The Growth and Structure of Dark Matter Haloes

In this paper, we analyse in detail the mass-accretion histories and structural properties of dark haloes in high-resolution N-body simulations. Modeling the density distribution in individual haloes with the NFW profile, we find, for all main progenitors of a given halo, there is a tight correlation between its inner scale radius $r_s$ and the mass within it, $M_s$, which is the basic reason why halo structural properties are closely related to their mass-accretion histories. This correlation can be used to predict accurately the structural properties of a dark halo at any time from its mass-accretion history. We also test our model with a large sample of GIF haloes. The build-up of dark haloes in CDM models generally consists of an early phase of fast accretion and a late phase of slow accretion [where $M_h$ increases with time approximately as the expansion rate]. These two phases are separated at a time when the halo concentration parameter $c\sim 4$. Haloes in the two accretion phases show systematically different properties, for example, the circular velocity $v_h$ increases rapidly with time in the fast accretion phase but remain almost constant in the slow accretion phase,the inner properties of a halo, such as $r_s$ and $M_s$ increase rapidly with time in the fast accretion phase but change only slowly in the slow accretion phase. The potential well associated with a halo is built up mainly in the fast accretion phase, even though a large amount of mass (over 10 times) can be accreted in the slow accretion phase. We discuss our results in connection to the formation of dark haloes and galaxies in hierarchical models.Comment: 26 pages, including 10 figures. v2: some conceptual changes. Accepted for publication in MNRA

The statistical nature of the brightest group galaxies

We examine the statistical properties of the brightest group galaxies (BGGs) using a complete spectroscopic sample of groups/clusters of galaxies selected from the Data Release 7 of the Sloan Digital Sky Survey. We test whether BGGs and other bright members of groups are consistent with an ordered population among the total population of group galaxies. We find that the luminosity distributions of BGGs do not follow the predictions from the order statistics (OS). The average luminosities of BGGs are systematically brighter than OS predictions. On the other hand, by properly taking into account the brightening effect of the BGGs, the luminosity distributions of the second brightest galaxies are in excellent agreement with the expectations of OS. The brightening of BGGs relative to the OS expectation is consistent with a scenario that the BGGs on average have over-grown about 20 percent masses relative to the other member galaxies. The growth ($\Delta M$) is not stochastic but correlated with the magnitude gap ($G_{1,2}$) between the brightest and the second brightest galaxy. The growth ($\Delta M$) is larger for the groups having more prominent BGGs (larger $G_{1,2}$) and averagely contributes about 30 percent of the final $G_{1,2}$ of the groups of galaxies.Comment: ApJ accepted, replaced with the accepted versio

A two-phase model of galaxy formation: II. The size-mass relation of dynamically hot galaxies

In Paper-I we developed a two-phase model to connect dynamically hot galaxies (such as ellipticals and bulges) with the formation of self-gravitating, turbulent gas clouds (SGC) associated with the fast assembly of dark matter halos. Here we explore the implications of the model for the size-stellar mass relation of dynamically hot galaxies. Star-forming sub-clouds produced by the fragmentation of the SGC inherit its spatial structure and dynamical hotness, which produces a tight and 'homologous' relation, $r_{\rm f}\approx\, 100 r_{\rm bulge}$, between the size of a dynamically hot galaxy ($r_{\rm bulge}$) and that of its host halo assembled in the fast assembly regime ($r_{\rm f}$), independent of redshift and halo mass. This relation is preserved by the 'dry' expansion driven by dynamical heating when a galaxy becomes gas-poor due to inefficient cooling, and is frozen during the slow assembly regime when the bulge stops growing in mass and dynamical heating is no longer effective. The size-stellar mass relation is thus a simple combination of the galaxy-halo homology and the non-linear relation between stellar mass and halo mass. Using a set of halo assembly histories we demonstrate that this model can reproduce all properties in the observed size-mass relation of dynamically hot galaxies, including the flattening of the relation in the low-mass end and the upturn in the very massive end. The predicted evolution of this relation matches observational data currently available to redshift $z \approx 4$, and can be tested in the future at higher $z$. Our results indicate that the sizes of dynamically hot galaxies are produced by the dissipation and collapse of gas in dark matter halos to establish self-gravitating systems of sub-clouds in which stars form.Comment: 9 pages, 4 figures, 1 table; submitted to MNRA