Gravitational instability of magnetized gaseous disks

The gravitational instability is investigated for an isothermal gaseous disk threaded perpendicularly by a uniform, frozen-in magnetic field with the linear perturbation analysis. It is found that the disk is stable when σ0/B0 < (4π2G)sup(-1/2), where σ0 and B0 are the column density of the disk and magnetic field strength in the unperturbed state, respectively, and G is the gravitational constant. When σ0/B0 > (4π2G)sup(-1/2), there is a critical wavelength above which the waves are unstable. Shorter waves are stabilized by the gas pressure. The critical wavelength decrease as σ0/B0 increases, but it neve becomes less than several times the scale height of the disk. (author)