Andrey V. Kravtsov

WHERE ARE THE MISSING GALACTIC SATELLITES

According to the hierarchical clustering scenario, galaxies are assembled by merging and accretion of numerous satellites of di†erent sizes and masses. This ongoing process is not 100% efficient in destroying all of the accreted satellites, as evidenced by the satellites of our Galaxy and of M31. Using published data, we have compiled the circular velocity distribution function (VDF) of galaxy satellites in the (V circ ) Local Group. We Ðnd that within the volumes of radius of 570 kpc (400 h~1 kpc assuming the Hubble constant1 h \ 0.7) centered on the Milky Way and Andromeda, the average VDF is roughly approx- imated as km s~1)~1.4B0.4 h3 Mpc~3 for in the range B10E70 km s~1. n( ( V circ ) B 55 ^ 11(V circ /10 V circ The observed VDF is compared with results of high-resolution cosmological simulations. We Ðnd that the VDF in models is very di†erent from the observed one : km s~1)~2.75 h3 n( ( V circ ) B 1200(V circ /10 Mpc~3. Cosmological models thus predict that a halo the size of our Galaxy should have about 50 dark matter satellites with circular velocity greater than 20 km s~1 and mass greater than 3 ) 108 within M _ a 570 kpc radius. This number is signiÐcantly higher than the approximately dozen satellites actually observed around our Galaxy. The di†erence is even larger if we consider the abundance of satellites in simulated galaxy groups similar to the Local Group. The models predict D300 satellites inside a 1.5 Mpc radius, while only D40 satellites are observed in the Local Group. The observed and predicted VDFs cross at B50 km s~1, indicating that the predicted abundance of satellites with km s~1 V circ Z 50 is in reasonably good agreement with observations. We conclude, therefore, that unless a large fraction of the Local Group satellites has been missed in observations, there is a dramatic discrepancy between observations and hierarchical models, regardless of the model parameters. We discuss several possible explanations for this discrepancy including identiÐcation of some satellites with the high-velocity clouds observed in the Local Group and the existence of dark satellites that failed to accrete gas and form stars either because of the expulsion of gas in the supernovae-driven winds or because of gas heating by the intergalactic ionizing background. Subject headings : cosmology : theory E galaxies : clusters : general E galaxies : interactions E Galaxy : formation E Local Group E methods : numerical

Profiles of dark haloes. Evolution, scatter, and environment

We study dark-matter halo density profiles in a high-resolution N-body simulation of aCDM cosmology. Our statistical sample contains �5000 haloes in the range 10 11 10 14 h −1 M⊙ and the resolution allows a study of subhaloes inside host haloes. The profiles are parameterized by an NFW form with two parameters, an inner radius rs and a virial radius Rvir, and we define the halo concentration cvirRvir/rs. We find that, for a given halo mass, the redshift dependence of the median concentration is cvir / (1 + z) −1 . This corresponds to rs(z) � constant, and is contrary to earlier suspicions that cvir does not vary much with redshift. The implications are that high- redshift galaxies are predicted to be more extended and dimmer than expected before. Second, we find that the scatter in halo profiles is large, with a 1� �(logcvir) = 0.18 at a given mass, corresponding to a scatter in maximum rotation velocities of �Vmax/Vmax = 0.12. We discuss implications for modelling the Tully-Fisher relation, which has a smaller reported intrinsic scatter. Third, subhaloes and haloes in dense environments tend to be more concentrated than isolated haloes, and show a larger scatter. These results suggest that cvir is an essential parameter for the theory of galaxy modelling, and we briefly discuss implications for the universality of the Tully- Fisher relation, the formation of low surface brightness galaxies, and the origin of the Hubble sequence. We present an improved analytic treatment of halo formation that fits the measured relations between halo parameters and their redshift dependence, and can thus serve semi-analytic studies of galaxy formation.

Toward a halo mass function for precision cosmology: The Limits of universality

We measure the mass function of dark matter halos in a large set of collisionless cosmological simulations of flat ΛCDM cosmology and investigate its evolution at -->z 2. Halos are identified as isolated density peaks, and their masses are measured within a series of radii enclosing specific overdensities. We argue that these spherical overdensity masses are more directly linked to cluster observables than masses measured using the friends-of-friends algorithm (FOF), and are therefore preferable for accurate forecasts of halo abundances. Our simulation set allows us to calibrate the mass function at -->z = 0 for virial masses in the range -->1011 h−1 M☉ ≤ M≤ 1015 h−1 M☉ to 5%, improving on previous results by a factor of 2-3. We derive fitting functions for the halo mass function in this mass range for a wide range of overdensities, both at -->z = 0 and earlier epochs. Earlier studies have sought to calibrate a universal mass function, in the sense that the same functional form and parameters can be used for different cosmologies and redshifts when expressed in appropriate variables. In addition to our fitting formulae, our main finding is that the mass function cannot be represented by a universal function at this level or accuracy. The amplitude of the universal function decreases monotonically by 20%-50%, depending on the mass definition, from -->z = 0 to 2.5. We also find evidence for redshift evolution in the overall shape of the mass function.

