Anatoly Klypin

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.

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.

ΛCDM-based Models for the Milky Way and M31. I. Dynamical Models

We apply standard disk formation theory with adiabatic contraction within cuspy halo models predicted by the standard cold dark matter (?CDM) cosmology. The resulting models are confronted with the broad range of observational data available for the Milky Way and M31 galaxies. We find that there is a narrow range of parameters that can satisfy the observational constraints, but within this range, the models score remarkably well. Our favored models have virial masses of 1012 and 1.6 ? 1012 M? for the Galaxy and for M31, respectively, average spin parameters ? ? 0.03-0.05, and concentrations Cvir = 10-17, typical for halos of this mass in the standard ?CDM cosmology. The models require neither dark matter modifications nor flat cores to fit the observational data. We explore two types of models, with and without the exchange of angular momentum between the dark matter and the baryons. The models without exchange give reasonable rotation curves, fulfill constraints in the solar neighborhood, and satisfy constraints at larger radii, but they may be problematic for fast rotating central bars. We explore models in which the baryons experience additional contraction due to loss of angular momentum to the surrounding dark matter. These models produce similar global properties, but the dark matter is only a 25% of the total mass in the central 3 kpc region, allowing a fast rotating bar to persist. According to preliminary calculations, our model galaxies probably have sufficient baryonic mass in the central ~3.5 kpc to reproduce recent observational values of the optical depth to microlensing events toward the Galactic center. Our dynamical models unequivocally require that about 50% of all the gas inside the virial radius must not be in the disk or in the bulge, a result that is obtained naturally in standard semianalytic models. Assuming that the Milky Way is typical, we investigate whether the range of virial masses allowed by our dynamical models is compatible with constraints from the galaxy luminosity function. We find that if the Milky Way has a luminosity MK = -24.0, then these constraints are satisfied, but if it is more luminous (as expected if it lies on the Tully-Fisher relation), then the predicted space density is larger than the observed space density of galaxies of the corresponding luminosity by a factor of 1.5-2. We conclude that observed rotation curves and dynamical properties of normal spiral galaxies appear to be consistent with standard ?CDM.

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.

Adaptive refinement tree: A New high resolution N body code for cosmological simulations

Abstract : We present a new high-resolution N-body algorithm for cosmological simulations. The algorithm employs a traditional particle-mesh technique on a cubic grid and successive multilevel relaxations on the finer meshes, introduced recursively in a fully adaptive manner in the regions where the density exceeds a predefined threshold. The mesh is generated to effectively match an arbitrary geometry of the underlying density field-a property particularly important for cosmological simulations. In a simulation the mesh structure is not created at every time step but properly adjusted to the evolving particle distribution. The algorithm is fast and effectively parallel: the gravitational relaxation solver is approximately two times slower than the FFT solver on the same number of mesh cells. The required CPU time scales with number of cells, N suc c, as ^O(Nc). It allows us to improve considerably the spatial resolution of the particle-mesh code without loss in mass resolution. We present a detailed description of the methodology, implementation, and tests of the code. We further use the code to study the structure of dark matter halos in high-resolution (^2/h kpc) simulations of standard CDM (Omega = 1, h = 0.5, sigma sub g = 0.63) and (Lambda)CDM (0A = 1 -Omega sub O = 0.7, h = 0.7, sigma sub g = 1.0) models. We find that halo density profiles in both CDM and ACDM models are well fit by the analytical model presented recently by Navarro et al. (1966) which predicts a singular (rho(r) oc 1/r) behavior of the halo density profiles at small radii. We therefore conclude that halos formed in the (Lambda)CDM model have structure similar to the CDM halos, and thus cannot explain dynamics of the central parts of dwarf spiral galaxies infrerred from their rotation curves.

