Interaction of a Pulsar Wind with the Expanding Supernova Remnant

Recent HST observations of the Crab Nebula show filamentary structures thatappear to originate from the Rayleigh-Taylor (R-T) instability operating on thesupernova ejecta accelerated by the pulsar-driven wind. In order to understandthe origin and formation of the filaments in the Crab Nebula, we study theinteraction of a pulsar wind with the uniformly expanding supernova remnant bymeans of numerical simulation. By performing two-dimensional numericalsimulations, we find three independent instabilities in the interaction regionbetween the pulsar wind and the expanding supernova remnant. The most importantinstability develops as the shock driven by the pulsar bubble becomesaccelerated ($r \propto t^{6/5}$). The instability produces pronouncedfilamentary structures that resemble the observed filaments in the Crab Nebula.Our numerical simulations can reproduce important observational features of theCrab Nebula. The high density heads in the R-T finger tips are produced becauseof the compressibility of the gas. The density of these heads is found to beabout 10 times higher than other regions in the fingers. The mass contained inthe R-T fingers is found to be $60 % - 75 %$ of the total shocked mass and thekinetic energy within the R-T fingers is $55 % - 72 %$ of the total kineticenergy of the shocked flow. The R-T fingers are found to accelerate with aslower rate than the shock front, which is consistent with the observations. Bycomparing our simulations and the observations, we infer that the somefinger-like filaments (region F or G in Hester's observation) started todevelop about 657 years ago.Comment: 16 pages, 9 figures, 1 table, accepted for Astrophysical Journa