Q criterion for disc stability modified by external tidal field

Understand

The standard Q criterion (with Q > 1) describes the local stability of a disc supported by rotation and random motion.

• Most astrophysical discs, however, are under the influence of an external gravitational field which can affect their stability.
• A typical example is a galactic disc embedded in a dark matter halo.
• Here we do a linear perturbation analysis for a disc in an external field, and obtain a generalized dispersion relation and a modified stability criterion.