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Using high resolution N-body simulations of stellar disks embedded in cosmologically motivated dark matter halos, we study the evolution of bars and the transfer of angular momentum between halos and bars. We find that dynamical friction results in some transfer of angular momentum to the halo, but the effect is much smaller than previously found in low resolution simulations and is incompatible with early analytical estimates. In simulations with millions of particles reaching a resolution of 20-40 pc, the pattern speed may not change over billions of years. Our high resolution models produce bars which are fast rotators, where the ratio of the corotation radius to the bar major semi-axis lies in the range R =1.2-1.7, marginally compatible with observational results. In contrast to many previous simulations, we find that bars are relatively short. As in many observed cases, the bar major semi-axis is close to the exponential length of the disk. The transfer of angular momentum between inner and outer parts of the disk plays a very important role in the secular evolution of the disk and the bar. The bar formation increases the exponential length of the disk by a factor of 1.2 -1.5. The transfer substantially increases the stellar mass in the centre of the galaxy and decreases the dark matter-to-baryons ratio. As the result, the central 2 kpc region is always strongly dominated by the baryonic component. At intermediate 3-10kpc scales the disk is sub-dominant. In summary, realistic models produce bar structure in striking agreement with observational results., Comment: updated version includes new 10M model, extensive tests, estimates of two-body scattering, corrected typos. High resolution version is in http://ganymede.nmsu.edu/aklypin/BARS/bars5.ps.gz

We use a novel statistical tool, the mark correlation functions (MCFs), to study clustering of galaxy-size halos as a function of their properties and environment in a high-resolution numerical simulation of the LambdaCDM cosmology. We applied MCFs using several types of continuous and discrete marks: maximum circular velocity of halos, merger mark indicating whether halos experienced or not a major merger in their evolution history, and a stripping mark indicating whether the halo underwent a tidal stripping. We find that halos which experienced a relatively early (z>1) major merger or mass loss (due to tidal stripping) in their evolution histories are over-abundant in halo pairs with separations < 3 Mpc/h. This result can be interpreted as spatial segregation of halos with different merger histories, qualitatively similar to the morphological segregation in the observed galaxy distribution. The analysis presented in this paper demonstrate that MCFs provide powerful, yet algorithmically simple, quantitative measures of segregation in the spatial distribution of objects with respect to their various properties (marks)., Comment: 10 pages, 7 figures, A&A accepted 05/03/02

We apply standard disk formation theory with adiabatic contraction within cuspy halo models predicted by the standard LCDM cosmology. The resulting models score remarkably well when confronted with the broad range of observational data available for the Milky Way and M31 galaxies, giving a Milky Way virial mass of 1-2x10^12Msun and concentration C=12-17. We consider two types of models, in which: (A) baryons conserve angular momentum and (B) some of the angular momentum of the baryons is transferred to the dark matter. Type-A models produce good agreement with observed rotation curves and obey constraints in the solar neighborhood, but may have too much dark matter in the center to allow a fast rotating bar. The type-B models with angular momentum transport have a slightly more massive disk and less dark matter in the central part, allowing a fast rotating bar to persist. Both classes of models probably have sufficient baryonic mass in the central 3.5kpc to reproduce recent observational values of the optical depth to microlensing events towards the Galactic center. All models require that about 1/2 of all baryons expected inside the virial radius must not be in the disk or bulge. We investigate whether the range of virial masses allowed by our dynamical models is compatible with constraints from the galaxy luminosity function, and find a range of parameter space that is allowed by this constraint. We conclude that rotation curves and dynamical properties of ``normal'' high surface brightness spiral galaxies appear to be consistent with standard LCDM., Comment: 26 pages, 11 figures, submited to ApJ

We present results of gasdynamics+N-body constrained cosmological simulations of the Local Supercluster region (LSC; about 30/h Mpc around the Virgo cluster), which closely mimic the real Universe within 100 Mpc by imposing constraints from Mark III catalog of galaxy peculiar velocities. The simulations are used to study the properties and possible observational signatures of intergalactic medium in the LSC region. We find that, in agreement with previous unconstrained simulations, about 30% of the gas in this region is in the warm/hot phase at T~10^5-10^7 K, and about 40% in the diffuse phase at T<10^5 K in low-density regions. The best prospects for detection of the warm/hot intergalactic medium of the LSC located in filaments and in the vicinity of virialized regions of groups and clusters are through absorption in resonant lines of OVII and OVIII in soft X-rays and in the OVI doublet in UV. If intergalactic gas in filaments (rho/~ 1-10) is enriched to typical metallicities of >0.05, the column densities of OVI, OVII, and OVIII along a random line of sight near the North Galactic Pole, especially near the supergalactic plane, have a significant probability to be in the range detectable by the current (FUSE,XMM) and future (Constellation-X) instruments. (Abridged), Comment: submitted to ApJ, 18 pages, 7 figures, LaTeX (AASTeX), high-resolution figures are available at ftp://charon.nmsu.edu/pub/kravtsov/LSC2/

We present cosmological simulations which closely mimic the real Universe within 100Mpc of the Local Group. The simulations, called Constrained Simulations, reproduce the large-scale density field with major nearby structures, including the Local Group, the Coma and Virgo clusters, the Great Attractor, the Perseus-Pices, and the Local Supercluster, in approximately correct locations. The MARK III survey of peculiar velocities of the observed structures inside 80Mpc/h sphere is used to constrain the initial conditions. Fourier modes on scales larger then 5Mpc/h are dominated by the constraints, while small scale waves are random. The main aim of this paper is the structure of the Local Supercluster (LSC; 30Mpc/h around the Virgo cluster) and the Local Group environment. We find that at the current epoch most of the mass (7.5e14Msun/h) of the LSC is located in a filament roughly centered on the Virgo cluster and extending over 40Mpc/h. The simulated Local Group (LG) is located in an adjacent smaller filament, which is not a part of the main body of the LSC, and has a peculiar velocity of 250kms toward the Virgo cluster. The peculiar velocity field in the LSC region is complicated and is drastically different from the field assumed in the Virgocentric infall models. The peculiar velocity flow in the vicinity of the LG in the simulation is ``cold'': the peculiar line-of-sight velocity dispersion within 7Mpc/h of the LG is less than 60km/s, comparable to the observed velocity dispersion of nearby galaxies., Comment: 22 pages, 9 figures, submitted to ApJ, high resolution version is available at http://astro.nmsu.edu/~aklypin/HOFFMAN

[Abridged] We study the angular-momentum profiles of a statistical sample of halos drawn from a high-resolution N-body simulation of the LCDM cosmology. We find that the cumulative mass distribution of specific angular momentum, j, in a halo of mass Mv is well fit by a universal function, M(

