We study velocity moments of elliptical galaxies in the Coma cluster using Jeans equations. The dark matter distribution in the cluster is modelled by a generalized formula based upon the results of cosmological N‐body simulations. Its inner slope (cuspy or flat), concentration and mass within the virial radius are kept as free parameters, as well as the velocity anisotropy, assumed independent of position. We show that the study of line‐of‐sight velocity dispersion alone does not allow us to constrain the parameters. By a joint analysis of the observed profiles of velocity dispersion and kurtosis, we are able to break the degeneracy between the mass distribution and velocity anisotropy. We determine the dark matter distribution at radial distances larger than 3 per cent of the virial radius and we find that the galaxy orbits are close to isotropic. Due to limited resolution, different inner slopes are found to be consistent with the data and we observe a strong degeneracy between the inner slope α and concentration c; the best‐fitting profiles have the two parameters related with c= 19−9.6α. Our best‐fitting Navarro–Frenk–White profile has concentration c= 9, which is 50 per cent higher than standard values found in cosmological simulations for objects of similar mass. The total mass within the virial radius of 2.9h−170 Mpc is 1.4 × 1015h−170 M⊙ (with 30 per cent accuracy), 85 per cent of which is dark. At this distance from the cluster centre, the mass‐to‐light ratio in the blue band is 351h70 solar units. The total mass within the virial radius leads to estimates of the density parameter of the Universe, assuming that clusters trace the mass‐to‐light ratio and baryonic fraction of the Universe, with Ω0= 0.29 ± 0.1.

Using the standard dynamical theory of spherical systems, we calculate the properties of spherical galaxies and clusters whose density profiles obey the universal form first obtained in high‐resolution cosmological N‐body simulations by Navarro, Frenk & White (NFW). We adopt three models for the internal kinematics: isotropic velocities, constant anisotropy and increasingly radial Osipkov–Merritt anisotropy. Analytical solutions are found for the radial dependence of the mass, gravitational potential, velocity dispersion, energy and virial ratio and we test their variability with the concentration parameter describing the density profile and amount of velocity anisotropy. We also compute structural parameters, such as half‐mass radius, effective radius and various measures of concentration. Finally, we derive projected quantities, the surface mass density and line‐of‐sight as well as aperture‐velocity dispersion, all of which can be directly applied in observational tests of current scenarios of structure formation. On the mass scales of galaxies, if constant mass‐to‐light is assumed, the NFW surface density profile is found to fit Hubble–Reynolds laws well. It is also well fitted by Sérsic R1/m laws, for but in a much narrower range of m and with much larger effective radii than are observed. Assuming in turn reasonable values of the effective radius, the mass density profiles imply a mass‐to‐light ratio that increases outwards at all radii.

Elliptical galaxies are modelled with a four‐component model: Sérsic stars, Λ‐cold dark matter (ΛCDM), a β‐model for the hot gas and a central black hole, with the aim of establishing how accurately can one measure the total mass within their virial radii. Dark matter (DM) is negligible in the inner regions, which are dominated by stars and the central black hole. This prevents any kinematic estimate (using a Jeans analysis) of the inner slope of the DM density profile. The gas fraction rises, but the baryon fraction decreases with radius, at least out to 10 effective radii (Re). Even with line‐of‐sight velocity dispersion (VD) measurements at 4 or 5Re with 20 km s−1 accuracy and perfectly known velocity anisotropy, the total mass within the virial radius (rv≡r200) is uncertain by a factor of over 3. The DM distributions found in ΛCDM simulations appear inconsistent with the low VDs measured by Romanowsky et al. of planetary nebulae between 2 and 5Re. Some of Romanowsky et al.'s orbital solutions for NGC 3379 imply a dark matter content at least as large as cosmologically predicted, and the lower M/L values of most of their solutions lead to a baryonic fraction within rv that is larger than the universal value. Replacing the Navarro–Frenk–White (NFW) DM model by the new model of Navarro et al. decreases the VD slightly at a given radius. So, given the observed VD measured at 5Re, the inferred M/L within rv is 40 per cent larger than that predicted by the NFW model. Folding in the slight (strong) radial anisotropy found in ΛCDM (merger) simulations, which is well modelled (much better than with the Osipkov–Merritt formula) with , the inferred M/L within rv is 1.6 (2.4) times higher than for the isotropic NFW model. Thus, the DM model and radial anisotropy can partly explain the low planetary nebula VDs, but not in full. The logarithmic slope of the VD at radii of 1–5Re, which is insensitive to radius, is another measure of the DM mass within the virial radius, but it is similarly affected by the a priori unknown DM mass profile and stellar velocity anisotropy. In an , single integral expressions are derived for the VDs in terms of general radial profiles for the tracer density and total mass, for various anisotropic models (general constant anisotropy, radial, Osipkov–Merritt and the model above).

