Merge or survive: Number of Population III stars per minihalo

Abstract

The formation process of Population III (PopIII) stars in the mass accretion phase is investigated by numerical experiments. The barotropic relation of primordial gas and artificial stiffening of the equation of state in very dense regions ($> 10^{15}~{\rm cm}^{-3}$) enables us to follow the fragmentation of PopIII circumstellar disks and the merging processes of the fragments. The disk becomes gravitationally unstable to fragmentation , followed by a rapid merger process typically within 100 yrs, which roughly corresponds to one orbital time of the circumstellar disk. We also find that the fragmentation of the gas disk around a multiple system, a circumbinary disk, is rare; however, it is frequent in the disk around an individual protostar. We also perform a simulation with standard sink particles, where the number and total mass of sink particles are in rough agreement with those of the stiff equation of state runs. Based on the results of these numerical results, we model the evolution of the number of fragments with a simple phenomenological equation. We find that the average number of fragments is roughly proportional to $t^{0.3}$, where $t$ is the elapsed time since the formation of the first protostar. Next, we compare this trend with a number of published numerical studies by scaling the elapsed time according to the scale-free nature of the system. As a result, we find most of the results in the literature agree well with the relation. Present results combined with the previous studies in the literature imply that the PopIII stars tend to be born not as single stars, but in multiple systems.