Galaxies in N-Body Simulations: Overcoming the Overmerging Problem

We present analysis of the evolution of dark matter halos in dense environments of groups and clusters in dissipationless cosmological simulations. The premature destruction of halos in such environments, known as the overmerging, reduces the predictive power of N-body simulations and makes difficult any comparison between models and observations. We analyze the possible processes that cause the overmerging and assess the extent to which this problem can be cured with current computer resources and codes. Using both analytic estimates and high-resolution numerical simulations, we argue that the overmerging is mainly due to the lack of numerical resolution. We find that the force and mass resolution required for a simulated halo to survive in galaxy groups and clusters is extremely high and was almost never reached before: ~1-3 kpc and 108-109 M☉, respectively. We use the high-resolution Adaptive Refinement Tree (ART) N-body code to run cosmological simulations with particle mass ≈2 × 108 h-1 M☉ and spatial resolution ≈1-2 h-1 kpc and show that in these simulations the halos do survive in regions that would appear overmerged with lower force resolution. Nevertheless, the halo identification in very dense environments remains a challenge even with resolution this high. We present two new halo-finding algorithms developed to identify both isolated and satellite halos that are stable (existed at previous moments) and gravitationally bound. To illustrate the use of the satellite halos that survive the overmerging, we present a series of halo statistics, which can be compared with those of observed galaxies. Particularly, we find that, on average, halos in groups have the same velocity dispersion as the dark matter particles; i.e., they do not exhibit significant velocity bias. The small-scale (100 kpc to 1 Mpc) halo correlation function in both models is well described by the power law ξ r-1.7 and is in good agreement with observations. It is slightly antibiased (b≈0.7-0.9) relative to the dark matter. To test other galaxy statistics, we use the maximum of the halo rotation velocity and the Tully-Fisher relation to assign luminosity to the halos. For two cosmological models, a flat model with the cosmological constant and Ω0=1-ΩΛ=0.3,h=0.7 and a model with a mixture of cold and hot dark matter and Ω0=1.0,Ων=0.2,h=0.5, we construct luminosity functions and evaluate mass-to-light ratios in groups. Both models produce luminosity functions and mass-to-light ratios ( ~200-400) that are in reasonable agreement with observations. The latter implies that the mass-to-light ratio in galaxy groups (at least for Mvir 3 × 1013 h-1 M☉ analyzed here) is not a good indicator of Ω0.

The Santa Barbara Cluster Comparison Project: A Comparison of Cosmological Hydrodynamics Solutions

We have simulated the formation of an X-ray cluster in a cold dark matter universe using 12 different codes. The codes span the range of numerical techniques and implementations currently in use, including smoothed particle hydrodynamics (SPH) and grid methods with fixed, deformable, or multilevel meshes. The goal of this comparison is to assess the reliability of cosmological gasdynamical simulations of clusters in the simplest astrophysically relevant case, that in which the gas is assumed to be nonradiative. We compare images of the cluster at different epochs, global properties such as mass, temperature and X-ray luminosity, and radial profiles of various dynamical and thermodynamical quantities. On the whole, the agreement among the various simulations is gratifying, although a number of discrepancies exist. Agreement is best for properties of the dark matter and worst for the total X-ray luminosity. Even in this case, simulations that adequately resolve the core radius of the gas distribution predict total X-ray luminosities that agree to within a factor of 2. Other quantities are reproduced to much higher accuracy. For example, the temperature and gas mass fraction within the virial radius agree to within about 10%, and the ratio of specific dark matter kinetic to gas thermal energies agree to within about 5%. Various factors, including differences in the internal timing of the simulations, contribute to the spread in calculated cluster properties. Based on the overall consistency of results, we discuss a number of general properties of the cluster we have modeled.

The large-scale bias of dark matter halos: numerical calibration and model tests

We measure the clustering of dark matter halos in a large set of collisionless cosmological simulations of the flatCDM cosmology. Halos are identified using the spherical over density algorithm, which finds the mass around isolated peaks in the density field such that the m ean density istimes the background. We calibrate fitting functions for the large scale bias that are adaptable to any value ofwe examine. We find a � 6% scatter about our best fit bias relation. Our fitting functi ons couple to the halo mass functions of Tinker et. al. (2008) such that bias of all dark matter is normalized to unity. We demonstrate that the bias of massive, rare halos is higher than that predicted in the modified ellip soidal collapse model of Sheth, Mo, & Tormen (2001), and approaches the predictions of the spherical collapse model for the rarest halos. Halo bias results based on friends-of-friends halos identified with linking l ength 0.2 are systematically lower than for halos with the canonical � = 200 overdensity by � 10%. In contrast to our previous results on the mass function, we find that the universal bias function evolves very weakly with redshift, if at all. We use our numerical results, both for the mass function and the bias relation, to test the peak- background split model for halo bias. We find that the peak-background split achieves a reasonable agreement with the numerical results, but � 20% residuals remain, both at high and low masses. Subject headings:cosmology:theory — methods:numerical — large scale structure of the universe