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We use the recently completed one billion particle Via Lactea II LambdaCDM simulation to investigate local properties like density, mean velocity, velocity dispersion, anisotropy, orientation and shape of the velocity dispersion ellipsoid, as well as structure in velocity space of dark matter haloes. We show that at the same radial distance from the halo centre, these properties can deviate by orders of magnitude from the canonical, spherically averaged values, a variation that can only be partly explained by triaxiality and the presence of subhaloes. The mass density appears smooth in the central relaxed regions but spans four orders of magnitude in the outskirts, both because of the presence of subhaloes as well as of underdense regions and holes in the matter distribution. In the inner regions the local velocity dispersion ellipsoid is aligned with the shape ellipsoid of the halo. This is not true in the outer parts where the orientation becomes more isotropic. The clumpy structure in local velocity space of the outer halo can not be well described by a smooth multivariate normal distribution. Via Lactea II also shows the presence of cold streams made visible by their high 6D phase space density. Generally, the structure of dark matter haloes shows a high degree of graininess in phase space that cannot be described by a smooth distribution function., Comment: 22 pages, 14 figures, 1 table, accepted for publication by MNRAS

The final inspiral and coalescence of a black hole binary can produce highly beamed gravitational wave radiation. To conserve linear momentum, the black hole remnant can recoil with "kick" velocity as high as 4000 km/s. We present two sets of full N-body simulations of recoiling massive black holes (MBH) in high-resolution, non-axisymmetric potentials. The host to the first set of simulations is the main halo of the Via Lactea I simulation (Diemand et al. 2007). The nature of the resulting orbits is investigated through a numerical model where orbits are integrated assuming an evolving, triaxial NFW potential, and dynamical friction is calculated directly from the velocity dispersion along the major axes of the main halo of Via Lactea I. By comparing the triaxial case to a spherical model, we find that the wandering time spent by the MBH is significantly increased due to the asphericity of the halo. For kicks larger than 200 km/s, the remnant MBH does not return to the inner 200 pc within 1 Gyr, a timescale an order of magnitude larger than the upper limit of the estimated QSO lifetime. The second set of simulations is run using the outcome of a high-resolution gas-rich merger (Mayer et al. 2007) as host potential. In this case, a recoil velocity of 500 km/s cannot remove the MBH from the nuclear region., Comment: 4 pages, 4 figures. Proceedings of the conference Galactic & Stellar Dynamics In the Era of High Resolution Surveys

We perform a series of simulations of a Galactic mass dark matter halo at different resolutions, our largest uses over three billion particles and has a mass resolution of 1000 M_sun. We quantify the structural properties of the inner dark matter distribution and study how they depend on numerical resolution. We can measure the density profile to a distance of 120 pc (0.05% of R_vir) where the logarithmic slope is -0.8 and -1.4 at (0.5% of R_vir). We propose a new two parameter fitting function that has a linearly varying logarithmic density gradient which fits the GHALO and VL2 density profiles extremely well. Convergence in the density profile and the halo shape scales as N^(-1/3), but the shape converges at a radius three times larger at which point the halo becomes more spherical due to numerical resolution. The six dimensional phase-space profile is dominated by the presence of the substructures and does not follow a power law, except in the smooth under-resolved inner few kpc., Comment: 6 pages, 4 figures, submitted to MNRAS Letters, for full sized images, see http://www.itp.uzh.ch/news.html

We present quantitative predictions for the detectability of individual Galactic dark matter subhalos in gamma-rays from dark matter pair annihilations in their centers. Our method is based on a hybrid approach, employing the highest resolution numerical simulations available (including the recently completed one billion particle Via Lactea II simulation) as well as analytical models for the extrapolation beyond the simulations' resolution limit. We include a self-consistent treatment of subhalo boost factors, motivated by our numerical results, and a realistic treatment of the expected backgrounds that individual subhalos must outshine. We show that for reasonable values of the dark matter particle physics parameters (M_X ~ 50 - 500 GeV and ~ 10^-26 - 10^-25 cm^3/s) GLAST may very well discover a few, even up to several dozen, such subhalos, at 5 sigma significance, and some at more than 20 sigma. We predict that the majority of luminous sources would be resolved with GLAST's expected angular resolution. For most observer locations the angular distribution of detectable subhalos is consistent with a uniform distribution across the sky. The brightest subhalos tend to be massive (median Vmax of 24 km/s) and therefore likely hosts of dwarf galaxies, but many subhalos with Vmax as low as 5 km/s are also visible. Typically detectable subhalos are 20 - 40 kpc from the observer, and only a small fraction are closer than 10 kpc. The total number of observable subhalos has not yet converged in our simulations, and we estimate that we may be missing up to 3/4 of all detectable subhalos., Comment: 19 pages, 12 figures, ApJ accepted, a version with higher resolution figures can be downloaded from http://www.sns.ias.edu/~mqk/transfer/VL2_GLAST_predictions.pdf

