Linear Stability of Magnetized Massive Protoplanetary Disks

Magnetorotational instability (MRI) and gravitational instability (GI) are the two principle routes to turbulent angular momentum transport in accretion disks. Protoplanetary disks (PPDs) may develop both. This paper aims to reinvigorate interest in the study of magnetized massive PPDs, starting from the basic issue of stability. The local linear stability of a self-gravitating, uniformly magnetized, differentially rotating, three-dimensional stratified 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 (SG) can decrease MRI growth rates; the MRI becomes global in the vertical direction, and MRI modes with small radial length scales are stabilized. The maximum vertical field strength that permits the MRI in a strongly self-gravitating polytropic disk with polytropic index Γ = 1 is estimated to be B_{z,{max}} \simeq c_{s0}\Omega \sqrt{\mu _0/16\pi G}, where c _s0 is the midplane sound speed and Ω is the local angular velocity. 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, SG can enhance density perturbations, an effect that becomes significant in the presence of a strong toroidal field, and which depends on the symmetry of the underlying MRI mode. 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 nonlinear simulations are discussed briefly.