[Abridged] The interaction rates of dark-matter halos and subhalos, are computed using high-resolution cosmological N-body simulations of the Lambda-CDM model. Although the number fraction of subhalos of mass $>2x10^{11}\hsolmass$ is only ~10%, we find that the interaction rate of such subhalos is relatively high because they reside in high density environments. At low redshift, the subhalo collisions dominate the total collision rate, and even at z=3 they are involved in more than 30% of all collisions. About 40% of the "major" mergers are between subhalos. Therefore subhalo interactions must be incorporated in models of structure formation. We find that the collision rate between halos in physical density units, is $\propto (1+z)^\delta $, with $\delta = 3-4$, in agreement with earlier simulations and most observational data. We test previous analytic estimates of the interaction rates of subhalos based on statistical models, which could be very inaccurate because of the small number of subhalos and the variation of conditions within small host halos. We find that, while such statistical estimates may severely overestimate the rate within hosts $< 10^{13} \hsolmass$, typical of high redshifts, they are valid for larger hosts regardless of the number of subhalos in them. We find the Makino & Hut (1997) estimate of the subhalo merger rate to be valid for hosts $ > 6x10^{11}\hsolmass$ at all redshifts. The collision rate between subhalos and the central object of their host halo is approximated relatively well using the timescale for dynamical friction in circular orbits. This approximation fails in ~40% of the cases, partly because of deviations from the assumption of circular orbits and partly because of the invalidity of the assumption that the subhalo mass is negligible., Comment: 18 pages, submitted to MNRAS

[Abridged] We analyze the exchange of dark matter between halos, subhalos, and their environments in a high-resolution cosmological N-body simulation of a Lambda CDM cosmology. At each analyzed redshift z we divide the dark matter particles into 4 components: (i) isolated galactic halos, (ii) subhalos, (iii) the diffuse medium of group and cluster halos, and (iv) the background outside of virialized halos. We follow the time evolution of the mass distribution and flows between these components and provide fitting functions for the exchange rates. We use our derived exchange rates to gauge the importance of metal redistribution in the universe due solely to gravity-induced interactions. The diffuse metallicity in clusters is predicted to be ~40% that in isolated galaxies (~55% of groups) at z=0, and should be lower only slightly by z=1, consistent with observations. The metallicity of the diffuse media in poor groups is expected to be lower by a factor of 5 by z~2, in agreement with the observed metallicity of damped Ly$\alpha$ systems. The metallicity of the background IGM is predicted to be (1-3)x10^{-4} that of z=0 clusters, also consistent with observations. The agreement of predicted and observed trends indicates that gravitational interaction alone may play an important role in metal enrichment of the intra-cluster and intergalactic media., Comment: 12 pages, submitted to MNRAS

We study the effects of mass and force resolution on the density profiles of galaxy-size Cold Dark Matter (CDM) halos in a flat, low-density cosmological model with vacuum energy. We show thatalthough increasing the mass and force resolution allows us to probe deeper into the inner halo regions, it does not lead to steeper inner density profiles. Instead, the halo profiles converge at scales larger than four times the formal resolution or the radius containing more than 200 particles, whichever is larger. In the simulations presented in this paper, we are able to probe density profile of a relaxed isolated galaxy-size halo at scales r=(0.005-1)r_vir. We find that the density distribution can be well approximated by the profile suggested by Moore etal (1998): rho= x^{-1.5}(1+x^{1.5})^-1, where x=r/r_s and r_s is the characteristic radius. The analytical profile proposed by Navarro et al. (1996) rho= x^{-1}(1+x)^-2, also provides a good fit, with the same relative errors of about 10% for radii larger than 1% of the virial radius. Both analytical profiles fit equally well because for high-concentration galaxy-size halos the differences between these profiles become significant only at scales well below 0.01r_vir. We also find that halos of similar mass may have somewhat different parameters (characteristic radius, maximum rotation velocity, etc.) and shapes of their density profiles. We associate this scatter in properties with differences in halo merger histories and the amount of substructure present in the analyzed halos., Comment: substantially revised, accepted to ApJ, 19 pages, 9 figures, uses aastex and natbib

We give a summary of recent results on spatial and velocity biases in cosmological models. Progress in numerical techniques made it possible to simulate halos in large volumes with a such accuracy that halos survive in dense environments of groups and clusters of galaxies. Halos in simulations look like real galaxies, and, thus, can be used to study the biases -- differences between galaxies and the dark matter. The biases depend on scale, redshift, and circular velocities of selected halos. Two processes seem to define the evolution of the spatial bias: (1) statistical bias and (2) merger bias (merging of galaxies, which happens preferentially in groups, reduces the number of galaxies, but does not affect the clustering of the dark matter). There are two kinds of velocity bias. The pair-wise velocity bias is b_12=0.6-0.8 at r< 5Mpc/h, z=0. This bias mostly reflects the spatial bias and provides almost no information on the relative velocities of the galaxies and the dark matter. One-point velocity bias is a better measure of the velocities. Inside clusters the galaxies should move slightly faster (b_v =1.1-1.3) than the dark matter. Qualitatively this result can be understood using the Jeans equations of the stellar dynamics. For the standard LCDM model we find that the correlation function and the power spectrum of galaxy-size halos at z=0 are antibiased on scales r<5Mpc/h and k=(0.15-30)h/Mpc., Comment: Lecture at the Summer School "Relativistic Cosmology: Theory and Observations", Italy, Como, May 2000. AASTeX and natbib

Properties of dark matter halos are reviewed. Taken from different publications, we present results on (1) the mass and velocity functions, (2) density and velocity profiles, and (3) concentration of halos. In the range of radii r=(0.005-1)rvir the density profile for a quiet isolated halo is very accurately approximated by a fit suggested by Moore etal (1997): rho=1/x^1.5(1+x^1.5), where x=r/rs and rs is a characteristic radius. The fit suggested by Navarro et al (1995) rho= 1/x(1+x)^2, also gives a very satisfactory approximation with relative errors of about 10% for radii not smaller than 1% of the virial radius. The mass function of z=0 halos with mass below 10^{13}Msun/h is approximated by a power law with slope alpha =-1.85. The slope increases with the redshift. The velocity function of halos with Vmax< 500km/s is also a power law with the slope beta= -3.8-4. The power-law extends to halos at least down to 10km/s. It is also valid for halos inside larger virialized halos. The concentration of halos depends on mass (more massive halos are less concentrated) and environment, with isolated halos being less concentrated than halos of the same mass inside clusters. Halos have intrinsic scatter of concentration: at 1sigma level halos with the same mass have Delta(log{c_vir})=0.18 or, equivalently, DeltaVmax/Vmax =0.12. Velocity anisotropy for both subhalos and the dark matter is approximated by beta(r) =0.15+2x/[x^2+4], where x is radius in units of the virial radius., Comment: Lecture at the Summer School "Relativistic Cosmology: Theory and Observations", Italy, Como, May 2000. AASTeX and natbib

This lecture gives a short introduction to different methods used in cosmology. The focus is on major features of N-body simulations: equations, main numerical techniques, effects of resolution, and methods of halo identification., Comment: Lecture at the Summer School "Relativistic Cosmology: Theory and Observations", Italy, Como, May 2000. AASTeX and natbib