The Via Lactea simulation of the dark matter halo of the Milky Way predicts the existence of many thousands of bound subhalos distributed approximately with equal mass per decade of mass. Here we show that: a) a similar steeply rising subhalo mass function is also present at redshift 0.5 in an elliptical-sized halo simulated with comparable resolution in a different cosmology. Compared to Via Lactea, this run produces nearly a factor of two more subhalos with large circular velocities; b) the fraction of Via Lactea mass brought in by subhalos that have a surviving bound remnant today with present-day peak circular velocity Vmax>2 km/s (>10 km/s) is 45% (30%); c) because of tidal mass loss, the number of subhalos surviving today that reached a peak circular velocity of >10 km/s throughout their lifetime exceeds half a thousand, five times larger than their present-day abundance and more than twenty times larger than the number of known satellites of the Milky Way; e) unless the circular velocity profiles of Galactic satellites peak at values significantly higher that expected from the stellar line-of-sight velocity dispersion, only about one in five subhalos with Vmax>20 km/s today must be housing a luminous dwarf; f) small dark matter clumps appear to be relatively inefficient at forming stars even well beyond the virial radius; g) the observed Milky Way satellites appear to follow the overall dark matter distribution of Via Lactea, while the largest simulated subhalos today are found preferentially at larger radii; h) subhalos have central densities that increase with Vmax and reach 0.1-0.3 Msun/pc3 comparable to the central densities inferred in dwarf spheroidals with core radii >250 pc., Comment: 14 pages, 8 figures, ApJ in press. A few typos corrected

Numerical simulations of Milky-Way size Cold Dark Matter (CDM) halos predict a steeply rising mass function of small dark matter subhalos and a substructure count that greatly outnumbers the observed satellites of the Milky Way. Several proposed explanations exist, but detailed comparison between theory and observation in terms of the maximum circular velocity (Vmax) of the subhalos is hampered by the fact that Vmax for satellite halos is poorly constrained. We present comprehensive mass models for the well-known Milky Way dwarf satellites, and derive likelihood functions to show that their masses within 0.6 kpc (M_0.6) are strongly constrained by the present data. We show that the M_0.6 mass function of luminous satellite halos is flat between ~ 10^7 and 10^8 M_\odot. We use the ``Via Lactea'' N-body simulation to show that the M_0.6 mass function of CDM subhalos is steeply rising over this range. We rule out the hypothesis that the 11 well-known satellites of the Milky Way are hosted by the 11 most massive subhalos. We show that models where the brightest satellites correspond to the earliest forming subhalos or the most massive accreted objects both reproduce the observed mass function. A similar analysis with the newly-discovered dwarf satellites will further test these scenarios and provide powerful constraints on the CDM small-scale power spectrum and warm dark matter models., Comment: 8 pages, 6 figures

We discuss the possibility of GLAST detecting gamma-rays from the annihilation of neutralino dark matter in the Galactic halo. We have used "Via Lactea", currently the highest resolution simulation of Galactic cold dark matter substructure, to quantify the contribution of subhalos to the annihilation signal. We present a simulated allsky map of the expected gamma-ray counts from dark matter annihilation, assuming standard values of particle mass and cross section. In this case GLAST should be able to detect the Galactic center and several individual subhalos., Comment: 4 pages, 2 figures, to be published in "The Proceedings of the First International GLAST Symposium", February 5-8, 2007, Stanford University, AIP, Eds. S. Ritz, P.F. Michelson, and C. Meegan

