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Register a new userHierarchical Formation of Dark Matter Halos and the Free Streaming Scale
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Authors
Tomoaki Ishiyama
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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.
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We use a 200 $h^{-1}Mpc$ a side N-body simulation to study the mass accretion history (MAH) of dark matter halos to be accreted by larger halos, which we call infall halos. We define a quantity $a_{rm nf}equiv (1+z_{rm f})/(1+z_{rm peak})$ to characterize the MAH of infall halos, where $z_{rm peak}$ and $z_{rm f}$ are the accretion and formation redshifts, respectively. We find that, at given $z_{rm peak}$, their MAH is bimodal. Infall halos are dominated by a young population at high redshift and by an old population at low redshift. For the young population, the $a_{rm nf}$ distribution is narrow and peaks at about $1.2$, independent of $z_{rm peak}$, while for the old population, the peak position and width of the $a_{rm nf}$ distribution both increases with decreasing $z_{rm peak}$ and are both larger than those of the young population. This bimodal distribution is found to be closely connected to the two phases in the MAHs of halos. While members of the young population are still in the fast accretion phase at $z_{rm peak}$, those of the old population have already entered the slow accretion phase at $z_{rm peak}$. This bimodal distribution is not found for the whole halo population, nor is it seen in halo merger trees generated with the extended Press-Schechter formalism. The infall halo population at $z_{rm peak}$ are, on average, younger than the whole halo population of similar masses identified at the same redshift. We discuss the implications of our findings in connection to the bimodal color distribution of observed galaxies and to the link between central and satellite galaxies.
The impact of the streaming between baryons and dark matter on the first structures has been actively explored by recent studies. We investigate how the key results are affected by two popular approximations. One is to implement the streaming by accounting for only the relative motion while assuming ``baryons trace dark matter spatially at the initialization of simulation. This neglects the smoothing on the gas density taking place before the initialization. In our simulation initialized at $z_i=200$, it overestimates the gas density power spectrum by up to 40% at $kapprox10^2~h~mbox{Mpc}^{-1}$ at $z=20$. Halo mass ($M_h$) and baryonic fraction in halos ($f_{b,h}$) are also overestimated, but the relation between the two remains unchanged. The other approximation tested is to artificially amplify the density/velocity fluctuations in the cosmic mean density to simulate the first minihalos that form in overdense regions. This gives a head start to the halo growth while the subsequent growth is similar to that in the mean density. The growth in a true overdense region, on the other hand, is accelerated gradually in time. For example, raising $sigma_8$ by 50% effectively transforms $zrightarrowsqrt{1.5}z$ in the halo mass growth history while in 2-$sigma$ overdensity, the growth is accelerated by a constant in redshift: $zrightarrow{z+4.8}$. As a result, halos have grown more in the former than in the latter before $zapprox27$ and vice versa after. The $f_{b,h}$-$M_h$ relation is unchanged in those cases as well, suggesting that the Pop III formation rate for a given $M_h$ is insensitive to the tested approximations.
Dissipative dark matter self-interactions can affect halo evolution and change its structure. We perform a series of controlled N-body simulations to study impacts of the dissipative interactions on halo properties. The interplay between gravitational contraction and collisional dissipation can significantly speed up the onset of gravothermal collapse, resulting in a steep inner density profile. For reasonable choices of model parameters controlling the dissipation, the collapse timescale can be a factor of 10-100 shorter than that predicted in purely elastic self-interacting dark matter. The effect is maximized when energy loss per collision is comparable to characteristic kinetic energy of dark matter particles in the halo. Our simulations provide guidance for testing the dissipative nature of dark matter with astrophysical observations.
Using the self-consistent modeling of the conditional stellar mass functions across cosmic time by Yang et al. (2012), we make model predictions for the star formation histories (SFHs) of {it central} galaxies in halos of different masses. The model requires the following two key ingredients: (i) mass assembly histories of central and satellite galaxies, and (ii) local observational constraints of the star formation rates of central galaxies as function of halo mass. We obtain a universal fitting formula that describes the (median) SFH of central galaxies as function of halo mass, galaxy stellar mass and redshift. We use this model to make predictions for various aspects of the star formation rates of central galaxies across cosmic time. Our main findings are the following. (1) The specific star formation rate (SSFR) at high $z$ increases rapidly with increasing redshift [$propto (1+z)^{2.5}$] for halos of a given mass and only slowly with halo mass ($propto M_h^{0.12}$) at a given $z$, in almost perfect agreement with the specific mass accretion rate of dark matter halos. (2) The ratio between the star formation rate (SFR) in the main-branch progenitor and the final stellar mass of a galaxy peaks roughly at a constant value, $sim 10^{-9.3} h^2 {rm yr}^{-1}$, independent of halo mass or the final stellar mass of the galaxy. However, the redshift at which the SFR peaks increases rapidly with halo mass. (3) More than half of the stars in the present-day Universe were formed in halos with $10^{11.1}msunh < M_h < 10^{12.3}msunh$ in the redshift range $0.4 < z < 1.9$. (4) ... [abridged]
A self-interacting dark matter halo can experience gravothermal collapse, resulting in a central core with an ultrahigh density. It can further contract and collapse into a black hole, a mechanism proposed to explain the origin of supermassive black holes. We study dynamical instability of the core in general relativity. We use a truncated Maxwell-Boltzmann distribution to model the dark matter distribution and solve the Tolman-Oppenheimer-Volkoff equation. For given model parameters, we obtain a series of equilibrium configurations and examine their dynamical instability based on considerations of total energy, binding energy, fractional binding energy, and adiabatic index. The numerical results from our semi-analytical method are in good agreement with those from fully relativistic N-body simulations. We further show for the instability to occur in the classical regime, the boundary temperature of the core should be at least $10%$ of the mass of dark matter particles; for a $10^9~{rm M_odot}$ seed black hole, the particle mass needs to be larger than a few keV. These results can be used to constrain different collapse models, in particular, those with dissipative dark matter interactions.
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