Propagation of spiral density waves in a magneto-active disk (Q1331344)

The wave propagation problem is investigated in a differentially rotating, self-gravitating, magneto-active and highly flattened disk. The main purpose is the study of spiral density waves, esp. using the formalism for tightly wound spirals. Since the equations are nonlinear ones, even those obtained after the linearization are rather complicated, and more rigorous treatment offered by the WKB-approximation procedure is needed for the following results. Local dispersion relations can be obtained, and the effect of magnetic field and rotation on the growth rate and other parameters can be evaluated. The fate of the disc can be sketched; the disk stability largely depends on the fight among stabilizing effects of the finite pressure and the conservation of momentum on one hand, and the destabilizing effects of Jeans' tendency on the other. If the latter win, the result is Jeans' collapse. A more detailed discussion of the effects is also given, as well as of the importance of this problem to different branches of astrophysics.