Using high resolution N-body simulations we address the problem of emptiness of giant 20 Mpc/h diameter voids found in the distribution of bright galaxies. Are the voids filled by dwarf galaxies? Do cosmological models predict too many small dark matter haloes inside the voids? Can the problems of cosmological models on small scales be addressed by studying the abundance of dwarf galaxies inside voids? We find that voids in the distribution of 10^12 Msun/h haloes (expected galactic magnitudes ~ M_*) are almost the same as the voids in 10^11 Msun/h haloes. Yet, much smaller haloes with masses 10^9 Msun/h and circular velocities v_circ about 20 km/s readily fill the voids: there should be almost 1000 of these haloes in a 20 Mpc/h void. A typical void of diameter 20 Mpc/h contains about 50 haloes with v_circ > 50 km/s. The haloes are arranged in a pattern, which looks like a miniature Universe: it has the same structural elements as the large-scale structure of the galactic distribution of the Universe. There are filaments and voids; larger haloes are at the intersections of filaments. The only difference is that all masses are four orders of magnitude smaller. There is severe (anti)bias in the distribution of haloes, which depends on halo mass and on the distance from the centre of the void. Large haloes are more antibiased and have a tendency to form close to void boundaries. The mass function of haloes in voids is different from the ``normal'' mass function. It is much steeper for high masses resulting in very few M33-type galaxies (v_circ about 100 km/s). We present an analytical approximation for the mass function of haloes in voids.Comment: 12 pages, 10 figures (paper with high resolution figure 2 available at http://www.aip.de/People/SGottloeber/papers/void_struc.ps.gz (8.5 Mb)), MNRA

The tidal stirring model posits the formation of dwarf spheroidal galaxies (dSphs) via the tidal interactions between late-type, rotationally-supported dwarfs and Milky Way-sized host galaxies. Using a comprehensive set of collisionless N-body simulations, we investigate the efficiency of the tidal stirring mechanism for the origin of dSphs. In particular, we examine the degree to which the tidal field of the primary galaxy affects the sizes, masses, shapes, and kinematics of the disky dwarfs for a range of dwarf orbital and structural parameters. Our study is the first to employ self-consistent, equilibrium models for the progenitor dwarf galaxies constructed from a composite distribution function and consisting of exponential stellar disks embedded in massive, cosmologically-motivated dark matter halos. Exploring a wide variety of dwarf orbital configurations and initial structures, we demonstrate that in the majority of cases the disky dwarfs experience significant mass loss and their stellar distributions undergo a dramatic morphological, as well as dynamical, transformation. Specifically, the stellar components evolve from disks to bars and finally to pressure-supported, spheroidal systems with kinematic and structural properties akin to those of the classic dSphs in the Local Group (LG) and similar environments. The self-consistency of the adopted dwarf models is crucial for confirming this complex transformation process via tidally-induced dynamical instabilities and impulsive tidal heating of the stellar distribution. Our results suggest that such tidal transformations should be common occurrences within the currently favored cosmological paradigm and highlight the key factor responsible for an effective metamorphosis to be the strength of the tidal shocks at the pericenters of the orbit. We also demonstrate that the combination of short orbital times and small pericentric distances, characteristic of dwarfs being accreted by their hosts at high redshift, induces the strongest and most complete transformations. Our models also indicate that the efficiency of the transformation via tidal stirring is affected significantly by the structure of the progenitor disky dwarfs. While the mass-to-light ratios, M/L, of the dwarf galaxies typically decrease monotonically with time as the extended dark matter halos are efficiently tidally stripped, we identify a few cases where this trend is reversed later in the evolution when stellar mass loss becomes more effective. We also find that the dwarf remnants satisfy the relation V max = √ 3 σ * , where σ * is the one-dimensional, central stellar velocity dispersion and V max is the maximum halo circular velocity, which has intriguing implications for the missing satellites problem. Assuming that the distant dSphs in the LG, such as Leo I, Tucana, and Cetus are the products of tidal stirring, our findings suggest that these galaxies should have only been partially stirred by the tidal field of their hosts. We thus predict that these remote dwarfs should exhibit higher val...