We use the ``Via Lactea'' simulation to study the co-evolution of a Milky Way-size LambdaCDM halo and its subhalo population. While most of the host halo mass is accreted over the first 6 Gyr in a series of major mergers, the physical mass distribution [not M_vir(z)] remains practically constant since z=1. The same is true in a large sample of LambdaCDM galaxy halos. Subhalo mass loss peaks between the turnaround and virialization epochs of a given mass shell, and declines afterwards. 97% of the z=1 subhalos have a surviving bound remnant at the present epoch. The retained mass fraction is larger for initially lighter subhalos: satellites with maximum circular velocities Vmax=10 km/s at z=1 have today about 40% of their mass back then. At the first pericenter passage a larger average mass fraction is lost than during each following orbit. Tides remove mass in substructure from the outside in, leading to higher concentrations compared to field halos of the same mass. This effect, combined with the earlier formation epoch of the inner satellites, results in strongly increasing subhalo concentrations towards the Galactic center. We present individual evolutionary tracks and present-day properties of the likely hosts of the dwarf satellites around the Milky Way. The formation histories of ``field halos'' that lie today beyond the Via Lactea host are found to strongly depend on the density of their environment. This is caused by tidal mass loss that affects many field halos on eccentric orbits., Comment: 20 pages, 18 figures. Figures 6,7 and 8 corrected in this version, for details see the erratum in ApJ 679, 1680 and http://www.ucolick.org/~diemand/vl/publ/vlevolerr.pdf. Data, movies and images are available at http://www.ucolick.org/~diemand/vl/

We combine newly measured rotation velocities, velocity dispersions, and stellar masses to construct stellar mass Tully-Fisher relations (M*TFRs) for 544 galaxies with strong emission lines at 0.1

We present initial results from ``Via Lactea'', the highest resolution simulation to date of Galactic CDM substructure. It follows the formation of a Milky Way-size halo with Mvir=1.8x10^12 Msun in a WMAP 3-year cosmology, using 234 million particles. Over 10,000 subhalos can be identified at z=0: Their cumulative mass function is well-fit by N(>Msub)= 0.0064 (Msub/Mvir)^(-1) down to Msun=4x10^6 Msun. The total mass fraction in subhalos is 5.3%, while the fraction of surface mass density in substructure within a projected distance of 10 kpc from the halo center is 0.3%. Because of the significant contribution from the smallest resolved subhalos, these fractions have not converged yet. Sub-substructure is apparent in all the larger satellites, and a few dark matter lumps are resolved even in the solar vicinity. The number of dark satellites with peak circular velocities above 10 km/s (5 km/s) is 124 (812): of these, 5 (26) are found within 0.1 Rvir, a region that appeared practically smooth in previous simulations. The neutralino self-annihilation gamma-ray emission from dark matter clumps is approximately constant per subhalo mass decade. Therefore, while in our run the contribution of substructure to the gamma-ray luminosity of the Galactic halo amounts to only 40% of the total spherically-averaged smooth signal, we expect this fraction to grow significantly as resolution is increased further. An all-sky map of the expected annihilation gamma-ray flux reaching a fiducial observer at 8 kpc from the Galactic center shows that at the current resolution a small number of subhalos start to be bright enough to be visible against the background from the smooth density field surrounding the observer., Comment: 15 pages, 10 figures. ApJ accepted. Movies, images and a version with higher resolution figures are available at http://www.ucolick.org/~diemand/vl/

We have recently shown that both the Prugniel-Simien model and Sersic's function (hereafter referred to as the Einasto model when applied to internal density profiles) describe simulated dark matter halos better than an NFW-like model with equal number of parameters. Here we provide analytical expressions for the logarithmic slopes of these models, and compare them with data from real galaxies. Depending on the Einasto parameters of the dark matter halo, one can expect an extrapolated, inner (0.01--1 kpc), logarithmic profile slope ranging from -0.2 to -1.5, with a typical value at 0.1 kpc around -0.7. Application of this (better fitting) model therefore alleviates some of the past disagreement with observations on this issue. We additionally provide useful expressions for the concentration and assorted scale radii: r_s, r_{-2}, r_e, R_e, r_virial, and r_max -- the radius where the circular velocity profile has its maximum value. We also present the circular velocity profiles and the radial behavior of rho(r)/sigma(r)^3 for both the Einasto and Prugniel-Simien models. We find this representation of the phase-space density profile to be well approximated by a power-law with slope slightly shallower than -2 near r=r_{-2}., Comment: AJ, in press. (Paper I can be found at astro-ph/0509417)

