We apply two new state-of-the-art methods that model the distribution of observed tracers in projected phase space to lift the mass / velocity anisotropy (VA) degeneracy and deduce constraints on the mass profiles of galaxies, as well as their VA. We
first show how a distribution function based method applied to the satellite kinematics of otherwise isolated SDSS galaxies shows convincing observational evidence of age matching: red galaxies have more concentrated dark matter (DM) halos than blue galaxies of the same stellar or halo mass. Then, applying the MAMPOSSt technique to M87 (traced by its red and blue globular clusters) we find that very cuspy DM is favored, unless we release priors on DM concentration or stellar mass (leading to unconstrained slope). For the Fornax dwarf spheroidal (traced by its metal-rich and metal-poor stars), the inner DM slope is unconstrained, with weak evidence for a core if the stellar mass is fixed. This highlights how priors are crucial for DM modeling. Finally, we find that blue GCs around M87 and metal-rich stars in Fornax have tangential outer VA.
Mass modelling of spherical systems through internal motions is hampered by the mass/velocity anisotropy (VA) degeneracy inherent in the Jeans equation, as well as the lack of techniques that are both fast and adaptable to realistic systems. A new fa
st method, called MAMPOSSt, which performs a maximum likelihood fit of the distribution of observed tracers in projected phase space, is developed and thoroughly tested. MAMPOSSt assumes a shape for the gravitational potential, but instead of postulating a shape for the distribution function in terms of energy and angular momentum, or supposing Gaussian line-of-sight velocity distributions, MAMPOSSt assumes a VA profile and a shape for the 3D velocity distribution, here Gaussian. MAMPOSSt requires no binning, differentiation, nor extrapolation of the observables. Tests on cluster-mass haloes from LambdaCDM cosmological simulations show that, with 500 tracers, MAMPOSSt is able to jointly recover the virial radius, tracer scale radius, dark matter scale radius and outer or constant VA with small bias (<10% on scale radii and <2% on the two other quantities) and inefficiencies of 10%, 27%, 48% and 20%, respectively. MAMPOSSt does not perform better when some parameters are frozen, and even worse when the virial radius is set to its true value, which appears to be the consequence of halo triaxiality. The accuracy of MAMPOSSt depends weakly on the adopted interloper removal scheme, including an efficient iterative Bayesian scheme that we introduce here, which can directly obtain the virial radius with as good precision as MAMPOSSt. Our tests show that MAMPOSSt with Gaussian 3D velocities is very competitive with, and up to 1000x faster than other methods. Hence, MAMPOSSt is a very powerful and rapid tool for the mass and anisotropy modeling of systems such as clusters and groups of galaxies, elliptical and dwarf spheroidal galaxies.
Understanding galaxy formation is one of the most pressing issues in cosmology. We review the current status of galaxy formation from both an observational and a theoretical perspective, and summarise the prospects for future advances.
A simple, 1-equation, galaxy formation model is applied to both the halo merger tree derived from a high-resolution dissipationless cosmological simulation and to 1/4 million Monte-Carlo halo merger trees. The galaxy formation model involves a sharp
entropy barrier against the accretion of gas onto low-mass halos, the shock heating of infalling gas far from the central regions of massive halos, and supernova feedback that drives the gas out of shallow halo potential wells. With the first approach, we show that the large majority of galaxies within group- and cluster-mass halos, known to be mainly dwarf ellipticals, have acquired the bulk of their stellar mass through gas accretion and not via galaxy mergers. With the second approach, we qualitatively reproduce the downsizing trend of greater ages at greater masses in stars and predict an upsizing trend of greater ages as one proceeds to masses lower than 10^10 M_Sun. We find that the fraction of galaxies with very young stellar populations (more than half the stellar mass formed within the last 1.5 Gyr) is a function of present-day stellar mass, which peaks at 0.5% at m_crit=10^7.5-9.5 M_Sun, roughly corresponding to the masses of blue compact dwarfs. We predict that the stellar mass function of galaxies should not show a maximum at m_stars > 10^{5.5}, M_Sun, with a power-law stellar mass function with slope approx -1.6 if the IGM temperature in the outskirts of halos before reionization is set by H2 cooling. We speculate on the nature of the lowest mass galaxies.
We apply a simple, one-equation, galaxy formation model on top of the halos and subhalos of a high-resolution dark matter cosmological simulation to study how dwarf galaxies acquire their mass and, for better mass resolution, on over 10^5 halo merger
trees, to predict when they form their stars. With the first approach, we show that the large majority of galaxies within group- and cluster-mass halos have acquired the bulk of their stellar mass through gas accretion and not via galaxy mergers. We deduce that most dwarf ellipticals are not built up by galaxy mergers. With the second approach, we constrain the star formation histories of dwarfs by requiring that star formation must occur within halos of a minimum circular velocity set by the evolution of the temperature of the IGM, starting before the epoch of reionization. We qualitatively reproduce the downsizing trend of greater ages at greater masses and predict an upsizing trend of greater ages as one proceeds to masses lower than m_crit. We find that the fraction of galaxies with very young stellar populations (more than half the mass formed within the last 1.5 Gyr) is a function of present-day mass in stars and cold gas, which peaks at 0.5% at m_crit=10^6-8 M_Sun, corresponding to blue compact dwarfs such as I Zw 18. We predict that the baryonic mass function of galaxies should not show a maximum at masses above 10^5.5, M_Sun, and we speculate on the nature of the lowest mass galaxies.
