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 \ Koc, to take account of the temperature change during the collapse. Our numerical simulations have two model parameters, b and c, which specify the initial rotation velocity and polytropic index, respectively. We show three models, b \ 1.0, 0.5, and 0.2, for each c, 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 (c \ 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 increases with time (t) inThis collapse is qualitatively similar in density and velocity distributions o c P (t [ t 0 )~2. to the runaway collapse of a rotating isothermal cloud. The surface density of the disk, &, is proportional to the power of the radial distance, &(r) P r1~2c, in the envelope. Models with c [ 1 have geometrically thick disks (aspect ratio while those with c \ 1 have very thin disks 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 for models with c [ 1. The accretion phase t [ t 0 starts at a stage in which the central density is still Ðnite. The central density at the beginning of the accretion phase is lower when b and c are larger. Our models with c \ 1 are applicable to star formation in turbulent gas clouds in which the e †ective sound speed decreases with increase in the density. Our models with c [ 1 are applicable to star formation in primordial clouds in which the temperature increase during the collapse is due to less efficient cooling.

Formation Scenario for Wide and Close Binary Systems

“…Fragmentation does not occur in the isothermal phase when the cloud collapses in a self-similar fashion because the self-similar solution with ¼ 1 exists even in a rotating collapsing cloud ( Matsumoto et al 1997;Matsumoto & Hanawa 1999). On the other hand, the clouds with > 1 form rotating disks and stop the contraction because no self-similar solution exists (Saigo et al 2000). These clouds can fragment as shown in Saigo et al (2004).…”

Evolution of First Cores in Rotating Molecular Cores

“…This power-law index is steeper than that of the spherically collapsing polytropic gas of r À2/(2À) ¼ r À2:22 ( ¼ 1:1; Suto & Silk 1988). In the case of > 1, the ratio of the centrifugal force to the pressure gradient force increases gradually during the runaway collapse phase (Saigo et al 2000). Such a rapid increase in the centrifugal force effectively makes the gas stiffer.…”

The Formation of Population III Binaries

“…The formation of a rotationally sup-19 Ϫ3 n p 1.82 # 10 c ported disk is an important consequence for the binary formation. If the equation of state is perfectly isothermal (g p ), the runaway collapse of a rotating cloud continues to form 1 the central singularity without forming a rotationally supported disk (Saigo & Hanawa 1998;Saigo et al 2000). However, the present simulation shows that the runaway collapse stops before producing the central singularity in the case of .…”