We study the distribution functions of mass and circular velocity for dark matter halos in N-body simulations of the $\Lambda$CDM cosmology, addressing redshift and environmental dependence. The dynamical range enables us to resolve subhalos and distinguish them from "distinct" halos. The mass function is compared to analytic models, and is used to derive the more observationally relevant circular velocity function. The distribution functions in the velocity range 100--500 km/s are well fit by a power-law with two parameters, slope and amplitude. We present the parameter dependence on redshift and provide useful fitting formulae. The amplitudes of the mass functions decrease with z, but, contrary to naive expectation, the comoving density of halos of a fixed velocity ~200 km/s actually increases out to z=5. This is because high-z halos are denser, so a fixed velocity corresponds to a smaller mass. The slope of the velocity function at z=0 is as steep as ~ -4, and the mass and velocity functions of distinct halos steepen with increasing z, while the functions of subhalos do not steepen with $z$, and become even flatter at z>2. A simple observable prediction is that the slope of the velocity function of isolated galaxies is steeper than that of galaxies in groups by as much as unity, reflecting the density biasing of high-velocity halos. We confirm that the Press-Schechter approximation typically overestimates the halo mass function by a factor of ~2, while modified approximations provide improved predictions., Comment: 26 pages, 9 figures. submitted to MNRAS

We have simulated the evolution of a large sample of X-ray clusters in a Lambda-CDM universe at high spatial resolution using adaptive mesh refinement and placed the results in an online archive for public access. The Simulated Cluster Archive website http://sca.ncsa.uiuc.edu provides tools for interactive 2D and 3D analysis of gas and dark matter fields, X-ray and SZ imaging, and data export. We encourage community use and solicit their feedback., Comment: 2 pages, 0 figures. Poster paper presented at "Large-Scale Structure in the X-Ray Universe", Santorini, Greece 20-22 September 1999. Eds. M. Plionis & I. Georgantopoulos, (Atlantisciences, Athens). Visit the Simulated Cluster Archive at http://sca.ncsa.uiuc.edu

According to the hierarchical scenario, galaxies form via merging and accretion of small objects. Using N-body simulations, we study the frequency of merging events in the history of the halos. We find that at z<~2 the merging rate of the overall halo population can be described by a simple power law (1+z)^3. The main emphasis of the paper is on the effects of environment of halos at the present epoch (z=0). We find that the halos located inside clusters have formed earlier (dz \approx 1) than isolated halos of the same mass. At low redshifts (z<1), the merger rate of cluster halos is 3 times lower than that of isolated halos and 2 times lower than merger rate of halos that end up in groups by z=0. At higher redshifts (z~1-4), progenitors of cluster and group halos have 3--5 times higher merger rates than isolated halos. We briefly discuss implications of our results for galaxy evolution in different environments., Comment: submitted to the Astrophys. Journal; 11 pages, 9 figs., LaTeX (uses emulateapj.sty)

We present a study of numerical effects in dissipationless cosmological simulations. The numerical effects are evaluated and studied by comparing results of a series of 64^3-particle simulations of varying force resolution and number of time steps, performed using three different N-body techniques: the Particle Mesh (PM), the adaptive P3M (AP3M) code, and the Adaptive Refinement Tree (ART) code. This study can therefore be interesting both as an analysis of numerical effects and as a systematic comparison of different codes. We find that the AP3M and the ART codes produce similar results, given that convergence is reached within the code type. We also find that numerical effects may affect the high-resolution simulations in ways that have not been discussed before. In particular, our study revealed the presence of two-body scattering, effects of which can be greatly amplified by inaccuracies of time integration. This process appears to affect the correlation function of matter, mass function and inner density of dark matter halos and other statistics at scales much larger than the force resolution, although different statistics may be affected in different fashion. We discuss the conditions at which strong two-body scattering is possible and discuss the choice of the force resolution and integration time step. Furthermore, we discuss recent claims that simulations with force softening smaller than the mean interparticle separation are not trustworthy and argue that this claim is incorrect in general and applies only to the phase-sensitive statistics. Our conclusion is that, depending on the choice of mass and force resolution and integration time step, a force resolution as small as 0.01 of the mean interparticle separation can be justified., Comment: submitted to MNRAS, LaTeX (uses mn.sty), 19 pages, 15 figs, high-res figures can be found at http://www-thphys.physics.ox.ac.uk/users/AlexanderKnebe/publications.html

We give a summary of our recent studies of spatial and velocity biases of galaxy-size halos in cosmological models. Recent progress in numerical techniques made it possible to simulate halos in large volumes with a such accuracy that halos survive in dense environments of groups and clusters of galaxies. Dark matter halos in simulations look like real galaxies, and, thus, can be used to study the biases - differences between galaxies and the dark matter. For the standard LCDM model we find that the correlation function and the power spectrum of galaxy-size halos at z=0 are antibiased on scales r<5Mpc/h and k=(0.15-30)h/Mpc. The biases depend on scale, redshift, and circular velocities of selected halos. Two processes seem to define the evolution of the spatial bias: (1) statistical bias (or peak bias) and merger bias (merging of galaxies, which happens preferentially in groups, reduces the number of galaxies, but does not affect the clustering of the dark matter). There are two kinds of velocity bias. The pair-wise velocity bias is b_12=0.6-0.8 at r<5Mpc/h, z=0. This bias mostly reflects the spatial bias and provides almost no information on the relative velocities of the galaxies and the dark matter. One-point velocity bias is a better measure of the velocities. Inside clusters the galaxies should move slightly faster (b_v=1.1-1.3) than the dark matter. Qualitatively this result can be understood using the Jeans equations of the stellar dynamics., Comment: 8 pages, 6 figures, Proceedings of "Cosmic Flows", Victoria, UVic, July 1999, paspconf and epsf

We discuss the impact of the cosmological environment on the evolution of dark matter halos using a high-resolution simulation within a spatially flat LCDM cosmology., Comment: 4 pages, 1 figure, contribution to the Morphology Conference in Johannesburg, September 1999

We study dark-matter halo density profiles in a high-resolution N-body simulation of an LCDM cosmology. Our statistical sample contains ~5000 haloes in the range 10^{11}-10^{14} M_sun. The profiles are parameterized by an NFW form with two parameters, an inner radius r_s and a virial radius r_v, and we define the halo concentration c_v = r_v/r_s. First, we find that, for a given halo mass, the redshift dependence of the median concentration is c_v ~ 1/(1+z), corresponding to a roughly constant r_s with redshift. We present an improved analytic treatment of halo formation that fits the measured relations between halo parameters and their redshift dependence. 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 log(c_v) is ~0.18, corresponding to a scatter in maximum rotation velocities of dV/V ~ 0.12. We discuss implications for modelling the Tully-Fisher relation, which has a smaller reported intrinsic scatter. Third, haloes in dense environments tend to be more concentrated than isolated haloes. These results suggest that c_v 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., Comment: Version accepted by MNRAS, includes additional resolution tests, 18 pages, 13 figures Toy model code made available: http://www.astronomy.ohio-state.edu/~james/CVIR/parts.html

