Interaction of a Pulsar Wind with the Expanding Supernova Remnant

Recent Hubble Space Telescope observations of the Crab Nebula show filamentary structures that appear to originate from the Rayleigh-Taylor (R-T) instability operating on the supernova ejecta accelerated by the pulsar-driven wind. In order to understand the origin and formation of the filaments in the Crab Nebula, we study the interaction of a pulsar wind with the uniformly expanding supernova remnant by means of numerical simulation. We derive the self-similar solution of this model for a general power-law density profile of supernova ejecta.

By performing two-dimensional numerical simulations, we find three independent instabilities in the interaction region between the pulsar wind and the expanding supernova remnant. The first weak instability occurs in the very beginning and is caused by the impulsive acceleration of supernova ejecta by the pulsar wind. The second instability occurs in the postshock flow (shock wave driven by pulsar bubble) during the intermediate stage. This second instability develops briefly while the gradients of density and pressure are of opposite signs (satisfying the criterion of the R-T instability). The third and most important instability develops as the shock driven by the pulsar bubble becomes accelerated (r ∝ t^6/5). This is the strongest instability and produces pronounced filamentary structures that resemble the observed filaments in the Crab Nebula. Our numerical simulations can reproduce important observational features of the Crab Nebula. The high-density heads in the R-T fingertips are produced because of the compressibility of the gas. The density of these heads is found to be about 10 times higher than other regions in the fingers. The mass contained in the R-T fingers is found to be 60%-75% of the total shocked mass, and the kinetic energy within the R-T fingers is 55%-72% of the total kinetic energy of the shocked flow. The R-T fingers are found to accelerate with a slower rate than the shock front, which is consistent with the observations. By comparing our simulations and the observations, we infer that the some finger-like filaments (region F or G in Hester's observations) started to develop about 657 yr ago.