We use the Delaunay Tessellation Field Estimator (DTFE) to study the one-point density distribution functions of the Millennium (MS) and Millennium-II (MS-II) simulations. The DTFE technique is based directly on the particle positions, without requir
ing any type of smoothing or analysis grid, thereby providing high sensitivity to all non-linear structures resolved by the simulations. In order to identify the detailed origin of the shape of the one-point density probability distribution function (PDF), we decompose the simulation particles according to the mass of their host FoF halos, and examine the contributions of different halo mass ranges to the global density PDF. We model the one-point distribution of the FoF halos in each halo mass bin with a set of Monte Carlo realizations of idealized NFW dark matter halos, finding that this reproduces the measurements from the N-body simulations reasonably well, except for a small excess present in simulation results. This excess increases with increasing halo mass. We show that its origin lies in substructure, which becomes progressively more abundant and better resolved in more massive dark matter halos. We demonstrate that the high density tail of the one-point distribution function in less massive halos is severely affected by the gravitational softening length and the mass resolution. In particular, we find these two parameters to be more important for an accurate measurement of the density PDF than the simulated volume. Combining our results from individual halo mass bins we find that the part of the one-point density PDF originating from collapsed halos can nevertheless be quite well described by a simple superposition of a set of NFW halos with the expected cosmological abundance over the resolved mass range. The transition region to the low-density unbound material is however not well captured by such an analytic halo model.
We present a new statistical method to determine the relationship between the stellar masses of galaxies and the masses of their host dark matter haloes over the entire cosmic history from z~4 to the present. This multi-epoch abundance matching (MEAM
) model self-consistently takes into account that satellite galaxies first become satellites at times earlier than they are observed. We employ a redshift-dependent parameterization of the stellar-to-halo mass relation to populate haloes and subhaloes in the Millennium simulations with galaxies, requiring that the observed stellar mass functions at several redshifts be reproduced simultaneously. Using merger trees extracted from the dark matter simulations in combination with MEAM, we predict the average assembly histories of galaxies, separating into star formation within the galaxies (in-situ) and accretion of stars (ex-situ). The peak star formation efficiency decreases with redshift from 23% at z=0 to 9% at z=4 while the corresponding halo mass increases from 10^11.8Modot to 10^12.5Modot. The star formation rate of central galaxies peaks at a redshift which depends on halo mass; for massive haloes this peak is at early cosmic times while for low-mass galaxies the peak has not been reached yet. In haloes similar to that of the Milky-Way about half of the central stellar mass is assembled after z=0.7. In low-mass haloes, the accretion of satellites contributes little to the assembly of their central galaxies, while in massive haloes more than half of the central stellar mass is formed ex-situ with significant accretion of satellites at z<2. We find that our method implies a cosmic star formation history and an evolution of specific star formation rates which are consistent with those inferred directly. We present convenient fitting functions for stellar masses, star formation rates, and accretion rates as functions of halo mass and redshift.
We present the first and so far the only simulations to follow the fine-grained phase-space structure of galaxy haloes formed from generic LCDM initial conditions. We integrate the geodesic deviation equation in tandem with the N-body equations of mo
tion, demonstrating that this can produce numerically converged results for the properties of fine-grained phase-space streams and their associated caustics, even in the inner regions of haloes. Our effective resolution for such structures is many orders of magnitude better than achieved by conventional techniques on even the largest simulations. We apply these methods to the six Milky Way-mass haloes of the Aquarius Project. At 8 kpc from halo centre a typical point intersects about 10^14 streams with a very broad range of individual densities; the ~10^6 most massive streams contribute about half of the local dark matter density. As a result, the velocity distribution of dark matter particles should be very smooth with the most massive fine-grained stream contributing about 0.1% of the total signal. Dark matter particles at this radius have typically passed 200 caustics since the Big Bang. The peak densities on present-day caustics in the inner halo almost all lie well below the mean local dark matter density. As a result caustics provide a negligible boost (<0.1%) to the predicted local dark matter annihilation rate. The effective boost is larger in the outer halo but never exceeds about 10%. Thus fine-grained streams and their associated caustics have no effect on the detectability of dark matter, either directly in Earth-bound laboratories, or indirectly through annihilation radiation, with the exception that resonant cavity experiments searching for axions may see the most massive local fine-grained streams because of their extreme localisation in energy/momentum space. (abridged)
We have resimulated the six galaxy-sized haloes of the Aquarius Project including metal-dependent cooling, star formation and supernova feedback. This allows us to study not only how dark matter haloes respond to galaxy formation, but also how this r
esponse is affected by details of halo assembly history. In agreement with previous work, we find baryon condensation to lead to increased dark matter concentration. Dark matter density profiles differ substantially in shape from halo to halo when baryons are included, but in all cases the velocity dispersion decreases monotonically with radius. Some haloes show an approximately constant dark matter velocity anisotropy with $ beta approx 0.1-02$, while others retain the anisotropy structure of their baryon-fre
We use the very large Millennium Simulation of the concordance $Lambda$CDM cosmogony to calibrate the bias and error distribution of Timing Argument estimators of the masses of the Local Group and of the Milky Way. From a large number of isolated spi
ral-spiral pairs similar to the Milky Way/Andromeda system, we find the interquartile range of the ratio of timing mass to true mass to be a factor of 1.8, while the 5% and 95% points of the distribution of this ratio are separated by a factor of 5.7. Here we define true mass as the sum of the ``virial masses $M_{200}$ of the two dominant galaxies. For current best values of the distance and approach velocity of Andromeda this leads to a median likelihood estimate of the true mass of the Local Group of $5.27times 10^{12}msun$, or $log M_{LG}/M_odot = 12.72$, with an interquartile range of $[12.58, 12.83]$ and a 5% to 95% range of $[12.26, 13.01]$. Thus a 95% lower confidence limit on the true mass of the Local Group is $1.81times 10^{12}msun$. A timing estimate of the Milky Ways mass based on the large recession velocity observed for the distant satellite Leo I works equally well, although with larger systematic uncertainties. It gives an estimated virial mass for the Milky Way of $2.43 times 10^{12}msun$ with a 95% lower confidence limit of $0.80 times 10^{12}msun$.
