Date of Award


Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy (PhD)

Degree Program


First Advisor

Houjun Mo

Second Advisor

Martin D. Weinberg

Third Advisor

Todd M. Tripp

Subject Categories

Astrophysics and Astronomy


I carried out systematic studies on the assembly history of dark matter halos, using numerical simulations and semi-analytical methods. First, I look into dark halo mass assembly history. I confirmed that the halo mass assembly is divided into a fast accretion phase and a slow accretion phase. These two phases are found to be separated by the epoch when the dark halo potential reaches its maximum. The fast accretion phase is dominated by mergers, especially major mergers; the slow accretion phase is dominated by slow mass accretion. Each halo experiences about 3±2 major mergers since its main progenitor had a mass equal to 1 percent of halo mass. However, the average redshift at which these major mergers occur is strongly mass dependent. Secondly, I investigate the formation times and the assembly bias of dark halos. I use eight different definitions of halo formation times to characterize the different aspects of the halo assembly history. I find that these formation times have different dependence on halo mass. While some formation times characterize well the hierarchical nature of halo formation, the trend is reversed for other definitions of the formation time. In addition, the formation-time dependence of halo bias is quite strong for some definitions of formation time but weak or absent for others. Thirdly, I study sub-halo mass function in the halo assembly history, with the generally known unevolved sub-halo mass functions (USMFs). I find that for subhalos that merge into the main progenitor of a present-day halo, their USMF can be well described by a universal functional form; the same conclusion can also be reached for the USMF of all sub-halos that have merged during the entire halo merging history. In these two cases, the USMFs do not seem to depend on the redshift of the host halo either. However, due to the mass loss caused by dynamical effects, only small part of the accreted halos survived and became sub-structures in the present-day dark halos. In the cluster-sized halos, 30% survived sub-halos are sub-subhalos. The sub-halo mass function at given accretion time (redshift) is also investigated to find the origin of the statistics mentioned above.