Amplification, Saturation, and Q Thresholds for Runaway: Growth of Self-Gravitating Structures in Models of Magnetized Galactic Gas Disks

We investigate the susceptibility of gaseous, magnetized galactic disks to formation of self-gravitating condensations using two-dimensional, local models. We focus on two issues: (1) determining the threshold condition for gravitational runaway, taking into account nonlinear effects, and (2) distinguishing the magneto-Jeans instability (MJI) that arises under inner-galaxy rotation curves from the modified swing amplification (MSA) that arises under outer-galaxy rotation curves. For axisymmetric density fluctuations, instability is known to require a Toomre parameter Q<1. For nonaxisymmetric fluctuations, any nonzero shear $q \equiv -d\ln \Omega /d \ln R$ winds up wavefronts such that in linear theory amplification saturates. Any Q threshold for nonaxisymmetric gravitational runaway must originate from nonlinear effects. We use numerical magnetohydrodynamic simulations to demonstrate the anticipated threshold phenomenon, to analyze the nonlinear processes involved, and to evaluate the critical value $Q_c$ for stabilization. We find $Q_c \sim 1.2-1.4$ for a wide variety of conditions, with the largest values corresponding to nonzero but subthermal mean magnetic fields. Our findings for $Q_c$ are similar to those inferred from thresholds for active star formation in the outer regions of spiral galaxies. MJI is distinct from MSA in that opposition to Coriolis forces by magnetic tension, rather than cooperation of epicyclic motion with kinematic shear, enables nonaxisymmetric density perturbations to grow. We suggest that under low-shear inner-disk conditions, $Q_c$ will be larger than that in outer disks by a factor $\sim (v_A/q c_s)^{1/2}$, where $v_A$ and $c_s$ are the respective Alfven and sound speeds.