Dynamic instabilities in rotating, low-mass protostars during early disk formation

Abstract

We have recently constructed evolutionary model sequences for the equilibrium cores of rotating, low-mass protostars during their accretion phase. The cloud that collapses to form the core is assumed to be a pressure-supported, singular isothermal sphere in uniform rotation. The equilibrium core is assumed to be an isentropic, monatomic ideal gas. When T/∥ W∥ ≥ 0.1, where T is the rotational kinetic energy and W is the gravitational potential energy, these core models represent the early disk formation stage. A linear stability analysis suggests that, for T/∥ W∥ ≥ 0.13, the star/disk systems are dynamically unstable to nonaxisymmetric disturbances, with the fastest growth predicted for disturbances with four- or fivefold symmetry. By using one of our protostellar core models with T/∥ W∥ = 0.157 as the initial configuration in a three-dimensional hydrodynamics code, we have confirmed the dynamic instability of numerous multiarmed spiral disturbances. A disturbance with fourfold symmetry has the fastest growth rate and dominates in the linear regime. Swing amplification seems to be the mechanism that drives the dynamic growth. In the nonlinear regime, power shifts to threefold and then to twofold disturbances, but we do not detect any significant transport of mass or angular momentum nor any tendency for the disk to fragment by the end of a calculation spanning six and a half rotations. In one calculation, we also detect dynamic growth of a onefold disturbance. We conclude that fast-growing nonaxisymmetric instabilities set in as soon as Keplerian disks form during star formation, even when the disks have only limited radial extent.