of unassociated LAT sources with pulsar-like characteristics \citep[e.g.,][]{Ransom11,Cognard11,Keith11,Ray12,Barr13,Bhatt13}, suggesting that MSPs are generally gamma-ray emitters. Of these new radio MSPs, over 75\% are in binaries and 11 are ``black-widow'' systems \citep[with extremely low-mass companions thought to have been ablated by the pulsar wind, see][for a review]{Roberts11}, further supporting the recycling scenario. The origin of HE pulsed emission remains an important question in gamma-ray pulsar physics. It is commonly accepted that the observed HE gamma rays are primarily the result of curvature radiation from electrons/positrons accelerated along the magnetic field lines by the rotationally-induced electric field, but the recent detections of pulsations from the Crab pulsar at energies up to $\sim$400 GeV by VERITAS \citep{Aliu11} and MAGIC \citep{Aleksic11,Aleksic12} suggest that either an additional component is necessary or a different process is at work \citep[e.g.,][]{Lyutikov12}. The exact location in the magnetosphere where the acceleration occurs is still uncertain. The light curves of gamma-ray pulsars detected with the LAT strongly suggest that emission occurs in the outer magnetosphere rather than near the polar caps, in narrow gaps bordering the closed-field-line boundary, but it is not yet clear how the acceleration or emission is distributed. Several authors have attempted to address these questions by generating simulated light curves using either geometric models \citep[e.g.,][]{Cheng86b,Venter09,BS10b,WR11} or full radiation models \citep[e.g.,][]{Harding08,Wang11}. We have simulated gamma-ray and radio MSP light curves assuming the vacuum retarded-dipole (VRD) magnetic field geometry of \citet{Deutsch55}. These simulations have been used to fit the observed light curves of the 40 gamma-ray MSPs from which significant pulsed signals have been detected with the LAT in three years of sky-survey operations as reported in the second LAT catalog of gamma-ray pulsars \citep[2PC hereafter,][]{2PC}, all of which satisfy the inequality in Equation \ref{eqn-LeeMSPs}. We fit the simulated light curves to the observed profiles and estimate uncertainties on the best-fit model parameters, using either one or two-dimensional likelihood profiles, and discuss the implications of trends in the best-fit parameters. Similar to \citet{Venter12}, we define three model classes as follows: MSPs with gamma-ray peaks trailing the radio peaks (by $\lesssim0.5$ in phase) are Class I, those with gamma-ray and radio peaks nearly aligned in phase (to within 0.1) are Class II, and those with gamma-ray peaks leading the radio peaks (by between 0.3 and 0.1 in phase, corresponding to radio lags between 0.7 and 0.9 in phase) are Class III. In Appendix \ref{app-fits} we provide, for each MSP, the observed and best-fit light curves, summarize the observational characteristics, discuss how the models match the data, and compare our results to those from other methods when possible. Appendices \ref{app-contours} and \ref{app-skymaps} provide confidence contours and maps of simulated emission on the sky for selected MSPs, respectively. Due to the choice of radio phase zero in 2PC, PSRs J0034$-$0534 and J1810$-$1744 have radio lags of 0.866 and 0.849, respectively, but have wide double-peaked radio and gamma-ray light curves with similar morphology and thus are considered Class II for our purposes. Additionally, PSRs J1744$-$1134 and J2214+3000 have radio lags of 0.2 to 0.3 in phase but are considered Class III in our studies. For PSR J1744$-$1134 this is due to the use of the `h' method for shifting the profile, which puts phase zero at the weaker radio interpulse. For PSR J2214+3000, phase zero is placed at the peak radio intensity, the `p' method, and the radio lag is referenced to the first gamma-ray peak appearing later in phase, but we note that the highest gamma-ray peak occurs just before the highest radio peak. \citet{Espinoza13} separated the gamma-ray MSPs known at the time into three types based on the characteristics of their gamma-ray and radio light curves. Their A-type MSPs, those that have the main gamma-ray peak aligned with the main radio pulse, overlap exactly with our Class II MSPs with the exception of PSR J1810+1744, which was not known to be a gamma-ray emitter prior to 2PC. Their N-type and W-type MSPs are a mix of our Class I (3) and III (1) MSPs. Both N-type and W-type MSPs are defined as those without the main gamma-ray and radio peaks occurring at or near the same phase, with the radio profile of the former dominated by a single pulse and the latter consisting of wide peaks covering most of the pulse phase. \citet{Espinoza13} hypothesized that the W-type MSPs were possibly aligned rotators, explaining the wide radio profiles and high duty cycles. | 14 | 4 | 1404.2264 |
|
1404 | 1404.3732_arXiv.txt | We present 855 cataclysmic variable candidates detected by the Catalina Real-time Transient Survey (CRTS) of which at least 137 have been spectroscopically confirmed and 705 are new discoveries. The sources were identified from the analysis of five years of data, and come from an area covering three quarters of the sky. We study the amplitude distribution of the dwarf novae CVs discovered by CRTS during outburst, and find that in quiescence they are typically two magnitudes fainter compared to the spectroscopic CV sample identified by SDSS. However, almost all CRTS CVs in the SDSS footprint have $ugriz$ photometry. We analyse the spatial distribution of the CVs and find evidence that many of the systems lie at scale heights beyond those expected for a Galactic thin disc population. We compare the outburst rates of newly discovered CRTS CVs with the previously known CV population, and find no evidence for a difference between them. However, we find that significant evidence for a systematic difference in orbital period distribution. We discuss the CVs found below the orbital period minimum and argue that many more are yet to be identified among the full CRTS CV sample. We cross-match the CVs with archival X-ray catalogs and find that most of the systems are dwarf novae rather than magnetic CVs. | Cataclysmic variables (CVs) are a common state of evolved compact binary systems. Such systems consist of a main-sequence, sub-giant or brown dwarf star that is filling its Roche lobe and transferring mass onto a white dwarf (Warner 2003). The accretion process can be either directly onto a strongly magnetic white dwarf or by way of an intervening accretion disc. Many CV systems with accretion discs undergo thermal instabilities within their discs (Meyer \& Meyer-Hofmeister 1981) that give rise to outbursts of up to eight magnitudes, and make up the CV sub-class termed dwarf novae (e.g. Patterson et al. 1981; Howell et al. 1995). These outbursting events in dwarf novae-type CVs can last from days to weeks (e.g. Szkody \& Mattel 1984). Apart from their role in binary star evolution, understanding such systems is important for cosmology, since CVs remain possible progenitors to type-Ia supernovae explosions (Patat et al.~2007; Kafka et al.~2012; Immer et al.~2006; Zorotovic et al.~2011). Historically, the discovery of dwarf nova type CVs has been in large part due to serendipitous detection and subsequent follow-up studies (G\"ansicke 2005). More recently, confirmation of dwarf nova candidates has been undertaken routinely by a large network of small telescopes (Kato et al.~2009). The discovery of these systems is aided by the large intrinsic variations of the sources. However, the lack of deep synoptic wide-field surveys has meant that most historical CV discoveries have been, either relatively bright nearby CV systems, or fainter systems undergoing very large outbursts. An exception to this discovery method has been the Sloan Digital Sky Survey (SDSS), which undertook a spectroscopic survey of more than a hundred thousand QSO targets (Schneider et al. 2010; Paris et al. 2012). Due to the similar optical colours of QSOs and CVs, besides large numbers of QSOs, a few hundred CVs were discovered (Szkody et al.~2002, 2003, 2004, 2005, 2006, 2007, 2009, 2011). Since these CV systems were identified from quiescent spectra rather than optical variation, this survey presented an unprecedented insight into the variety of system properties within the CV population, and led to the firm detection of the predicted accumulation of CVs near the orbital period minimum (G\"ansicke et al.~2009). However, as spectroscopic observations require more flux than photometry, the SDSS CV sample was limited to sources with $i < 19.1$ (although later work followed some targets as faint as $i=20.2$; Richards et al.~2002). The fact that dwarf novae brighten by many magnitudes during their outbursts enables the discovery of CV systems that are very faint in quiescence. However, intrinsically faint systems have lower accretion rates and less frequent outbursts compared to bright sources, thus introducing a bias in variability-based searches (Wils et al.~2010). To find large numbers of the faintest CV systems, it is necessary to repeatedly survey large areas of the sky. A number of surveys have begun to systematically explore the astronomical time domain in order to discover optical transient events, such as CV outbursts. These projects include the Catalina Real-time Transient Survey (CRTS; Drake et al. 2009a, Djorgovski et al. 2011), the Panoramic Survey Telescope and Rapid Response System (PanSTARRS; Hodapp et al.~2004), the Palomar Transient Factory (PTF; Law et al.~2009) and the La Silla Quest survey (LSQ; Rabinowitz et al.~2011). All these surveys are capable of discovering hundreds of intrinsically faint CVs during outbursts. However, only CRTS openly reports the discovery of CVs. Future surveys such as SkyMapper (Keller et al. 2007), Gaia (Perryman et al.~2001) and the Large Synoptic Survey Telescope (LSST; Ivezic et al.~2008) are also expected to detect numerous CVs. In this paper we describe the CV systems that were detected by CRTS in data taken by the Catalina Sky Survey between 2007 November 8th and 2012 July 31st. We will then investigate the basic properties of these systems and outline areas where additional work is required to better understand their nature. | In this work we have cataloged 855 CV candidates detected by CRTS. Of these 705 are new discoveries and at least 137 are spectroscopically confirmed. These sources were primarily selected among CRTS optical transient sources using information about prior outbursts and their amplitudes, combined with archival information such as optical colours, and the presence of radio and X-ray sources. We have investigated the resulting outburst amplitude and colour distributions and confirm the expected differences from other common types of optical transients (such as supernovae and blazars). We find that the CRTS CV sample extends two magnitudes deeper compared to the CVs that were spectroscopically identified by SDSS (Szkody 2002-2011). In contrast to the recent work on quantifying the CV population based on CRTS data by Thorstensen \& Skinner (2012), our analysis includes the additional CVs discovered using MLS and SSS telescopes, as well as more accurate details of the CRTS CV detection and classification. Nevertheless, given that only 45\% of the CRTS CVs have been detected in outburst more than once, we agree with the suggestion of Thorstensen \& Skinner (2012) that a large fraction of the galactic CV population must remain to be discovered. While it is clear that the Galactic latitude limits of the Catalina survey ($|b| > 10\arcdeg $) create a bias towards sources at large scale heights, the absolute magnitudes predicted from CV outbursts suggest a significant fraction of the CVs discovered have scale heights well beyond that expected for the Galactic thin disc. This strongly supports the idea that many of the CRTS CVs belong to a thick disc population. Since CRTS detects CVs by searching for optical transient sources, this inherently biases the detections toward dwarf nova systems. To better understand the CV population we identified candidates that coincide with hard sources from X-ray catalogs. We find that most of the CV systems with X-ray matches appear to be non-magnetic systems. Nevertheless, CRTS has discovered both eclipsing systems and magnetic CVs. It is likely that more magnetic CVs remain to be identified. By analysing the orbital periods of the CVs, we find that the period distribution of CRTS CVs includes a much more significant contribution from short-period systems compared to the bulk of the previously known CVs, which are, on average, both brighter, and have more frequent outbursts. This result is in agreement with prior analyses by Wils et al.~(2010) and Woudt et al.~(2012), and also with the work by G\"ansicke et al.~(2009) based on SDSS CVs, and Uemura et al.~(2010) on WZ Sge stars. This underlines that new CV samples that have much deeper limiting magnitudes probe a different population of systems compared to the previously discovered bright CVs. However, in contrast to the orbital period distribution, we find no evidence for a difference in the outburst rates of the dwarf nova CVs. Recent work on CVs from CRTS and other synoptic surveys has led to the discovery of a number of ultra-short-period CVs. These have been identified as AM CVn types (eg. Woudt \& Warner 2010; Levitan et al.~2013) as well as those that systems are evolving into AM CVns (eg. Breedt et al.~2012), or have substellar companions (eg. Garnavich et al.~2012). Given that less than quarter of the CRTS CVs currently have orbital period determinations, it is likely that a large number of ultra-short-period systems remain to be found. | 14 | 4 | 1404.3732 |
1404 | 1404.3218_arXiv.txt | We have obtained a series of deep X-ray images of the nearby galaxy M83 using \chandra, with a total exposure of 729 ks. Combining the new data with earlier archival observations totaling 61 ks, we find 378 point sources within the D$_{25}$ contour of the galaxy. We find 80 more sources, mostly background AGN, outside of the D$_{25}$ contour. Of the X-ray sources, 47 have been detected in a new radio survey of M83 obtained using the Australia Telescope Compact Array. Of the X-ray sources, at least 87 seem likely to be supernova remnants (SNRs), based on a combination of their properties in X-rays and at other wavelengths. We attempt to classify the point source population of M83 through a combination of spectral and temporal analysis. As part of this effort, we carry out an initial spectral analysis of the 29 brightest X-ray sources. The soft X-ray sources in the disk, many of which are SNRs, are associated with the spiral arms, while the harder X-ray sources, mostly X-ray binaries (XRBs), do not appear to be. After eliminating AGN, foreground stars and identified SNRs from the sample, we construct the cumulative luminosity function (CLF) of XRBs brighter than \EXPU{8}{35}{\LUM}. Despite M83's relatively high star formation rate, the CLF indicates that most of the XRBs in the disk are low mass XRBs. % Subject Headings: galaxies: individual (M83) -- galaxies: ISM -- supernova remnants -- X-rays: general -- X-rays: binaries -- X-rays: individual (M83) -- SN: individual (SN1923A) | } M83 (NGC~5236) is a large, grand-design spiral galaxy at a distance of 4.61 Mpc \citep{saha06} that has been the site of six historical supernovae (SNe; see \citet{stockdale06} and references therein). It has very active star formation, estimated by \cite{boissier05} at between 3 and 4$\MSOL\peryr$. Due to its nearly face-on inclination \cite[i=24$^{\circ}$, ][]{talbot79}, very well defined spiral arms, and location along a line of sight with low Galactic absorption \cite[N$_H$=\EXPU{4}{20}{cm^{-2};}][]{kalberla05}, M83 provides an outstanding laboratory for understanding X-ray source populations in star-forming galaxies. Given the nature of M83, it is not surprising that it has been observed many times at X-ray wavelengths. \cite{trinchieri85} were the first to obtain spatially resolved images of M83 using the $Einstein~Observatory$ and to discuss its X-ray properties. \cite{immler99} used the improved sensitivity of the ROSAT HRI to resolve about half of the total luminosity of the galaxy (\EXPU{1.1}{40}{\LUM}, corrected to our assumed distance of 4.61 Mpc) into 21 X-ray point sources, and to show that some of the diffuse emission was associated with the spiral arms of M83. However, detailed study of the galaxy has become possible only with the increased sensitivity of \chandra\ (and {\em XMM/Newton}). Soria \& Wu (2002, 2003) analyzed a 51 Ks observation of M83 with \chandra's ACIS-S instrument, identifying 127 sources to a limiting sensitivity of $\sim \EXPU{4.6}{36}{\LUM}$ (also adjusted to a distance of 4.61 Mpc), and showed that many of the discrete sources as well as much of the emission from hot gas and unresolved sources is associated with the spiral arms. Most of the sources have been tentatively identified as X-ray binaries (XRBs), based on their spectral characteristics, but a number of supernova remnants (SNRs) and possible supersoft sources (SSS) have been identified as well. Here we provide an overview of a very deep set of \chandra\ observations of M83 and an analysis of the X-ray point source populations. We also describe new radio observations of M83 made with the Australia Telescope Compact Array (ATCA), which were obtained to support the \chandra\ observations. We have previously used these data to report the discovery of a new ultra-luminous X-ray source (ULX) in M83 \citep{soria12}, to report the recovery of the remnant of the historical SN1957D in X-rays in M83 \citep{long12} and more recently to describe the properties of a new micro-quasar in M83 \citep{soria14}. | } Our results on the CLF of M83 can be summarized as follow: \begin{itemize} \item The CLF of the nuclear starburst and bulge of M83, as derived from our point source catalog, resembles, {\it prima facie}, that of a population of LMXB. However, this result appears to be misleading, reflecting, primarily, the effects of source confusion in the innermost 0$\farcm$3 and the bright, diffuse, strongly structured background there. In fact, the outer bulge (the region between 0$\farcm$3 and 0$\farcm$6 of the center) surrounding the inner nuclear starburst region has the power law luminosity function expected from a HMXB population. \item The CLF of the disk shows a complex shape, with an inflection at \POW{36.5}{\LUM} and a break at \POW{37.5}{\LUM}. The \POW{37.5}{\LUM} break is common to all the subregions of the disk, and appears to be a fundamental characteristic of the M83 XRB population. As this break is at roughly the luminosity expected for the break in the canonical LMXB luminosity function, the interpretation may be straight-forward. The \POW{36.5}{\LUM} inflection is stronger in the arms than in the inter-arm regions, and disappears if one removes the soft and very soft sources. We suspect that a large fraction of the soft sources and part of the very soft source population (not currently identified) are in fact SNRs, and their association with spiral arms supports this hypothesis. The true XRB CLF below \POW{37.5}{\LUM} is thus likely to be more like the CLF with the soft and very soft sources removed than the CLF. The CLF for the XRBs in the disk of M83 is thus well characterized as a broken power law. The index below the break is consistent with that of canonical LMXB luminosity functions, as is the break luminosity. That the index above the break does not roll off as quickly as the canonical LMXB luminosity function indicates the presence of {\it some} HMXB despite the dominance of LMXB. We would have significantly overestimated the HMXB contribution had we not removed (the majority of) the SNRs. \end{itemize} Since M83 clearly has a mixture of HMXBs and LMXBs, we may test the extent to which scaling of the canonical HMXB and LMXB luminosity functions \citep{gilfanov04,grimm03} provides a reasonable match to our observed CLFs. \citet{gilfanov04} provides the canonical LMXB luminosity function with a normalization per galactic stellar mass (as measured from the K band luminosity) while \citet{grimm03} provides the canonical HMXB luminosity function with a normalization per unit star-formation rate. The Milky Way version of these functions are only slightly different and extend to \EXPU{\sim3}{35}{\LUM}. Our estimate of the mass in stars follows directly from from the K-band magnitude, which we take to be 4.62 from the 2MASS Large Galaxy Catalog \citep{jarrett03}, the distance to M83, the absolute K magnitude of the Sun (3.39), and a mass-to light-ratio estimate of 0.59 for M83 based on the B -- V color of the galaxy \citep{bell01}. We expect M83 to have a stellar mass of \EXPU{4}{10}{\MSOL}. We take the star-formation rate of 3.5{\MSOL}yr$^{-1}$ from the value of 3-4 {\MSOL}yr$^{-1}$ estimated by \cite{boissier05}. In Figure~\ref{fig_gg}, we compare the broad band CLF for the entire galaxy within the D$_{25}$ after the removal of the AGN and SNRs (both with and without the removal of the soft and very soft sources) with the Grimm \& Gilfanov canonical luminosity functions, scaled to the mass and star-formation rate of M83. The scaled combination of canonical luminosity functions fails to match the one we have derived from the observations rather badly. For the CLF including the soft and very soft sources that we propose are dominated by SNRs, a better agreement can be found if the star-formation is only $\sim2$ {\MSOL} yr$^{-1}$ and the stellar mass increased by a factor of 1.5-2.0. However, it is not clear that either of these is allowed; the alternative is that the scaling factors provided by \cite{gilfanov04} are simply averages and vary significantly from galaxy to galaxy, depending on the star formation history and perhaps the metallicity. Better agreement would be obtained if one also allows the LMXB function to shift to higher luminosities by factors of two to four; variation in the cut-offs of individual galaxies have been observed previously \citep{gilfanov04}. In any event, the X-ray CLF suggests that the current starburst has provided a very thin icing of HMXB over a substantial population of LMXB that has built up over a long period of steady star-formation over the last Gyr. A recent study of the luminosity functions of star-forming galaxies \citep{mineo12} examined only galaxies with a star-formation rate/stellar mass ratio $>10^{-10} yr^{-1}$. M83 falls just below this value, suggesting that it is not HMXB dominated. Using the Gilfanov scaling from stellar mass to LMXB rate, \citet{mineo12} found an unexpectedly large number of LMXB in their ``HMXB-dominated'' galaxies. M83 suggests that LMXB scaling may not need to be reduced so much for the galaxies at the low end of the