Ewa L. Łokas

Dark matter distribution in the Coma cluster from galaxy kinematics: breaking the mass–anisotropy degeneracy

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 a 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 - 1 70 Mpc is 1.4 x 10 1 5 h - 1 70 M O . (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 351h 7 0 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 Ω 0 = 0.29 ′ 0.1.

Properties of spherical galaxies and clusters with an NFW density profile

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 Sersic 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.

The structure of voids

Using high resolution N-body simulations we address the problem of emptiness of giant � 20h −1 Mpc–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 h −1 M⊙ haloes (expected galactic magnitudes � M∗) are almost the same as the voids in 10 11 h −1 M⊙ haloes. Yet, much smaller haloes with masses 10 9 h −1 M⊙ and circular velocities vcirc � 20 km/s readily fill the voids: there should be almost 1000 of these haloes in a 20h −1 Mpc–diameter void. A typical void of diameter 20h −1 Mpc contains about 50 haloes with vcirc > 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 (vcirc � 100 km/s). We present an analytical approximation for the mass function of haloes in voids.

Dark matter in elliptical galaxies — II. Estimating the mass within the virial radius

Elliptical galaxies are modelled with a a 4-component model: Sersic stars, �CDM dark matter (DM), 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. DM is negligible in the inner regions, which are dominated by stars and the central black hole. This prevents any kinematical estimate (using a Jeans analysis) of the inner slope of the DM density profile. The gas fraction rises, but the baryon fra ction decreases with radius, at least out to 10 effective radii (Re). Even with line-of-sight velocity dispersion (VD) measure- ments at 4 or 5 Re with 20kms 1 accuracy and perfectly known velocity anisotropy, the total mass within the virial radius (rvr200) is uncertain by a factor over 3. The DM distributions found inCDM simulations appear inconsistent with the low VDs measured by Romanowsky et al. (2003) of planetary nebulae between 2 and 5 Re, which typically (but not always) imply very low M/Ls, and a baryon fraction within rv that is greater than the universal value. Re- placing the NFW DM model by the new model of Navarro et al. (2004) decreases slightly the VD at a given radius. So, given the observed VD measured at 5 Re, the inferred M/L within rv is 40% larger than predicted with the NFW model. Folding in the slight (strong) radial anisotropy found inCDM (merger) simulations, which is well modelled (much better than with the Osipkov-Merritt formula) with β(r) = 1/2 r/(r + a), 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 PN VDs, but not in full. The logarithmic slope of the VD at radii of 1 to 5 Re, 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. Some of the orbital solutions produced by Romanowsky et al. (2003) indicate that NGC 3379 has a dark matter content at least as large as cosmologically predicted, and the lower M/Ls of most of their solutions lead to a baryonic fraction withi n rv that is larger than the universal value. In an appendix, single integral expres sions are derived for the VDs in terms of general radial profiles for the tracer density and to tal mass, for various anisotropic models (general constant anisotropy, radial, Osipkov-Merritt, and the model above).

ON THE EFFICIENCY OF THE TIDAL STIRRING MECHANISM FOR THE ORIGIN OF DWARF SPHEROIDALS: DEPENDENCE ON THE ORBITAL AND STRUCTURAL PARAMETERS OF THE PROGENITOR DISKY DWARFS

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 , 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 values of V rot/σ*, where V rot is the stellar rotational velocity, compared with those of dSphs located closer to the primary galaxies. Overall, we conclude that the action of tidal forces from the hosts constitutes a crucial evolutionary mechanism for shaping the nature of dwarf galaxies in environments such as that of the LG. Environmental mechanisms of this type should thus be included as ingredients in models of dwarf galaxy formation and evolution.

Dark matter distribution in dwarf spheroidal galaxies

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.

The mass and velocity anisotropy of the Carina, Fornax, Sculptor and Sextans dwarf spheroidal galaxies

We model the large kinematic data sets for the four Milky Way dwarf spheroidal (dSph) satellites: Carina, Fornax, Sculptor and Sextans, recently published by Walker et al. The member stars are selected using a reliable dynamical interloper removal scheme tested on simulated data. Our member selection is more restrictive than the one based on metallicity indicators as it removes not only contamination due to Milky Way stars but also the unbound stars from the tidal tails. We model the cleaned data sets by adjusting the solutions of the Jeans equations to the profiles of the projected velocity dispersion and kurtosis. The data are well reproduced by models where mass follows light and the best-fitting stellar orbits are isotropic to weakly tangential, as expected from the tidal stirring scenario. The Fornax dwarf, with more than 2400 member stars, is a dSph galaxy with the most accurately determined mass to date: its 1σ error following from the sampling errors of the velocity moments is below 5 percent. With mass-to-light ratio of 97 solar units, Sextans seems to be the most dark matter dominated of the four dSph galaxies.