We have recently shown that the 3-parameter density-profile model from Prugniel & Simien provides a better fit to simulated, galaxy- and cluster-sized, dark matter halos than an NFW-like model with arbitrary inner profile slope gamma (Paper I). By construction, the parameters of the Prugniel-Simien model equate to those of the Sersic R^{1/n} function fitted to the projected distribution. Using the Prugniel-Simien model, we are therefore able to show that the location of simulated (10^{12} M_sun) galaxy-sized dark matter halos in the _e-log(R_e) diagram coincides with that of brightest cluster galaxies, i.e., the dark matter halos appear consistent with the Kormendy relation defined by luminous elliptical galaxies. These objects are also seen to define the new, and equally strong, relation log(rho_e) = 0.5 - 2.5log(R_e), in which rho_e is the internal density at r=R_e. Simulated (10^{14.5} M_sun) cluster-sized dark matter halos and the gas component of real galaxy clusters follow the relation log(rho_e) = 2.5[1 - log(R_e)]. Given the shapes of the various density profiles, we are able to conclude that while dwarf elliptical galaxies and galaxy clusters can have dark matter halos with effective radii of comparable size to the effective radii of their baryonic component, luminous elliptical galaxies can not. For increasingly large elliptical galaxies, with increasingly large profile shapes `n', to be dark matter dominated at large radii requires dark matter halos with increasingly large effective radii compared to the effective radii of their stellar component., Comment: AJ, in press. (Paper I can be found at astro-ph/0509417)

If the dark matter particle is a neutralino then the first structures to form are cuspy cold dark matter (CDM) haloes collapsing after redshifts z ~ 100 in the mass range 10^{-6} - 10^{-3} Msun. We carry out a detailed study of the survival of these micro-haloes in the Galaxy as they experience tidal encounters with stars, molecular clouds, and other dark matter substructures. We test the validity of analytic impulsive heating calculations using high resolution N-body simulations. A major limitation of analytic estimates is that mean energy inputs are compared to mean binding energies, instead of the actual mass lost from the system. This energy criterion leads to an overestimate of the stripped mass and underestimate of the disruption timescale since CDM haloes are strongly bound in their inner parts. We show that a significant fraction of material from CDM micro-haloes can be unbound by encounters with Galactic substructure and stars, however the cuspy central regions remain relatively intact. Furthermore, the micro-haloes near the solar radius are those which collapse significantly earlier than average and will suffer very little mass loss. Thus we expect a fraction of surviving bound micro-haloes, a smooth component with narrow features in phase space, which may be uncovered by direct detection experiments, as well as numerous surviving cuspy cores with proper motions of arc-minutes per year, which can be detected indirectly via their annihilation into gamma-rays., Comment: 9 pages, 12 figures, submitted to MNRAS, v2: references added

Earth-mass ``microhalos'' may be the first objects to virialize in the early universe. Their ability to survive the hierarchical clustering process as substructure in the larger halos that form subsequently has implications for dark matter detection experiments. We present a large N-body simulation of early substructure in a supersymmetric cold dark matter (SUSY-CDM) scenario characterized by an exponential cutoff in the power spectrum at M_c=10^-6 Msun. The simulation resolves a 0.014 Msun parent ``SUSY'' halo at z=75 with 14 million particles. On these scales the effective index of the power spectrum approaches -3, and a range of mass scales collapse almost simultaneously. Compared to a z=0 galaxy cluster substructure within our SUSY host is less evident both in phase-space and in physical space, and it is less resistant against tidal disruption. As the universe expands by a factor of 1.3, we find that between 20 and 40 percent of well-resolved SUSY substructure is destroyed, compared to only about 1 percent in the low-redshift cluster. Nevertheless SUSY substructure is just as abundant as in z=0 galaxy clusters, i.e. the normalized mass and circular velocity functions are very similar. The dark matter self-annihilation gamma-ray luminosity from bound subhalos and other deviations from a smooth spherical configuration is at least comparable to the spherically-averaged signal in the SUSY host, and at least three times larger than the spherically-averaged signal in the cluster host. Such components must be taken into account when estimating the total cosmological extragalactic gamma-ray annihilation background.(ABRIDGED), Comment: 14 pages, 11 figures, ApJ in press. Added a discussion of halo formation below the cutoff scale (Section 3.3). A version with high-resolution figures is available at http://www.ucolick.org/~diemand/earlysubs.pdf

