Juerg Diemand

Empirical Models for Dark Matter Halos. I. Nonparametric Construction of Density Profiles and Comparison with Parametric Models

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 ΛCDM simulations of gravitational clustering, as well as isolated spherical collapses. The logarithmic density slopes γ ≡ d log ρ/d log r of the ΛCDM halos are found to vary as power laws in radius, reaching values of γ ≈ -1 at the innermost resolved radii, ~10-2rvir. This behavior is significantly different from that of broken-power-law models like the Navarro-Frenk-White (NFW) profile but similar to that of models like de Vaucouleurss. 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 & McLaughlins anisotropic model; Einastos model (identical in functional form to Sersics model but fitted to the space density); and the density model of Prugniel & Simien that was designed to match the deprojected form of Sersics R1/n law. Overall, the best-fitting model to the ΛCDM halos is Einastos, 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 4 times smaller than that obtained with either the NFW-like model or the three-parameter Dehnen-McLaughlin model. Finally, we confirm recent claims of a systematic variation in profile shape with halo mass.

Dark matter substructure and gamma-ray annihilation in the milky way halo

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-sized halo with Mhalo = 1.8 ? 1012 M? in a WMAP three-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/Mhalo)-1 down to Msub = 4 ? 106 M?. 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-1 (5 km s-1) is 124 (812): of these, five (26) are found within 0.1rvir, a region that appeared practically smooth in previous simulations. The neutralino self-annihilation ?-ray emission from dark matter clumps is approximately constant per subhalo mass decade. Therefore, while in our run the contribution of substructure to the ?-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 ?-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.

Velocity and spatial biases in cold dark matter subhalo distributions

We present a statistical study of substructure within a sample ofCDM 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 = σsub/σDM � 1.12±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 before the cluster forms, rather than a subsequent transformation of disks to S0s by virtue of the cluster environment.

Earth-mass dark-matter haloes as the first structures in the early Universe

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 1015 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 γ-rays (from particle–particle annihilation).

Haloes gone MAD: The Halo-Finder Comparison Project

We present a detailed comparison of fundamental dark matter halo properties retrieved by a substantial number of different halo finders. These codes span a wide range of techniques including friends-of-friends, spherical-overdensity and phase-space-based algorithms. We

Convergence and scatter of cluster density profiles

We present new results from a series of ACDM simulations of cluster mass haloes 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 per cent 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 per cent of the virial radius is y = 1.26 with a scatter of ±0.17. Over the entire resolved regions the density profiles are well fitted by a smooth function that asymptotes to a central cusp p oc r -γ , where we find y = 1.16 ± 0.14 from the mean of the fits to our six highest-resolution clusters.

Globular clusters, satellite galaxies and stellar haloes from early dark matter peaks

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.

Cusps in cold dark matter haloes

We resolve the inner region of a massive cluster forming in a cosmological ΛCDM simulation with a mass resolution of 2 × 106M⊙ and before z=4.4 even 3 × 10 5M⊙. This is a billion times less than the clusters final virial mass and a substantial increase over current ΛCDM 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 ρ ∝ r 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. (2004b) and its inner slope of about γ = 1.2 lies close to the sample average.

The distribution and kinematics of early high-σ peaks in present-day haloes: implications for rare objects and old stellar populations

We show that the hierarchical assembly of cold dark matter 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 to which they originally belonged. Only for objects forming at lower redshifts does the exact formation site within the progenitor halo (e.g. whether near the centre or in an extended disc) become 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, 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 ≥2.5σ fluctuations would follow today an 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 the recent work of Battaglia et al. and with the anisotropic orbits of nearby halo stars.

Empirical Models for Dark Matter Halos. II. Inner Profile Slopes, Dynamical Profiles, and ρ/σ 3

We have recently shown that both the Prugniel-Simien model and Sersics function (hereafter referred to as the Einasto model when applied to internal density profiles) describe simulated dark matter halos better than a Navarro-Frenk-White-like model with an 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 approximately -0.2 to approximately -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. In addition, we provide useful expressions for the concentration and assorted scale radii: rs, r-2, re, Re, rvir, and rmax, the radius where the circular velocity profile has its maximum value. We also present the circular velocity profiles and the radial behavior of ρ(r)/σ(r)3 for both the Einasto and Prugniel-Simien models, where σ(r) is the velocity dispersion associated with the density profile ρ(r). We find this representation of the phase-space density profile to be well approximated by a power law with a slope slightly shallower than -2 near r = r-2.