Collapse of Rotating Gas Clouds and Formation of Protostellar Disks: Effects of Temperature Change during Collapse

Abstract

We show two-dimensional numerical simulations of the gravitational collapse of rotating gas clouds. We assume the polytropic equation of state, P = Kργ, to take account of the temperature change during the collapse. Our numerical simulations have two model parameters, β and γ, which specify the initial rotation velocity and polytropic index, respectively. We show three models, β= 1.0, 0.5, and 0.2, for each γ, which is taken to be 0.8, 0.9, 0.95, 1.05, 1.1, or 1.2. These 18 models are compared with previously reported isothermal models (γ = 1). In each model a rotating cylindrical cloud initially in equilibrium fragments periodically because of the growth of a velocity perturbation and forms cloud cores. The cloud core becomes a dynamically collapsing gaseous disk whose central density (ρc) increases with time (t) in proportion to ρc ∝ (t - t0)-2. This collapse is qualitatively similar in density and velocity distributions to the runaway collapse of a rotating isothermal cloud. The surface density of the disk, Σ, is proportional to the power of the radial distance, Σ(r) ∝ r1 - 2γ, in the envelope. Models with γ > 1 have geometrically thick disks (aspect ratio rd/zd ≃ 2), while those with γ < 1 have very thin disks (rd/zd > 10). While the former disks are stable, the latter disks are unstable against fragmentation if we adopt the Toomre stability criterion for a thin gaseous disk. Our numerical simulations also show the growth of a rotationally supported disk by radial accretion in a period t > t0 for models with γ > 1. The accretion phase starts at a stage in which the central density is still finite. The central density at the beginning of the accretion phase is lower when β and γ are larger. Our models with γ < 1 are applicable to star formation in turbulent gas clouds in which the effective sound speed decreases with increase in the density. Our models with γ > 1 are applicable to star formation in primordial clouds in which the temperature increase during the collapse is due to less efficient cooling.