We use N-body simulations to study the velocity bias of dark matter halos, the difference in the velocity fields of dark matter and halos, in a flat low- density LCDM model. The high force, 2kpc/h, and mass, 10^9Msun/h, resolution allows dark matter halos to survive in very dense environments of groups and clusters making it possible to use halos as galaxy tracers. We find that the velocity bias pvb measured as a ratio of pairwise velocities of the halos to that of the dark matter evolves with time and depends on scale. At high redshifts (z ~5) halos move generally faster than the dark matter almost on all scales: pvb(r)~1.2, r>0.5Mpc/h. At later moments the bias decreases and gets below unity on scales less than r=5Mpc/h: pvb(r)~(0.6-0.8) at z=0. We find that the evolution of the pairwise velocity bias follows and probably is defined by the spatial antibias of the dark matter halos at small scales. One-point velocity bias b_v, defined as the ratio of the rms velocities of halos and dark matter, provides a more direct measure of the difference in velocities because it is less sensitive to the spatial bias. We analyze b_v in clusters of galaxies and find that halos are ``hotter'' than the dark matter: b_v=(1.2-1.3) for r=(0.2-0.8)r_vir, where r_vir is the virial radius. At larger radii, b_v decreases and approaches unity at r=(1-2)r_vir. We argue that dynamical friction may be responsible for this small positive velocity bias b_v>1 found in the central parts of clusters. We do not find significant difference in the velocity anisotropy of halos and the dark matter. The dark matter the velocity anisotropy can be approximated as beta(x)=0.15 +2x/(x^2+4), where x is measured in units of the virial radius., Comment: 13 pages, Latex, AASTeXv5 and natbib

We use a high-resolution dissipationless simulation to study the evolution of the dark matter and halo distributions in a spatially flat cosmological model dominated by a cosmological constant $\Lambda$ and cold dark matter ($\Lambda$CDM). In order to quantify the evolution of structure, we calculate the Minkowski functionals of the halos and the dark matter component at various redshifts. A comparison of Minkowski functionals and the more standard correlation function analysis shows that the Minkowski functionals contain information about correlation functions of arbitrary order. While little evolution of the Minkowski functionals of halos between $z=4$ and $z=0$ is observed, we find that the Minkowski functionals of the dark matter evolve rapidly with time. The difference of the Minkowski functionals of halos and dark matter can be interpreted as a scale dependent bias. This implies that scale-dependent bias is a property of not only the two-point halo correlation function, but also of correlation functions of higher order., Comment: 10 pages including 6 figures. Accepted for publication in Monthly Notices

Lyman break galaxies (LBGs) at $z \sim 3$ exhibit number densities and clustering similar to local $L_*$ galaxies; however, their star formation rates (SFRs) are much higher. We explore the scenario in which LBGs are starburst galaxies triggered by collisions, and thus provide an explanation for these key properties. The relative paucity of starburst galaxies at low redshift can be attributed to a much higher collision rate in the past. We use high-resolution cosmological $N$-body simulations and a hierarchical halo finder to estimate the galaxy collision rate as a function of time in the popular $\Lambda$CDM cosmological model. We find that bright collisional starbursts are frequent enough to account for most of the high-$z$ ($2.5-4.5$) LBGs. Moreover, many of the objects are of relatively small mass, but they cluster about large-mass halos. They therefore exhibit strong clustering, similar to that observed and stronger than that of the relevant massive halos., Comment: 7 pages, three figures (one jpg), submitted to the Astrophysical Journal Letters

Using published data, we have compiled the circular velocity (Vc) distribution function (VDF) of galaxy satellites in the Local Group. We find that within the volumes of radius of 570 kpc (400/h kpc for h=0.7) centered on the Milky Way and Andromeda, the average VDF is roughly approximated as n(>Vc)~ 45(Vc/10 km/s)^{-1} h^3 Mpc^{-3} for Vc in the range ~10-70 km/s. The observed VDF is compared with results of high-resolution cosmological simulations. We find that the VDF in models is very different from the observed one: n(>Vc)~1200(Vc/10 km/s)^{-2.75}h^3 Mpc^{-3}. Cosmological models thus predict that a halo of the size of our Galaxy should have about 50 dark matter satellites with circular velocity >20 km/s and mass >3x10^8/h Msun within a 570 kpc radius. This number is significantly higher than the approximate dozen satellites actually observed around our Galaxy. The observed and predicted VDFs cross at ~50 km/s, indicating that the predicted abundance of satellites with Vc> 50 km/s 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 identification 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 due either to the expulsion of gas in the supernovae-driven winds or to gas heating by the intergalactic ionizing background. (Abridged), Comment: missing Table 3 added; submitted to the Astrophys.Journal; 10 pages, 5 Figures, LaTeX (uses emulateapj.sty)

We present results from a study of bias and its evolution for galaxy-size halos in a large, high-resolution simulation of a LCDM model. We consider the evolution of bias estimated using two-point correlation function (b_xi), power spectrum (b_P), and a direct correlation of smoothed halo and matter overdensity fields (b_d). We present accurate estimates of the evolution of the matter power spectrum probed deep into the stable clustering regime (k~[0.1-200]h/Mpc at z=0). The halo power spectrum evolves much slower than the power spectrum of matter and has a different shape which indicates that the bias is time- and scale-dependent. At z=0, the halo power spectrum is anti-biased with respect to the matter power spectrum at wavenumbers k~[0.15-30]h/Mpc, and provides an excellent match to the power spectrum of the APM galaxies at all probed k. In particular, it nicely matches the inflection observed in the APM power spectrum at k~0.15h/Mpc. We complement the power spectrum analysis with a direct estimate of bias using smoothed halo and matter overdensity fields and show that the evolution observed in the simulation in linear and mildly non-linear regimes can be well described by the analytical model of Mo & White (1996), if the distinction between formation redshift of halos and observation epoch is introduced into the model. We present arguments and evidence that at higher overdensities, the evolution of bias is significantly affected by dynamical friction and tidal stripping operating on the satellite halos in high-density regions of clusters and groups; we attribute the strong anti-bias observed in the halo correlation function and power spectrum to these effects. (Abridged), Comment: submitted to the Astrophys.Journal; 19 pages, 9 figures LaTeX (uses emulateapj.sty)

A significant fraction of mass in the universe is believed to be in the form of dark matter (DM). Due to gravitational instability, the DM collapses hierarchically into DM halos. In this contribution we present a study of the formation and evolution of such DM halos in a COBE-normalized spatially flat LCDM model (Omega_0=1-Omega_L=0.3; h=0.7) using high-resolution N-body simulations. The novelty of this study is use of the newly developed halo-finding algorithms to study the evolution of both isolated and satellite (located inside virial radii of larger group- and cluster-size systems) halos. The force and mass resolution required for a simulated halo to survive in the high-density environments typical of groups and clusters is high: ~1-3 kpc and \~10^9 M_sun, respectively. We use the high-resolution Adaptive Refinement Tree (ART) N-body code to follow the evolution of 256^3 dark matter particles with dynamic range in spatial resolution of 32,000 in a box of 60/h Mpc. We show that the correlation function of these halos is anti-biased with respect to the dark matter correlation function and is high and steeper than the correlation function of the isolated virialized objects. The correlation function evolves only mildly between z=3 and z=1. The mass evolution of isolated virialized objects determined from the simulation is in good agreement with prediction of semi-analytical models. The differences exist, however, if we include satellite halos in the halo catalogs., Comment: Contributions to the Proceedings of the MPA/ESO Conference "Evolution of LSS: from Recombination to Garching", Garching, August 2-7, 1998. LaTeX (uses tp.sty, psfig.sty), 5 pages, 5 figs

