The $ u^2$GC Simulations : Quantifying the Dark Side of the Universe in the Planck Cosmology

We present the evolution of dark matter halos in six large cosmological N-body simulations, called the $ u^2$GC (New Numerical Galaxy Catalog) simulations on the basis of the LCDM cosmology consistent with observational results obtained by the Planck satellite. The largest simulation consists of $8192^3$ (550 billion) dark matter particles in a box of $1.12 , h^{-1} rm Gpc$ (a mass resolution of $2.20 times 10^{8} , h^{-1} M_{odot}$). Among simulations utilizing boxes larger than $1 , h^{-1} rm Gpc$, our simulation yields the highest resolution simulation that has ever been achieved. A $ u^2$GC simulation with the smallest box consists of eight billions particles in a box of $70 , h^{-1} rm Mpc$ (a mass resolution of $3.44 times 10^{6} , h^{-1} M_{odot}$). These simulations can follow the evolution of halos over masses of eight orders of magnitude, from small dwarf galaxies to massive clusters. Using the unprecedentedly high resolution and powerful statistics of the $ u^2$GC simulations, we provide statistical results of the halo mass function, mass accretion rate, formation redshift, and merger statistics, and present accurate fitting functions for the Planck cosmology. By combining the $ u^2$GC simulations with our new semi-analytic galaxy formation model, we are able to prepare mock catalogs of galaxies and active galactic nuclei, which will be made publicly available in the near future.

Hierarchical Formation of Dark Matter Halos and the Free Streaming Scale

The smallest dark matter halos are formed first in the early universe. According to recent studies, the central density cusp is much steeper in these halos than in larger halos and scales as $rho propto r^{-(1.5-1.3)}$. We present results of very large cosmological $N$-body simulations of the hierarchical formation and evolution of halos over a wide mass range, beginning from the formation of the smallest halos. We confirmed early studies that the inner density cusps are steeper in halos at the free streaming scale. The cusp slope gradually becomes shallower as the halo mass increases. The slope of halos 50 times more massive than the smallest halo is approximately $-1.3$. No strong correlation exists between inner slope and the collapse epoch. The cusp slope of halos above the free streaming scale seems to be reduced primarily due to major merger processes. The concentration, estimated at the present universe, is predicted to be $60-70$, consistent with theoretical models and earlier simulations, and ruling out simple power law mass-concentration relations. Microhalos could still exist in the present universe with the same steep density profiles.

4.45 Pflops Astrophysical N-Body Simulation on K computer -- The Gravitational Trillion-Body Problem

As an entry for the 2012 Gordon-Bell performance prize, we report performance results of astrophysical N-body simulations of one trillion particles performed on the full system of K computer. This is the first gravitational trillion-body simulation in the world. We describe the scientific motivation, the numerical algorithm, the parallelization strategy, and the performance analysis. Unlike many previous Gordon-Bell prize winners that used the tree algorithm for astrophysical N-body simulations, we used the hybrid TreePM method, for similar level of accuracy in which the short-range force is calculated by the tree algorithm, and the long-range force is solved by the particle-mesh algorithm. We developed a highly-tuned gravity kernel for short-range forces, and a novel communication algorithm for long-range forces. The average performance on 24576 and 82944 nodes of K computer are 1.53 and 4.45 Pflops, which correspond to 49% and 42% of the peak speed.

The Cosmogrid Simulation: Statistical Properties of Small Dark Matter Halos

We present the results of the Cosmogrid cosmological N-body simulation suites based on the concordance LCDM model. The Cosmogrid simulation was performed in a 30Mpc box with 2048^3 particles. The mass of each particle is 1.28x10^5 Msun, which is sufficient to resolve ultra-faint dwarfs. We found that the halo mass function shows good agreement with the Sheth & Tormen fitting function down to ~10^7 Msun. We have analyzed the spherically averaged density profiles of the three most massive halos which are of galaxy group size and contain at least 170 million particles. The slopes of these density profiles become shallower than -1 at the inner most radius. We also find a clear correlation of halo concentration with mass. The mass dependence of the concentration parameter cannot be expressed by a single power law, however a simple model based on the Press-Schechter theory proposed by Navarro et al. gives reasonable agreement with this dependence. The spin parameter does not show a correlation with the halo mass. The probability distribution functions for both concentration and spin are well fitted by the log-normal distribution for halos with the masses larger than ~10^8 Msun. The subhalo abundance depends on the halo mass. Galaxy-sized halos have 50% more subhalos than ~10^{11} Msun halos have.

Gamma-ray Signal from Earth-mass Dark Matter Microhalos

Earth-mass dark matter microhalos with size of ~100 AUs are the first structures formed in the universe, if the dark matter of the Universe are made of neutralino. Here, we report the results of ultra-high-resolution simulations of the formation and evolution of these microhalos. We found that microhalos have the central density cusps of the form $rho propto r^{-1.5}$, much steeper than the cusps of larger dark halos. The central regions of these microhalos survive the encounters with stars except in very inner region of the galaxy down to the radius of a few hundreds pcs from the galactic center. The annihilation signals from nearest microhalos are observed as gamma-ray point-sources (radius less than 1), with unusually large proper motions of ~0.2 degree per year. Their surface brightnesses are ~10% of that of the galactic center. Their S/N ratios might be better if they are far from the galactic plane. Luminosities of subhalos are determined only by their mass, and they are more than one order of magnitude luminous than the estimation by Springel et al. (2008): A boost factor can be larger than 1000. Perturbations to the millisecond pulsars by gravitational attractions of nearby earth-mass microhalos can be detected by the observations of Parkes Pulsar Timing Array (PPTA).

Variation of the subhalo abundance in dark matter halos

We analyzed the statistics of subhalo abundance of galaxy-sized and giant-galaxy-sized halos formed in a high-resolution cosmological simulation of a 46.5Mpc cube with the uniform mass resolution of $10^6 M_{odot}$. We analyzed all halos with mass more than $1.5 times 10^{12}M_{odot}$ formed in this simulation box. The total number of halos was 125. We found that the subhalo abundance, measured by the number of subhalos with maximum rotation velocity larger than 10% of that of the parent halo, shows large halo-to-halo variations. The results of recent ultra-high-resolution runs fall within the variation of our samples. We found that the concentration parameter and the radius at the moment of the maximum expansion shows fairly tight correlation with the subhalo abundance. This correlation suggests that the variation of the subhalo abundance is at least partly due to the difference in the formation history. Halos formed earlier have smaller number of subhalos at present.