Collapse of rotating gas clouds and formation of protostellar disks: Effects of temperature change during collapse

We show two-dimensional numerical simulations of the gravitational collapse of rotating gas clouds. We assume the polytropic equation of state, P = K rho(gamma), to take account of the temperature change during the collapse. Our numerical simulations have two model parameters, beta and gamma, which specify the initial rotation velocity and polytropic index, respectively. We show three models, beta = 1.0, 0.5, and 0.2, for each gamma, 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 (gamma = 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 (rho(c)) increases with time (t) in proportion to rho(c) proportional to (t - t(0))(-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, Sigma, is proportional to the power of the radial distance, Sigma(r) proportional to r(1-2 gamma), in the envelope. Models with gamma > 1 have geometrically thick disks (aspect ratio r(d)/z(d) similar or equal to 2), while those with gamma < 1 have very thin disks (r(d)/z(d) > 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 > t(0) for models with gamma > 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 beta and gamma are larger. Our models with gamma > 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 gamma > 1 are applicable to star formation in primordial clouds in which the temperature increase during the collapse is due to less efficient cooling.