specific star-formation rate, and that the HMXB scaling may need to be reduced as well. Overall, M83 falls below their $L_X$-SFR relation, but within the observed scatter for that relation. As we noted at the beginning of this Section, our current examination of the CLF in M83 was intended primarily to provide an initial exploration of the properties of the CLF. That the canonical luminosity functions do not describe the M83 CLF {\it well} was probably to be expected; more sophisticated models based on calculating the evolution of stellar populations \citep[e.g. StarTrack,][]{belczynski08} show that even simple star formation histories can produce complex CLFs \citep{luo12,fragos08,tzanavaris13}. We anticipate applying these more sophisticated models to these data in the near future. However, even before applying them, it is clear that the faint populations in M83 may pose some significant challenges. Further studies, including those we are carrying out with HST \citep{blair14}, are needed to identify as many of the soft and very soft sources as possible. Since a small variation in the number of high luminosity sources can make a significant change in the shape of the CLF, and those source should be dominated by HMXB, optical efforts to identify HMXB hold are likely to shed some light on this mystery. } We have presented an overview of the sources identified from a series of new \chandra\ observations of M83 that total 729 ks of observing time distributed over a year, along with a new radio survey of M83 with ATCA. Combined with archival observations from a decade earlier, we have found 378 X-ray sources within the D$_{25}$ contours of the galaxy to a limiting luminosity of about \EXPU{8}{35}{\LUM}, of which 45 are coincident with ATCA sources. About 1/4 of the X-ray sources are seen to be variable in our initial analysis. Despite the sensitivity of the survey, a large majority of the sources are associated with M83, as opposed to background or foreground objects. The luminosity of the X-ray point sources totals \EXPU{1.30\pm0.15}{40}{\LUM}. The brightest source in the galaxy is a ULX, discussed in detail by \cite{soria12}, located in an interarm region of the galaxy. The total luminosity of the galaxy is about \EXPU{1.85\pm0.2}{40}{\LUM}, and so about 70\% of the X-ray luminosity has been resolved into point sources. Our main results are as follows: \begin{itemize} \item Most of the sources in the galaxy are binary X-ray sources. The binary X-ray sources in the disk are not strongly correlated with the spiral arms. The luminosity function of the binary X-ray sources in the disk resembles that expected from LMXBs, despite the fact that M83 has a high star formation rate of between 3 and 4 \MSOL\ yr$^{-1}$ \citep{boissier05}. The CLF outer bulge/nuclear region appears to be dominated by high mass X-ray binaries. The CLF of the inner bulge/nuclear starburst has the shape expected for a low mass binary population, contrary to expectations, but this unexpected result may be attributable to the effects of source crowding and strong diffuse emission in the region. \item There is a substantial number of SNRs in the sample, a higher percentage than has been found in studies of most (but not all) other galaxies. A total of about 67 (73) sources lie within 1\arcsec\ (2\arcsec) of SNRs identified by \cite{blair12} from optical interference filter imagery. The spectra of these sources are soft, and in X-ray hardness-ratio diagrams they occupy a region where SNRs are expected. Counting sources from other optical surveys \citep{dopita10} and objects with soft spectra coincident with ATCA radio sources, we find that 87 X-ray sources are most likely SNRs, fully 24\% of the sample within the D$_{25}$ contours of the galaxy, and 31\% after AGN have been statistically removed. There are 82 other sources in the same region of the hardness-ratio diagram as SNRs; many of these are likely SNRs as well. The large number of SNRs detected in the survey is most likely due to a combination of factors, including the high sensitivity of the survey to soft sources, the fact that the density in the ISM in M83 is high, making SNRs relatively bright, and the fact that M83 lies along a line of sight with low foreground column. This is also consistent with the high SF and SN rates in M83. Unlike the binary X-ray sources, the SNRs (and indeed the soft sources as a whole) are concentrated in the spiral arms of the galaxy. \end{itemize} This data set represents a resource for understanding the X-ray properties of galaxies with active star formation, which we plan to exploit in conjunction with our on-going efforts to acquire additional data with \hst\ and the JVLA. Future reports will address areas such as the global properties of the supernova remnant population in M83, the characteristics of the diffuse emission, and X-ray emission from the nuclear region. | 14 | 4 | 1404.3218 |
1404 | 1404.6926_arXiv.txt | We analyze the formation histories of 19 galaxies from cosmological smoothed particle hydrodynamics zoom-in resimulations. We construct mock three-colour images and show that the models reproduce observed trends in the evolution of galaxy colours and morphologies. However, only a small fraction of galaxies contains bars. Many galaxies go through phases of central mass growth by in-situ star formation driven by gas-rich mergers or misaligned gas infall. These events lead to accretion of low-angular momentum gas to the centres and leave imprints on the distributions of $z=0$ stellar circularities, radii and metallicities as functions of age. Observations of the evolution of structural properties of samples of disc galaxies at $z=2.5 - 0.0$ infer continuous mass assembly at all radii. Our simulations can only explain this if there is a significant contribution from mergers or misaligned infall, as expected in a $\Lambda$CDM universe. Quiescent merger histories lead to high kinematic disc fractions and inside-out growth, but show little central growth after the last `destructive' merger at $z>1.5$. For sufficiently strong feedback, as assumed in our models, a moderate amount of merging does not seem to be a problem for the $z=0$ disc galaxy population, but may rather be a requirement. The average profiles of simulated disc galaxies agree with observations at $z\ge 1.5$. At $z\le1$, there is too much growth in size and too little growth in central mass, possibly due to the under-abundance of bars. The discrepancies may partly be caused by differences between the star formation histories of the simulations and those assumed for observations. | Galaxies with masses similar to that of the Milky Way (MW) are thought to have been most efficient of all galaxies in turning available baryons into stars \citep{guo}. At $z=0$, a majority of them are dominated by discs \citep{delgado}. It is therefore a key question in astrophysics to understand the formation histories of MW-like disc galaxies. Recently, \citet{vD} (D13 hereafter) and \citet{patel} (P13 hereafter) presented observational data on the growth and structural evolution of such galaxies from $z=2.5$ to $z=0$. To achieve this, D13 selected samples of galaxies in six disjoint redshift intervals at the same cumulative co-moving number density, assuming that this would reproduce the typical formation history of a $z=0$ galaxy with a stellar mass of $\sim5\times 10^{10}\;M_{\odot}$. P13 selected samples of galaxies at six redshifts from $z=1.3$ to $z=0$ according to their star formation rates (SFRs) and masses under the assumption that a typical selected galaxy stays on the evolving main sequence of star formation (e.g. \citealp{karim}) and has a $z=0$ mass of $3.2\times10^{10}\;M_{\odot}$. \begin{figure*} \centering \vspace{-0.5cm} \includegraphics[width=17.4cm]{leg1.pdf}\\ \vspace{-0.15cm} \hspace{-0.15cm} \includegraphics[width=1.35cm]{leg2.pdf} \hspace{-0.15cm} \includegraphics[width=16.4cm]{evol.png} \caption[Evolution of face-on mock three-colour images 1] {Evolution of face-on mock three-colour $ugr$-band images of the model galaxies. From right to left redshifts $z=2.5,2.0,1.5,1.1,0.85,0.37,0.0$. From top to bottom models 0997-1, 0997-2, 1646, AqB, AqE, 1196, 1192, AqD, AqC, AqA. Each image comprises 40 x 40 kpc.} \label{evolution1} \end{figure*} Both papers concluded that the galaxy populations under consideration grew only mildly in effective radius over the studied time. Stellar mass growth in the centre occurs at all times with outer growth being only mildly more efficient at late times. This behaviour differs strongly from the stellar mass growth as observed in massive elliptical galaxies, some of which apparently formed dense cores at high redshifts ($z>2$), and which as a population grew strongly in outer mass and effective radius at later times \citep{vD2, patel2}. This evolutionary path has been explained as a result of the continuous accretion of stars in dry major and minor mergers \citep{naab, bezanson, hopkins10, oser, oser12, hilz}. Major mergers destroy thin galactic discs \citep{toomre77}, so disc dominated galaxies are thought to form in haloes with quiescent merger histories from the cooling of gas from increasingly large radii. This leads to an inside-out formation process (e.g. \citealp{fall, mo}), for which observational evidence in the form of radial stellar age gradients has been presented (e.g. \citealp{califa}). Results from abundance matching support the idea that most stars in disc galaxies formed in-situ \citep{behroozi,moster, yang}. Additionally, it has been suggested that for $\Lambda$CDM haloes, feedback processes that preferentially remove low-angular momentum gas are needed to explain the observed structure of galactic discs \citep{donghia, dutton, brook}. Several processes that modify the simple inside-out formation picture for disc galaxies are, however, known and can lead to substantial star formation (SF) in the central galactic regions. These include clump migration in violently unstable discs \citep{noguchi}, bar-induced gas inflows \citep{atha}, gas-rich minor mergers \citep{barnes}, angular momentum loss due to the reorientation of the disc rotation axis \citep{aw, okamoto} and the infall of gas with misaligned angular momentum \citep{cs09}. The fact that a large fraction of local disc galaxies show small bulge fractions or even no evidence for a classical bulge at all (e.g. \citealp{kormendy}) has, on the one hand, been identified as a possible challenge to hierarchical galaxy formation in a $\Lambda$CDM universe (e.g. \citealp{freeman}). On the other hand, it has also been shown that discs can (re)form after gas-rich mergers \citep{barnes02, sprihern, naab6, robertson}. Observational evidence for this process has been presented in the form of peculiar morphologies, anomalous kinematics and episodic star formation histories (SFHs) of spiral galaxies at $z\sim 0.5$ (e.g. \citealp{hammer,hammer9,puech}). Additionally, \citet{zavala} have shown that a semi-empirical model for the bulge growth through mergers in a $\Lambda$CDM universe can correctly reproduce the observed $z=0$ distribution of galactic bulge fractions. They have, however, ignored other channels of bulge growth. In this work we use recent cosmological hydrodynamical simulations by \citet{a13} to better understand the observed structural evolution of disc galaxies. Our paper is organized as follows: In Section 2 we describe the sample of simulated galaxies. In Section 3 we illustrate the diverse formation histories of the models. In Section 4 we discuss the influence of mergers and misaligned infall. In Section 5 we compare to recent observations. Finally, we conclude in Section 6. | We have presented an analysis of the evolution of the structural properties of a sample of 19 simulated disc galaxies. These are cosmological re-simulations with multiphase SPH which were recently presented by A13. We have created mock three-colour $u/g/r$ band images to visualize the evolution of the models. We have investigated, how the complexity of light profiles and variations with orientation can complicate the interpretation of observed data if rest-frame $g$ or $i$ band light is used as a proxy for mass, as in the work of D13 or P13. The model galaxies show a variety of structural evolution histories, ranging from inside-out growing discs around older, more centrally concentrated stellar populations to continuous SF at all radii. Our models show only a small number of bars and no unstable, clumpy discs, so that not all known mechanisms for central mass growth in disc galaxies are well represented. However, gas-rich mergers with mass fractions up to $1:3$ and misaligned infall of gas can be clearly linked to episodes of central mass growth. In a $\Lambda$CDM universe, these events are common and are thus likely to be major contributors to the continuous central growth observed in mean surface density profiles of samples of galaxies selected at various redshifts in order to represent the typical evolution history of galaxies with $z=0$ masses similar to that of the MW (D13 and P13). Further observational evidence for such a scenario was recently presented by \citet{kaviraj}, who estimated that SFR enhancements in morphologically disturbed disc galaxies contribute significantly to present-day SF in spiral galaxies. These disturbed galaxies also exhibit central mass growth and are plausibly undergoing minor mergers or misaligned infall as discussed above. We have also shown that model galaxies which have undergone mergers or misaligned infall events after $z=1$ can have very low values of $B/T<0.1$ for the bulge-to-total ratio if mock face-on $i$-band profiles are decomposed into an exponential disc plus a Sersic bulge profile. Despite their appearance as good disc galaxies, their kinematic disc fractions are often below 50 per cent (see also \citealp{cs10}). Observed galaxies with low photometric $B/T$ might thus not all have had quiescent merger histories. Model galaxies which do not experience mergers or misaligned infall events, grow inside-out and show no or little central mass growth. We have shown that mergers or misaligned infall leave distinct features in the distributions of present-day radii, circularities and metallicities as functions of stellar age. Observational detection of such features is complicated by the fact that the timescales of these events are smaller than the typical errors in age determinations of stars. In our simulations, metallicities effectively increase during events that drive central SF, as these events enrich the ISM. The evolution of metallicities in discs due to interactions has been studied in detail by several groups \citep{montuori, perez, torrey}. All these papers discuss non-cosmological simulations of mergers of pairs of disc galaxies. They all apply SPH codes without a prescription for the turbulent diffusion of metals, which is included in our fully cosmological models and has been shown to significantly change the metallicity distributions in discs \citep{pilkington} and the circumgalactic medium \citep{shen}. All these models find a strong initial dilution of central metallicities caused by the inflow of gas originating from the outer disc which, due to the metallicity gradients assumed in the set-up, is metal poor. In A13 we showed that the discs in our simulations have gradients that are shallower than observed and \citet{Gibson} recently showed that the details of feedback models significantly influence gradients. Because of the shallow gradients, only very weak metallicity dilution features in the form of slightly lowered metallicities at the beginning of the events can be found in Fig. \ref{archae}. For the idealized simulations, it has, however, also been shown that enrichment due to SF in gas-rich mergers leads to an effective increase of metallicities at the end of the merger, in agreement with our findings. We conclude that events which trigger central SF are likely to leave an imprint on the age-metallicity relation of stars in that region and possibly also throughout the whole disc, but the shape of this feature is uncertain on account of modelling uncertainties. When we compare our sample of simulated galaxies directly to observed samples, we have to take into account that the allowed scatter in the observers' selection criteria on evolution histories is much narrower than the scatter of the evolution histories displayed by our simulated galaxies. Moreover, the shapes of the SFHs of our galaxies differ significantly from that assumed by D13, although in A13 we have shown that the models with similar $z=0$ masses as targeted by D13 agree well with abundance matching predictions for SFHs by \citet{moster}. Agreement with the assumptions of P13 in terms of SFH at slightly lower galaxy masses is better. Nevertheless, independent of sample selection, the mean profiles of the simulated galaxies agree with observations at $z\ge1.5$. At later times, galaxies show too little central mass growth and effective radii that increase too rapidly. At $z=0$ galaxies are typically a factor of $\sim2$ too extended. Disagreement at low $z$ is significant both for mass and light profiles and strongest if $g$-band light is used. It is not, however, clear how much this result is influenced by the biased selection of haloes, as a significant number of galaxies with effective radii $R_{50}\sim 10$ kpc have been observed \citep{sargent}. Moreover, in a comparison of our $z=0$ model gas discs with observed HI discs, we find that the observed and simulated samples show the same range of gas disc diameters \citep{wang} and follow the same HI mass-size relation. Size growth is strongest for galaxies with masses similar to that of the MW and several of those models show strong inside-out growth. Although our full sample of galaxies shows better agreement with observations, we caution that this behaviour is driven by the high central SFRs and high central stellar mass densities at $z=0$ of the most massive galaxies, which are likely unrealistic. \citet{fang} recently showed that low-redshift galaxies with high central mass densities are preferentially quenched. The lack of a model of AGN feedback in our simulations is a possible cause for this. It is interesting to note that our models agree best with observations at high $z$, as, until recently, simulations matched observational data particularly poorly at early formation stages (e.g. \citealp{aquila,moster}). As already discussed in A13, our new simulations show better agreement with a variety of observations at $z\sim 1$ than at $z=0$. One clearly identified problem is the lack of bars, which predominantly form at low $z$ and can lead to inflow of gas to the centres of discs. One reason for this are overly high velocity dispersions in our model discs (see A13), which can prevent the formation of dynamically cold structures. Coarse resolution prevents low velocity dispersions (see e.g. \citealp{house}), but other simulations at the same resolution have produced many barred systems (e.g. \citealp{cs09}). Our models differ from these as they have lower surface densities and lower baryon conversion efficiencies. The main reason for the differences is the strong stellar feedback applied in our models. As was shown in \citet{hannah}, our feedback implementation is very efficient at removing low angular momentum material. In general, the angular momentum of accreted gas in our models also increases with time. Moreover, low angular momentum gas that is blown out in early formation stages can re-accrete after several Gyr, but then has on average gained angular momentum. All these points combine to keep central baryonic surface densities low and to reduce bulge fractions. They thus also help in preventing disc instabilities, which could lead to bar formation and thus enhance central surface densities, which in turn would make the discs more unstable due to the increase in surface gravity. \citet{marinacci} recently simulated five of our haloes with a different galaxy formation code. Interestingly, in these haloes, they found more massive and less extended galaxies compared to our models. On average, their sizes lie mildly above the observed mass-size relation of \citet{shen03}. They used a very different prescription for stellar feedback and also find a higher fraction of bars. These arguments seem to suggest that the effects of the stellar feedback models applied in our simulations are too strong at low redshifts, as was also indicated by the underproduction of stars at low $z$ in lower mass galaxies, as discussed in A13. It is interesting that the model for feedback from radiation pressure from young massive stars already invokes a significantly stronger feedback for high $z$ gas-rich, turbulent galaxies than for quiescently star-forming discs at low $z$. It is possible that the calibration on galaxies similar in mass to the MW is problematic. At this halo mass the quenching mechanism needed for high mass galaxies, be it AGN or something else, but not implemented here, probably already plays a role. Moreover, in our simulations, feedback is particularly efficient in removing material during mergers \citep{hannah}, so that central mass growth during these events might actually be underestimated in our models. Simulations of disc galaxy formation have long been struggling with removing sufficient amounts of low angular momentum material from the inner regions and avoiding the formation of overly compact galaxies. Apparently our efforts in A13 to overcome this have led to the opposite problem. Weakening feedback seems an obvious solution, but the success of the model at high redshifts suggests that this should only be effective at late times. Evidently, our models are still far from capturing all relevant astrophysical processes accurately. | 14 | 4 | 1404.6926 |
