Although rare, tidal disruption events, the dismemberment of a star by a massive black hole, are now observable. These events provide a special window on accretion dynamics because they violate many of the standard assumptions: they are intrinsically transient, the fluid orbits are far from circular, the density distribution is strongly asymmetric, the mass accretion rate can be substantially super-Eddington, and shocks are important to both angular momentum transport and orbital energy dissipation. Recent hydrodynamical simulations have uncovered some of the consequences of these departures from standard accretion theory; at a semi-quantitative level, predictions based upon them agree well with observations.
The highly eccentric character of the stellar debris orbits also motivates development of an improved theory for accretion dynamics in such a situation, beginning with how eccentricity alters the character of the magneto-rotational instability, the fundamental mechanism generating the internal stresses that ordinarily make accretion possible. I will report results from the first step in this program, a linear theory of the magneto-rotational instability in eccentric accretion flows.