The Milky Way contains several distinct old stellar components that provide a fossil record of its formation. We can understand their spatial distribution and kinematics in a hierarchical formation scenario by associating the proto-galactic fragments envisaged by Searle and Zinn (1978) with the rare peaks able to cool gas in the cold dark matter density field collapsing at redshift z>10. We use hierarchical structure formation simulations to explore the kinematics and spatial distribution of these early star-forming structures in galaxy haloes today. Most of the proto-galaxies rapidly merge, their stellar contents and dark matter becoming smoothly distributed and forming the inner Galactic halo. The metal-poor globular clusters and old halo stars become tracers of this early evolutionary phase, centrally biased and naturally reproducing the observed steep fall off with radius. The most outlying peaks fall in late and survive to the present day as satellite galaxies. The observed radial velocity dispersion profile and the local radial velocity anisotropy of Milky Way halo stars are successfully reproduced in this model. If this epoch of structure formation coincides with a suppression of further cooling into lower sigma peaks then we can reproduce the rarity, kinematics and spatial distribution of satellite galaxies as suggested by Bullock et al. (2000). Reionisation at z=12+/-2 provides a natural solution to the missing satellites problem. Measuring the distribution of globular clusters and halo light on scales from galaxies to clusters could be used to constrain global versus local reionisation models. If reionisation occurs contemporary, our model predicts a constant frequency of blue globulars relative to the host halo mass, except for dwarf galaxies where the average relative frequencies become smaller., Comment: Submitted to MNRAS

We use techniques from nonparametric function estimation theory to extract the density profiles, and their derivatives, from a set of N-body dark matter halos. We consider halos generated from LCDM simulations of gravitational clustering, as well as isolated, spherical collapses. The logarithmic density slopes gamma = d(log rho)/d(log r) of the LCDM halos are found to vary as power-laws in radius, reaching values of gamma ~ -1 at the innermost resolved radii (~0.01 r_virial). This behavior is significantly different from that of broken power-law models like the NFW profile, but similar to that of models like de Vaucouleurs'. Accordingly, we compare the N-body density profiles with various parametric models to find which provide the best fit. We consider an NFW-like model with arbitrary inner slope; Dehnen & McLaughlin's anisotropic model; Einasto's model (identical in functional form to Sersic's model but fit to the space density); and the density model of Prugniel & Simien that was designed to match the deprojected form of Sersic's R^{1/n} law. Overall, the best-fitting model to the LCDM halos is Einasto's, although the Prugniel-Simien and Dehnen-McLaughlin models also perform well. With regard to the spherical collapse halos, both the Prugniel-Simien and Einasto models describe the density profiles well, with an rms scatter some four times smaller than that obtained with either the NFW-like model or the 3-parameter Dehnen-McLaughlin model. Finally, we confirm recent claims of a systematic variation in profile shape with halo mass., Comment: AJ in press