1404 | 1404.6117_arXiv.txt | {Solar type III radio bursts are an important diagnostic tool in the understanding of solar accelerated electron beams. They are a signature of propagating beams of nonthermal electrons in the solar atmosphere and the solar system. Consequently, they provide information on electron acceleration and transport, and the conditions of the background ambient plasma they travel through. We review the observational properties of type III bursts with an emphasis on recent results and how each property can help identify attributes of electron beams and the ambient background plasma. We also review some of the theoretical aspects of type III radio bursts and cover a number of numerical efforts that simulate electron beam transport through the solar corona and the heliosphere.} | The Sun is the most efficient and prolific particle accelerator in our solar system. Electrons are regularly accelerated to near-relativistic energies by the unstable magnetic field of the solar atmosphere. Solar flares are the most violent example of such acceleration, with vast amounts of energy released when the solar magnetic field reconfigures to a lower energy state, releasing energy on the order of $10^{32}$~ergs and accelerating up to $10^{36}$ electrons per second in the solar atmosphere \citep[e.g.][]{Emslie_etal2012}. Solar radio bursts come in a variety of forms, classified by how their frequency changes in time, known as their frequency drift rate. Initially three types of radio emission were named type I, II and III in order of ascending drift frequency \citep{WildMccready1950}, with types IV and V introduced later. Each type has subtypes that further describe the array of complex behaviour these radio bursts display. In this study we are going to concentrate on the most prolific type of solar radio burst, the type III radio burst. These are a common signature of near-relativistic electrons streaming through the background plasma of the solar corona and interplanetary space, offering a means to remotely trace these electrons. Moreover, their dependence on the local plasma conditions means they act as a probe of the solar coronal plasma and the plasma of the solar wind. The example type III burst in Figure \ref{fig:typeIII} shows their main features; they are very bright, transient bursts that usually drift from higher to lower frequencies over time The precise mechanism for the acceleration of solar electrons is still debated but it is generally attributed to the reconfiguration of an unstable coronal magnetic field, resulting in the conversion of free magnetic energy to kinetic energy. This acceleration usually occurs at solar active regions but can occur when the magnetic field in a coronal hole interacts with the surrounding magnetic field (a process known as interchange reconnection). Moreover, type III radio bursts are observed in relation with X-ray bright points \citep{Kundu_etal1994}. \begin{SCfigure} \centering \includegraphics[width=0.59\columnwidth]{ms1742_fig1.png} \caption{An example of an interplanetary type III radio burst dynamic spectrum on the 28th January 2014. The 900 - 200 MHz frequencies are observed by the Bleien telescope \citep{Benz_etal2009}. The 80 to 15 MHz are obsered by the Nancay Decametre Array \citep{Lecacheux2000}. The 14 to 0.1 MHz are obsreved by the WAVES experient onboard the WIND spacecraft \citep{Bougeret_etal1995}. You can observe a number of different type III bursts starting at different frequencies from $<100$~MHz at 11:32 UT to from $>1$~GHz at 11:37 UT. All the radio bursts merge into one at the lowest frequencies $< 1$~MHz.} \label{fig:typeIII} \end{SCfigure} The first theory of type III bursts was described by \citet{GinzburgZhelezniakov1958}. They considered the two-stream instability of an electron beam which generates Langmuir (plasma) waves at the local plasma frequency that can be converted into electromagnetic emission. They proposed that scattering by plasma ions would produce radiation at the plasma frequency (the fundamental component), while the coalescence of two Langmuir waves could produce the second harmonic. The theory has been subsequently discussed and refined by many authors \citep[e.g.][]{Sturrock1964,ZheleznyakovZaitsev1970, 1970SoPh...15..202S,1976SoPh...46..515S,1980SSRv...26....3M, 1983SoPh...89..403G,1985ARA&A..23..169D, 1987SoPh..111...89M}, but the basic two-step process, production of Langmuir waves followed by their conversion into EM emission, remains the same. An overview of the dominant processes is shown in Figure \ref{fig:typeIII_flow}. This \emph{plasma emission mechanism} is now the generally accepted model for type III burst generation. Analytical calculations over many years have shown it is certainly capable of explaining the drift, brightness and harmonic structure of bursts. Alternatives, such as strong turbulence effects like Langmuir wave collapse \citep[e.g.][]{1983SoPh...89..403G}; conversion of Langmuir waves directly into EM waves \citep[e.g.][]{Huang1998} and emission via the maser mechanism \citep[e.g.][]{2002ApJ...575.1094W} can explain some of the properties of type IIIs. Where relevant, we assume plasma emission throughout this review. The purpose of this study is to give an overview on the type III radio burst as a probe of both accelerated electrons and the background plasma it travels through. In Section \ref{sec:observations} we give a detailed account of the observational characteristics of type III radio bursts and we describe how they relate to the properties of the generating electron beam. Section \ref{sec:electrons} reviews in-situ plasma observations connected with type III bursts. In Section \ref{sec:theory} we will cover some of the theoretical work that has been done on electron beams responsible for type III radio bursts. In Section \ref{sec:em} we will give an overview of the theory involved with the generation of electromagnetic emission from plasma waves. Finally we look towards the future in Section \ref{sec:conclusion} by covering the ``state of the art'' simulation codes and the next generation radio telescopes. \begin{figure} \centering \includegraphics[width=0.59\columnwidth]{ms1742_fig2.png} \caption{A flow diagram indicating the stages in plasma emission in an updated version on the original theory (adapted from \citep{Melrose2009})} \label{fig:typeIII_flow} \vspace{20pt} \end{figure} | \label{sec:conclusion} It is our opinion that solar radio physics is beginning to enter a new era. Regarding type IIIs, new technology is allowing simulations to generate synthetic dynamic spectra for comparison to observations to probe relevant electron beam and background plasma properties. At the same time new technology is giving birth to the next generation of radio telescope. Interferometers with large baselines and huge collecting areas are being trained on the Sun o produce images of radio bursts over many frequencies with impressive angular resolution. We conclude this article by summarising the future of type III radio burst analysis, both numerically and observationally. \subsection{``State of the Art'' simulations} While initially plasma emission work was mainly theoretical, simulations have always played a key role. Early work by e.g. \citet{TakakuraShibahashi1976,Takakura1982} allowed the simulation of bursts at a few wavelengths, and was key to the adoption of the ion-sound wave dependent model. Only recently have large-scale kinetic simulations become possible, as computing power is a strong limitation. The series of papers by \citet{2008JGRA..11306104L,2008JGRA..11306105L,2009JGRA..11402104L} were the first to trace an electron beam from the injection site into the corona and solar wind, and calculate the resulting radio emission fully numerically, rather than by analytical estimates. These simulations have more recently been extended to cover a wider frequency range, and used to explore the effects of the background plasma on the emission. In the solar wind, observations often show a kappa-distribution rather than a Maxwellian background plasma, and this contains more electrons of higher velocity. A similar power-law electron injection forms a higher velocity beam due to time-of-flight effects, and the emission may be expected to show a faster drift. This is confirmed by the simulations of \citet{LiCairns2014}, although these consider only instantaneous electron injection. Ongoing work by the authors aims to combine the large-scale simulations of e.g. \citet{ReidKontar2013} with a model for plasma radio emission used in a different context in \citet{2014A&A_RatcliffeKontar}. This aims to explore the effects of plasma density fluctuations on the emission. On the other hand, the fully numerical approach is not the only possibility. The simulations of \citet{RobinsonCairns1998,CairnsRobinson1999,Li_etal2006b,Li_etal2006c} used a combination of numerics and analytical estimates from Stochastic Growth Theory to reproduce emission. The relevance of SGT remains in question, but the results are useful nonetheless. The localisation of Langmuir waves into discrete clumps, or wave packets, is investigated using the Zakharov equations in e.g. \citet{Zaslavsky_etal2010,Krafft_etal2013}. Continued work on the propagation of electrons and their Langmuir wave generation and non-linear evolution is also essential. Langmuir waves can help to explain the observed non-Maxwellian thermal electron distribution in the solar wind \citep[e.g.][]{2012SSRv..173..459Y}. They may affect the hard-X ray emission from downward electron beams in the corona \citep[e.g.][]{Hannah_etal2013}. Plasma emission has even been suggested as a source of sub-THz radio emission \citep{2013AstL...39..650Z}. \subsection{Next generation radio observations} There are many solar telescopes all around the world that are able to observe the dynamic spectra of type III radio bursts, too many to mention individually. On the global scale we would like to mention the e-Callisto project \citep{Benz_etal2009b}, an international network of solar radio spectrometers that has more than 66 instruments in more than 35 locations with users from more than 92 countries. Regarding imaging, the most notable dedicated solar interferometer for type III radio bursts is the Nan\c{c}ay Radioheliograph \citep{KerdraonDelouis1997} (NRH), based in France, that has been making dedicated solar images since the 1960s and not images between 150 MHz and 450 MHz The next generation radio observatories being developed around the world are taking observational solar radio astronomy into a revolutionary new phase. Large baseline interferometers are making high resolution imaging spectroscopy observations of type III bursts. This will enable us to address fundamental questions about the energy release site in solar flares and the transport of energetic electrons through the heliosphere. In Europe there is the LOw Frequency ARray \citep{vanHaarlem_etal2013} (LOFAR), a network of observatories spread across Europe (Netherlands, UK, Germany, France and Sweden). LOFAR operates between the frequencies of 10 MHz and 250 MHz and is providing interferometric imaging with 10s arcsec resolutions. In North America there is the recently upgraded Expanded Very Large Array \citep{Perley_etal2011} (EVLA) that operates between 1 GHz and 50 GHz and has started solar observing at the end of 2011. In Western Australia there is the Murchison Widefield Array (MWA) \citep{Lonsdale_etal2009,Bowman_etal2013} that is a low-frequency radio telescope operating between 80 MHz and 300 MHz, is one of the precursors to the Square Kilometer Array (SKA) and has recently started to observe the Sun \citep{Oberoi_etal2011}. Other next generation radio telescopes are on the horizon and will soon be ready for solar observations. We now cover them (in no particular order). In China the Chinese Spectral Radio Heliograph (CSRH) \citep{Yan_etal2009} will be operational in 2014 and will produce dedicated solar imaging between 400 MHz and 15 GHz, an ideal frequency range for type III bursts in the deep corona. In Russia there is the Siberian Solar Radio Telescope (SSRT) that is being upgraded to create interferometric images of the Sun at GHz frequencies. In India an upgrade is currently under way to the GMRT Giant Metrewave Radio Telescope (GMRT) to operate between the frequencies between 50 MHz and 1500 MHz. In America, improvements to the existing array will create the Expanded Owens Valley Solar Array (EOVSA) that will operate between the frequency range 1 GHz to 18 GHz. In South America we will have the Brazilian Decimeric Array that will operate between the frequencies of 1 GHz and 6 GHz. In New Mexico there is the Long Wavelength Array (LWA) \citep{Lazio_etal2010,Taylor_etal2012} that will operate at the low frequencies between 10 - 88 MHz. Extending into space, the upcoming ESA Solar Orbiter mission and NASA Solar Probe Plus mission are journeying close to the Sun to 10s solar radii, and should launch in 2017 and 2018 respectively. Both missions will be armed with in-situ plasma measuring devices to explore the radial dependence of type III radio signals and the plasma properties of electron beams and the ambient solar wind. | 14 | 4 | 1404.6117 |
1404 | 1404.3168_arXiv.txt | The {\em Lyman-$\alpha$ forest} is a portion of the observed light spectrum of distant galactic nuclei which allows us to probe remote regions of the Universe that are otherwise inaccessible. The observed Lyman-$\alpha$ forest of a quasar light spectrum can be modeled as a noisy realization of a smooth curve that is affected by a `damping effect' which occurs whenever the light emitted by the quasar travels through regions of the Universe with higher matter concentration. To decode the information conveyed by the Lyman-$\alpha$ forest about the matter distribution, we must be able to separate the smooth {\em continuum} from the noise and the contribution of the damping effect in the quasar light spectra. To predict the continuum in the Lyman-$\alpha$ forest, we use a nonparametric functional regression model in which both the response and the predictor variable (the smooth part of the damping-free portion of the spectrum) are function-valued random variables. We demonstrate that the proposed method accurately predicts the unobservable continuum in the Lyman-$\alpha$ forest both on simulated spectra and real spectra. Also, we introduce distribution-free prediction bands for the nonparametric functional regression model that have finite sample guarantees. These prediction bands, together with bootstrap-based confidence bands for the projection of the mean continuum on a fixed number of principal components, allow us to assess the degree of uncertainty in the model predictions. | \begin{figure}[h!] \begin{center} \includegraphics[width=\columnwidth]{Figures/quasarhighNEWNEW.pdf} \caption{Light spectrum of a quasar. To the left of the Lyman-$\alpha$ line, the flux is damped at a dense set of wavelengths and the unabsorbed flux continuum is not clearly recognizable (blue side of the figure). To the right of the Lyman-$\alpha$ line, the flux continuum is easily guessed (red portion of the figure). The spectrum is perturbed by heteroskedastic noise with higher variance at the extremes of the observed wavelength range.} \label{fig:quasarhigh} \end{center} \end{figure} Technological advances over the last quarter-century have allowed astronomers to collect data of unprecedented richness and scope, gathered from previously inaccessible regions of space. By exploiting the information about the spatial distribution of the neutral hydrogen atoms contained in these data, cosmologists are placing ever-tighter constraints on the fundamental parameters governing the Universe's structure and evolution. Today, quasar spectra are one of the only means for probing the distribution of neutral hydrogen and they allow us to investigate the Universe at distances that are far beyond the reach of other available methods. Quasars are luminous distant galactic nuclei that appear as point-like sources of light in our sky. Many properties of a quasar, and of the regions of the Universe through which its light passes on its way to us, can be inferred from its {\em light spectrum}. This is a curve that relates the light's intensity, or {\em flux}, to its wavelength. Figure~\ref{fig:quasarhigh} shows an example of a quasar light spectrum. For wavelengths greater than what is called the Lyman-$\alpha$ wavelength, the observed light spectrum $f_{\text{obs}}$ can be well modeled as a smooth {\em continuum} $f$ plus noise: \begin{equation*} f_{\text{obs}}(\lambda) = f(\lambda) + \text{noise}(\lambda). \end{equation*} \noindent For wavelengths below the Lyman-$\alpha$ wavelength -- a region of the spectrum known as the {\em Lyman-$\alpha$ forest} -- a third contribution comes from a nonsmooth random absorption effect that originates whenever the light emitted by the quasar travels through regions of the Universe that are richer in neutral hydrogen: \begin{equation} \label{eq:absorptionmodeleasy} f_{\text{obs}}(\lambda) = \text{absorption}(\lambda) \cdot f(\lambda) + \text{noise}(\lambda). \end{equation} We want to decode the information in the Lyman-$\alpha$ forest to learn about the distribution of the neutral hydrogen in otherwise unreachable regions of the Universe. To do this, however, we need to separate the smooth part of the quasar spectrum, which we call the {\em unabsorbed flux continuum} (UFC), from the noise and (especially) from the absorption component. The task of separating the three components is not an easy one because there is no immediately available information about the UFC in the Lyman-$\alpha$ forest (which we label UFC$\alpha$). However, the smooth part of the spectrum above the Lyman-$\alpha$ wavelength, henceforth abbreviated with UFC+, could be informative about the structure of UFC$\alpha$. In fact, these two curves belong to the same object, and one may be used to predict the other. For a particular spectrum, let $X$ represent UFC+ (where the quasar spectrum is absorption-free) and let $Y$ denote UFC$\alpha$. We develop a nonparametric functional regression model to estimate the regression operator \begin{equation} \label{eq:firstregressionoperator} r(X)(\cdot) = E(Y | X )(\cdot), \end{equation} \noindent where \begin{equation*} \lambda \mapsto r(X)(\lambda) \end{equation*} \noindent is a curve that has the same domain as $Y$. Then, we use the estimate $\hat r$ to predict $Y^*$ of a new quasar spectrum from $X^*$ according to \begin{equation*} \hat Y^*(\lambda) = \hat r(X^*)(\lambda). \end{equation*} Reliable predictions of UFC$\alpha$ have important implications in cosmological studies. The detection of Baryon Acoustic Oscillations (BAOs) is only one example of the many goals which require good quality predictions of the UFC. BAOs are `typical' distances that characterize the geometry of our Universe. They provide a valuable ruler to measure the separation between pairs of distant objects and to study large scale structures. Our ability to detect BAOs using Lyman-$\alpha$ forest data relies on the accuracy of the predicted UFC$\alpha$. Thus, while on the one hand the prediction of UFC$\alpha$ has a high scientific payoff, on the other hand it also constitutes a challenging statistical task for three main reasons. First, the target quasar spectra are those of {\em high redshift} (i.e. very distant) quasars. Because of the strength of the absorption effect in the Lyman-$\alpha$ forest of their spectra, the UFC is indiscernible in the observed spectrum of high redshift quasars. One then necessarily has to use low redshift quasar spectra (in which the absorption effect is absent or mild) to fit the regression model, and the goodness of the predictions is then conditional, at least in part, on the redshift invariance of the regression operator $r$. Secondly, the amplitude of the spectra in the Lyman-$\alpha$ forest is characterized by a high degree of variability. For some spectra, the variability in the amplitude represents a natural limit in the ability of statistical models to predict UFC$\alpha$. Finally, there are no natural candidate predictors for UFC$\alpha$ other than the absorption-free part of the spectrum, UFC+. Despite these challenges, we demonstrate that nonparametric functional regression provides a natural framework for this prediction problem and that the proposed nonparametric functional regression model produces satisfying predictions of UFC$\alpha$. Our work also introduces distribution-free prediction bands for the nonparametric functional regression model with a function-valued predictor and a function-valued response. Prediction bands for nonparametric functional models are not yet well developed in the Functional Data Analysis literature: we contribute by providing a straightforward method to obtain prediction bands with finite sample coverage guarantees. We use these bands to assess the uncertainty of the model predictions in the Lyman-$\alpha$ continuum prediction problem. Thus, by combining some recent advances in nonparametric functional regression modeling with distribution-free prediction bands, we provide a complete and statistically sound methodology for the prediction of UFC$\alpha$ and the assessment of the uncertainty in the predictions. The remainder of the paper is organized as follows. The next section provides more scientific details and background on quasars, the Lyman-$\alpha$ forest, and the motivation behind the need of statistical methods to predict UFC$\alpha$. Section \ref{sec:nonparametricfunctionalmodeling} presents the nonparametric estimator of the regression operator $r$ of equation \eqref{eq:firstregressionoperator}. In Section \ref{sec:conformalsets}, we derive distribution-free prediction bands for the UFC while Section \ref{sec:confidencebands} describes the implementation of a {\em wild bootstrap} procedure which can be used to generate pseudo-confidence bands for the mean of UFC$\alpha$. The prediction bands and the confidence bands allow us to visually evaluate the degree of uncertainty of the model predictions. Sections \ref{sec:simulationstudy} and \ref{sec:realspectraapplication} are devoted to describing the application of the nonparametric functional regression model to a set of realistic simulated spectra and to two sets of real quasar spectra. Finally, in Section \ref{sec:conclusions} we summarize the results of our study and give some perspective on future research directions stemming from this analysis. | \label{sec:conclusions} In this paper, we demonstrate how the nonparametric functional regression model for function-valued predictor and function-valued response and the estimator of equation \eqref{eq:model} can be used to predict the unknown flux continuum in the Lyman-$\alpha$ forest UFC$\alpha$ from the flux continuum UFC+ in the absorption-free portion of the spectrum using a set of realistic mock spectra and a set of real spectra from the HST-FOS and from the BOSS catalogs. Our results suggest that the methodology that we describe can expand and complement the toolkit of methods that are used to predict the unknown UFC of spectra of large scale studies, which is an important challenge in today cosmology. We hope this study will draw the attention of other astronomers, astrostatisticians and scientists working with Lyman-$\alpha$ forest data to the potential of functional modeling. Furthermore, we introduce a methodology to construct prediction bands with finite sample coverage guarantees and no assumption on the distribution of the function-valued pairs $(X_i,Y_i)$'s for the nonparametric functional regression model proposed by \cite{ferraty2012regression}. It is worth pointing out that current estimates of the correlation function of the relative flux absorption $\delta$ of equation \eqref{eq:relativefluxabsorption} use weighting schemes of the spectra that generally do not account for the uncertainty in the prediction of UFC$\alpha$. The conformal prediction bands proposed in this paper offer a starting point to improve the weighing of the spectra in the computation of the correlation function by including some measure of uncertainty (e.g. the width of the bands) along with the other sources of uncertainty that are already taken into consideration. Our study raises additional questions, both applied and theoretical. On the applied side, it would be interesting to examine if and how strongly the mean flux regulation post-processing step proposed by \cite{lee2012mean} would positively affect the accuracy of the predictions obtained using the nonparametric functional regression model that we describe (especially on BOSS spectra). From a methodological perspective, efforts should be made to devise an extended model that incorporates information about the break in the power law of the spectrum, which we mention in Section \ref{sec:simulationstudy}. Furthermore, information contained in the observed pixels of the Lyman-$\alpha$ forest about the amplitude of UFC$\alpha$ and its shape should be incorporated in the model in such a way to mitigate the inaccuracy in the predicted amplitude of the continuum and to reduce the potential for the slight bias in the predictions which we observed in the simulation study of Section \ref{sec:simulationstudy} (perhaps thus permitting to get around the need for post-processing). Finally, we will investigate refinements of both the conformal prediction bands and of the confidence bands in a future paper. | 14 | 4 | 1404.3168 |