Erratum: "Chandra Sample of Nearby Relaxed Galaxy Clusters: Mass, Gas Fraction, and Mass-Temperature Relation"

We present gas and total mass profiles for 13 low-redshift, relaxed clusters spanning a temperature range 0.7-9 keV, derived from all available Chandra data of sufficient quality. In all clusters, gas-temperature profiles are measured to large radii (Vikhlinin et al.) so that direct hydrostatic mass estimates are possible to nearly r500 or beyond. The gas density was accurately traced to larger radii; its profile is not described well by a beta model, showing continuous steepening with radius. The derived ρtot profiles and their scaling with mass generally follow the Navarro-Frenk-White model with concentration expected for dark matter halos in ΛCDM cosmology. However, in three cool clusters, we detect a central mass component in excess of the Navarro-Frenk-White profile, apparently associated with their cD galaxies. In the inner region (r < 0.1r500), the gas density and temperature profiles exhibit significant scatter and trends with mass, but they become nearly self-similar at larger radii. Correspondingly, we find that the slope of the mass-temperature relation for these relaxed clusters is in good agreement with the simple self-similar behavior, M500 Tα, where α = (1.5-1.6) ± 0.1, if the gas temperatures are measured excluding the central cool cores. The normalization of this M-T relation is significantly, by ≈30%, higher than most previous X-ray determinations. We derive accurate gas mass fraction profiles, which show an increase with both radius and cluster mass. The enclosed fgas profiles within r2500 0.4r500 have not yet reached any asymptotic value and are still far (by a factor of 1.5-2) from the universal baryon fraction according to the cosmic microwave background (CMB) observations. The fgas trends become weaker and its values closer to universal at larger radii, in particular, in spherical shells r2500 < r < r500.

CHANDRA CLUSTER COSMOLOGY PROJECT III: COSMOLOGICAL PARAMETER CONSTRAINTS

Chandra observations of large samples of galaxy clusters detected in X-rays by ROSAT provide a new, robust determination of the cluster mass functions at low and high redshifts. Statistical and systematic errors are now sufficiently small, and the redshift leverage sufficiently large for the mass function evolution to be used as a useful growth of a structure-based dark energy probe. In this paper, we present cosmological parameter constraints obtained from Chandra observations of 37 clusters withz �= 0.55 derived from 400 deg 2 ROSAT serendipitous survey and 49 brightest z ≈ 0.05 clusters detected in the All-Sky Survey. Evolution of the mass function between these redshifts requires ΩΛ > 0 with a ∼ 5σ significance, and constrains the dark energy equation- of-state parameter to w0 =− 1.14 ± 0.21, assuming a constant w and a flat universe. Cluster information also significantly improves constraints when combined with other methods. Fitting our cluster data jointly with the latest supernovae, Wilkinson Microwave Anisotropy Probe, and baryonic acoustic oscillation measurements, we obtain w0 =− 0.991 ± 0.045 (stat) ±0.039 (sys), a factor of 1.5 reduction in statistical uncertainties, and nearly a factor of 2 improvement in systematics compared with constraints that can be obtained without clusters. The joint analysis of these four data sets puts a conservative upper limit on the masses of light neutrinos mν < 0.33 eV at 95% CL. We also present updated measurements of ΩMh and σ8 from the low-redshift cluster mass function.

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 that 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, where r and 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.

Reionization and the abundance of galactic satellites

One of the main challenges facing standard hierarchical structure formation models is that the predicted abundance of Galactic subhalos with circular velocities vc ~ 10-30 km s-1 is an order of magnitude higher than the number of satellites actually observed within the Local Group. Using a simple model for the formation and evolution of dark halos, based on the extended Press-Schechter formalism and tested against N-body results, we show that the theoretical predictions can be reconciled with observations if gas accretion in low-mass halos is suppressed after the epoch of reionization. In this picture, the observed dwarf satellites correspond to the small fraction of halos that accreted substantial amounts of gas before reionization. The photoionization mechanism naturally explains why the discrepancy between predicted halos and observed satellites sets in at vc ~ 30 km s-1, and for reasonable choices of the reionization redshift (zre ~ 5-12) the model can reproduce both the amplitude and shape of the observed velocity function of galactic satellites. If this explanation is correct, then typical bright galaxy halos contain many low-mass dark matter subhalos. These might be detectable through their gravitational lensing effects, through their influence on stellar disks, or as dwarf satellites with very high mass-to-light ratios. This model also predicts a diffuse stellar component produced by large numbers of tidally disrupted dwarfs, perhaps sufficient to account for most of the Milky Ways stellar halo.

