Tidal stability of interstellar clouds

The strong gravitational tidal field of supermassive black holes is thought to disrupt nearby interstellar gas clouds, preventing star formation. Recently, bipolar outflows, a "smoking- gun" for recent star formation, have been found within 2 parsecs of Sgr A* - the 4 × 10 6 M black hole at the centre of our galaxy. This work employs a semi-analytic approach based on the tensor virial theorem to describe the gross dynamics of interstellar clouds including tidal fields, external pressure, figure rotation, and internal streaming. A set of coupled ordinary differential equations describing the evolution of the cloud's axes, velocities, and figure are solved for equilibrium states, and their stability is examined by following their evolution in response to a transient perturbation. Solutions are presented where the physical sizes of the clouds are found as a function of density and axis ratios, which are dependent on the strength of the tidal field. Allowing counter-rotating internal streaming gives rise to two new classes of equilibria, one of which is stable, and for low masses, violates the Roche criterion for tidal disruption.