We study the evolution of the halo-halo correlation function and bias in a LCDM model using very high-resolution N-body simulations. The high force and mass resolution allows dark matter (DM) halos to survive in the tidal fields in high-density regions and thus prevents the ambiguities related with the ``overmerging problem.'' Numbers of galaxy-size halos in cluster-like objects in our simulation are similar to the numbers of galaxies observed in real clusters. This allows us to estimate for the first time the evolution of the correlation function and bias at small (down to ~100/h kpc) scales. We compare particle distribution, dark matter correlation function, density profiles, and halo mass function produced with our N-body code and corresponding results of the AP3M simulations. We find that at all epochs the 2-point correlation function of galaxy-size halos xihh is well approximated by a power-law with slope ~1.6-1.8. The difference between the shape of xihh and the shape of the correlation function of matter results in the scale-dependent bias at scales <7/h Mpc, which we find to be a generic prediction of the hierarchical models, independent of the epoch and of the model details. We find that our results agree well with existing clustering data at different redshifts, indicating the general success of the picture of structure formation in which galaxies form inside the host DM halos. Particularly, we find an excellent agreement in both slope and the amplitude between xihh(z=0) in our simulation and the galaxy correlation function measured using the APM galaxy survey. At high redshifts, the observed clustering of the Lyman-break galaxies is also reasonably well reproduced by the models., Comment: Contributions to the Proceedings of the MPA/ESO Conference "Evolution of LSS: from Recombination to Garching", Garching, August 2-7, 1998. LaTeX (uses tp.sty, psfig.sty), 5 pages, 4 figs. Full-resolution version of Fig.2 is available at ftp://charon.nmsu.edu/pub/kravtsov/PAPERS/Garching98/

We study the evolution of the halo-halo correlation function and bias in four cosmological models (LCDM, OCDM, tauCDM, and SCDM) using very high-resolution N-body simulations. The high force and mass resolution allows dark matter (DM) halos to survive in the tidal fields of high-density regions and thus prevents the ambiguities related with the ``overmerging problem.'' This allows us to estimate for the first time the evolution of the correlation function and bias at small (down to ~100/h kpc) scales. We find that at all epochs the 2-point correlation function of galaxy-size halos xi_hh is well approximated by a power-law with slope ~1.6-1.8. The difference between the shape of xi_hh and the shape of the correlation function of matter results in the scale-dependent bias at scales <7/h Mpc, which we find to be a generic prediction of the hierarchical models. The bias evolves rapidly from a high value of ~2-5 at z~3-7 to the anti-bias of b~0.5-1 at small <5/h Mpc scales at z=0. We find that our results agree well with existing clustering data at different redshifts. Particularly, we find an excellent agreement in both slope and the amplitude between xi_hh(z=0) in our LCDM simulation and the galaxy correlation function measured using the APM galaxy survey. At high redshifts, the observed clustering of the Lyman-break galaxies is also well reproduced by the models. The agreement with the data at high and low z indicates the general success of the hierarchical models of structure formation in which galaxies form inside the host DM halos. (Abridged), Comment: submitted to the Astrophys.Journal; 21 pages, LaTeX (uses emulateapj.sty); full resolution versions of figs.1 and 2 are available at http://astro.nmsu.edu/~akravtso/GROUP/group_publications.html or at ftp://charon.nmsu.edu/pub/kravtsov/PAPERS/Bias/

Formation of luminous matter in the Universe is a complicated process, which includes many processes and components. It is the vastly different scales involved in the process (from star formation on few parsec scales to galaxy clusters and superclusters on megaparsecs scales) and numerous ill-understood processes, which make the whole field a maze of unsolved, but exciting problems. We present new approximations for numerical treatment of multiphase ISM forming stars. The approximations were tested and calibrated using N-body+fluid numerical simulations. We specifically target issues related with effects of unresolved lumpinesses of the gas. We show that the degree of freedom is much smaller than naively expected because of self-regulating nature of the process of global star formation. One of the problems of numerical simulations is related with the uncertainties of approximation of the supernovae (SN) feedback. It is often assumed that the feedback is mainly due to momentum transferred by SN in to the ISM. We argue that this may not be true. We present a realistic example of gas actively forming stars with short cooling time for which the SF feedback is important, but the kinetic energy of the gas motion due to SN is negligibly small as compared with the thermal energy of gas., Comment: 5 pages, 2 PS figures, uses epsf.sty. Talk presented at the 12-th Postdam Cosmology Workshop, ``Large Scale Structure: Tracks and Traces'', World Scientific 1998. Available at http://astro.nmsu.edu/~aklypin/index.html

Particle-Mesh (PM) codes are still very useful tools for testing predictions of cosmological models in cases when extra high resolution is not very important. We release for public use a cosmological PM N-body code. We provide a complete package of routines needed to set initial conditions, to run the code, and to analyze the results. The package allows you to simulate models with numerous combinations of parameters: open/flat/closed background, with or without the cosmological constant, different values of the Hubble constant, with or without hot neutrinos, tilted or non-tilted initial spectra, different amount of baryons. Routines are included to measure the power spectrum and the density distribution function in your simulations, and a bound-density-maxima code for halo finding. We also provide results of test runs. A simulation with 256^3 mesh and 128^3 particles can be done in a couple of days on a typical workstation (70Mb of RAM are needed). To run simulations with 800^3 mesh and 256^3 particles one needs a computer with 1Gb memory and 1Gb disk space. The code has been successfully tested on an HP workstation and on a Sun workstation running Solaris. Most of the files (not tests) can be obtained from ftp://astro.nmsu.edu/pub/aklypin/PMCODE The package can be downloaded from http://astro.nmsu.edu/~aklypin/PM/pmcode/index.html We provide this tool as a service to the astronomical community, but we cannot guarantee results or publications., Comment: 18 pages, 3 Postscript figures, uses epsf.sty

We present two matched sets of five simulations each, covering five presently favored simple modifications to the standard cold dark matter (CDM) scenario. One simulation suite, with a linear box size of 75 Mpc/h, is designed for high resolution and good statistics on the group/poor cluster scale, and the other, with a box size of 300 Mpc/h, is designed for good rich cluster statistics. All runs had 57 million cold particles, and models with massive neutrinos had an additional 113 million hot particles. We consider separately models with massive neutrinos, tilt, curvature, and a nonzero cosmological constant in addition to the standard CDM model. We find that our tilted Omega+Omega_Lambda=1 (TLCDM) model produces too much small-scale power by a factor of ~3, and our open Lambda=0 (OCDM) model also exceeds observed small-scale power by a factor of 2. In addition, we take advantage of the large dynamic range in detectable halo masses our simulations allow to check the shape of the Press-Schechter approximation. We find good fits at cluster masses for delta_c=1.27--1.35 for a Gaussian filter and delta_c=1.57--1.73 for a tophat filter. However, Press-Schechter overpredicts the number density of halos compared to the simulations in the high resolution suite by a weakly cosmology-dependent factor of 1.5--2 at galaxy and group masses, which cannot be fixed by adjusting delta_c within reasonable bounds. An appendix generalizes the spherical collapse model to any isotropic cosmology., Comment: 18 pages Latex using Monthly Notices style, with 13 inlined EPS figures. This version matches the one accepted by MNRAS. The appendix has been removed and may now be found instead at http://fozzie.gsfc.nasa.gov/thesis/appendixC.ps.gz