1404 | 1404.0304.txt | {By means of idealized, dissipationless N-body simulations which follow the formation and subsequent buckling of a stellar bar, we study the characteristics of boxy/peanut-shaped bulges and compare them with the properties of the stellar populations in the Milky Way bulge. The main results of our modeling, valid for the general family of boxy/peanut shaped bulges, are the following: \emph{(i)} because of the spatial redistribution in the disk initiated at the epoch of bar formation, stars from the innermost regions to the outer Lindblad resonance of the stellar bar are mapped into a boxy bulge; \emph{(ii)} the contribution of stars to the local bulge density depends on their birth radius: stars born in the innermost disk tend to dominate the innermost regions of the boxy bulge, while stars originating closer to the OLR are preferentially found in the outer regions of the boxy/peanut structure; \emph{(iii)} stellar birth radii are imprinted in the bulge kinematics, the larger the birth radii of stars ending up in the bulge, the greater their rotational support and the higher their line-of-sight velocity dispersions (but note that this last trend depends on the bar viewing angle); \emph{(iv)} the higher the classical bulge-over-disk ratio, the larger its fractional contribution of stars at large vertical distance from the galaxy mid-plane. Comparing these results with the properties of the stellar populations of the Milky Way's bulge recently revealed by the ARGOS survey, we conclude that: \emph{(I)} the two most metal-rich populations of the MW bulge, labeled A and B in the ARGOS survey, originate in the disk, with the population of A having formed on average closer to the Galaxy center than the population of component B; \emph{(II)} a massive (B/D$\sim$0.25) classical spheroid can be excluded for the Milky Way, thus confirming previous findings that the Milky Way bulge is composed of populations that mostly have a disk origin. On the basis of their chemical and kinematic characteristics, the results of our modeling suggests that the populations A, B and C, as defined by the ARGOS survey, can be associated, respectively, with the inner thin disk, to the young thick and to the old thick disk, following the nomenclature recently suggested for stars in the solar neighborhood by Haywood et al. (2013).} | Boxy and peanut shaped bulges are present in about half of edge-on disk galaxies \citep{lut00}. The closest example of a boxy bulge can be found in our Galaxy \citep{okuda77, maihara78, weiland94, dwek95}. Even if some studies \citep{binney85, whit88} have proposed that these structures can be formed during accretion events, their high frequency and relation to the fraction of barred galaxies in disks \citep{eskridge00, menendez07, marinova07, aguerri09} suggest that a more common mechanism may be responsible for shaping the central regions of galaxies, giving them their boxy- or peanut-shaped morphology. A number of numerical investigations \citep{combes81, pfenniger91, athanassoula05, martinez06} have indeed shown that boxy bulges can be manifestations of secular processes that occur in disk galaxies such as thick stellar bars seen edge on. During their evolution, stellar bars can indeed go through one (or multiple) buckling phase(s), which are the consequences of vertical instabilities, and depending on the bar viewing angle, the resulting thick structure can appear boxy, if observed mainly along the bar major axis, or peanut-shaped, if observed mainly along the bar minor axis. It is also possible that a combination of these mechanisms, satellite accretion and bar instability, may be responsible for some of the observed bulge morphologies \citep{mihos95}. Observations suggest that boxy bulges do not represent a homogeneous class of objects. Studies of galaxies indeed demonstrate that boxy bulges display a range of properties in their kinematics and stellar populations \citep{williams11}. Some of them show a constant rotation with height above the plane, while some others do not, thus indicating that cylindrical rotation does not necessarily characterize these structures; some of them show negative vertical metallicity gradients, that can be accompanied by positive [$\alpha$/Fe] gradients, while some are more homogenous, indicating that different stellar populations can dominate these structures at different vertical distances from the galaxy midplane. The complexity of the observed characteristics may be also due to the concomitant presence of a classical\footnote{In the following, by classical bulge we mean a spheroidal component, not formed by disk instabilities, but rather through mergers or some dissipative collapse at early phases of the galaxy formation.} bulge in the inner regions of some galaxy disks. It is not simple to identify the presence of such components in boxy or peanut-shaped structures by the characteristics of their stellar populations and/or kinematics. The existence of a vertical metallicity gradient, for example, does not necessarily imply the presence of a classical bulge \citep{bekki11, martinez13}; the detection of cylindrical rotation does not necessarily imply that the boxy bulge is the result of pure bar instabilities \citep{saha12, saha13}. The question of understanding how much of a classical bulge is present in structures otherwise mostly shaped by secular evolution processes is fundamental not only in interpreting observations of galaxies, but also for understanding the formation and evolution of the central regions of the Milky Way. Indeed, over the last two decades, a number of studies have elucidated the complexity of the boxy, peanut-shaped structure at the center of our Galaxy \citep{mcwilliam94, zoccali06, lecureur07, zoccali08, babusiaux10, shen10, ness12, ness13a, ness13b, gonzalez13, bensby13}, but no consensus has yet been reached on how to interpret these important results. A number of studies have shown evidence of the presence of a metal poor, $\alpha$-enriched component, whose kinematic properties are significantly different from that of the metal-rich, nearly solar [$\alpha$/Fe] bulge component \citep{babusiaux10, hill11, ness13b}. \citet{babusiaux10}, for example, have pointed out the presence of two distinct populations along the bulge minor axis, with distinct kinematic properties: a metal-poor population ([Fe/H]$\sim$-0.3 dex) whose radial velocity dispersion is constant with latitude, and a metal rich population ([Fe/H]$>$~0.1 dex) whose radial velocity dispersion decreases substantially with the distance from the Galactic mid-plane. The contribution of these two populations changes with latitude, the metal rich component disappearing when moving away from the plane, where the metal poor population is becoming dominant. By comparing the data with the N-body model of \citet{fux99}, \citet{babusiaux10} interpreted these two populations as being the signature in the inner Galactic disk of the simultaneous presence of a classical metal-poor bulge and a metal-rich population with bar-like kinematics. However, the presence of a classical bulge in the Milky Way disk and even its role in explaining the characteristics of the observed metal poor, $\alpha$-enhanced population is debated. \citet{shen10}, for example, have questioned the existence of any classical bulge in the Milky Way, ruling out the possibility that our Galaxy has a classical bulge with a mass greater than $\sim$15$\%$ of the stellar disk mass. In addition, recent studies have pointed out the similarities between the metal poor populations of the galactic bulge and the thick disk population at the solar vicinity \citep{melendez08, ryde10, alves10, bensby10, gonzalez11, ness13a}. The ARGOS survey \citep{freeman13}, in particular, is currently mapping the Galactic bulge over a large extent of latitudes and longitudes, contributing significantly to our understanding of how the bulge populations differ in their spatial redistribution, chemical properties and kinematics \citep{ness12, ness13a, ness13b}. The results of this survey mainly suggest the existence of at least three primary components in the Milky Way bulge. Two components (defined respectively as component A and B in their paper), with [Fe/H]$>$$-$0.5 dex, are part of the boxy/peanut shaped bulge, with component B ([Fe/H]$\sim$-0.25 dex) being dynamically hotter than component A ([Fe/H]$\sim$0.1 dex), rotating 20$\%$ faster than A, and being more prominent at high latitudes; component C ([Fe/H]$<$-0.5 dex) has the highest radial velocity dispersions in the fields analyzed, nearly constant both in latitude and longitude, and has been explained by Ness and collaborators as part of the inner thick disk. Is it possible to explain the complexity and richness of these data with a ``simple'' scenario for the formation of the Milky Way bulge? How many of the observed characteristics, for example, are due to a complex accretion history for the Galaxy and how much is due to secular evolution of the disk, with the possible contribution of an older and more metal-poor thick-disk component and/or a classical spheroid? In this paper, we try to answer to some of these questions by showing that at least part of the characteristics observed among the stellar populations of the Galactic bulge, such as the angular momentum support, radial velocity dispersions, and dependence of the fractional contribution of different stellar populations on latitude, can be explained as the simple result of the mapping of a stellar disk onto a boxy/peanut-shaped bulge. We will show that \emph{a large portion of the stellar disk, from the innermost regions to the outer Lindblad resonance of the bar,} is involved in the formation of a boxy/peanut structure, as a result of the radial migration initiated before the buckling instability of the formation of the bar. In particular, we will show that the two populations contributing to the boxy structure (component A and B in Ness et al papers) have kinematic and spatial characteristics compatible with a origin in different regions of the disk. Specifically, we show that, on average, component B formed from stars with initial radii larger than the stars that comprise component A. On the basis of the observed characteristics, the spatial distribution, chemistry and kinematics, we propose that component B is mostly made of the young MW thick disk \citep[stellar ages between 8 and 10 Gyr, as observed at the solar neighborhood;][]{haywood13}, while A is mostly made of stars that originated in the inner thin disk. The presence of a small (B/D=0.1), classical bulge is not excluded and we propose a possible signature of its presence should be searched for in observations of the bulge. We will discuss the possibility that the old thick disk \citep[ages greater than 10 Gyr;][]{haywood13} is the main contributor to component C, which is not part of the boxy/peanut structure. The paper is organized as follows: after describing the N-body models used for the analysis (Sect.~\ref{method}), we will present the main results from an analysis of these simulations in Sects.~\ref{results} and ~\ref{discussion}; then in Sect.~\ref{conclusions}, we state the main conclusions of our work. \begin{figure} \centering \includegraphics[width=4.8cm,angle=270]{pface_initfin2_BD0p00.ps} \includegraphics[width=4.8cm,angle=270]{pvcirc_initfin_BD0p00.ps} \caption{\emph{(Top panel):} Surface density profiles of the initial modeled bulgeless galaxy seen face-on (black curve), after 1.0 Gyr of evolution (blue curve) and after 3.9 Gyr of evolution (red curve). \emph{(Bottom panel):} The initial circular velocity of disk stars (black curve), after 1.0 Gyr of evolution (blue curve) and 3.9 Gyr of evolution (red curve).} \label{density} \end{figure} \begin{figure} \centering \includegraphics[width=4.8cm,angle=270]{Avstime_gS0BD0p00.ps} \includegraphics[width=3.2cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapxy_out395.dat.ps} \includegraphics[width=3.2cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapxz_out395.dat.ps} \caption{\emph{(Top panel:)} Evolution of the $A_1$ (black line), $A_2$ (red line), $A_4$ (blue line) asymmetries versus time for the model with B/D=0. The $A_i$ values are normalized to the $m=0$ value, $A_0$. \emph{(Bottom panels:)} Face-on and edge-on views of the stellar component of the bulgeless disk galaxy at the end of the simulation. } \label{asym} \end{figure} \begin{figure*} \centering \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg1xy_out040.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg1xy_out080.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg1xy_out110.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg1xy_out175.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg1xy_out210.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg1xy_out275.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg2xy_out040.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg2xy_out080.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg2xy_out110.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg2xy_out175.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg2xy_out210.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg2xy_out275.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg3xy_out040.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg3xy_out080.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg3xy_out110.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg3xy_out175.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg3xy_out210.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg3xy_out275.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg4xy_out040.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg4xy_out080.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg4xy_out110.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg4xy_out175.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg4xy_out210.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg4xy_out275.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg5xy_out040.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg5xy_out080.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg5xy_out110.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg5xy_out175.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg5xy_out210.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg5xy_out275.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg6xy_out040.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg6xy_out080.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg6xy_out110.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg6xy_out175.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg6xy_out210.dat.ps} \includegraphics[width=3.cm,angle=270]{gS0_q1p8_BD0p00.ini_pstrmapreg6xy_out275.dat.ps} \caption{\emph{(From top to bottom:)} Face-on density distribution of stars of various birth radii: $\rm{r_{ini}} \le 0.4r_{bar}$; $0.4r_{bar} \le \rm{r_{ini}} \le 0.7r_{bar}$; $0.7r_{bar} \le \rm{r_{ini}} \le r_{bar}$; $r_{bar}\le \rm{r_{ini}} \le 1.3r_{bar}$; $1.3r_{bar} \le \rm{r_{ini}} \le 1.6r_{bar}$; $1.6r_{bar} \le \rm{r_{ini}} \le 1.9r_{bar}$. Different columns correspond to different times, as indicated. In each panel, the average initial radius is indicated by a white circle.} \label{redistrib} \end{figure*} | By means of idealized, dissipationless N-body simulations that follow dynamical influence of the formation and subsequent buckling of a stellar bar on disk stars, we have studied the formation and characteristics of boxy/peanut-shaped bulges and compared them with the properties of the stellar populations of the Milky Way's bulge. The main general results of our modeling, valid for the general family of boxy/peanut shaped bulges, are the following: \begin{enumerate} \item Because of the radial migration initiated at the time of the bar formation, boxy bulges are populated by stars born both in the inner disk and in the outermost regions of the disk, up to the OLR. That is, it is essentially the entirety of stellar disk that is mapped into the stellar populations that comprise the boxy bulge. \item Stars formed outside the bar radius can constitute a non-negligible fraction of the stars that currently comprise the boxy bulge, in our modeling up to 30\% of the stellar mass at high latitudes. \item The fraction of outside-in migrators in a boxy bulge increases both with galactic latitude and longitude. \item The contribution of stars to the local bulge density depends on their birth radius: stars born in the inner disk tend to stay confined in the innermost regions of the boxy bulge, while stars born close to or beyond the vertical inner Lindblad resonance tend to populate the more extended regions of the boxy/peanut-shaped structure. \item The stellar birth radii are imprinted on the stellar kinematics of the bulge stars: bulge stars with larger birth radii have higher levels of rotational support and line-of-sight velocity dispersions compared with stars with smaller birth radii (but note that the trends in the line-of-sight velocity dispersion depend on the angle at which the bar is viewed). \item If a classical spheroid is hidden among the stellar components of a boxy bulge, then our modeling and empirical relationships between spheroidal mass and size and metallicity indicate the following: \begin{itemize} \item Because of the existence of a mass-size relation for spheroids, its contribution to the local density of the boxy bulge depends on its mass: the larger the classical bulge-to-disk ratio, the greater is its fractional contribution to the stellar densities at high vertical distances from the galaxy mid-plane. \item A boxy bulge which contains a small classical spheroid (B/D=0.1) is dominated everywhere by stars originating in the disk. In our models, the classical spheroid indeed contributes, at most, about 20\% of the local mass density regardless of galactic longitude or latitude. \item For a more massive classical spheroid (B/D=0.25), its contribution to the boxy bulge mass density stays constant or increases with latitude. In the absence of a thick disk component, our models predict that the ratio between the classical spheroid and disk stars mass can become equal to 1 at high latitudes, that is the classical spheroid becomes a non-negligible fraction of the stellar content of the boxy structure far from the mid-plane. \item Even if classical spheroids acquires some rotational angular momentum during the secular evolution of the bar \citep[see also][]{saha12, saha13}, their rotational support is generally smaller than that of disk stars at the same location: classical spheroids may be thus be revealed as a low velocity tail in the line-of-sight velocity distribution of stars in the boxy bulge, whose strength increases with longitude. \end{itemize} \end{enumerate} Comparing these results with the properties of the stellar populations in the Milky Way bulge obtained by the ARGOS survey, we conclude that: \begin{enumerate}[I] \item The two most metal-rich components of the MW bulge have a disk origin, with component B formed, on average, at larger radial distances than component A. \item Because of their chemical and kinematic characteristics, we suggest that component A and B are dominated by the Galactic inner thin disk and by the young \citep[ages $\le$ 10 Gyr; see][]{haywood13} thick disk, respectively. \item Because of the existence of a mass-metallicity relation for spheroids, and because of the properties of extra-galactic classical bulges, it is difficult to associate component C with a classical spheroid. Its high level of rotational support, as deduced by radial velocity measurements, suggests a disk origin for this component as well. On the basis of its chemical characteristics, we suggest that it is indeed associated to the old galactic thick disk \citep[ages in the range 8 --10 Gyr; see][]{haywood13}. \item The presence of a massive classical spheroid, with B/D$\sim$0.2 can be excluded for the MW. If present, such a massive component would indeed be significant at high latitudes (30--50\% of the local stellar density) and should have metallicities comparable to those of population B in the bulge. The bar-like kinematic and morphology of population B excludes this possibility. As a result, if a classical bulge is hidden in the populations of the boxy-peanut structure, it cannot be massive (B/D$\le$0.1). This result is in agreement with those found by \citet{shen10, kunder12}, on the basis of kinematic arguments, thus supporting the scenario that most of the mass of the MW's bulge has a disk origin. \end{enumerate} Many observational arguments discussed in this paper support the presence of a massive thick disk in the inner Galactic regions. Such a component cannot be neglected when tallying the mass budget of the MW bulge and inner disk. Modeling its interplay with and contribution to the bar and the thin disk will be the focus of future studies. | 14 | 4 | 1404.0304 |