We show that the hierarchical assembly of cold dark matter (CDM) haloes preserves the memory of the initial conditions. Using N-body cosmological simulations, we demonstrate that the present-day spatial distribution and kinematics of objects that formed within early (z > 10) protogalactic systems (old stars, satellite galaxies, globular clusters, massive black holes, etc.) depends mostly on the rarity of the peak of the primordial density field which they originally belonged to. Only for objects forming at lower redshifts the exact formation site within the progenitor halo (e.g. whether near the center or in an extended disk) becomes important. In present-day haloes, material from the rarer early peaks is more centrally concentrated and falls off more steeply with radius compared to the overall mass distribution, it has a lower velocity dispersion, moves on more radial orbits, and has a more elongated shape. Population II stars that formed within protogalactic haloes collapsing from >2.5 sigma fluctuations would follow today a r^{-3.5} density profile with a half-light radius of 17 kpc and a velocity anisotropy that increases from isotropic in the inner regions to nearly radial at the halo edge. This agrees well with the radial velocity dispersion profile of Galaxy halo stars from Battaglia et al. (2005) and with the anisotropic orbits of nearby halo stars., Comment: 19 pages, 12 figures, matches the published version. Increased line-width of plots for better reproduction. A version with higher resolution figures is available at http://www.ucolick.org/~diemand/highpeaks.pdf

We analyse the number density and radial distribution of substructures and satellite galaxies using cosmological simulations that follow the gas dynamics of a baryonic component, including shock heating, radiative cooling and star formation within the hierarchical concordance LCDM model. We find that the dissipation of the baryons greatly enhances the survival of subhaloes, expecially in the galaxy core, resulting in a radial distribution of satellite galaxies that closely follows the overall mass distribution in the inner part of the halo. Hydrodynamical simulations are necessary to resolve the adiabatic contraction and dense cores of galaxies, resulting in a total number of satellites a factor of two larger than found in pure dark matter simulation, in good agreement with the observed spatial distribution of satellite galaxies within galaxies and clusters. Convergence tests show that the cored distribution found by previous authors in pure N-body simulations was due to physical overmerging of dark matter only structures. We proceed to use a ray-shooting technique in order to study the impact of these additional substructures on the number of violations of the cusp caustic magnification relation. We develop a new approach to try to disentangle the effect of substructures from the intrinsic discreteness of N-Body simulations. Even with the increased number of substructures in the centres of galaxies, we are not able to reproduce the observed high numbers of discrepancies observed in the flux ratios of multiply lensed quasars., Comment: 11 pages, 15 figures, comparison with previous works updated, one more plot added, minor changes to match the accepted version by MNRAS

We resolve the inner region of a massive cluster forming in a cosmological LCDM simulation with a mass resolution of 2*10^6 Msun and before z=4.4 even 3*10^5 Msun. This is a billion times less than the clusters final virial mass and a substantial increase over current LCDM simulations. We achieve this resolution using a new multi-mass refinement procedure and are now able to probe a dark matter halo density profile down to 0.1 percent of the virial radius. The inner density profile of this cluster halo is well fitted by a power-law rho ~ r^-gamma down to the smallest resolved scale. An inner region with roughly constant logarithmic slope is now resolved, which suggests that cuspy profiles describe the inner profile better than recently proposed profiles with a core. The cluster studied here is one out of a sample of six high resolution cluster simulations of Diemand et al. (2004) and it's inner slope of gamma = 1.2 lies close to the sample average., Comment: 10 pages,10 figures. Matches version in press. Added Figure 7 and section 3.3. about upper limits of inner slopes, text (incl, title and abstract) revised, conclusions unchanged

Neutralino dark matter leads to the formation of numerous earth mass dark matter haloes at redshifts z\approx 60 (Diemand et al. 2005). These abundant CDM micro-haloes have cuspy density profiles that can easily withstand the Galactic tidal field at the solar radius. Zhao, Taylor, Silk & Hooper (astro-ph/0502049) concluded that ``...the majority of dark matter substructures with masses \sim 10^{-6}M_o will be tidally disrupted due to interactions with stars in the Galactic halo''. However these authors assumed a halo density of stars that is at least an order of magnitude higher than observed. We show that the appropriate application of the impulse approximation is to the regime of multiple encounters, not single disruptive events as adopted by Zhao et al., which leads to a survival time of several Hubble times. Therefore we do not expect the tidal heating by Galactic stars to affect the abundance of micro-haloes. Disk crossing will cause some mass loss but the central cores are likely to survive and could be detected as gamma-ray sources with proper motions of several arc minutes per year., Comment: Comment on Zhao etal (astro-ph/0502049)

