2017ApJ...845..139B

For pulsars born in supernovae, the expansion of the shocked pulsar wind nebula is initially in the freely expanding ejecta of the supernova. While the nebula is in the inner flat part of the ejecta density profile, the swept-up, accelerating shell is subject to the Rayleigh-Taylor instability. We carried out two- and three-dimensional simulations showing that the instability gives rise to filamentary structure during this initial phase but does not greatly change the dynamics of the expanding shell. The flow is effectively self-similar. If the shell is powered into the outer steep part of the density profile, the shell is subject to a robust Rayleigh-Taylor instability in which the shell is fragmented and the shocked pulsar wind breaks out through the shell. The flow is not self-similar in this phase. For a wind nebula to reach this phase requires that the deposited pulsar energy be greater than the supernova energy, or that the initial pulsar period be in the ms range for a typical 10⁵¹ erg supernova. These conditions are satisfied by some magnetar models for Type I superluminous supernovae. We also consider the Crab Nebula, which may be associated with a low energy supernova for which this scenario applies.