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 10^8-10^9 Msun, respectively. We use the high-resolution Adaptive Refinement Tree (ART) N-body code to run cosmological simulations with the particle mass of \approx 2x10^8/h Msun} and the spatial resolution of \approx 1-2/h 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 the 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, that can be compared with those of observed galaxies. (Abridged), Comment: Accepted for publication in ApJ, substantional revisions after the first version, LaTeX 23 pages, 18 figs. (uses emulateapj.sty), Full-resolution version of Fig.9 is available upon request

We use the rotation curves of a sample of dark matter dominated dwarf and low-surface brightness (LSB) late-type galaxies to study their radial mass distributions. We find that the shape of the rotation curves is remarkably similar for all (both dwarf and LSB) galaxies in the sample, suggesting a self-similar density distribution of their dark matter (DM) halos. This shape can be reproduced well by a density profile with a shallow central cusp (rho(r)\propto 1/r^gamma, gamma\approx 0.2-0.4), corresponding to a steeply rising velocity curve (v(r)\propto r^g, g\approx 0.9-0.8). We further show that the observed shape of the rotation curves is well matched by the density profiles of DM halos formed in very high resolution simulations of the CDM, LCDM, and CHDM models of structure formation. This is surprising in light of several previous studies which suggested that the structure of simulated DM halos is inconsistent with the dynamics of dwarf galaxies. We discuss possible explanations for this discrepancy. We show that although the mass distribution in the hierarchically formed halos is on average consistent with the shape of rotation curves of dark matter dominated galaxies, the scatter of the individual profiles around the average is substantial and should not be neglected in comparisons with the data. Finally, we show that the DM halos in our hierarchical simulations and the real galaxies in our sample exhibit a similar decrease in their characteristic densities with increasing characteristic radial scales, and increase in their maximum rotation velocities with increasing radii at which their maximum velocity occurs. (Abridged), Comment: to appear in July 20, 1998 issue of ApJ; revised to match the published version; LaTeX (uses emulateapj.sty); available at http://astro.nmsu.edu/~akravtso/GROUP/group_publications.html or at ftp://charon.nmsu.edu/pub/kravtsov/PAPERS/RC

Reconstruction of the linear power spectrum from observational data provides a way to compare cosmological models to a large amount of data, as Peacock & Dodds (1994, 1996) have shown. By applying the appropriate corrections to the observational power spectrum it is possible to recover the underlying linear power spectrum for any cosmological model. Using extensive N-body simulations we demonstrate that the method is applicable to a wide range of cosmological models. However, we find that the recovery of the linear power spectrum from observations following PD94 is misleading because the corrections are model- dependent. When we apply the proper corrections for a given model to the observational power spectrum, we find that no model in our test group recovers the linear power spectrum well for the bias suggested by PD94 between Abell, Radio, Optical, and IRAS catalogs 4.5:1.9:1.3:1, with b_IRAS=1. When we allow b_IRAS to vary we find that: (i)CHDM models give very good fits to observations if optically-selected galaxies are slightly biased b_Opt=1.1 (ii) Most LCDM models give worse but acceptable fits if blue galaxies are considerably antibiased: 0.6

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 is properly adjusted to the evolving particle distribution. The algorithm is fast and effectively parallel. 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_8=0.63) and LCDM (Omega_Lambda=1-Omega_0=0.7, h=0.7, sigma_8=1.0) models. We find that halo density profiles in both CDM and LCDM models are well fitted by the analytical model presented recently by Navarro et al., which predicts a singular [$\rho(r)\propto r^{-1}$] behavior of the halo density profiles at small radii. We therefore conclude that halos formed in the $\Lambda$CDM model have structure similar to CDM halos and thus cannot explain the dynamics of the central parts of dwarf spiral galaxies, as inferred from the galaxies' rotation curves., Comment: revised in accord with published version, LaTeX (uses aaspp4.sty), 42 pages, 12 figures, all PostScript figures are available at http://astro.nmsu.edu/~akravtso/GROUP/group_publications.html or at ftp://charon.nmsu.edu/pub/kravtsov/PAPERS/ART

A new class of geometric statistics for analyzing galaxy catalogs is presented. Filament statistics quantify filamentarity and planarity in large scale structure in a manner consistent with catalog visualizations. These statistics are based on sequences of spatial links which follow local high-density structures. From these link sequences we compute the discrete curvature, planarity, and torsion. Filament statistics are applied to CDM and CHDM ($\Omega_\nu = 0.3$) simulations of Klypin \etal (1996), the CfA1-like mock redshift catalogs of Nolthenius, Klypin and Primack (1994, 1996), and the CfA1 catalog. We also apply the moment-based shape statistics developed by Babul \& Starkman (1992), Luo \& Vishniac (1995), and Robinson \& Albrecht (1996) to these same catalogs, and compare their robustness and discriminatory power versus filament statistics. For 100 Mpc periodic simulation boxes ($H_0 = 50$ km s$^{-1}$ Mpc$^{-1}$), we find discrimination of $\sim 4\sigma$ (where $\sigma$ represents resampling errors) between CHDM and CDM for selected filament statistics and shape statistics, including variations in the galaxy identification scheme. Comparing the CfA1 data versus the models does not yield a conclusively favored model; no model is excluded at more than a $\sim 2\sigma$ level for any statistic, not including cosmic variance which could further degrade the discriminatory power. We find that CfA1 discriminates between models poorly mainly due to its sparseness and small number of galaxies, not due to redshift distortion, magnitude limiting, or geometrical effects. We anticipate that the proliferation of large redshift surveys and simulations will enable the statistics presented here to provide robust discrimination between large-scale structure in various cosmological models., Comment: 17 pages, 12 figures, LaTex (uses mn.sty). Accepted by MNRAS

Here we discuss what are perhaps the two most popular variants of CDM that might agree with the data: \lcdm\ and CHDM. While the predictions of COBE-normalized \lcdm\ and CHDM both agree well with the available data on scales of $\sim 10$ to $100 \hMpc$, each has potential virtues and defects. \lcdm\ with $\Omega_0 \sim 0.3$ has the possible virtue of allowing a higher expansion rate $H_0$ for a given cosmic age $t_0$, but the defect of predicting too much fluctuation power on small scales. CHDM has less power on small scales, so its predictions appear to be in good agreement with data on the galaxy distribution, but it remains to be seen whether it predicts early enough galaxy formation to be compatible with the latest high-redshift data. Also, two very recent observational results favor high cosmic density, and thus favor $\Omega=1$ models such as CHDM over \lcdm\ --- (1) the positive deceleration parameter $q_0>0$ measured using high-redshift Type Ia supernovae, and (2) the low primordial deuterium/hydrogen ratio measured in two different quasar absorption spectra. We try to identify ``best'' variants of both \lcdm\ and CHDM, and discuss critical observational tests for both models., Comment: 9 pages, postscript only, includes 3 figures, to be published in Proceedings of the International Conference on Sources and Detection of Dark Matter in the Universe, UCLA, February 1996, D. Cline and D. Sanders, editors, Nucl. Phys. B Proc. Suppl., in press

We present the first X-ray Luminosity Function (XLF) for an optically-selected sample of 49 nearby poor clusters of galaxies and a sample of 67 Abell clusters with z < 0.15. We have extended the measured cluster XLF by more than a factor of 10 in X-ray luminosity. Our poor cluster sample was drawn from an optical catalog of groups with 0.01

