Center Of Dark Matter Halos Research Articles

Cosmology: small-scale issues

The abundance of dark matter satellites and subhalos, the existence of density cusps at the centers of dark matter halos and problems producing realistic disk galaxies in simulations are issues that have raised concerns about the viability of the standard cold dark matter (ΛCDM) scenario for galaxy formation. This paper reviews these issues and considers the implications for cold versus various varieties of warm dark matter (WDM). The current evidence appears to be consistent with standard ΛCDM, although improving data may point toward a rather tepid version of ΛWDM—tepid since the dark matter cannot be very warm without violating observational constraints. (This is a substantially updated and expanded version of my talk at the DM08 meeting at Marina Del Rey, arXiv:0902.2506.)

Evolution of the dark matter phase-space density distributions of ΛCDM haloes

We study the evolution of phase-space density during the hierarchical structure formation of LCDM halos. We compute both a spherically-averaged surrogate for phase-space density (Q) and the coarse-grained distribution function f(x,v) for dark matter particles that lie within~2 virial radii of four Milky-Way-sized dark matter halos. The estimated f(x,v) spans over four decades at any radius. Dark matter particles that end up within two virial radii of a Milky-Way-sized DM halo at $z=0$ have an approximately Gaussian distribution in log(f) at early redshifts, but the distribution becomes increasingly skewed at lower redshifts. The value corresponding to the peak of the Gaussian decreases as the evolution progresses and is well described by a power-law in (1+z). The highest values of f are found at the centers of dark matter halos and subhalos, where f can be an order of magnitude higher than in the center of the main halo. The power-law Q(r) profile likely reflects the distribution of entropy (K = sigma^2/rho^{2/3} \propto r^{1.2}), which dark matter acquires as it is accreted onto a growing halo. The estimated f(x, v), on the other hand, exhibits a more complicated behavior. Although the median coarse-grained phase-space density profile F(r) can be approximated by a power-law in the inner regions of halos and at larger radii the profile flattens significantly. This is because phase-space density averaged on small scales is sensitive to the high-f material associated with surviving subhalos, as well as relatively unmixed material (probably in streams) resulting from disrupted subhalos, which contribute a sizable fraction of matter at large radii. (ABRIDGED)

DISTRIBUTION FUNCTION IN THE CENTER OF THE DARK MATTER HALO

N-body simulations of dark matter halos show that the density profiles of the halos behave as ρ(r) ∝ r-α(r), where the density logarithmic slope α ≃ 1–1.5 in the center and α ≃ 3–4 in the outer parts of the halos. However, some observations are not in agreement with simulations in the very central region of the halos. The simulations also show that the velocity dispersion anisotropy parameter β ≈ 0 in the inner part of the halo and the so-called pseudo–phase-space density ρ/σ3 behaves as a power law in radius r. With these results in mind, we study the distribution function and the pseudo–phase-space density ρ/σ3 of the center of dark matter halos and find that they are closely related.

The formation of compact massive self-gravitating discs in metal-free haloes with virial temperatures of ∼13 000-30 000 K

We have used the hydrodynamical adaptive mesh refinement code ENZO to investigate the dynamical evolution of the gas at the centre of dark matter haloes with virial velocities of ∼20-30 km s -1 and virial temperatures of ∼ 13 000-30 000K at z ∼ 15 in a cosmological context. The virial temperature of the dark matter haloes is above the threshold where atomic cooling by hydrogen allows the gas to cool and collapse. We neglect cooling by molecular hydrogen and metals, as may be plausible if H 2 cooling is suppressed by a metagalactic Lyman-Werner background or an internal source of Lyman-Werner photons, and metal enrichment has not progressed very far. The gas in the haloes becomes gravitationally unstable and develops turbulent velocities comparable to the virial velocities of the dark matter haloes. Within a few dynamical times, it settles into a nearly isothermal density profile over many decades in radius losing most of its angular momentum in the process. About 0.1-1 per cent of the baryons, at the centre of the dark matter haloes, collapse into a self-gravitating, fat, ellipsoidal, centrifugally supported exponential disc with scalelength of ∼0.075-0.27 pc and rotation velocities of 25-60 km s -1 . We are able to follow the settling of the gas into centrifugal support and the dynamical evolution of the compact disc in each dark matter halo for a few dynamical times. The dynamical evolution of the gas at the centre of the haloes is complex. In one of the haloes, the gas at the centre fragments into a triple system leading to strong tidal perturbations and eventually to the infall of a secondary smaller clump into the most massive primary clump. The formation of centrifugally supported self-gravitating massive discs is likely to be an important intermediary stage en route to the formation of a massive black hole seed.