The Universe was nearly smooth and homogeneous before a redshift of z = 100, about 20 million years after the Big Bang. After this epoch, the tiny fluctuations imprinted upon the matter distribution during the initial expansion began to collapse because of gravity. The properties of these fluctuations depend on the unknown nature of dark matter, the determination of which is one of the biggest challenges in present-day science. Here we report supercomputer simulations of the concordance cosmological model, which assumes neutralino dark matter (at present the preferred candidate), and find that the first objects to form are numerous Earth-mass dark-matter haloes about as large as the Solar System. They are stable against gravitational disruption, even within the central regions of the Milky Way. We expect over 10^15 to survive within the Galactic halo, with one passing through the Solar System every few thousand years. The nearest structures should be among the brightest sources of gamma-rays (from particle-particle annihilation)., Comment: 11 pages, 3 figures, published in Nature, January 27, 2005

We explore the region of influence of a galaxy cluster using numerical simulations of cold dark matter halos. Many of the observed galaxies in a cluster are expected to be infalling for the first time. Half of the halos at distances of one to two virial radii today have previously orbited through the cluster, most of them have even passed through the dense inner regions of the cluster. Some halos at distances of up to three times the virial radius have also passed through the cluster core. We do not find a significant correlation of ``infall age'' versus present day position for substructures and the scatter at a given position is very large. This relation may be much more significant if we could resolve the physically overmerged galaxies in the central region., Comment: To appear in the proceedings of IAU Colloquium 195: "Outskirts of galaxy clusters: intense life in the suburbs", Torino, Italy, March 12-16, 2004

We present new results from a series of LCDM simulations of cluster mass halos resolved with high force and mass resolution. These results are compared with recently published simulations from groups using various codes including PKDGRAV, ART, TPM, GRAPE and GADGET. Careful resolution tests show that with 25 million particles within the high resolution region we can resolve to about 0.3% of the virial radius and that convergence in radius is proportional to the mean interparticle separation. The density profiles of 26 high resolution clusters obtained with the different codes and from different initial conditions agree very well. The average logarithmic slope at one percent of the virial radius is $\gamma = 1.26$ with a scatter of $\pm 0.17$. Over the entire resolved regions the density profiles are well fitted by a smooth function that asymptotes to a central cusp $\rho \propto r^{-\gamma}$, where we find $\gamma=1.16\pm 0.14$ from the mean of the fits to our six highest resolution clusters., Comment: MNRAS accepted version. Due to an error in the initial conditions these simulations have a lower sigma_8 than the published value, 0.7 instead of 0.9. We thank Mike Kuhlen who helped us finding this mistake. See the erratum at http://www-theorie.physik.unizh.ch/~diemand/proerr.pdf . Images and movies available at http://www-theorie.physik.unizh.ch/~diemand/clusters/

We present a statistical study of substructure within a sample of LCDM clusters and galaxies simulated with up to 25 million particles. With thousands of subhalos per object we can accurately measure their spatial clustering and velocity distribution functions and compare these with observational data. The substructure properties of galactic halos closely resembles those of galaxy clusters with a small scatter in the mass and circular velocity functions. The velocity distribution function is non-Maxwellian and flat topped with a negative kurtosis of about -0.7. Within the virial radius the velocity bias $b=\sigma_{\rm sub}/\sigma_{\rm DM}\sim 1.12 \pm 0.04$, increasing to b > 1.3 within the halo centers. Slow subhalos are much less common, due to physical disruption by gravitational tides early in the merging history. This leads to a spatially anti-biased subhalo distribution that is well fitted by a cored isothermal. Observations of cluster galaxies do not show such biases which we interpret as a limitation of pure dark matter simulations - we estimate that we are missing half of the halo population which has been destroyed by physical overmerging. High resolution hydrodynamical simulations are required to study these issues further. If CDM is correct then the cluster galaxies must survive the tidal field, perhaps due to baryonic inflow during elliptical galaxy formation. Spirals can never exist near the cluster centers and the elliptical galaxies there will have little remaining dark matter. This implies that the morphology-density relation is set {\it before} the cluster forms, rather than a subsequent transformation of disks to S0's by virtue of the cluster environment., Comment: MNRAS accepted version. Due to an error in the initial conditions these simulations have a lower sigma_8 than the published value, 0.7 instead of 0.9. We thank Mike Kuhlen who helped us finding this mistake. See the erratum at http://www-theorie.physik.unizh.ch/~diemand/suberr.pdf . Images and movies available at http://www-theorie.physik.unizh.ch/~diemand/clusters/