Mass modelling of dwarf spheroidal galaxies: the effect of unbound stars from tidal tails and the Milky Way

We study the origin and properties of the population of unbound stars in the kinematic samples of dwarf spheroidal (dSph) 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. In agreement with the tidal stirring scenario of Mayer et al., the dwarf is placed on a highly eccentric orbit, its initial stellar component is in the form of an exponential disc and it has a NFW-like dark matter (DM) halo. After 10 Gyr of evolution the dwarf produces a spheroidal stellar component and is strongly tidally stripped so that mass follows light and the stars are on almost isotropic orbits. From this final state, we create mock kinematic data sets for 200 stars by observing the dwarf in different directions. We find that when the dwarf is observed along the tidal tails the kinematic samples are strongly contaminated by unbound stars from the tails. We also study another source of possible contamination by adding stars from the Milky Way. We demonstrate that most of the unbound stars can be removed by the method of interloper rejection proposed by den Hartog & Katgert and recently tested on simulated DM haloes. We model the cleaned-up kinematic samples using solutions of the Jeans equation with constant mass-to-light ratio (M/L) and velocity anisotropy parameter. 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 M/L of the dwarf with accuracy typically better than 25 per cent and almost exactly in the case when the line of sight is perpendicular to the tidal tails. The analysis was applied to the new data for the Fornax dSph galaxy. We show that after careful removal of interlopers the velocity dispersion profile of Fornax can be reproduced by a model in which mass traces light with a M/L of 11 solar units and isotropic orbits. We demonstrate that most of the contamination in the kinematic sample of Fornax probably originates from the Milky Way.

The grouping, merging and survival of subhaloes in the simulated Local Group

We use a simulation performed within the Constrained Local Universe Simulation (CLUES) project to study a realistic Local Group (LG)-like object. We employ this group as a numerical laboratory for studying the evolution of the population of its subhaloes from the point of view of the effects it may have on the origin of different types of dwarf galaxies. We focus on the processes of tidal stripping of the satellites, their interaction, merging and grouping before infall. The tidal stripping manifests itself in the transition between the phase of mass accretion and mass loss seen in most subhaloes, which occurs at the moment of infall on to the host halo, and the change of the shape of their mass function with redshift. Although the satellites often form groups, they are loosely bound within them and do not interact with each other. The infall of a large group could however explain the observed peculiar distribution of the LG satellites, but only if it occurred recently. Mergers between prospective subhaloes are significant only during an early stage of evolution, i.e. more than 7 Gyr ago, when they are still outside the host haloes. Such events could thus contribute to the formation of more distant early-type Milky Way companions. Once the subhaloes enter the host halo the mergers become very rare.

Tidal evolution of discy dwarf galaxies in the Milky Way potential: the formation of dwarf spheroidals

We conduct high-resolution collisionless N-body simulations to investigate the tidal evolution of dwarf galaxies on an eccentric orbit in the Milky Way (MW) potential. The dwarfs originally consist of a low surface brightness stellar disk embedded in a cosmologically motivated dark matter halo. During 10 Gyr of dynamical evolution and after 5 pericentre passages the dwarfs suffer substantial mass loss and their stellar component undergoes a major morphological transformation from a disk to a bar and finally to a spheroid. The bar is preserved for most of the time as the angular momentum is transferred outside the galaxy. A dwarf spheroidal (dSph) galaxy is formed via gradual shortening of the bar. This work thus provides a comprehensive quantitative explanation of a potentially crucial morphological transformation mechanism for dwarf galaxies that operates in groups as well as in clusters. We compare three cases with different initial inclinations of the disk and find that the evolution is fastest when the disk is coplanar with the orbit. Despite the strong tidal perturbations and mass loss the dwarfs remain dark matter dominated. For most of the time the 1D stellar velocity dispersion, �, follows the maximum circular velocity, Vmax, and they are both good tracers of the bound mass. Specifically, we find that Mbound / V 3.5 max � )