The origin of globular cluster systems from cosmological simulations

We investigate the structural, kinematical and chemical properties of globular cluster systems (GCSs) in galaxies of different Hubble types in a self-consistent manner based on high-resolution cosmological N-body simulations combined with semi-analytic models of galaxy and globular cluster (GC) formation. We focus on correlations between the physical properties of GCSs and those of their host galaxies for ∼10 5 simulated galaxies located at the centres of dark matter haloes (i.e. we do not consider satellite galaxies in subhaloes). Our principal results, which can be tested against observations, are as follows. The majority (∼90 per cent) of GCs currently in haloes are formed in low-mass galaxies at redshifts greater than 3 with mean formation redshifts of z = 5.7 (12.7Gyr ago) and 4.3 (12.3Gyr ago) for metal-poor GCs (MPCs) and metal-rich GCs (MRCs), respectively. About 52 per cent of galaxies with GCs show clear bimodality in their metallicity distribution functions, though less luminous galaxies with M B fainter than -17 are much less likely to show bimodality owing to little or no MRCs. The number fraction of MRCs does not depend on Hubble type but is generally smaller for less luminous galaxies. The specific frequencies (S N ) of GCSs are typically higher in ellipticals (S N ∼ 4.0) than in spirals (S N ∼ 1.8), and higher again (S N ∼ 5.0) for galaxies located at the centres of clusters of galaxies. The total number of GCs per unit halo mass does not depend strongly on M B or Hubble type of the host galaxy. The mean metallicities of MPCs and MRCs depend on M B such that they are higher in more luminous galaxies, though the dependence is significantly weaker for MPCs. The spatial distributions of MRCs are more compact than those of MPCs and we find that the half-number radii of MPCs (r e,mpc ) correlate with the halo masses (M h ) such that r e,mpc oc M h 0.18 . There is no significant difference in velocity dispersions between MPCs and MRCs. We qualitatively compare our results to observational data where possible. Finally, we discuss these results in the wider context of galaxy formation and evolution.

An improved model for contraction of dark matter haloes in response to condensation of baryons

The cooling of gas in the centres of dark matter haloes is expected to lead to a more concentrated dark matter distribution. The response of dark matter to the condensation of baryons is usually calculated using the model of adiabatic contraction, which assumes spherical symmetry and circular orbits. Following Gnedin et al., we improve this model by modifying the assumed invariant from M(r)r to M(r)r, where r and r are the current and orbit-averaged particle positions. We explore the effect of the bulge in the inner regions of the halo for different values of the bulge-to-disc mass ratio. We find that the bulge makes the velocity curve rise faster in the inner regions of the halo. We present an analytical fitting curve that describes the velocity curve of the halo after dissipation. The results should be useful for dark matter detection studies.

Contraction of Dark Matter Halos in Response to Condensation of Baryons

The cooling of baryons in the centers of dark matter halos leads to a more concentrated dark matter distribution. This effect has traditionally been calculated using the model of adiabatic contraction, which assumes spherical symmetry, while in hierarchical formation scenarios halos grow via multiple violent mergers. We test the adiabatic contraction model in high-resolution cosmological simulations and find that the dissipation of gas indeed increases the density of dark matter and steepens its radial profile compared to the case without cooling. Although the standard model systematically overpredicts the increase of dark matter density, a simple modification of the assumed invariant from M(r)r to M( )r, where is the orbit-averaged particle position, reproduces the simulated profiles within 10%.

Response of Dark Matter Halos to Condensation of Baryons: Cosmological Simulations and Improved Adiabatic Contraction Model

The cooling of gas in the centers of dark matter halos is expected to lead to a more concentrated dark matter distribution. The response of dark matter to the condensation of baryons is usually calculated using the model of adiabatic contraction, which assumes spherical symmetry and circular orbits. In contrast, halos in the hierarchical structure formation scenarios grow via multiple violent mergers and accretion along filaments, and particle orbits in the halos are highly eccentric. We study the effects of the cooling of gas in the inner regions of halos using high-resolution cosmological simulations which include gas dynamics, radiative cooling, and star formation. We find that the dissipation of gas indeed increases the density of dark matter and steepens its radial profile in the inner regions of halos compared to the case without cooling. For the first time, we test the adiabatic contraction model in cosmological simulations and find that the standard model systematically overpredicts the increase of dark matter density in the inner 5% of the virial radius. We show that the model can be improved by a simple modification of the assumed invariant from M(r)r to M(r_av)r, where r and r_av are the current and orbit-averaged particle positions. This modification approximately accounts for orbital eccentricities of particles and reproduces simulation profiles to within 10-20%. We present analytical fitting functions that accurately describe the transformation of the dark matter profile in the modified model and can be used for interpretation of observations.