Cosmological models with a positive cosmological constant and $\Omega_0<1$ have a number of attractive features. A larger Hubble constant, which can be compatible with the recent HST estimate, and a large fraction of baryon density in galaxy clusters make them current favorites. Early galaxy formation also is considered as a welcome feature of these models But early galaxy formation implies that fluctuations on few megaparsec scales spent more time in the nonlinearregime, as compared with standard Cold Dark Matter (CDM) or Cold+Hot Dark Matter models. This results in excessive clustering on small scales. We show that a typical LCDM model with $H_0=70$ km/s/Mpc, $\Omega_0=0.3$ normalized to COBE on large scales and compatible with the number-density of galaxy clusters, predicts a power spectrum of galaxy clustering in real space which is too high: {\it at least} twice larger than CfA estimates (Park \etal 1994) and 3 times larger than APM estimates (Baugh \& Efstathiou 1994) for wavenumbers $k=(0.4-1)h/{\rm Mpc}$. This conclusion holds if we assume either that galaxies trace the dark matter ($\sigma_8\approx 1.1$ for this model) or just that a region with higher density produces more galaxies than a region with lower density. The only way to reconcile the model with the observed power spectrum is to assume that regions with high dark matter density produce fewer galaxies than regions with low density. Theoretically this is possible, but it seems very unlikely: X-ray emission from groups and clusters indicates that places with a large density of dark matter produce a large number of galaxies. Since it follows that the low- $\Omega$ LCDM models are in serious trouble, we discuss which LCDM models have the best hope of surviving the confrontation with available observational data., Comment: 12 pages + 2 tables + 4 figures are available from http://charon.nmsu.edu/ftp/aklypin/LCDM

We discuss the structure of clusters in a class of flat cosmological models with the fraction of mass \Omega_{CDM} ~0.8 in cold dark matter, and the rest in hot dark matter in the form of massive neutrinos. We consider such Cold+Hot Dark Matter (CHDM) models with one, two or three massive neutrinos, with total mass ~4.6eV. Neutrinos of such low mass cannot constitute halos of galaxies and groups, but only of clusters of galaxies. The limit on the density of neutrinos in the central parts of galaxy clusters is estimated from the phase space den- sity constraints. The ratio of the neutrino density to that of CDM through the cluster is found analytically. It appears that the density of neutrinos is suppressed within the Abell radius. However, neutrinos contribute ~20% of the mass density to the cluster halo. Our numerical simulations match analytical results. The simulations indicate that the cluster halo dark matter density profile has the power-law slope ~-2.5 which is close to that in the model with cosmological constant. We also found that in the CHDM models the velocity dispersion is almost constant across the cluster. This is quite different from the model with cosmological constant or the open model where the velocity dispersion falls in the cluster outskirts. We discuss X-ray emission and weak gravitational lensing by clusters in the model. We input the found spherically symmetrical fit to the CHDM mass density profile and the X-ray surface brightness for the cluster A2256 into simple equation of hydrostatic equilibrium of the hot gas. X-ray temperature derived this way departures from both the data and actual prediction of the model, which give almost constant temperature. We found also that the problem of high baryonic fraction in clusters is not resolved in the CHDM models., Comment: 19 pages + 9 figures, self-expanding uuencoded compressed tar archive of postscript files. Complete paper is also available via anon ftp at ftp://ftp.cita.utoronto.ca/ftp/cita/pogosyan/cita-95-19/cita-95-19_full.uu

We use N-body simulations to study evolution of galaxy clusters over the redshift interval 0 <= z <= 0.5 in cosmological models with a mixture of cold and hot dark matter (CHDM). Four different techniques are utilized: the cluster-cluster correlation function, axial ratios and quadrupoles of the dark matter distribution in individual clusters, and virial properties. We find that the correlation function for clusters of the same mass limit was larger and steeper at high redshifts. The slope increases from 1.8 at z=0 to 2.1 at z=0.5. Comoving correlation length r_c scales with the mass limit M within comoving radius 1.5 h^-1 Mpc and the redshift z as r_c ~= 20(1+z)(M/M_*)^1/3, where M_* = 3*10^14 h^-1 M_sun. When the correlation length is normalized to the mean cluster separation d_c, it remains almost constant: r_c~=(0.45-0.5) d_c. For small masses (M_clust <2*10^14 h^-1 M_sun) there is an indication that r_c goes slightly above the relation with the constant of proportionality being ~= 0.55-0.6. Anisotropy of density distribution in a cluster shows no change over redshift with axial ratios remaining constant around 1.2. In other words, clusters at present are as elongated as they were at the epoch of their first appearance. While the anisotropy of clusters does not change with time, the density profile shows visible evolution: the slope of density profile changes from gamma ~= -3.5 at z=0.5 to gamma ~= -2.5 at the present. We find that the core of a cluster remains essentially the same over time, but the density of the outlying regions increases noticeably. The virial relation M ~ v^2 is a good approximation, but there is a large fraction of clusters with peculiar velocities greater than given by this relation, and clusters with the same rms velocities have smaller masses in the past, a factor of 2 at z=0.5., Comment: 16 pages, used aaspp.sty V3.0 13 figures are available from http://charon.nmsu.edu/ftp/cwalter/CHDM

A new class of geometric statistics for analyzing galaxy catalogs is presented. {\it Filament statistics} quantify filamentarity and planarity in large scale structure in a manner consistent with catalog visualizations. These statistics are based on sequences of spatial links which follow local high-density structures. From these link sequences we compute the discrete curvature, planarity, and torsion. Filament statistics are applied to CDM and CHDM ($\Omega_\nu = 0.3$) simulations of Klypin \etal (1995), the CfA1-like sky catalogs of Nolthenius, Klypin and Primack (1994, 1995), and the CfA1 catalog. For 100 Mpc periodic simulation boxes ($H_0 = 50$ km s$^{-1}$ Mpc$^{-1}$), we find robust discrimination of over 4$\sigma$ (where $\sigma$ represents resampling errors) between CHDM and CDM. The {\it reduced filament statistics} show that CfA1 data is intermediate between CHDM and CDM, but more consistent with the CHDM models. Filament statistics provide robust and discriminatory shape statistics with which to test cosmological simulations of various models against present and future redshift survey data., Comment: 29 pages total LaTex format. 6 compressed, tarred, uuencoded postscript figures. Or, PS figs available from Romeel Dav\'e at rad@lick.ucolick.org. Submitted to MNRAS

This paper presents an angular correlation analysis of the Green Bank 4.85 GHz radio catalog (Gregory \& Condon 1991) of 54,579 sources (S \gsim 25 mJy). The Green Bank catalog is found to be complete to S $\geq$ 35 mJy over 20$^{\circ} \leq \delta < 74^{\circ}$, 0$^h \leq \alpha < 24^h$, and Galactic latitude $|b| \geq 10^{\circ}$. The 2-point angular correlation function shows evidence for the clustering of radio sources, with a power-law distribution consistent with a slope $\gamma = -0.8$. This may well provide the $first$ detection of an angular correlation in a large area, complete deep radio survey., Comment: 14 pages, compressed, uuencoded postscript. Plots and text: anonymous ftp://charon.nmsu.edu/pub/PAPERS/aklypin, apj.uu and apjfigs.uu

Cold + Hot Dark Matter (CHDM) $\Omega=1$ cosmological models require a total neutrino mass $\sim 5$ eV. Because recent data support the $\nu_\mu \to \nu_\tau$ oscillation explanation of the cosmic ray $\nu_\mu$ deficit, which requires that $m(\nu_\mu) \approx m(\nu_\tau)$, this suggests that $m(\nu_\mu) \approx m(\nu_\tau) \approx 2.4$ eV. The linear calculations and N-body simulation reported here indicate that an $\Omega=1$ CHDM model with two 2.4 eV neutrinos (designated C$\nu^2$DM) agrees remarkably well with all available observations, but only if the Hubble parameter $h \approx 0.5$. We also show that even one 2.4 eV neutrino raises serious difficulties for low-$\Omega$ flat CDM models.