Modeling Luminosity-dependent Galaxy Clustering through Cosmic Time

We employ high-resolution dissipationless simulations of the concordance ΛCDM cosmology (Ω0 = 1 - ΩΛ = 0.3, h = 0.7, σ8 = 0.9) to model the observed luminosity dependence and evolution of galaxy clustering through most of the age of the universe, from z ~ 5 to z ~ 0. We use a simple, nonparametric model, which monotonically relates galaxy luminosities to the maximum circular velocity of dark matter halos (Vmax) by preserving the observed galaxy luminosity function in order to match the halos in simulations with observed galaxies. The novel feature of the model is the use of the maximum circular velocity at the time of accretion, V, for subhalos, the halos located within virial regions of larger halos. We argue that for subhalos in dissipationless simulations, V reflects the luminosity and stellar mass of the associated galaxies better than the circular velocity at the epoch of observation, V. The simulations and our model L-Vmax relation predict the shape, amplitude, and luminosity dependence of the two-point correlation function in excellent agreement with the observed galaxy clustering in the SDSS data at z ~ 0 and in the DEEP2 samples at z ~ 1 over the entire probed range of projected separations, 0.1 < rp/(h-1 Mpc) < 10.0. In particular, the small-scale upturn of the correlation function from the power-law form in the SDSS and DEEP2 luminosity-selected samples is reproduced very well. At z ~ 3-5, our predictions also match the observed shape and amplitude of the angular two-point correlation function of Lyman break galaxies (LBGs) on both large and small scales, including the small-scale upturn. This suggests that, like galaxies in lower redshift samples, the LBGs are fair tracers of the overall halo population and that their luminosity is tightly correlated with the circular velocity (and hence mass) of their dark matter halos.

The Tumultuous Lives of Galactic Dwarfs and the Missing Satellites Problem

Hierarchical cold dark matter (CDM) models predict that Milky Way-sized halos contain several hundred dense low-mass dark matter satellites (the substructure), an order of magnitude more than the number of observed satellites in the Local Group. If the CDM paradigm is correct, this prediction implies that the Milky Way and Andromeda are filled with numerous dark halos. To understand why these halos failed to form stars and become galaxies, we need to understand their history. We analyze the dynamical evolution of the substructure halos in a high-resolution cosmological simulation of Milky Way-sized halos in the ?CDM cosmology. We find that about 10% of the substructure halos with the present masses 108-109 M? (circular velocities Vm 30 km s-1) had considerably larger masses and circular velocities when they formed at redshifts z 2. After the initial period of mass accretion in isolation, these objects experience dramatic mass loss because of tidal stripping. Our analysis shows that strong tidal interaction is often caused by actively merging massive neighboring halos, even before the satellites are accreted by their host halo. These results can explain how the smallest dwarf spheroidal galaxies of the Local Group were able to build up a sizable stellar mass in their seemingly shallow potential wells. We propose a new model in which all the luminous dwarf spheroidals in the Local Group are descendants of the relatively massive (109 M?) high-redshift systems, in which the gas could cool efficiently by atomic line emission, and which were not significantly affected by the extragalactic ultraviolet radiation. We present a simple galaxy formation model based on the trajectories extracted from the simulation, which accounts for the bursts of star formation after strong tidal shocks and the inefficiency of gas cooling in halos with virial temperatures Tvir 104 K. Our model reproduces the abundance, spatial distribution, and morphological segregation of the observed Galactic satellites. The results are insensitive to the redshift of reionization.

Chandra Cluster Cosmology Project. II. Samples and X-Ray Data Reduction

We discuss the measurements of the galaxy cluster mass functions at z 0.05 and z 0.5 using high-quality Chandra observations of samples derived from the ROSAT PSPC All-Sky and 400 deg2 surveys. We provide a full reference for the data analysis procedures, present updated calibration of relations between the total cluster mass and its X-ray indicators (TX , M gas, and YX ) based on a subsample of low-z relaxed clusters, and present a first measurement of the evolving LX -M tot relation (with M tot estimated from YX ) obtained from a well defined statistically complete cluster sample and with appropriate corrections for the Malmquist bias applied. Finally, we present the derived cluster mass functions, estimate the systematic uncertainties in this measurement, and discuss the calculation of the likelihood function. We confidently measure the evolution in the cluster comoving number density at a fixed mass threshold, e.g., by a factor of 5.0 ? 1.2 at M 500 = 2.5 ? 1014 h ?1 M ? between z = 0 and 0.5. This evolution reflects the growth of density perturbations, and can be used for the cosmological constraints complementing those from the distance-redshift relation.