1404 | 1404.2996_arXiv.txt | Weakly interacting massive particle (WIMP) as a dark matter (DM) candidate is further inspired by recent AMS-02 data, which confirm the excess of positron fraction observed earlier by PAMELA and Fermi-LAT experiments. Additionally, the excess of positron+electron flux is still significant in the measurement of Fermi-LAT. For solving the problems of massive neutrinos and observed excess of cosmic-ray, we study the model with an inert Higgs doublet (IHD) in the framework of type-II seesaw model by imposing a $Z_2$ symmetry on the IHD, where the lightest particle of IHD is the DM candidate and the neutrino masses originate from the Yukawa couplings of Higgs triplet and leptons. We calculate the cosmic-ray production in our model by using three kinds of neutrino mass spectra, which are classified by normal ordering, inverted ordering and quasi-degeneracy. We find that when the constraints of DM relic density and comic-ray antiproton spectrum are taken into account, the observed excess of positron/electron flux could be explained well in normal ordered neutrino mass spectrum. Moreover, excess of comic-ray neutrinos is implied in our model. We find that our results on $\langle \sigma v \rangle$ are satisfied with and close to the upper limit of IceCube analysis. More data from comic-ray neutrinos could test our model. | Two strong direct evidences indicate the existence of new physics: one is the observations of neutrino oscillations, which lead to massive neutrinos~\cite{PDG2012}, and another one is the astronomical evidence of dark matter (DM), where a weakly interacting massive particle (WIMP) is the candidate in particle physics. The Planck best-fit for the DM density, which combines the data of WMAP polarization at low multipoles, high-$\ell$ experiments and baryon acoustic oscillations (BAO), etc., now is given by \cite{Ade:2013ktc} \be \Omega h^2=0.1187\pm0.0017\,. \label{eq:omega} \ed Until now, we have not concluded what the DM is and what the masses of neutrinos originate. It is interesting if we can accommodate both DM issue and neutrino masses in the same framework. Although the probe of DM could be through the direct detection experiments, however according to the recent measurements by LUX Collaboration~\cite{Akerib:2013tjd} and XENON100~\cite{XENON100}, we are still short of clear signals and the cross section for elastic scattering of nuclei and DM has been strictly limited. In contrast, the potential DM signals have been observed by the indirect detections. For instance, the recent results measured by AMS-02~\cite{Aguilar:2013qda} have confirmed the excess of positron fraction which was observed earlier by PAMELA~\cite{Adriani:2008zr} and Fermi-LAT~\cite{FermiLAT:2011ab} experiments. Additionally, the excess of positron+electron flux above the calculated backgrounds is also observed by PAMELA~\cite{Adriani:2011xv}, Fermi-LAT~\cite{Ackermann:2010ij}, ATIC~\cite{Chang:2008aa} and HESS~\cite{Aharonian:2008aa, Aharonian:2009ah}. Inspired by the observed anomalies, various interesting possible mechanisms to generate the high energy positrons and electrons are proposed, such as pulsars \cite{pulsar1,pulsar2}, dark matter annihilations \cite{DManni,Baek:2008nz,Ko:2010at} and dark matter decays \cite{Baek:2014goa,DMdecay,Chen:2009mf}. The origin of neutrino masses is one of most mysterious problems in high energy physics. Before nonzero neutrino masses were found, numerous mechanisms had been proposed to understand the source of neutrino masses, such as type-I seesaw \cite{SeeSaw} and type-II seesaw \cite{ Magg:1980ut,Konetschny:1977bn} mechanisms, where the former introduced the heavy right-handed neutrinos and the latter extended the standard model (SM) by including a $SU(2)$ Higgs triplet. Since the triplet scalars only couple to leptons, based on this character, it may have interesting impacts on the cosmic-ray positrons, electrons and neutrinos. We therefore study a simple extension of conventional type-II seesaw model by including the possible DM effects. For studying the excess of cosmic rays by DM annihilation and the masses of neutrinos, we add an extra Higgs doublet $(\Phi)$ and a Higgs triplet ($\Delta$) to the SM. Besides the gauge symmetry $SU(2)_L\times U(1)_Y$, in order to get a stable DM, we impose a discrete $Z_2$ symmetry in our model, where the $\Phi$ is $Z_2$-odd and the $\Delta$ and SM particles are $Z_2$-even. The $Z_2$ odd doublet is similar to the one in inert Higgs doublet (IHD) model~\cite{Ma:2006km,Barbieri:2006dq}, where the IHD model has been studied widely in the literature, such as DM direct detection \cite{Barbieri:2006dq,LopezHonorez:2006gr,Arhrib:2013ela}, cosmic-ray gamma spectrum~\cite{Gustafsson:2007pc}, cosmic-ray positrons and antiproton fluxes~\cite{Nezri:2009jd}, collider signatures~\cite{Cao:2007rm,Dolle:2009ft}, etc. The lightest neutral odd particle could be either CP-odd or CP-even, in this work we will adopt the CP-even boson as the DM candidate. For explaining the observed excess of cosmic rays, we set the odd particle masses at TeV scale. There are two motivations to introduce the Higgs triplet. First, like the type-II seesaw mechanism \cite{Magg:1980ut,Konetschny:1977bn}, the small neutrino masses could be explained by the small VEV of triplet without introducing heavy right-handed neutrinos. Second, the excess of cosmic-ray appears in positrons and electrons, however, by the measurements of AMS~\cite{Aguilar:2002ad}, PAMELA~\cite{Adriani:2010rc} and HESS~\cite{Asaoka:2001fv}, no excess is found in cosmic-ray antiproton spectrum. Since triplet Higgs bosons interact with leptons but do not couple to quarks, it is interesting to explore if the observed excess of positron fraction and positron+electron flux could be explained by the leptonic decays of Higgs triplet in DM annihilation processes. The model with one odd singlet and one $SU(2)_L$ triplet has been studied and one can refer to Ref.~\cite{Dev:2013hka}. Furthermore, the search of doubly charged Higgs now is an important topic at colliders. If doubly charged Higgs is 100\% leptonic decays, the experimental lower bound on its mass has been limited in the range between 375 and 409 GeV~\cite{Chatrchyan:2012ya, ATLAS:2012hi}. The detailed analysis and the implications at collider physics could consult the Refs.~\cite{triplet search, Perez:2008ha,Arhrib:2011uy,delAguila:2013mia}. The decays of triplet particles to leptons depend on the Yukawa couplings. As known, the Yukawa couplings could be constrained by the measured neutrino mass-squared differences and the mixing angles of Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix \cite{Pontecorvo:1957cp,Maki:1962mu}, where the current data are given by \cite{PDG2012} \be \Delta m^2_{21}&=&(7.50\pm 0.20)\times 10^{-5} eV^2 \,, \non \\ | \Delta m^2_{31} | &=& (2.32 ^{+0.12}_{-0.08} ) \times 10^{-3} eV^2\,, \non \\ \sin^2(2\theta_{12}) &=& 0.857 \pm 0.024\,, \sin^2(2\theta_{23}) > 0.95\,, \non \\ \sin^2(2\theta_{13})&=&0.095 \pm 0.01. \ed Since the data can not tell the mass pattern from various neutrino mass spectra, in our study, we classify the mass spectra to be normal ordering (NO), inverted ordering (IO) and quasi-degeneracy (QD) \cite{PDG2012} and investigate their influence on the production of cosmic rays. Because we do not have any information on the Dirac $(\delta)$ and Majorana $(\alpha_{31, 21})$ phases in PMNS matrix, we adopt four benchmark points that are used by CMS Collaboration for the search of doubly charged Higgs \cite{Chatrchyan:2012ya}. The first three benchmark points stand for the NO, IO and QD with $\delta=\alpha_{31}=\alpha_{21}=0$ while the fourth one denotes the QD with $\delta=\alpha_{31}=0$ and $\alpha_{21}=1.7$. We note that the necessary boost factor (BF) for fitting the measured cosmic-ray electron/positron flux by DM annihilation is regarded as astrophysical effects \cite{Kuhlen:2012ft}. We take the BF as a parameter and use the data of antiproton spectrum to bound it. Furthermore, since the singly charged and neutral triplet particles couple to neutrinos, an excess of cosmic-ray neutrinos is expected in the model. We find that a Breit-Wigner enhancement could occur at the production of neutrinos; therefore, without BF, a large neutrino flux from DM annihilation could be accomplished. Accordingly, with the same values of free parameters that fit the excess of cosmic-ray positron/electron flux, our results on neutrino excess from galactic halo could be close to the upper bound measured by IceCube~\cite{Abbasi:2011eq, Aartsen:2013mla}. The paper is organized as follows. We introduce the gauge interactions of IHD and triplet, Yukawa couplings of triplet, and scalar potential in Sec II. The set of free parameters and the branching fractions of triplet particle decays are introduced in Sec III. In Sec IV, we discuss the constraints from relic density of DM and cosmic-ray antiproton spectrum. With the values of constrained parameters, we study the fluxes of cosmic-ray positrons, electrons and neutrinos. % We give a summary in Sec V. | For explaining the measured positron excess by the DM annihilation, we have studied the extension of the SM by adding an odd IHD $\Phi$ and an even Higgs triplet $\Delta$. The LOP of $\Phi$ can be a WIMP DM candidate. Due to the unbroken $Z_2$-parity, the DM candidate is stable. We take the CP-even component $S$ as the DM candidate. The neutrinos become massive through the type-II seesaw mechanism. In order to suppress the effects from IHD model and emerge the triplet contributions, we have set $\lambda_L=0$, $m_A - m_S= 1$ GeV and $m_{H^\pm}=m_A$. Even though, the antiproton spectrum is dominated by triple interactions $SH^\pm W^\mp$ and $SAZ$ and quadratic interactions $SS(W^\pm W^\mp,ZZ)$ which appear in IHD model. With the measurement of antiproton spectrum, we study the correlation between the upper bound of BF and $m_S$. In terms of the Feynman diagrams, three scenarios are involved in our analysis. In scenario-I, we further use three schemes to describe the parameters $\chi_A$ and $\chi_B$. In our model, the excess of positrons/electrons is mainly arisen from the triplet decays. Since the neutrino mass spectrum is still uncertain, we also study the influence of neutrino mass in the cases of NO, IO and QD. From Figs.~\ref{fig:positronBP1}-\ref{fig:positronBP4}, we see that scenario-I$_a$ and -I$_{b}$ have similar contributions. Moreover, the normal ordered mass spectrum could fit well to the excess of positrons/electron measured by PAMELA, Fermi-LAT and AMS-02. Although we have not observed the excess of comic-ray neutrinos, however if the source of excess of positrons/electrons is from triplet decays, the same effects will also increase the abundance of cosmic-ray neutrinos. We find that the quasi-resonance effects at $m_\Delta \approx 2m_S$ could occur in scenario-III so that large neutrino flux can be obtained without BF. We calculate $\langle \sigma v \rangle $ for cosmic-ray neutrinos and realize that our results in some parameter region are close to the recent IceCube data for neutrino flux from galactic halo. Hence, our model could be tested if more data for cosmic-ray neutrinos are observed. \\ \noindent{\bf Acknowledgments} We thank Dr. A. Pukhov for providing the revised code of micrOMEGAs. This work is supported by the National Science Council of R.O.C. under Grant \#: NSC-100-2112-M-006-014-MY3 (CHC) and NSC-102-2811-M-006-035 (TN). We also thank the National Center for Theoretical Sciences (NCTS) for supporting the useful facilities. | 14 | 4 | 1404.2996 |
1404 | 1404.5578_arXiv.txt | The Gaia-ESO Public Spectroscopic Survey (GES) is conducting a large-scale study of multi-element chemical abundances of some $100~000$ stars in the Milky Way with the ultimate aim of quantifying the formation history and evolution of young, mature and ancient Galactic populations. However, in preparing for the analysis of GES spectra, it has been noted that atomic oscillator strengths of important Fe~I lines required to correctly model stellar line intensities are missing from the atomic database. Here, we present new experimental oscillator strengths derived from branching fractions and level lifetimes, for 142 transitions of Fe~I between 3526~\AA~and 10864~\AA, of which at least 38 are urgently needed by GES. We also assess the impact of these new data on solar spectral synthesis and demonstrate that for 36 lines that appear unblended in the Sun, Fe abundance measurements yield a small line-by-line scatter (0.08 dex) with a mean abundance of 7.44 dex in good agreement with recent publications. | The Gaia-ESO Public Spectroscopic Survey (GES) is currently taking place at the European Southern Observatory (ESO), employing the Fibre Large Array Multi Element Spectrograph (FLAMES) instrument at the Very Large Telescope (VLT) facility. Its aim is to obtain high quality spectroscopy of some 100~000 stars from all major components of the Milky Way to quantify the ``kinematic multi-chemical element abundance distribution functions of the Milky Way Bulge, the thick Disc, the thin Disc, and the Halo stellar components, as well as a very significant sample of 100 open clusters" \citep{ref:gilmore12}. Over the course of the survey, chemical abundances will be measured for alpha and iron-peak elements in all stars with visual magnitude less than nineteen. These data will probe stellar nucleosynthesis by examining nuclear statistical equilibrium and the alpha-chain. Ultimately, the abundances and radial velocities will be combined with high-precision position and proper motion measurements from the European Space Agency's \emph{Gaia} mission, to ``quantify the formation history and evolution of young, mature and ancient Galactic populations" \citep{ref:perryman01}. \cite{ref:gilmore12} also state that ``Considerable effort will be invested in abundance calibration and ESO archive re-analysis to ensure maximum future utility." To achieve these high-level aims, it is vital that fundamental atomic data be available for lines in the GES spectral range: $4800$ \AA~to $6800$ \AA~ for measurements with the high-resolution FLAMES Ultraviolet and Visual Echelle Spectrograph (UVES) and $8500$ \AA~to $9000$ \AA~for measurements with the mid-resolution FLAMES \emph{Giraffe} spectrograph. The availability of absorption oscillator strengths, f (usually used as the $\log(gf)$, where $g$ is the statistical weight of the lower level), is particularly important for the correct modelling and analysis of stellar line intensities; especially so for abundant elements such as iron, which is also used to infer fundamental stellar parameters. However, in preparing a list of iron lines to be targeted during the analysis of GES spectra, the GES line list team noted that of $449$ well-resolved lines of neutral iron (Fe~I) expected to be visible with sufficient signal-to-noise ratio, only 167 have published log(gf) values measured in the laboratory with uncertainties below 25 \%. Experimental log(gf) values with large uncertainties (greater than 50 \% in many cases) were available for an additional 162 lines. For the final $120$ lines, no experimental $\log(gf)$s were available at all. A similar observation was made by \cite{ref:bigot06} for lines of interest to the \emph{Gaia} mission. As a result of this inadequacy in the atomic database, and similar inadequacies observed by other astronomers (see \cite{ref:ruffoni13b} and \cite{ref:pickering11}, for example), we have undertaken a new study of the Fe~I spectrum with the aim of providing accurate $\log(gf)$ values for lines of astrophysical significance. In Section \ref{section:results} of this paper, we report accurate $\log(gf)$s for 142 Fe~I lines, 64 of which have been measured experimentally for the first time. The $\log(gf)$ values of at least 38 of these lines are urgently needed for the GES survey. % | \label{section:summary} In Table \ref{table:results}, we have provided new $\log(gf)$ values for 142 Fe~I lines from 12 upper levels, which include 38 lines of particular interest for the analysis of stellar spectra obtained by the GES survey. Where $\log(gf)$s existed for these lines in the literature, we have found good agreement with our new values, which in many cases have smaller experimental uncertainties than those previously reported. This is especially true for uncertainties in $\log(gf)$s from \cite{ref:may74}, which have been reduced from $50 \%$ or more to less than $25 \%$ in most cases. This work represents part of an on-going collaboration between Imperial College London, U. Wisconsin, and NIST to provide the astronomy community with Fe~I $\log(gf)$ values needed for the analysis of astrophysical spectra. Further publications will follow in the near future. | 14 | 4 | 1404.5578 |
1404 | 1404.0677_arXiv.txt | We investigate the process of rapid star formation quenching in a sample of 12 massive galaxies at intermediate redshift ($z\sim0.6$) that host high-velocity ionized gas outflows ($v > 1000$~km~s$^{-1}$). We conclude that these fast outflows are most likely driven by feedback from star formation rather than active galactic nuclei (AGN). We use multiwavelength survey and targeted observations of the galaxies to assess their star formation, AGN activity, and morphology. Common attributes include diffuse tidal features indicative of recent mergers accompanied by bright, unresolved cores with effective radii less than a few hundred parsecs. The galaxies are extraordinarily compact for their stellar mass, even when compared with galaxies at $z\sim2$~--~3. For 9/12 galaxies, we rule out an AGN contribution to the nuclear light and hypothesize that the unresolved core comes from a compact central starburst triggered by the dissipative collapse of very gas-rich progenitor merging disks. We find evidence of AGN activity in half the sample but we argue that it accounts for only a small fraction ($\lesssim10$\%) of the total bolometric luminosity. We find no correlation between AGN activity and outflow velocity and we conclude that the fast outflows in our galaxies are not powered by on-going AGN activity, but rather by recent, extremely compact starbursts. | \label{section:intro} Cosmological simulations based on a $\Lambda$CDM framework overpredict by an order of magnitude the fraction of baryons that will form stars by the present day \citep[e.g.,][]{keres09}. This ``overcooling" problem is manifested at the massive end ($M_{\ast} \sim 10^{11} M_{\sun}$) by simulated galaxies that are too luminous and blue to match observations \citep[e.g.,][]{croton06,gabor11}. The preferred solution is that feedback from massive stars and accreting supermassive black holes (SMBHs) regulates the cold gas supply for star formation by ejecting cold gas from galaxies and preventing hot gas from cooling. The global effect of this feedback can be tuned to match the observed stellar mass function by reducing the efficiency of star formation in both low-mass and high-mass dark matter halos \citep[e.g.,][]{somerville09,behroozi13}. However, the relevant gas physics (e.g., shocks, dissipation, heating, cooling) occurs on scales that are unresolved by modern simulations. At the massive end, the central problem is how to quench star formation to form the population of elliptical galaxies found in the local universe and the ``red sequence" galaxies observed out to $z\ge2$. The most massive ellipticals have high $\alpha$/Fe abundance ratios implying very short formation times ($\Delta t \lesssim 1$~Gyr; \citealt{thomas05,thomas10}). The ejective feedback that is necessary to quench star formation quickly in simulations is predicted to be most effective in major mergers of massive gas-rich galaxies \citep[e.g.,][]{wuyts10}. Under the assumption that such mergers form dynamically hot spheroids and quench subsequent star formation \citep[e.g.,][]{springel05}, this merger-driven model has been proposed to be the dominant formation mechanism for red elliptical galaxies \citep{hopkins08a}. Feedback from an active galactic nucleus (AGN) is commonly invoked as the mechanism for heating up and driving out large fractions of cold gas, effectively quenching star formation \citep[e.g.,][]{booth13,granato04,hopkins06,menci06}. These models have been successful in reproducing a number of empirical trends, including the color-magnitude relation and the correlation between supermassive black hole (SMBH) mass and bulge stellar velocity dispersion. AGN feedback models accomplish this by assuming that $\sim5$\% of the radiated quasar luminosity can couple thermally and isotropically to the surrounding gas. However, linking galaxy-wide outflows to feedback processes (e.g., radiation pressure, jets) from a SMBH that originate on parsec scales remains a challenging problem because momentum coupling is not fully understood. Therefore, it is crucial to search for direct evidence of merger-induced quasar feedback. Unfortunately, even recent evidence for AGN feedback is still largely circumstantial \citep[e.g.,][]{cano-diaz12,veilleux13}. Only in a limited number of cases in very low-redshift galaxies where powerful, kiloparsec-scale outflows can be resolved and examined in detail can quasar feedback be most clearly traced back to the SMBH \citep[e.g.,][]{lipari09,rupke11,greene11,greene12,hainline13}. Several observational studies have found that massive, quiescent galaxies at $z \sim 2$~--~3 are remarkably compact, with sizes a factor of 4~--~6 smaller than local galaxies \citep{zirm07,trujillo07,vandokkum08,buitrago08}. Highly dissipational mergers between gas-rich progenitors, which are more common at high redshift, have been invoked to explain these super-compact massive galaxies \citep{covington11}. It has been suggested that these massive galaxies evolve ``inside out'' in order to arrive on the local size-mass relation \citep{hopkins09b,fan13,vandesande13}. There have been considerable recent efforts to identify the $z\sim3$ star-forming progenitors of massive, compact, quiescent galaxies \citep{patel12,barro13,stefanon13}. Studying such faint systems in sufficient detail to gain insight into the physical mechanisms responsible for shutting down their star formation is very difficult at these redshifts. By identifying and studying lower redshift analogues, we may be able to more readily learn about higher redshift massive galaxy evolution. With the preceding ideas in mind, we have been studying a sample of massive galaxies ($log(M_*/M_{\sun}) = 10.5 - 11.5$) at $z=0.40$~--~$0.75$ selected to be in the midst of star formation quenching. They have very blue B- and A-star dominated stellar continua but relatively weak nebular emission lines (H$\beta$ EW$ < 12$~\AA). \citet{tremonti07} inferred that the star formation rate in the last 10~Myr was significantly lower than it was in the past 100~Myr, and labeled them young post-starburst galaxies. Subsequent restframe mid-infrared (IR) measurements revealed large luminosities, which might be explained if these galaxies are unusually compact young post-starbursts \citep{groves08}. However, modeling of the ultraviolet (UV) to near IR spectral energy distribution (SED) suggests