Non-Stationary Rayleigh-Taylor Instabilities in Pulsar Wind Interaction with a Supernova Shell.

The Rayleigh-Taylor instability (RTI) plays an important role in the dynamics of several astronomical objects, in particular, in the supernovae (SN) evolution. In the present paper we examine the dynamics of a shell (representing a type II SN remnant) blown-up by a wind emitted by a central pulsar. The shell is accelerated by the pulsar wind and its inner surface experiences the RTI. We develop an analytical approach by using a specific transformation into the coordinate frame co-moving with the SN ejecta. We first derive a non-stationary spherically symmetric solution describing an expansion of a gas shell under the pressure of a central source (pulsar). Then, we analyze its 3D stability with respect to a small perturbation on the inner shell surface. The dispersion relation is derived in the co-moving reference frame. The growth rate of the perturbation is found and its temporal evolution is discussed. We compare our result with the previous published studies and apply it to the Crab nebula evolution. [ABSTRACT FROM AUTHOR]