Damped Ly$\alpha$ systems provide possibly the most significant evidence for early structure formation, and thus a stringent constraint on the Cold + Hot Dark Matter (CHDM) cosmology. Using the numbers of halos in N-body simulations to normalize Press-Schechter (PS) estimates of the number densities of protogalaxies as a function of redshift, we find that CHDM with $\Omega_c/\Omega_\nu/\Omega_b = 0.6/0.3/0.1$ is compatible with the damped Ly$\alpha$ data only at $z<2.5$, but that it is probably incompatible with data at $z>3$. The predictions of CHDM are quite sensitive to the neutrino fraction. We find that $\Omega_c/\Omega_\nu/\Omega_b = 0.725/0.20/0.075$ is compatible with the $z>3$ data. With one massive neutrino species, this corresponds to lowering the neutrino mass from 7.0 to 4.7 eV, for $H_0=50\kmsMpc$ and $T=2.726$ K. By analysing our numerical simulations with different resolutions and box sizes as well as those of Ma \& Bertchinger (1994), we show that for the CHDM models with $\Omega_\nu$=0.2--0.3 the PS approximation should be used with Gaussian filter with $\delta_c=1.3-1.4$ if one tries to recover the total mass of a collapsed halo and to include nonlinear effects, due to waves both longer and shorter than those within the simulation box., Comment: submitted to ApJ, 31 pages including one table and 6 figures, uuencoded compressed postscript, SCIPP 94/09

We present the first self-consistently computed results on the evolution of X-ray properties of galaxy clusters in a Cold + Hot Dark Matter (CHDM) model. We have performed a hydrodynamic plus N-body simulation for the COBE-compatible CHDM model with standard mass components: Omega(hot) = 0.3, Omega(cold) = 0.6 and Omega(baryon) = 0.1 (h = 0.5). In contrast with the CDM model, which fails to reproduce the observed temperature distribution function dN/dT (Bryan et al. 1994b), the CHDM model fits the observational dN/dT quite well. Our results on X-ray luminosity are less firm but even more intriguing. We find that the resulting X-ray luminosity functions at redshifts z = 0.0, 0.2, 0.4, 0.7 are well fit by observations, where they overlap. The fact that both temperatures and luminosities provide a reasonable fit to the available observational data indicates that, unless we are missing some essential physics, there is neither room nor need for a large fraction of gas in rich clusters: 10% (or less) in baryons is sufficient to explain their X-ray properties. We also see a tight correlation between X-ray luminosity and gas temperature., Comment: 11 pages, 3 figures uuencoded postscript file, (92 kb), accepted for publication in Astrophysical Journal Letters. Also available via anonymous ftp at zeus.ncsa.uiuc.edu in gc3/publications/gc3005, LCA017

This letter presents results of new high resolution $\Omega=1$ Cold + Hot Dark Matter (CHDM) and Cold Dark Matter (CDM) simulations. Properties of groups in these simulations reflect the lower small-scale velocities and the greater tendency to form distinct filaments on both small and large scales in CHDM as compared to CDM. The fraction of galaxies in groups and the median group rms velocity are found to be powerful discriminators between models. We combine these two features into a very robust statistic, median group rms velocity $v_{\rm gr}(f_{\rm gr})$ as a function of the fraction $f_{\rm gr}$ of galaxies in groups. Using this statistic, we compare ``observed'' simulations to CfA data in redshift space in a careful and consistent way. We find that CHDM remains a promising model, with for example $v_{\rmgr}(0.45) \approx 125 \pm 25 \kms$ in agreement with the CfA data, while CDM with bias b=1.0 (COBE-compatible) or b=1.5, both giving $v_{\rm gr}(0.45) \approx 400 \pm 25 \kms$, can be virtually ruled out. Using median $M/L$, the observed value of $\Omega$ is $0.10$ (CHDM) to $0.38$ (CDM)., Comment: to appear in Ap J Letters, 12 pages including 3 figures, uuencoded compressed postscript, preprint SCIPP 93/46

We propose the zero-point of the cluster-cluster correlation function as a sensitive test for the shape of the power spectrum of initial fluctuations. It is now possible to go beyond the power law description to measure the point at which the correlation function becomes zero. Four independent measurements indicate that the zero point, $r_0$, should be in the range (40-60)$h^{-1}$Mpc. The large value of $r_0$ at which the zero-point occurs rules out conventional CDM models independently of the assumed amplitude. Models with $\Omega < 0.25$ should be rejected because they predict too large $r_0$. If the age of the Universe is assumed to be larger than 15 Gyr, models with either $\Omega<0.5$ or $h> 0.55$ are rejected. We present the results of numerical simulations of clusters in an $\Omega=1$ cosmological model with a mixture of cold plus hot dark matter (CHDM). The correlation function we determined for the simulated clusters has a zero-point, $r_0=55h^{-1}$Mpc that accurately matches the zero point of the observed function., Comment: 16 pages, tex, UNLV/93/32

We report results from high-resolution particle-mesh (PM) N-body simulations of structure formation in an $\Omega=1$ cosmological model with a mixture of Cold plus Hot Dark Matter (C+HDM) having $\Omega_{\rm cold}=0.6$, $\Omega_\nu=0.3$, and $\Omega_{\rm baryon}=0.1$. We present analytic fits to the C+HDM power spectra for both cold and hot ($\nu$) components, which provide initial conditions for our nonlinear simulations. In order to sample the neutrino velocities adequately, these simulations included six times as many neutrino particles as cold particles. Our simulation boxes were 14, 50, and 200~Mpc cubes (with $H_0=50$ km s$^{-1}$ Mpc$^{-1}$); we also did comparison simulations for Cold Dark Matter (CDM) in a 50~Mpc box. C+HDM with linear bias factor $b=1.5$ is consistent both with the COBE data and with the galaxy correlations we calculate. We find the number of halos as a function of mass and redshift in our simulations; our results for both CDM and C+HDM are well fit by a Press-Schechter model. The number density of galaxy-mass halos is smaller than for CDM, especially at redshift $z>2$, but the numbers of cluster-mass halos are comparable. We also find that on galaxy scales the neutrino velocities and flatter power spectrum in C+HDM result in galaxy pairwise velocities that are in good agreement with the data, and about 30\% smaller than in CDM with the same biasing factor. On scales of several tens of Mpc, the C+HDM streaming velocities are considerably larger than CDM. Thus C+HDM looks promising as a model of structure formation., Comment: 33pp., 16+ figures not included (available by mail), SCIPP-92/52