a high level of heavily obscured star formation \citep{diamond-stanic12b}. In either case, the galaxies are very different from classic post-starburst galaxies \citep[i.e., E+A or K+A galaxies][]{dressler83,zabludoff96,poggianti99}, which do not exhibit such unusual properties and have been shown to have very little obscured star formation \citep{nielsen12}. Therefore, the galaxies in our sample are likely to be very close to their peak star formation rate, when quenching processes are expected to be the most active. Notably, two-thirds of the galaxies exhibit $\ge 1000$~km~s$^{-1}$ outflows \citep{tremonti07}, the largest outflow velocities observed in star-forming galaxies at any redshift, suggesting that feedback may play a significant role in quenching. We present detailed multiwavelength analysis of a small sub-sample of these galaxies. The 12 galaxies in this study are a subset of the 29 galaxies initially considered by \cite{diamond-stanic12b}. They presented the basic result that many of these galaxies have compact morphologies (as small as $r_e \sim 100$~pc). The compact morphologies of these galaxies suggested that their high-velocity outflows could have been driven by extreme star-formation feedback \citep{heckman11}. \cite{diamond-stanic12b} highlighted the UV though IR SEDs, Hubble Space Telescope (HST) images, and optical spectra for three galaxies with extraordinarily high star-formation rate surface densities (up to $\Sigma_{\textnormal{\scriptsize{SFR}}}\approx3000$~M$_{\odot}$~yr$^{-1}$~kpc$^{-2}$) that approach the theoretical Eddington limit \citep{lehnert96,meurer97,murray05,thompson05}. One of these galaxies, J1506+54, which is one of the 12 galaxies in our sub-sample, has also been investigated by \cite{geach13}. Their recent CO observations of this galaxy indicate that it contains $\sim10^{10}~M_{\odot}$ of cold gas. However, the very high $L_{IR}$ / $L_{CO}$ ratio implies that it is being consumed with near 100\% efficiency, and will be exhausted in a few tens of Myr. Thus, we surmise that our galaxies are in the midst of starburst quenching. An important issue is whether feedback from an AGN contributes to these outflows and whether the presence of an AGN could have affected the size measurements from {\em HST}. We consider whether the galaxies' recent activity is related to a merger, and we examine whether there is any evidence that the black hole plays a role in driving the fast outflows we observe and in quenching the starburst. For our investigation, we use multi-wavelength diagnostics to build a comprehensive view of these galaxies. We combine targeted MMT UV-optical spectroscopy, \emph{Chandra} X-ray observations, \emph{HST} optical imaging, Jansky Very Large Array (JVLA) radio observations, and {\em Spitzer Space Telescope} \citep{werner04} near IR imaging with survey imaging from the {\it Galaxy Evolution Explorer} \citep[GALEX;][]{martin05a}, Sloan Digital Sky Survey \citep[SDSS;][]{york02}, and {\em Wide-field Infrared Survey Explorer} \citep[WISE;][]{wright10}. This paper is organized as follows. Our sample selection is discussed in \S~\ref{section:sample}; data reduction and basic analysis of our multiwavelength observations is presented in \S~\ref{section:data_red} and in the Appendix. Readers wishing to go straight to the results are encouraged to begin reading in \S~\ref{section:analysis_agn}, which provides a summary of the preceding analysis. In this section, we estimate the accretion rate of the three broad-line AGN and consider the available evidence for AGN activity in the other nine galaxies. We also include a case study of a galaxy in our sample with one of most extreme starbursts currently known (\S~\ref{section:j1506}). In \S~\ref{section:discussion}, we summarize the HST morphological analysis and highlight the very high star formation surface densities implied by the compact sizes of the galaxies. We assess whether AGN feedback is responsible for starburst quenching and the ultra-fast outflows in our sample. Finally, we summarize this work and state our most important conclusions in \S~\ref{section:conclusions}. Throughout this paper, we adopt the AB magnitude system, unless otherwise noted, and standard cosmological parameters: $H_0 = 70$~km~s$^{-1}$~Mpc$^{-1}$, $\Omega_M = 0.3$, and $\Omega_\Lambda = 0.7$. | \label{section:conclusions} We have analyzed \emph{HST} and \emph{Chandra} images, UV-optical spectra, UV-MIR photometric data, and JVLA radio data on a a sub-sample of massive galaxies at $z=0.4$~--~0.75 in the midst of star formation quenching. These galaxies were selected from a larger parent sample as the most likely to host AGN. Our primary goal is to understand the activity of their SMBHs and the morphology of their host galaxies to gain insight into whether the SMBHs drove the galaxy-wide outflows and played the primary role in shutting down their recent star formation. A summary of our findings is presented below. \begin{itemize} \item{Restframe V-band \emph{HST} imaging reveals tidal tails or disturbed morphologies indicative of a recent major or minor merger in 9/12 galaxies. Given the shallow depth of our images, we cannot rule out the presence of such features in the remaining galaxies. We conclude that the recent starburst in all of our galaxies was likely triggered by a merger.} \item{All of the galaxies have very compact light profiles. J1558+39, J1613+28, J1713+28, and J2118+00 appear to be in the midst of nuclear coalescence and have not relaxed yet. Excluding these galaxies and the three Type~I AGN, we measure effective radii of 0.1~--~0.2~kpc using a single S\'{e}rsic fit. These objects are better fit by a combination of a S\'{e}rsic profile and a nuclear point source which contains 40~--~60\% of the total light. We argue that the unresolved light is not due to an AGN because we see no evidence of broad Mg~II or H$\beta$ emission lines in the optical spectrum and the probability that these galaxies are consistent with weak-lined AGN is small based on their $\alpha_{ox}$ ratios. We conclude that the nuclear light is likely due to a compact ($<0.5$~kpc) central starburst triggered by the dissipative collapse of very gas rich progenitor disks, as suggested by theoretical models \citep[c.f.,][]{hopkins09a}.} \item{Three of the galaxies (J1359+51, J1634+46, and J2140+12) are broad-line AGN. We use the width of the broad Mg~II emission lines to derive virial masses of $M_{SMBH} \sim 10^8$~--~$10^9$~M$_\odot$. Two of the AGN are X-ray-detected (J1359+51 and J1634+46) and one is radio-loud (J1634+46). We calculate that they are radiating at $\sim 1$~--~7\% of their Eddington luminosities.} \item{Based on high-excitation emission-line diagnostics, only 3/9 narrow-line galaxies (J1104+59, J1506+54, and J1713+28) exhibit signs of obscured AGN. The bolometric Eddington fractions are similar to those found for the broad-line AGN, but even more uncertain because the emission is also consistent with the presence of an ultra-compact starburst; this leads to somewhat ambiguous results. In one case, J1506+54, we find that only 11\% of the mid-IR luminosity of is due to the AGN with the remainder coming from star formation.} \item{The other six galaxies in the sample are completely consistent with compact starbursts. We have shown that analysis of BPT-type diagrams does not provide a clear indication of AGN activity for these galaxies primarily because the [O~III]/H$\beta$ ratio does not discriminate extreme starbursts well. In addition, although faint levels of X-ray emission are observed in three of these galaxies, the derived X-ray luminosities and stacked hardness ratio are entirely consistent with emission from XRBs given the large recent SFRs of these galaxies. While we cannot conclusively rule out Compton-thick AGN in these sources, we suggest that star formation is likely to be the dominant contributor to the galaxies' bolometric luminosities.} \item{Nine of our galaxies show evidence of ultra-fast ($v_{max} \gtrsim 1000$~km~s$^{-1}$) Mg~II outflows. Only one of the three unequivocally identified (broad-line) AGN has a detected outflow, and it is the slowest or second slowest in the sample, depending on how the outflow velocity is measured. The light from 5/9 of the galaxies with the ultra-fast outflows is completely consistent with compact starbursts (and in 3/9 cases, we are unable to conclusively differentiate between starburst and AGN activity). We conclude that outflow properties are not linked to ongoing AGN activity.} \end{itemize} These results support the primary conclusion of \cite{diamond-stanic12b}, who argued that our ultra-compact galaxies have the physical conditions necessary to launch the high-velocity outflows we observe by highlighting the $v\propto r^{-1/2}$ scaling for winds driven by either supernovae or radiation pressure from massive stars. To this argument we add the fact that the presence of a luminous AGN does not appear to have any positive correlation with Mg~II absorption strength or outflow velocity. This study and \cite{diamond-stanic12b} cannot and did not conclusively rule out that AGN play at least a minor role at some point in the evolution of these galaxies. However, we do not find any evidence directly in support of AGN feedback in this sample of galaxies, and AGN feedback is unnecessary to explain the observations. Overall, we conclude that these galaxies are massive merger remnants with high-velocity outflows primarily driven by powerful, unusually compact starbursts. | 14 | 4 | 1404.0677 |
1404 | 1404.5264_arXiv.txt | We carry out a nonadiabatic analysis of strange-modes in hot massive stars with time-dependent convection (TDC). In envelopes of such stars, convective luminosity is not so dominant as that in envelopes of stars in the redder side of the classical instability strip. Around the Fe opacity bump, however, convection contributes non-negligibly to energy transfer. Indeed, we find that instability of modes excited at the Fe bump is likely to be weaker with TDC compared with the case of adopting the frozen-in convection approximation. But we confirm that unstable strange-modes certainly remain in hot massive stars even by taking into account TDC. We also examine properties of the strange-mode instability, which is related to destabilization of strange-modes without adiabatic counterparts. In this type of instability, the phase lag between density and pressure varies from 0 to $180^{\circ}$ in an excitation zone unlike the case of the $\kappa$-mechanism. In addition, we confirm by comparing models with $Z=0$ and $Z=0.02$ that dominance of radiation pressure is important for this type of instability. | Strange-modes are one type of stellar pulsation modes, but have significantly different properties from those of ordinary modes appearing in most of pulsating stars. Although their physical properties have not been well established yet, they have been examined by many authors so far. \citet{Wood1976} found strange-modes for the first time in a numerical study for luminous helium stars. He pointed out that there is no one-to-one correspondence between solutions by adiabatic and nonadiabatic analyses. As a matter of fact, they were not called strange-modes at that time, but \citet{Cox1980} named them ``strange'' modes for the first time in the study of pulsations in hydrogen deficit carbon stars. \citet{Shibahashi1981} systematically analyzed radial and nonradial pulsations in models with different $L/M$ ratios, and found that strange-modes appear in models with $L/M\gtrsim 10^4L_{\odot}/M_{\odot}$. They also investigated the origin of strange-modes with a numerical experiment, in which they artificially changed the thermal time-scale. For the thermal time-scale reduced to zero, which generates an extremely nonadiabatic situation, the strange-mode eigenfrequencies are close to those obtained by a fully nonadiabatic analysis with the realistic and unchanged thermal time-scale. On the other hand, when increasing the thermal time-scale and generating an adiabatic situation, the real part of eigenfrequency decreases toward zero while the imaginary part remains large. And then the mode becomes an oscillatory convection ($g^{-}$) mode. \citet{Saio1984} performed a similar experiment, and found a relation to thermal waves. \citet{Gautschy1990} found strange-modes not related to thermal waves both in a fully nonadiabatic analysis and in the nonadiabatic reversible (NAR) approximation (equivalent with reducing the thermal time-scale to zero in \authorcite{Shibahashi1981}'s experiment). In the NAR approximation, the classical $\kappa$-mechanism can no longer work, and hence an alternative physical explanation for the excitation of the strange-modes has been needed. To understand about the instability of this type of strange-mode, which is called ``strange-mode instability'', \citet{Glatzel1994} suggested with a local analysis that dominance of radiation pressure leads to a large phase lag between density and pressure perturbations, and to the strange-mode instability. \citet{Saio1998} also carried out analytic investigations through different approaches, and obtained similar consequences. But in addition to this, they claimed that the opacity derivative with respect to density $\kappa_\rho$ is essential for the instability, and that the instability grows as radiation pressure gradient produces a restoring force. Since the strange-modes mentioned above appear in the environment with short thermal time-scale, the adiabatic approximation is no longer available for them. However, after new opacity tables \citep{Rogers1992} were released, strange modal sequences have been found even by adiabatic analyses in a modal diagram, i.e. a diagram plotting frequencies as a function of a stellar parameter (e.g. mass, effective temperature). Modes on such sequences appear since the Fe opacity bump, enhanced in the new opacity tables, causes a sound speed inversion. As a result, mode amplitude is confined around there, and the $\kappa$-mechanism works efficiently and leads to an extremely rapid growth of amplitude (Kiriakidis et al. \yearcite{Kiriakidis1993}; Saio et al. \yearcite{Saio1998}). Although the physical properties still remain puzzling, unstable strange-modes have been found in models of very luminous stars such as massive stars, Wolf-Rayet stars, helium stars, etc. by many studies (summarized by Saio et al. \yearcite{Saio1998}). Growth time-scales of unstable strange-modes are likely to be much shorter than those of ordinary modes, and comparable to their pulsational periods. Then, instability of the strange-modes might lead to nonlinear phenomena such as mass loss, and might be influential on stellar evolution. Indeed, the instability of strange-modes has been suggested as one of the candidates for a trigger of the \authorcite{Humphreys1979} (HD, 1979) limit phenomenon. In the Hertzsprung-Russel (HR) diagram, there are few observed stars over the HD limit. This implies that stars with $M\gtrsim 50M_{\odot}$ cannot evolve toward red supergiants. Just in the lower left side of the HD limit, luminous blue variables [LBVs or S Dor (SD) variables] are distributed. They intermittently show irregular variations in visible magnitude in a timescale of years to decades, while their bolometric magnitude almost keeps constant. In the HR diagram, this phenomenon can be shown as a horizontal transition. As an explanation for this, it is thought that sporadic eruptions would take place by some mechanism, and generate a thick envelope with a pseudo-photosphere. As the envelope expands, the apparent effective temperature decreases. When the eruptions cease, the core would be exposed again, and the effective temperature goes back to the original high value. After repeating this process and losing substantial mass, the stars are thought to evolve toward Wolf-Rayet stars. Although the mass-loss mechanism of LBVs has not been established yet, Kiriakidis, Fricke \& Glatzel (\yearcite{Kiriakidis1993}) found that strange-modes are unstable around the HD limit, and suggested that their instability could be responsible for the HD limit phenomenon. Recently, nonlinear calculations for radial strange-modes have been carried out (\cite{Dorfi2000}; Chernigovski et al. \yearcite{Chernigovski2004}; Grott et al. \yearcite{Grott2005}) to investigate pulsationally-driven mass-loss, although there seem to be no conclusive results so far. On the other hand, \citet{Aerts2010} observed a pulsation in a luminous B star, HD 50064, and found that its mass-loss rate changes in a time-scale of the pulsation period. \citet{Godart2011} suggested that a strange-mode could be a candidate for this pulsation in terms of the period. Stability of strange-modes has been so far investigated by nonadiabatic analyses with frozen-in convection (FC) approximation. Indeed, convection theories still have a lot of uncertainties. Moreover, convective energy transport in the envelopes of hot massive stars is not so dominant as that of stars in the redder side of the classical instability strip. However, around the Fe opacity bump, convective luminosity occupies a few dozen percent of luminosity. Therefore, we cannot definitively conclude that convection never affects pulsations. Note that \citet{Glatzel1996} performed nonadiabatic analyses by two types of FC with zero Lagrangian and Eulerian perturbations of convective luminosity, and obtained significantly different results between the two types of FC. In this study, we carry out a nonadiabatic analysis of the strange-modes in hot massive stars with time-dependent convection (TDC). Despite uncertainties of convection theories, nonadiabatic analyses with TDC have been able to roughly explain suppression of pulsational instability in the redder side of the classical instability strip \citep{Baker1979, Gonczi1980, Gonczi1981, Houdek2000, Xiong2001, Dupret2005}. Convection in the redder side of the strip is caused by the H and the He opacity bumps. In hot massive stars, on the other hand, the Fe bump generates a convection zone with a certain contribution of convective luminosity. Pulsations in massive stars are then worthy to analyze with TDC. | We carry out a nonadiabatic analysis of strange-modes with TDC for hot massive stars. Compared with results by FC, the instability is weaker for modes excited at the Fe bump. Convection certainly contributes to energy transfer around the Fe bump, and gives damping effects on pulsations. In spite of this, we confirm that instability of strange-modes certainly remains in hot massive stars even with taking into account TDC. We also carefully examine properties of the strange-mode instability, which acts on strange-modes without adiabatic counterparts. Unlike the case of the $\kappa$-mechanism, the phase lag between density and pressure perturbations varies from 0 to $180^{\circ}$ in an excitation zone. Besides, we confirm by comparing the models with $Z=0$ and $Z=0.02$ that dominance of radiation pressure is important for the strange-mode instability. These results are in agreement with the previous analytic works of \citet{Glatzel1994} and \citet{Saio1998}. Since the growth time-scale of strange-modes is extremely short, nonlinear phenomena are expected to take place. Then, nonlinear analyses are worth doing especially to understand associations with LBV phenomena and effects on evolution of Population III very massive stars toward PISN. \bigskip The authors are grateful to the anonymous referee for useful comments to improve our manuscript. They would like to thank M\'elanie Godart for her helpful advices and comments that led to the improvement of the original manuscript. They also thank Hideyuki Saio for his useful comments about strange-modes, and Takashi Sekii, Masao Takata, Othman Benomar and Kazuhiro Maeda for fruitful discussions. This study is financially supported by Japan Society for the Promotion of Science Grant-in-Aid for Research Fellows. | 14 | 4 | 1404.5264 |
1404 | 1404.1740.txt | Relic neutrinos play an important role in the evolution of the Universe, modifying some of the cosmological observables. We summarize the main aspects of cosmological neutrinos and describe how the precision of present cosmological data can be used to learn about neutrino properties. In particular, we discuss how cosmology provides information on the absolute scale of neutrino masses, complementary to beta decay and neutrinoless double-beta decay experiments. We explain why the combination of Planck temperature data with measurements of the baryon acoustic oscillation angular scale provides a strong bound on the sum of neutrino masses, 0.23~eV at the 95\% confidence level, while the lensing potential spectrum and the cluster mass function measured by Planck are compatible with larger values. We also review the constraints from current data on other neutrino properties. Finally, we describe the very good perspectives from future cosmological measurements, which are expected to be sensitive to neutrino masses close the minimum values guaranteed by flavour oscillations. | \label{20-sec:intro} The role of neutrinos in cosmology is one of the best examples of the very close ties that have developed between nuclear physics, particle physics, astrophysics and cosmology. Here we focus on the most interesting aspects related to the case of massive (and light) relic neutrinos, but many others that were left out can be found in specialised books \cite{20-NuCosmo} and reviews \cite{20-Dolgov:2002wy,20-Hannestad:2006zg,20-Lesgourgues:2006nd,20-Hannestad:2010kz,20-Wong:2011ip,Archidiacono:2013fha}. We begin with a description of the properties and evolution of the background of relic neutrinos that fills the Universe. The largest part of this paper is devoted to the impact of massive neutrinos on cosmological observables, that can be used to extract bounds on neutrino masses from present data, with emphasis on the results of the Planck satellite. Next, we review the implication of current cosmological data on other neutrino properties (relic density, leptonic asymmetry, extra sterile neutrino species). Finally, we discuss the sensitivities of future cosmological experiments to neutrino masses. % %A more general review on the connection between particle physics and cosmology can be found in %\cite{20-Kamionkowski:1999qc}. | Neutrinos, despite the weakness of their interactions and their small masses, can play an important role in cosmology that we have reviewed in this contribution. In addition, cosmological data can be used to constrain neutrino properties, providing information on these elusive particles that complements the efforts of laboratory experiments. In particular, the data on cosmological observables have been used to bound the radiation content of the Universe via the effective number of neutrinos, including a potential extra contribution from other relativistic particles. But probably the most important contribution of cosmology to our knowledge of neutrino properties is the information that provides on the absolute scale of neutrino masses. We have seen that the analysis of cosmological data can lead to either a bound or a measurement of the sum of neutrino masses, an important result complementary to terrestrial experiments such as tritium beta decay and neutrinoless double beta decay experiments. In the next future, thanks to the data from new cosmological experiments we could even hope to test the minimal values of neutrino masses guaranteed by the present evidences for flavour neutrino oscillations. For this and many other reasons, we expect that neutrino cosmology will remain an active research field in the next years. \ack SP was supported by the Spanish grants FPA2011-22975 and Multidark Consolider CSD2009-00064 (MINECO), and by PROMETEO/2009/091 (Generalitat Valenciana). | 14 | 4 | 1404.1740 |
