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 the formation of self-gravitating condensations using two-dimensional, loca l models. We focus on two issues: (1) determining the threshold condition f or gravitational runaway, taking into account nonlinear effects; and (2) di stinguishing the magneto-Jeans instability (MJI) that arises under inner ga laxy rotation curves from the modified swing amplification (MSA) that arise s under outer galaxy rotation curves. For axisymmetric density fluctuations , instability is known to require a Toomre parameter Q < 1. For nonaxisymme tric fluctuations, any nonzero shear q = - d ln <Omega>/d ln R winds up wav e fronts such that in linear theory amplification saturates. Any Q threshol d for nonaxisymmetric gravitational runaway must originate from nonlinear e ffects. We use numerical magnetohydrodynamic simulations to demonstrate the anticipated threshold phenomenon, to analyze the nonlinear processes invol ved, and to evaluate the critical value Q, for stabilization. We find Q(c) similar to 1.2-1.4 for a wide variety of conditions, with the largest value s corresponding to nonzero but subthermal mean magnetic fields. Our finding s for Q, are similar to those inferred from thresholds for active star form ation in the outer regions of spiral galaxies. MJI is distinct from MSA in that opposition to Coriolis forces by magnetic tension, rather than coopera tion of epicyclic motion with kinematic shear, enables nonaxisymmetric dens ity perturbations to grow. We suggest that under low-shear inner disk condi tions, Q(c) will be larger than that in outer disks by a factor similar to (v(A)/qc(s))(1/2), where v(A) and c(s) are the respective Alfven and sound speeds.