When clusters of galaxies are viewed in projection, one cannot avoid picking up foreground/background interlopers (FBIs), that lie within the virial cone (VC), but outside the virial sphere. Structural & kinematic deprojection equations are not known
for an expanding Universe, where the Hubble flow (HF) stretches the line-of-sight (LOS) distribution of velocities. We analyze 93 mock relaxed clusters, built from a cosmological simulation. The stacked mock cluster is well fit by an m=5 Einasto DM density profile (but only out to 1.5 virial radii [r_v]), with velocity anisotropy (VA) close to the Mamon-Lokas model with VA radius equal to that of density slope -2. The surface density of FBIs is nearly flat out to r_v, while their LOS velocity distribution shows a dominant gaussian cluster-outskirts component and a flat field component. This distribution of FBIs in projected phase space is nearly universal in mass. A local k=2.7 sigma velocity cut returns the LOS velocity dispersion profile (LOSVDP) expected from the NFW density and VA profiles measured in 3D. The HF causes a shallower outer LOSVDP that cannot be well matched by the Einasto model for any k. After this velocity cut, FBIs still account for 23% of DM particles within the VC (close to the observed fraction of cluster galaxies lying off the Red Sequence). The best-fit projected NFW/Einasto models underestimate the 3D concentration by 6+/-6% (16+/-7%) after (before) the velocity cut, unless a constant background is included in the fit. Assuming the correct mass profile, the VA profile is well recovered from the measured LOSVDP, with a slight bias towards more radial orbits in the outer regions. These small biases are overshadowed by large cluster-cluster variations caused by cosmic variance. An appendix provides an analytical approximation to the surface density, projected mass and tangential shear profiles of the Einasto model.
The nature of compact groups (CGs) of galaxies, apparently so dense that the galaxies often overlap, is still a subject of debate: Are CGs roughly as dense in 3D as they appear in projection? Or are they caused by chance alignments of galaxies along
the line-of-sight, within larger virialized groups or even longer filamentary structures? The nature of CGs is re-appraised using the z=0 outputs of three galaxy formation models, applied to the dissipationless Millennium Simulation. The same selection criteria are applied to mock galaxy catalogs from these models as have been applied by Hickson and co-workers in redshift space. We find 20 times as many mock CGs as the `HCGs found by Hickson within a distance corresponding to 9000 km/s. This very low (5%) HCG completeness is caused by Hickson missing groups that were either faint, near the surface brightness threshold, of small angular size, or with a dominant brightest galaxy. We find that most velocity-filtered CGs are physically dense, regardless of the precise threshold used in 3D group size and line-of-sight elongation, and of the galaxy formation model used. This result also holds for mock CGs with the same selection biases as was found for the HCGs.
Traditionally, the mass / velocity anisotropy degeneracy (MAD) inherent in the spherical, stationary, non-streaming Jeans equation has been handled by assuming a mass profile and fitting models to the observed kinematical data. Here, the opposite app
roach is considered: the equation of anisotropic kinematic projection is inverted for known arbitrary anisotropy to yield the space radial velocity dispersion profile in terms of an integral involving the radial profiles of anisotropy and isotropic dynamical pressure. Then, through the Jeans equation, the mass profile is derived in terms of double integrals of observable quantities. Single integral formulas for both deprojection and mass inversion are provided for several simple anisotropy models (isotropic, radial, circular, general constant, Osipkov-Merritt, Mamon-Lokas and Diemand-Moore-Stadel). Tests of the mass inversion on NFW models with these anisotropy models yield accurate results in the case of perfect observational data, and typically better than 70% (in 4 cases out of 5) accurate mass profiles for the sampling errors expected from current observational data on clusters of galaxies. For the NFW model with mildly increasing radial anisotropy, the mass is found to be insensitive to the adopted anisotropy profile at 7 scale radii and to the adopted anisotropy radius at 3 scale radii. This anisotropic mass inversion method is a useful complementary tool to analyze the mass and anisotropy profiles of spherical systems. It provides the practical means to lift the MAD in quasi-spherical systems such as globular clusters, round dwarf spheroidal and elliptical galaxies, as well as groups and clusters of galaxies, when the anisotropy of the tracer is expected to be linearly related to the slope of its density.
We investigate the LF in the very relaxed cluster Abell 496. Our analysis is based on deep images obtained at CFHT with MegaPrime/MegaCam in four bands (ugri) covering a 1x1 deg2 region, which is centered on the cluster Abell 496 and extends to near
its virial radius. The LFs are estimated by statistically subtracting a reference field taken as the mean of the 4 Deep fields of the CFHTLS survey. Background contamination is minimized by cutting out galaxies redder than the observed Red Sequence in the g-i versus i colour-magnitude diagram. In Abell 496, the global LFs show a faint-end slope alpha=-1.55+/-0.06 and vary little with observing band. Without colour cuts, the LFs are much noisier but not significantly steeper. The faint-end slopes show a statistically significant steepening from alpha=-1.4+/-0.1 in the central region (extending to half a virial radius) to -1.8+/-0.1 in the Southern envelope of the cluster. Cosmic variance and uncertain star-galaxy separation are our main limiting factors in measuring the faint-end of the LFs. The large-scale environment of Abell 496, probed with the fairly complete 6dFGS catalogue, shows a statistically significant 36 Mpc long filament at PA=137 deg, but we do not find an enhanced LF along this axis. Our LFs do not display the large number of dwarf galaxies (alpha ~ -2) inferred by several authors, whose analyses may suffer from field contamination caused by inexistent or inadequate colour cuts. Alternatively, different clusters may have different faint-end slopes, but this is hard to reconcile with the wide range of slopes found for given clusters and for wide sets of clusters.