1404 | 1404.5925_arXiv.txt | Determination of the coronal electron density by the inversion of white-light polarized brightness ($pB$) measurements by coronagraphs is a classic problem in solar physics. An inversion technique based on the spherically symmetric geometry (Spherically Symmetric Inversion, SSI) was developed in the 1950s, and has been widely applied to interpret various observations. However, to date there is no study about uncertainty estimation of this method. In this study we present the detailed assessment of this method using a three-dimensional (3D) electron density in the corona from 1.5 to 4 $R_\odot$ as a model, which is reconstructed by tomography method from STEREO/COR1 observations during solar minimum in February 2008 (Carrington rotation, CR 2066). We first show in theory and observation that the spherically symmetric polynomial approximation (SSPA) method and the Van de Hulst inversion technique are equivalent. Then we assess the SSPA method using synthesized $pB$ images from the 3D density model, and find that the SSPA density values are close to the model inputs for the streamer core near the plane of the sky (POS) with differences generally less than a factor of two or so; the former has the lower peak but more spread in both longitudinal and latitudinal directions than the latter. We estimate that the SSPA method may resolve the coronal density structure near the POS with angular resolution in longitude of about 50$^{\circ}$. Our results confirm the suggestion that the SSI method is applicable to the solar minimum streamer (belt) as stated in some previous studies. In addition, we demonstrate that the SSPA method can be used to reconstruct the 3D coronal density, roughly in agreement with that by tomography for a period of low solar activity (CR 2066). We suggest that the SSI method is complementary to the 3D tomographic technique in some cases, given that the development of the latter is still an ongoing research effort. | The electron density is a fundamental parameter in plasma physics. Knowledge of the three-dimensional (3D) electron density structure is very important for our understanding of physical processes in the solar corona, such as the coronal heating and the acceleration of the solar wind ({\it e.g.}, \opencite{mun77}; \opencite{cra99}). The density structure of the corona strongly affects the propagation of CMEs \cite{ods99, ril01, ods02, man04}. The density is also important for estimates of the Alfv\'{e}n Mach number and compression rate of CME-driven shocks \cite{rea99, sok04, man05}, and for the interpretation of solar radio emission such as type II and type IV radio bursts produced by coronal eruptions \cite{car04, cho07, she13, ram13, zuc14}. The K corona arises from Thomson scattering of photospheric white light from free electrons ({\it e.g.}, \opencite{bil66}). Because the emission is optically thin, the measured signal is a contribution from electrons all along the line of sight (LOS). The derivation of the electron density in the K corona from the total brightness ($B$) or polarized radiance ($pB$) is a classical problem of coronal physics, first addressed by \inlinecite{min30} and \inlinecite{van50}. Because of difficulties in generally separating the K-coronal component from the F-coronal component arising from interplanetary dust scattering ({\it e.g.}, \opencite{bil66}; \opencite{hay01}), most of the inversion techniques are practical for $pB$ measurements. The F-coronal polarization is not very well understood (see reviews by \opencite{kou85}; \opencite{kim98}). It is generally accepted that the polarized contribution of the F corona can be ignored within 5 $R_{\odot}$ \cite{man92, kou85, hay01}, but some observations show that the F corona is almost unpolarized even at elongations ranging from 10 to 16 $R_{\odot}$ (\opencite{bla66a}, \citeyear{bla66b}; \opencite{bla67}). In addition, the F corona dominates the total brightness of the corona beyond about 4 or 5 $R_{\odot}$ and make it difficult to recover the much fainter K-corona emission \cite{sai77, kou85, hay01}. To retrieve the electron density of the corona from a single 2D $pB$-image, one needs to assume some special geometries for the distribution of electrons along the LOS. The previous studies have modeled the electron density distribution in several ways, including the simple spherically symmetric model \cite{van50}, the axisymmetric model \cite{sai70, mun77, que02}, or the models that take into account large-scale structures, such as polar plumes in the coronal holes \cite{bar08}, or active streamers in the equatorial regions \cite{guh96}. \begin{figure} \centerline{\includegraphics[width=0.8\textwidth,clip=]{wang_fig1.eps}} \caption{Spherical cross section of the tomographic reconstructed 3D coronal electron density for CR 2066 at a heliocentric distance of 2.0 $R_{\odot}$. Two vertical solid lines marked with AE and AW indicate the positions of the east and west limbs in the COR1-A image observed at 12:00 UT on 8 February 2008, and those dashed lines with BE and BW the positions of east and west limbs in the COR1-B image at the same time. The symbols marked {\it diamonds} and {\it pluses} indicate the locations for the SSPA inversions shown in Figures~\ref{fig:neva} and~\ref{fig:nevb}. } \label{fig:necr} \end{figure} Among the above inversion methods, the spherically symmetric inversion (SSI) developed by \inlinecite{van50} (called the {\it Van de Hulst} inversion thereafter), was the most representative and commonly used. He found that the density integral for $pB$ signals becomes invertible if the latitudinal and azimuthal gradients in electron density are weaker than the radial gradient ({\it i.e.}, a local spherical symmetry approximation). This classic inversion technique has been applied to establish the standard density models of the coronal background at equator and pole in the solar minimum and maximum (see \opencite{all00}) and the density models of near-symmetric coronal structures such as streamers and coronal holes \cite{sai77, gib95, guh95, guh96, gib99}. The SSI method was also used to analyze detailed density distribution of fine coronal structures observed in eclipses ({\it e.g.}, \opencite{kou94}; \opencite{nov96}), and to derive the 2D density distribution of the entire corona \cite{hay01, que02}, when the spherical symmetry is assumed holding locally. The importance of the SSI method for coronal density determination has been demonstrated by wide applications of the derived densities such as in testing models of the acceleration mechanism of the fast solar wind \cite{que07, lal10}, interpreting sources of type II and type IV radio bursts \cite{cho07, she13, ram13, zuc14}, and determining the coronal magnetic field strengths from fast magnetosonic waves by global coronal seismology \cite{kwo13}. However, in contrast to extensive applications, studies on evaluation of the SSI method are few in the literature. \inlinecite{gib99} compared the white light densities to those determined from the density-sensitive EUV line ratios of Si\,{\sc{ix}} 350/342 \AA\ observed by SOHO/CDS, and found that densities determined from these two different analysis techniques match extremely well in the low corona for a very symmetric solar minimum streamer structure. Similarly, \inlinecite{lee08} compared densities of various coronal structures determined by inverting MLSO MK4 $pB$ maps and from the line ratios of O\,{\sc{vi}} 1032/1037.6 \AA\ observed by SOHO/UVCS, and found that the mean densities in a streamer by the two methods are consistent, while the coronal densities for a coronal hole and an active region are within a factor of two. These results are encouraging, and suggest that the 2D white-light density distribution in coronal structures can be very useful for other studies, but a detailed assessment is required for its better application, such as information about the limitation of the SSI method and the uncertainty of derived densities. To achieve this goal, one may use synthetic $pB$ images from 3D densities of the corona reconstructed by tomographic techniques (\opencite{fra02}; \opencite{fra07}, \citeyear{fra10}; \opencite{vas08}; \opencite{kra09}; \opencite{but10}; \opencite{bar13}), or simulated by global 3D MHD models \cite{mik99, lin99, usm00, gro00, hay05, ril06, fen07, hu08, lio09, van14}. \begin{figure} \centerline{\includegraphics[width=1.\textwidth,clip=]{wang_fig2.eps}} \caption{Cross sections of the tomographic 3D coronal density in the plane of the sky (POS), corresponding to positions of COR1-A (a) and COR1-B (b) at 12:00 UT on 8 February 2008. } \label{fig:nemap} \end{figure} The tomographic technique is a sophisticated method which reconstructs optically thin 3D coronal density structures using observations from multiple viewing directions. The use of this method in solar physics was previously proposed by \inlinecite{dav94}, and later this method has been applied to the SOHO/LASCO \cite{fra02} and STEREO/COR1 data \cite{kra09, kra14}. For a solar coronal tomography based on observations made by a single spacecraft or only from the Earth-based coronagraph, data typically need to be gathered over a period of half solar rotation, so, generally, only structures that are stationary over about two weeks can be reliably reconstructed. Therefore, this technique is not applicable to eclipses or, perhaps, periods of high level of solar activity, although the 3D coronal electron density can be routinely computed \cite{but05, kra09}. Similarly, as global MHD models of the corona need measurements of photospheric magnetic field data over a solar rotation, it is also difficult using the MHD method to reconstruct dynamic or rapidly-evolving coronal structures matching to observations. Thus, the SSI analysis could be very useful in some cases when the tomography is not suitable. In addition, the SSI method is also useful in order to investigate the coronal density variability over a long term period (several solar cycles) when modern quality synoptic observations were not available and relate it to the modern state of the art reconstructions. In this study, we choose the 3D coronal density obtained by tomography as a model in order to estimate uncertainties of the SSI method. \inlinecite{vas08} compared the tomographic reconstruction and a 3D MHD model of the corona, and found that at lower heights the MHD models have better agreement with the tomographic densities in the region below 3.5 $R_{\odot}$, but become more problematic at larger heights. They also showed that the tomographic reconstruction has more smaller-scale structures within the streamer belt than the model can reproduce. Moreover, the tomographic reconstruction is entirely based on {\it coronal} observations, while the MHD models are primary based on photospheric boundary conditions. This suggests that the tomographic reconstructions are more realistic and thus may be more suitable to be used as a model in order to evaluate uncertainties of the SSI method. This article is organized as follows. Section~\ref{sctssi} describes two SSI methods and their relationship. Section~\ref{sctrlt} presents the evaluation of the SSI method. We demonstrate the 3D density reconstruction by the SSI method based on real data in Section~\ref{sctd3d}. The discussion and conclusions as well as the potential extension of our work are given in Section~\ref{sctdc}. \begin{figure} \centerline{\includegraphics[width=1.\textwidth,clip=]{wang_fig3.eps}} \caption{Synthetic $pB$ images based on the 3D coronal density model reconstructed by tomography. (a) Viewed from COR1-A, and (b) from COR1-B at 12:00 UT on 8 February 2008. Carrington longitudes of the viewing direction are marked at the bottom of the images. Solid lines mark the positions where the $pB$ intensity profiles shown in Figure~\ref{fig:pblc} are extracted. Short bars with a size of 0.31 $R_{\odot}$ show the scale, over which the $pB$ intensity is averaged across the radial cut. Four circles (dotted lines) at 1.6, 2.0, 2.5 and 3.0 $R_{\odot}$ mark the paths along which the density profiles are shown in Figure~\ref{fig:neap}.} \label{fig:pbmap} \end{figure} \begin{figure} \centerline{\includegraphics[width=0.8\textwidth,clip=]{wang_fig4.eps}} \caption{Radial profiles of $pB$ for COR1-A (solid line) and COR1-B (dashed line), extracted along the radial cuts shown in Figure~\ref{fig:pbmap}. The error bars are the standard deviations for average over five pixels across the cut. } \label{fig:pblc} \end{figure} | \label{sctdc} In this study, we have, for the first time, evaluated the SSI method using the 3D model of the coronal electron densities reconstructed by tomography from the STEREO/COR1 $pB$ data. Our study is instructive for more efficient use of the SSI technique to invert the $pB$ observations from ground- and space-based coronagraphs, in particular, the COR1 data. We demonstrate both theoretically and observationally that the SSPA method and the Van de Hulst inversion are equivalent SSI techniques when the radial densities or $pB$ signals are assumed in the polynomial form of high degrees (more than two). The polynomial degree of five is suitable for COR1 data inversions. Thus, assessment results of the SSPA method can also be applied to the Van de Hulst inversion technique. We determine radial profiles of the streamer density from the COR1-A and -B synthetic $pB$ images as well as their longitudinal and latitudinal dependencies. We find that the SSPA density values are close to the model for the core of streamers near the POS, with differences (or uncertainties if we regard the model input as a true solution) typically within a factor of $\sim$2. This result is consistent with those evaluated using UV spectroscopy \cite{gib99, lee08}. We find that the SSPA density profiles tend to better match the model at lower heights ($\lesssim$ 2.5 $R_\odot$). Our results confirm the suggestion in some previous studies that the SSI assumption is appropriate for the edge-on streamers or the streamer belt during the solar minimum. We suggest that the edge-on condition for streamers may be determined by tomography method or by examining the consistency between simultaneous $pB$ measurements from COR1-A and -B in radial distribution, when the two spacecraft have a small angular separation ({\it e.g.}, less than 45$^{\circ}$). We also find the SSPA streamer densities are more spread in both longitudinal and latitudinal directions than in the model. We demonstrate the application of the SSPA inversion for reconstructions of the 3D coronal density near the solar minimum, and show that the SSPA 3D density for the streamer belt is roughly consistent in both position and magnitude with the tomographic reconstruction. The synoptic density maps derived by the SSPA method show some discontinuities at the longitudes that separate the regions made of the east- and west-limb inversions. These discontinuities may be due to temporal changes of coronal structures and/or the effect of tilt of the solar rotation axis on the poles' visibility that is not considered. They can be smoothed out during post-processing by smoothing and averaging the density distributions from COR1-A and -B, but such treatments will reduce the spatial resolution. In comparison, the tomographic inversion can fully take into account the tilt effect of the solar pole and produce the density distributions smoother in these discontinuity regions \cite{fra02, kra09}. We estimate that the SSPA method may resolve the coronal density structure near the POS with an angular resolution of $\sim$50$^{\circ}$ in longitudinal direction. Given this limitation, the SSPA reconstruction using $pB$ data with higher cadence ({\it e.g.}, more than three images per day) would not help improve its actual angular resolution. Although the current state of the tomographic method has allowed to routinely obtain the 3D coronal densities, we speculate that the SSI method could be complementary to the tomography when used for the interpretation of observations in such cases as during maximum of solar activity, in some regions where tomography gives zero density values, or in the regions near the edges of FOV. The zero density values in the tomographic reconstruction (so called ``zero-density artifacts", ZDAs) could be caused either (or both) due to coronal dynamics \cite{fra02, fra07, vas08, but10}, or due to real very small density in these coronal regions which are below the error limit in the tomography method \cite{kra09}. The latter reason is also supported by results of MHD modeling \cite{air11}. In the former case, the SSI method could be complementary to tomography, while in the latter case the SSPA method gives much larger values than in the tomographic model. The FOV artifacts in the tomography are due to the finite coronagraph FOV that causes the reconstructed density to increase at the regions close to the outer reconstruction domain \cite{fra10, kra09}. However, this FOV artifacts can be reduced by extending the outer reconstruction domain beyond the coronagraph FOV limit \cite{fra10, kra13}. Another way to obtain more correct density values in this region could be by using the SSPA method which does not imply strict outer boundaries for LOS integration. Thus the estimate of uncertainties of the SSPA method should be limited to the regions with distances less than about 3.5 $R_{\odot}$ for the tomographic model used. Also, the use of MHD model in order to produce artificial data can be useful for this test. However this will be a subject of future research. The tomography generally assumes that the structure of the corona is stable over the observational interval, {\it e.g.}, two weeks of observations made by a single spacecraft, although for some coronal regions that are exposed to the spacecraft for only about a week during the observation the stationary assumption can be reduced to about a week \cite{kra11}. However, such an assumption is hard to meet during solar maximum or times of enhanced coronal activity. The CME catalog in the NASA CDAW data center shows that the CME occurrence rate increases from $\sim$0.5 per day near solar minimum to $\sim$6 near solar maximum during Solar Cycle 23 \cite{gop03, yas04}. Although our assessment results for the SSPA method are based on a static coronal model, their validity may not be limited to the static assumption. Because the key factor for the SSPA inversion for obtaining a good estimate of the 2D coronal density is an instantaneous (local) symmetric condition for coronal densities along the LOS. The minimal size of this local symmetry is limited by the angular resolution in longitude which is about $50^\circ$. Therefore, the SSI method can be used to estimate the density of a dynamic coronal structure in terms of weighted average over the region with this angular size in longitude. For this reason it may be a better choice to use a combination of the tomography and the SSI inversions for interpretations of radio bursts and shocks produced by CMEs in the case when coronal structures of interest evolve quickly with time \cite{lee08, she13, ram13}. In addition, the SSI method is also often applied to the cases when observational data are not suitable for tomography, {\it e.g.}, solar eclipses. The 3D MHD models of the corona using the synoptic photospheric magnetic field data have been successfully used to interpret solar observations, including total eclipses and ground-based ({\it e.g.} MLSO/MK4) images of the corona ({\it e.g.}, \opencite{lin99}; \opencite{mik99}). We suggest that the evaluation of the SSI method based on such a global MHD model may be necessary in the future. The profits using such MHD models to estimate the uncertainties of the SSI method could be in avoidance of the ZDA and FOV effects. The modeled corona also allows evaluations of the SSI method down to very low heights ({\it e.g.}, the region between 1.1 and 1.5 $R_{\odot}$) where the corona is much more structured. Moreover, a simulated time dependent corona from a time-evolving MHD model would allow us to estimate the uncertainties in tomography and the SSI inversion when they are applied to the dynamic corona, especially during the solar maximum. This needs detailed investigations in the future. \appendix {\bf Estimates of Angular Resolution of the SSPA Method in Longitude}\\ To determine the angular resolution of the SSPA method in the longitudinal direction, a numerical experiment is performed using 2D coronal models. We construct a 2D density model by first using the \inlinecite{sai77} equatorial background density model to build a background corona of rotational symmetry in the equatorial plane, and then inserting two structures into it. The structures have the angular width of $\phi$, the density contrast ratio of $d$ to the background, and the longitudinal profile following a step function or Gaussian function. For the Gaussian-type structure, its FWHM is set as $\phi$. Figures~\ref{fig:reso}(a) and (b) show the two types of 2D coronal models with about the same FOV as COR1, where two structures are separated by an angle of 2$\phi$, thus the width of the gap between them is also equal to $\phi$ in the step-profile case. We assume that the two structures (marked A and B) are located at the longitudes of $\phi$ and $-\phi$, respectively, i.e. defining their middle position as the origin of longitude. So for the cases shown in Figures~\ref{fig:reso}(a) and (b), the origin of longitude is just located in the POS at the west limb. \begin{figure} \centerline{\includegraphics[width=1.0\textwidth,clip=]{wang_fig16.eps}} \caption{2D density models of the corona from 1.5 to 4.0 $R_{\odot}$ in the equatorial plane with two structures (marked A and B) of (a) the step profile and (b) the Gaussian profile in longitude. The horizontal dotted line represents the POS. (c)-(e): Comparisons of the SSPA density (in dashed line) with the model density (in solid line) in the POS at 2 $R_{\odot}$ as a function of longitudes for the two structures with angular separation of 40$^{\circ}$ (c), 50$^{\circ}$ (d), and 60$^{\circ}$ (e). The black curves represent the case for the model density with the step profile, and the red curves the case for the model density with the Gaussian profile. (f): The comparison between the SSPA and model densities at different heights. The black, red, and green dashed lines represent the SSPA density profiles at 2, 3 and 4 $R_{\odot}$, respectively. Note that the model density profiles (in solid line), normalized to the coronal background, are same for the three heights. (g): The case for the structures with different widths of 15$^{\circ}$ (red curves), 25$^{\circ}$ (black curves), and 35$^{\circ}$ (green curves). The solid lines represent the model density in the POS, and the dashed lines the SSPA density. (h): The case for the structures with different density contrast ratios to the background of 5 (red curves), 10 (black curves), and 20 (green curves). The solid lines represent the model density in the POS, and the dashed lines the SSPA density. In (f)-(h), except for one parameter that is set as different values, the other parameters are set to be 50$^{\circ}$ for angular separation, 2 $R_{\odot}$ for heliocentric height, 25 $^{\circ}$ for structure width, and 10 for density contrast ratio. The vertical dotted lines in (c)-(h) mark the central position in the structure.