Galaxies and subhaloes in ΛCDM galaxy clusters

We combine 10 high-resolution resimulations of cluster-sized dark haloes with semi-analytic galaxy formation modelling in order to compare the number density and velocity dispersion profiles of cluster galaxies with those of dark matter substructures (subhaloes). While the radial distribution of galaxies follows closely that of the dark matter, the distribution of dark matter subhaloes is much less centrally concentrated. The velocity dispersion profiles of galaxies are also very similar to those of the dark matter, while those for subhaloes are biased high, particularly in the inner regions of clusters. We explain how these differences, already clearly visible in earlier work, are a consequence of the formation of galaxies at the centres of dark matter haloes. Galaxies and subhaloes represent different populations and are not directly comparable. Evolution produces a complex and strongly position-dependent relation between galaxies and the subhaloes in which they reside. This relation can be properly modelled only by appropriate physical representation of the galaxy formation process.

Ionized Gas in Damped Lyα Protogalaxies. II. Comparison between Models and the Kinematic Data

We test semianalytic models for galaxy formation with accurate kinematic data of damped Lyα protogalaxies presented in a companion paper. The models envisage centrifugally supported exponential disks at the centers of dark matter halos, which are filled with ionized gas undergoing radial infall to the disks. The halo masses are drawn from cross section weighted mass distributions predicted by cold dark matter (CDM) cosmogonies, or by the null hypothesis that the dark matter mass distribution has not evolved since z ~ 3 (i.e., the Tully-Fisher [TF] models). In our models, C IV absorption lines detected in damped Lyα protogalaxies arise in infalling ionized clouds, while the low-ion absorption lines arise from neutral gas in the disks. Using Monte Carlo methods, we find that: (1) The CDM models are incompatible with the low-ion statistics at more than 99% confidence, whereas some TF models cannot be ruled out at more than 88% confidence. (2) Both CDM and TF models are in general agreement with the observed distribution of C IV velocity widths. (3) The CDM models generate differences between the mean velocities of C IV and low-ion profiles that are compatible with the data, while the TF model produces differences in the means that are too large. (4) Both CDM and TF models produce ratios of C IV to low-ion velocity widths that are too large. (5) Neither CDM nor TF models generate C IV versus low-ion cross-correlation functions compatible with the data. While it is possible to select model parameters resulting in agreement between the models and the data, the fundamental problem is that the disk-halo configuration assumed in both cosmogonies does not produce significant overlap in velocity space between C IV and low-ion velocity profiles. We conjecture that including the angular momentum of the infalling clouds will increase the overlap between C IV and low-ion profiles.

Dynamical biases in gravitational clustering

The centers of dark matter halos, where galaxies form, have spatial distributions and pairwise random velocities that misrepresent those in the general density field. The origin and evolution of these biases are studied with the aid of dissipationless n-body models. Velocity bias originates when the galaxies, along with their extended dark matter halos, fall into virialized regions and become subject to dynamical friction. As a consequence, galaxy random velocities are always less than those in the density field. A first-order model that includes the dynamical friction experienced by two gravitationally bound galaxies with their correlated dark halos reproduces the general features of the velocity-acceleration relation measured in n-body experiments roughly to the accuracy to which the Coulomb integral, ln {LAMBDA}, is known. The model predicts that the ratio of the mean pairwise peculiar velocity of galaxies to the dark matter dispersion tends to 3(π)^1/2^/[2(2)^1/2^ ln {LAMBDA}] ~ 0.7 in regions of high acceleration. To emphasize the distinction between dark halos and the locations of galaxies the relative correlation amplitudes of halos, ξ_hh_, and the general dark matter distribution, ξ<SUB>rho</SUB>ρ_, are compared as a function of epoch, finding that the two-point correlations of the halos have little dependence on epoch. Moreover ξ_hh_ of galaxy mass halos is always less than ξ_gg_, the observed correlation of galaxies. To match the n-body data to the amplitude of ξ_gg_ requires that galaxies be identified with the z = 0 locations of the centers of halos that are formed in the redshift range z ~ 1-3. By redshift zero these halos have undergone considerable dynamical evolution, including clustering, merging, and tidal stripping, but overall have become considerably more clustered than halos of the same mass and overdensity identified at z = 0. The correlation function of these "galaxies" is not too sensitive to the particular redshift choice, at separations where ξ_gg_ &gt;~ 10, although there are interesting enhancements at ξ_gg_ &lt;~ 1 with increasing redshift of selection. The mean cosmological density estimated with the cosmic virial theorem can be corrected to {OMEGA}_true_ = b^2^<SUB>xi</SUB>_ b^-2^_v_ {OMEGA}_CVT_, where the biases are estimated using a simple galaxy identification algorithm within the context of this particular {OMEGA} = 1 CDM model to be b<SUB>xi</SUB>_ = 1.08 +/- 0.20 and b_v_ = 0.6 +/- 0.2. Overall, these models and a variety of other observations suggest that standard luminous galaxies have a modest b<SUB>xi</SUB>_ ~ 1.4, and a velocity bias b_v_ ~ 07 which together imply that apparent {OMEGA}_CVT_ should be corrected upward by a factor of ~ 4.