Shock waves in astrophysical gaseous disks: Effects of finite disk thickness and of vertical motions

A proper quasi-two-dimensional model of thin astrophysical gaseous disks mu st take into account the generation of vertical motions in the disk, and fi nite and variable disk thickness. Using such a quasi-two-dimensional model, we consider the existence of a steady-state shock wave generated by a nona xisymmetric distribution of the gravitational field in the disk. We find co nditions under which the shock front cannot be in steady state in the vicin ity of a gravitational potential well. The significant differences between the results that we obtained using this model and standard quasi-two-dimens ional models, which assume either constant disk thickness or vertical hydro static equilibrium, lend support to the conclusion that the latter are impr oper. We discuss applications of the results in the theory of galactic shoc k waves in spiral galaxies and shock waves in accretion disks.