} \label{fig:reso} \end{figure} We synthesize $pB$ data for the west-limb region from 1.5 to 4 $R_{\odot}$ at longitudes in the range from $-90^{\circ}$ to 90$^{\circ}$ using Equation~(\ref{eqpb}), and then derive the electron density using the SSPA method by fitting the synthetic $pB$ data. The panels (c)-(e) show comparisons of the SSPA density with the model density in the POS at 2 $R_{\odot}$ as a function of longitudes for different angular distances between two artificial structures with the density contrast ratio $d$=10. We find that for both types of the structure (in the step or Gaussian profile), the minimum resolvable distance (or angular resolution) is about 50$^{\circ}$. To examine the effects of radial distance, structure width, and density contrast on the obtained resolution, we make a parametric study, and show the results in panels (f)-(h). We find that the resolution is only slightly dependent on the radial distance and structure width, which is better for the lower heights and narrower widths, but almost independent on the density contrast. In addition, we also find that the obtained SSPA peak density is about a half of the model density for the analyzed structures in most of the cases, which is consistent with our results for edge-on streamers. These numerical experiments suggest that for coronal structures with more smoothing profile and larger extension in the longitudinal direction and with lower density contrast to the background, which can be regarded as better conditions meeting the spherically symmetric assumption, the SSPA solutions are more accurate. \begin{acks} The work of TW was supported by the NASA Cooperative Agreement NNG11PL10A to the Catholic University of America and NASA grant NNX12AB34G. We very much appreciate to Dr. Maxim Kramar for his suggestions that led to an improved estimation of angular resolution of the SSPA method in Appendix. We also thank the anonymous referee for his/her valuable comments in improving the manuscript. \end{acks} | 14 | 4 | 1404.5925 |
1404 | 1404.2734_arXiv.txt | The focal-plane camera of $\gamma$-ray telescopes frequently uses light concentrators in front of light sensors. The purpose of these concentrators is to increase the effective area of the camera as well as to reduce the stray light coming at large incident angles. These light concentrators are usually based on the Winston cone design. In this contribution we present the design of an hexagonal hollow light concentrator with a lateral profile optimized using a cubic B\'ezier function to achieve a higher collection efficiency in the angular region of interest. The design presented here is optimized for a Davies-Cotton telescope with primary mirror of about 4 meters of diameter and focal length of 5.6 m. The described concentrators are part of an innovative camera made up of silicon-photomultipliers sensors, although a similar approach can be used for other sizes of single-mirror telescopes with different camera sensors, including photomultipliers. The challenge of our approach is to achieve a cost-effective design suitable for standard industrial productions of both the plastic concentrator substrate and the reflective coating. At the same time we maximize the optical performance. In this paper we also describe the optical set-up to measure the absolute collection efficiency of the light guides and demonstrate our good understanding of the measured data using a professional light tracing simulation. | The Cherenkov Telescope Array project (CTA)~\cite{CTA} will be the next generation observatory in $\gamma$-ray astronomy. It will consist of two arrays of imaging atmospheric Cherenkov telescopes (IACTs) of different sizes to be installed in the two hemispheres. The southern array will be composed of few Large Size Telescopes (LSTs) of $\sim 24$~m diameter, about 25 Middle Size Telescopes (MSTs) of about 12~m diameter and about 70 Small Size Telescopes (SSTs) of $\sim 4$ m diameter. An arrangement over an area of the order of few km$^2$ will make it possible to cover about 2 decades in energy, from about 20 GeV to 300 TeV, with an improved sensitivity by about a factor of 15 compared to existing experiments which also operate in a smaller energy range. Reflective light concentrators are a common element used in IACTs in order to increase the collection area of camera pixels~\cite{HESS, MAGIC, VERITAS, FACT}. The cross-section of these concentrators is usually hexagon-shaped so that they can be arranged in an array with equal distance between all pixel centers. If their mutual distance is kept constant along the camera, the response of the pixels for different orientations of the shower images is geometrically unbiased. These light concentrators are designed to maximize the collection efficiency of incoming rays within the angular range subtended by the primary mirror and the camera while at the same time limiting the amount of light from the night sky background (NSB) at larger angles. The NSB arises from airglow, stars, nearby cities, etc. and usually reaches the camera sensors directly without reflecting first on the telescope's primary mirror. These trajectories can be rejected geometrically by optimizing the shape of the light concentrator. The spectrum of the NSB is also different from the Cherenkov spectrum, the latter peaks at $\sim$~330 nm and begins to be dominated at wavelengths larger than 600 nm by the NSB that extends in the infrared. Therefore the wavelength dependency of the reflectivity material of the light concentrator can be optimized to further reduce this background. The Small Size Telescopes of CTA are characterized by a wide field-of-view (FoV) of about $9^{\circ}$ which is essential for the physics goals of these telescopes, such as the Galactic Plane survey, study of spectra to discriminate hadronic against electromagnetic emissions, and the search for the Galactic PeVatrons which produce the Galactic cosmic rays up to the {\it knee} at a few PeV~\cite{cta_science}. In the following we will explore the design of a light concentrator suitable for a single mirror IACT and so we present it as a feasible solution for the SSTs. Particularly we consider the Davies-Cotton design which provides a good imaging over a wide FoV. The dispersion in the arrival time of photons introduced by this design for small dish telescopes is negligible compared to the intrinsic dispersion of photons and therefore it is a suitable solution for the SSTs. We pay particular attention to the cost-effectiveness of our proposal and to the industrial producibility of the light concentrators given the large number (around 70) of the SSTs planned for CTA. Assuming the number of pixels for each camera to be around 1'300, the total number of light concentrators to be produced for the SSTs in CTA will be of the order of 91'000. Therefore it is clear that the design has not only to address the optical performance but has also the industrial producibility. The outline of the paper is the following: in Section~\ref{sec:design} we review the Davies-Cotton telescope design and evaluate the parameters needed for a wide FoV telescope with a $\sim$4~m diameter dish. We review the requirements of light concentrators for this kind of design. In Section~\ref{sec:simulations} we show how, using a professional ray-tracing simulation, we can optimize the geometrical shape of the light concentrator using cubic B\'ezier curves. We compare this design with the Compound Parabolic Concentrator (CPC), also called Winston's Cone~\cite{winston}. Even if solid concentrators can achieve larger compression factors than hollow ones~\cite{FACT, FACT2, Bretz}, the former start to suffer from limited transmissivity due to the thickness of $\sim$37~mm necessary in this design for the SST. In addition, hollow cones allow us to use a reflective coating optimized for high reflectivity in the wavelength region of interest. We consider a few coating options and their impact on the collection efficiency. Section~\ref{sec:measurements} shows the optical measurements performed with the first prototypes and their comparison with simulations. Conclusions are given in Sec.~\ref{sec:conclusions}. | \label{sec:conclusions} In this paper we showed the procedure used to design, optimize and manufacture a cost-effective light concentrator for Cherenkov astronomy. The selection of coating was driven by simulations and the final measured collection efficiency achieved a remarkable good agreement with the predictions from simulations. Furthermore, we showed that efficiencies of about 93\% at normal incident angles are possible with this approach. This work was focused on a light guide design suitable for the CTA single mirror small size telescopes with a camera consisting on SiPM as the active sensors. Nevertheless a similar optimized design can be adapted for larger size telescopes within the CTA project independently of the sensors (SiPM or the traditional photomultipliers) as well as for other projects working in the UV-light seeking to have an increased effective area of the camera such as fluorescence detectors used in cosmic-ray experiments. | 14 | 4 | 1404.2734 |
1404 | 1404.5336_arXiv.txt | We use 2D MHD simulations to examine the effects of radiative cooling and inverse Compton (IC) cooling on X-ray emission from magnetically confined wind shocks (MCWS) in magnetic massive stars with radiatively driven stellar winds. For the standard dependence of mass loss rate on luminosity $\Mdot \sim L^{1.7} $, the scaling of IC cooling with $L$ and radiative cooling with $\Mdot$ means that IC cooling become formally more important for lower luminosity stars. However, because the sense of the trends is similar, we find the overall effect of including IC cooling is quite modest. More significantly, for stars with high enough mass loss to keep the shocks radiative, the MHD simulations indicate a linear scaling of X-ray luminosity with mass loss rate; but for lower luminosity stars with weak winds, X-ray emission is reduced and softened by a {\em shock retreat} resulting from the larger post-shock cooling length, which within the fixed length of a closed magnetic loop forces the shock back to lower pre-shock wind speeds. A semi-analytic scaling analysis that accounts both for the wind magnetic confinement and this shock retreat yields X-ray luminosities that have a similar scaling trend, but a factor few higher values, compared to time-averages computed from the MHD simulations. The simulation and scaling results here thus provide a good basis for interpreting available X-ray observations from the growing list of massive stars with confirmed large-scale magnetic fields. | Hot luminous, massive stars of spectral type O and B are prominent sources of X-rays thought to originate from shocks in their high-speed, radiatively driven stellar winds. In putatively single, non-magnetic O stars, the intrinsic instability of wind driving by line-scattering leads to embedded wind shocks that are thought to be the source of their relatively soft X-rays ($\sim$0.5\,keV) X-ray spectrum, with a total X-ray luminosity that scales with stellar bolometric luminosity, $L_{\rm x} \sim L_{\rm bol}$ \citep{Chlebowski89, Naze11, Owocki13}. In massive binary systems the collision of the two stellar winds at up to the wind terminal speeds can lead to even higher $L_x$, generally with a significantly harder (up to 10\,keV) spectrum \citep{Stevens92, Gagne11}. The study here examines a third source of X-rays from OB winds, namely those observed from the subset ($\sim$10\%) of massive stars with strong, globally ordered (often significantly dipolar) magnetic fields \citep{Petit13}; in this case, the trapping and channeling of the stellar wind in closed magnetic loops leads to {\em magnetically confined wind shocks} (MCWS) \citep[hereafter BM97a,b]{Babel97,Babel97b}, with pre-shock flow speeds that are some fraction of the wind terminal speed, resulting in intermediate energies for the shocks and associated X-rays ($\sim$2\,keV). A prototypical example is provided by the magnetic O-type star $\theta^1$~Ori~C, which shows moderately hard X-ray emission with a rotational phase variation that matches well the expectations of the MCWS paradigm \citep{Gagne05}. Our approach here builds on our previous MHD simulation studies of the role of magnetic fields in wind channeling \citep[Paper I]{Uddoula02}, including its combined effect with stellar rotation in formation of centrifugally supported magnetospheres \citep[Paper II] {Uddoula08} and in enhancing the angular momentum loss from the stellar wind \citep[Paper III]{Uddoula09}. In contrast to the assumption of isothermal flow used in these studies, our examination here of X-ray emission now requires a full treatment of the wind energy balance, including the cooling of shock-heated gas. This follows our successful specific application of MHD simulations of MCWS with a full energy balance for modeling X-ray observations of $\theta^1$~Ori~C \citep{Gagne05}. But rather than focus on any specific star, the aim here is to derive broad scaling relations for how the X-ray luminosity and spectral properties depend on the stellar luminosity $L$ and mass loss rate $\Mdot$, with particular attention to how these affect the efficiency of shock cooling. The initial study here will neglect rotation, and so focus on stars with ``dynamical magnetospheres'' (DM), deferring to future work studies of the effect of rapid rotation on X-rays from ``centrifugal magnetospheres'' (CM) \citep{Sundqvist12c, Petit13}. For high-density winds with efficient shock cooling, the maximum shock strength depends on the speed reached before the flow from opposite footpoints of a closed loop collide near the loop top, and thus on the maximum loop height. The analyses in papers I-III show that this is generally somewhat below [see eqn.\ (\ref{eq:rcetas})] the characteristic wind Alfv\'{e}n radius $R_A$, which for a dipole field scales as a factor $\sim \eta_\ast^{1/4}$ times the stellar radius $\Rstar$, where \beq \eta_\ast \equiv \frac{B_{eq}^2 \Rstar^2}{\Mdot \vinf} \label{eq:etasdef} \eeq is the ``wind magnetic confinement parameter'' for an equatorial surface field $B_{eq}$, with $\Mdot$ and $\vinf$ the wind mass loss rate and terminal speed that would occur in {\em non-magnetic} star with the same stellar parameters. For magnetic O-stars with $\eta_\ast \approx 10-100$, the associated Alfv\'{e}n radii $R_A \approx 1.7 - 3 \Rstar$ allow acceleration up to half terminal speed, typically about 1500~km/s. This leads to shock energies $\sim$2\,keV that are sufficient to explain the moderately hard X-rays observed in $\theta^1$~Ori~C \citep{Gagne05}. For magnetic B-type stars, the combination of lower mass loss rates ($\Mdot < 10^{-9} \Msun$/yr) and very strong (1-10\,kG) fields leads to very strong magnetic confinement, with $\eta_\ast \sim 10^4 - 10^6$ and so much larger Alfv\'{e}n radii, $R_A \approx 10-30 \Rstar$. This would suggest a potential to accelerate the flow to near the wind terminal speed $\sim$\, 3000 km\,s$^{-1}$ within closed magnetic loops, and so yield much stronger shocks (up to 10\,keV) and thus much harder X-rays. \begin{figure} \begin{center} \vfill \includegraphics[scale=0.65]{shock-retreat.pdf} \caption {Schematic illustration of the ``shock retreat'' from inefficient cooling associated with a lower mass loss rate ${\dot M}$, showing a hemispheric, planar slice of a stellar dipole magnetic field. Wind outflow driven from opposite foot-points of closed magnetic loops is channeled into a collision near the loop top, forming magnetically confined wind shocks (MCWS). For the high ${\dot M}$ case in the upper panel, the efficient cooling keeps the shock-heated gas within a narrow cooling layer, allowing the pre-shock wind to accelerate to a high speed and so produce strong shocks with strong, relatively hard X-ray emission. For the low ${\dot M}$ case in the lower panel, the inefficient cooling forces a shock retreat down to lower radii with slower pre-shock wind, leading to weaker shocks with weaker, softer X-ray emission. } \label{fig:shockretreat} \end{center} \end{figure} However, as illustrated schematically in figure \ref{fig:shockretreat} (see also figure 13 of BM97a) and quantified further below, the much lower mass loss rates of such B-stars also implies much less efficient cooling of the post-shock flow. When the associated cooling length becomes comparable to the Alfv\'{e}n radius, the shock location is effectively forced to ``retreat'' back down the loop, to a lower radius where the lower wind speed yields a weaker shock, implying then a much softer X-ray spectrum. To quantify this {\em shock retreat} effect, and derive general scalings for how the X-ray luminosity and hardness depend on the stellar luminosity and associated wind mass loss rate, the analysis here carries out an extensive parameter study based on 2D MHD simulations with a detailed energy balance. To focus on the relative roles of magnetic confinement and shock cooling, we ignore here the effects of stellar rotation, since this would introduce a third free parameter to our variations of magnetic confinement and cooling efficiency. As a prelude to the detailed MHD simulation study in \S\S\,3-4, the next section (\S 2) develops the basic equations, and presents an analysis of the relative importance of both radiative and inverse Compton (IC) cooling in stars of various luminosities and mass loss rates. In \S 3, the full 2D MHD simulation results (for a standard model appropriate to O-type supergiant star with large mass loss rate and so strong radiative cooling) are used to derive differential emission measure (DEM) and associated dynamic X-ray spectra. \S\,4 then presents a general parameter study for how the X-ray emission in this standard model scales with a modified cooling efficiency, intended as a proxy for varying the wind mass loss rate. Comparisons with a semi-analytic scaling analysis (\S 4.4) indicate that X-ray luminosity depends on both the magnetic confinement parameters $\eta_\ast$ and a radiative cooling parameter $\chi_\infty$ [see eqn.\ (\ref{eq:chiinf})], providing then a generalized scaling law [eqn.\ (\ref{eq:lxlkin})] for interpreting X-ray observations for magnetic massive stars with a range of stellar parameters. The concluding section (\S 5) summarizes results and their implications for interpreting X-ray observations, and outlines directions of future work. | This paper uses MHD simulations to examine the effects of radiative and inverse-Compton (IC) cooling on X-ray emission from magnetically confined wind shocks (MCWS) in the dynamical magnetospheres (DM) that arise in slowly rotating magnetic massive stars with radiatively driven (CAK) stellar winds. The key results can be summarized as follows: \begin{itemize} \item The scaling of IC cooling with luminosity and radiative cooling with mass loss rate suggests that for CAK winds with $\Mdot \sim L^{1.7}$, IC cooling should become relatively more important for lower luminosity stars. However, because the sense of the trends is similar, including IC cooling has a quite modest overall effect on the broad scaling of X-ray emission. \item For the two fixed values of magnetic confinement ($\eta_\ast$=10, 100) used in MHD simulations here, the reduced efficiency of radiative cooling from a lower mass loss rate causes a shock retreat to lower speed wind, leading to weaker shocks. This lowers and softens the X-ray emission, making the $\Mdot$ dependence of $L_x$ steeper than the linear scaling seen at higher $\Mdot$ without shock retreat. \item These overall scalings of time-averaged X-rays in the numerical MHD simulations are well matched by the $L_x$ computed from a semi-analytic ``XADM'' model that accounts for both shock retreat and magnetic confinement within the context of steady feeding of the DM by a CAK wind with field-adjusted mass flux. However, the values of $L_x$ are about a factor 5 lower in the MHD models, mostly likely reflecting an overall inefficiency of X-ray emission from the repeated episodes of dynamical infall. \item Comparison with the previous power-law scaling ($L_x \sim \Mdot \vinf B^{0.4}$) suggested by BM97a shows a general agreement with XADM at intermediate $\Mdot$. But the XADM $L_x$ drops well below the power-law scaling at both low $\Mdot$ (due to shock retreat) and high $\Mdot$ (due to weakened magnetic confinement). \item The XADM reproduction of trends in MHD X-rays encourages application of this XADM scaling, with a factor 0.2 efficiency reduction, toward interpreting X-ray observations of slowly rotating magnetic massive stars with a broader range of field strength and wind parameters than considered in the MHD simulations here. \end{itemize} Within this theoretical framework, one focus of our future work will be to apply these results toward interpreting X-ray observations for the subset of confirmed magnetic massive stars \citep{Petit13} with available X-ray data from {\em Chandra} or {\em XMM-Newton}, with initial emphasis on slowly rotating O and B stars. (See \citet{Naze14}.) To facilitate analysis of the moderately fast rotating B-stars with centrifugal magnetospheres (CM), we also plan an extension of the present simulation study to examine the potential effects of rotation on the X-ray emission. | 14 | 4 | 1404.5336 |
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