We study the distribution of dark matter in dwarf spheroidal galaxies by modelling the moments of their line-of-sight velocity distributions. We discuss different dark matter density profiles, both cuspy and possessing flat density cores. The predictions are made in the framework of standard dynamical theory of two-component (stars and dark matter) spherical systems with different velocity distributions. We compare the predicted velocity dispersion profiles to observations in the case of Fornax and Draco dwarfs. For isotropic models the dark haloes with cores are found to fit the data better than those with cusps. Anisotropic models are studied by fitting two parameters, dark mass and velocity anisotropy, to the data. In this case all profiles yield good fits but the steeper the cusp of the profile, the more tangential is the velocity distribution required to fit the data. To resolve this well-known degeneracy of density profile versus velocity anisotropy we obtain predictions for the kurtosis of the line-of-sight velocity distribution for models found to provide best fits to the velocity dispersion profiles. It turns out that profiles with cores typically yield higher values of kurtosis which decrease more steeply with distance than the cuspy profiles, which will allow to discriminate between the profiles once the kurtosis measurements become available. We also show that with present quality of the data the alternative explanation of velocity dispersions in terms of Modified Newtonian Dynamics cannot yet be ruled out.Comment: 13 pages, 9 figures, 3 tables, accepted for publication in MNRAS. Significantly revised, conclusions weakened, predictions for the kurtosis of the line-of-sight velocity distribution adde

Abstract. We study the origin and properties of unbound stars in the kinematic samples of dwarf spheroidal galaxies. For this purpose we have run a high resolution N -body simulation of a two-component dwarf galaxy orbiting in a Milky Way potential. We create mock kinematic data sets by observing the dwarf in different directions. When the dwarf is observed along the tidal tails the kinematic samples are strongly contaminated by unbound stars from the tails. However, most of the unbound stars can be removed by the method of interloper rejection proposed by den Hartog & Katgert. We model the velocity dispersion profiles of the cleaned-up kinematic samples using solutions of the Jeans equation. We show that even for such a strongly stripped dwarf the Jeans analysis, when applied to cleaned samples, allows us to reproduce the mass and mass-to-light ratio of the dwarf with accuracy typically better than 25%.

We study the distribution function (DF) of dark matter particles in haloes of mass range 10^{14}--10^{15}\Msun. In the numerical part of this work we measure the DF for a sample of relaxed haloes formed in the simulation of a standard \LambdaCDM model. The DF is expressed as a function of energy E and the absolute value of the angular momentum L, a form suitable for comparison with theoretical models. By proper scaling we obtain the results that do not depend on the virial mass of the haloes. We demonstrate that the DF can be separated into energy and angular momentum components and propose a phenomenological model of the DF in the form f_{E}(E)[1+L^{2}/(2L_{0}^{2})]^{-\beta_{\infty}+\beta_{0}}L^{-2\beta_{0}}. This formulation involves three parameters describing the anisotropy profile in terms of its asymptotic values (\beta_{0} and \beta_{\infty}) and the scale of transition between them (L_{0}). The energy part f_{E}(E) is obtained via inversion of the integral for spatial density. We provide a straightforward numerical scheme for this procedure as well as a simple analytical approximation for a typical halo formed in the simulation. The DF model is extensively compared with the simulations: using the model parameters obtained from fitting the anisotropy profile, we recover the DF from the simulation as well as the profiles of the dispersion and kurtosis of radial and tangential velocities. Finally, we show that our DF model reproduces the power-law behaviour of phase space density Q=\rho(r)/\sigma^{3}(r).Comment: 16 pages, 12 figures, final version accepted for publication in MNRA