2006PASP..118..833C

We have expressed in linearized form the five classical coupled equations representing the rotating gas disk of a standard disk galaxy. We solve them in three limiting cases for the gas disk: (1) infinite thickness and uniform rotation, (2) finite thickness and uniform rotation, and (3) infinite thickness and a shearing box approximating differential rotation. We then tested the effect of a giant high-velocity cloud (HVC) colliding with a disk at velocities in excess of 100 km/s. We find that the usual Jeans criterion for the limit of cloud stability is modified by the additional term arising from the effect of the HVC collision with the gas disk. This term, which contains the velocity of the incoming cloud and a characteristic scale for the shock front, is closely comparable in magnitude to the original term (the square of the product of the sound speed and the characteristic wavenumber) in the static Jeans equation and is also similar in magnitude to the global effect of shear. This result shows that an HVC falling onto a disk that contains clouds close to Jeans equilibrium will generally be effective in triggering cloud collapse and subsequent star formation.