Relaxation of protostellar accretion shocks using the smoothed particle hydrodynamics

It is believed that protostellar accretion disks to be formed from nearly ballistic infall of the molecular matters in rotating core collapse. Collisions of these infalling matters lead to formation of strong supersonic shocks, which if they cool rapidly, result in accumulation of that material in a thin structure in the equatorial plane. Here, we investigate the relaxation time of the protostellar accretion post-shock gas using the smoothed particle hydrodynamics (SPH). For this purpose, a one-dimensional head-on collision of two molecular sheets is considered, and the time evolution of the temperature and density of the post-shock region simulated. The results show that in strong supersonic shocks, the temperature of the post-shock gas quickly increases proportional to square of the Mach number, and then gradually decreases according to the cooling processes. Using a suitable cooling function shows that in appropriate time-scale, the center of the collision, which is at the equatorial plane of the core, is converted to a thin dense molecular disk, together with atomic and ionized gases around it. This structure for accretion disks may justify the suitable conditions for grain growth and formation of proto-planetary entities.