The structural evolution of substructure in cold dark matter (CDM) models is investigated combining ``low-resolution'' satellites from cosmological N-body simulations of parent halos with N=10^7 particles with high-resolution individual subhalos orbiting within a static host potential. We show that, as a result of mass loss, convergence in the central density profiles requires the initial satellites to be resolved with N=10^7 particles and parsec-scale force resolution. We find that the density profiles of substructure halos can be well fitted with a power-law central slope that is unmodified by tidal forces even after the tidal stripping of over 99% of the initial mass and an exponential cutoff in the outer parts. The solution to the missing-satellites problem advocated by Stoehr et al. in 2002 relied on the flattening of the dark matter (DM) halo central density cusps by gravitational tides, enabling the observed satellites to be embedded within DM halos with maximum circular velocities as large as 60 km/s. In contrast, our results suggest that tidal interactions do not provide the mechanism for associating the dwarf spheroidal satellites (dSphs) of the Milky Way with the most massive substructure halos expected in a CDM universe. We compare the predicted velocity dispersion profiles of Fornax and Draco to observations, assuming that they are embedded in CDM halos. Models with isotropic and tangentially anisotropic velocity distributions for the stellar component fit the data only if the surrounding DM halos have maximum circular velocities in the range 20-35 km/s. If the dSphs are embedded within halos this large then the overabundance of satellites within the concordance LCDM cosmological model is significantly alleviated, but this still does not provide the entire solution., Comment: Accepted for publication in ApJ, 17 pages, 9 figures, LaTeX (uses emulateapj5.sty)

We present a technique for constructing equilibrium triaxial N-body haloes with nearly arbitrary density profiles, axial ratios and spin parameters. The method is based on the way in which structures form in hierarchical cosmological simulations, where prolate and oblate haloes form via mergers with low and high angular momentum, respectively. We show that major mergers between equilibrium spherical cuspy haloes produce similarly cuspy triaxial remnants and higher angular-momentum mergers produce systems with lower concentrations. Triaxial haloes orbiting within deeper potentials become more spherical and their velocity dispersion tensors more isotropic. The rate of mass loss depends sensitively on the halo shape: a prolate halo can lose mass at a rate several times higher than an isotropic spherical halo with the same density profile. Subhaloes within cosmological simulations are significantly rounder than field haloes with axial ratios that are ~ 30% larger., Comment: Accepted for publication in MNRAS, 8 pages, 8 figures, LaTeX (uses mn2e.cls)

N-body simulations of the hierarchical formation of cosmic structures suffer from the problem that the first objects to form always contain just a few particles. Although relaxation is not an issue for virialised objects containing millions of particles, collisional processes will always dominate within the first structures that collapse. First we quantify how the relaxation varies with resolution, softening, and radius within isolated equilibrium and non-equilibrium cuspy haloes. We then attempt to determine how this numerical effect propagates through a merging hierarchy by measuring the local relaxation rates of each particle throughout the hierarchical formation of a dark matter halo. The central few percent of the final structures - a region which one might naively think is well resolved at the final time since the haloes contains about 10^6 particles - suffer from high degrees of relaxation. It is not clear how to interpret the effects of the accumulated relaxation rate, but we argue that it describes a region within which one should be careful about trusting the numerical results. Substructure haloes are most affected by relaxation since they contain few particles at a constant energy for the entire simulation. We show that relaxation will flatten a cusp in just a few mean relaxation times of a halo. We explore the effect of resolution on the degree of relaxation and we find that increasing N slowly reduces the degree of relaxation proportional to N^{-0.25} rather than proportional to N. Simulated with the same relative mass resolution (i.e. equal numbers of particles) cluster mass objects suffer significantly more relaxation than galaxy mass objects since they form relatively late and therefore more of the particles spend more time in small N haloes., Comment: 11 pages, 14 figures. Accepted for publication in MNRAS. Movies available at http://www-theorie.physik.unizh.ch/~diemand/tbr