Simulating Stability of Massive Protoplanetary Disks

Linear stability of magnetized massive protoplanetary disks

Author:

Lin

Abstract:

Magneto-rotational instability (MRI) and gravitational instability (GI) are the two principle routes to turbulent angular momentum transport in accretion disks. Protoplanetary disks may develop both. This paper aims to reinvigorate interest in the study of magnetized massive protoplanetary disks, starting from the basic issue of stability. The local linear stability of a self-gravitating, uniformly magnetized, differentially rotating, three-dimensional disk subject to axisymmetric perturbations is calculated numerically. The formulation includes resistivity. It is found that the reduction in the disk thickness by self-gravity can decrease MRI growth rates; the MRI becomes global in the vertical direction, and MRI modes with small radial length scales are stabilized. In massive disks with layered resistivity, the MRI is not well-localized to regions where the Elsasser number exceeds unity. For MRI modes with radial length scales on the order of the disk thickness, self-gravity can enhance density perturbations, an effect that becomes significant in the presence of a strong toroidal field. In gravitationally unstable disks where GI and MRI growth rates are comparable, the character of unstable modes can transition smoothly between MRI and GI. Implications for non-linear simulations are discussed briefly.