Supercloud formation by gravitational collapse of magnetic gas in the crest of a spiral density wave

The dispersion relations for radial and azimuthal gravitational instabilities in a magnetic gas that flows through a spiral density wave are derived considering the time-dependent flow and shear fields in the linear wave. The results are approximately the same as the dispersion relations without the spiral wave except for the substitution of local values for the density, magnetic field strength, and epicyclic frequency. The instability leads to the formation of 10^7^ M_sun_ cloud complexes with a characteristic spacing of ~3 times the arm width. Spiral arms can trigger an excess of star formation if the arm density exceeds several times the average critical value at that radius and if Gμ/c^2^ > 1 for mass per unit length p along the arm and velocity dispersion c.