Recently obtained Hubble Space Telescope WFPC2 images of the Crab Nebula show that the emission-line filaments are dominated by structures that morphologically appear to be the result of magnetic RayleighTaylor (R-T) instabilities at the interface between the pulsar-driven synchrotron nebula and a shell of swept-up ejecta. We replace this morphological argument with a quantitative treatment of the growth rate and characteristic wavelength of such instabilities. Using published data on the rate of expansion of the synchrotron nebula and the density of the ejecta, together with a wavelength for the instability measured from the WFPC2 images, we calculate a magnetic field strength of ∼540 μG. This is within a factor of 2 of the canonical minimum energy equipartition field of 300 μG, and probably closer than that to a more realistic estimate of the field at the edge of the Crab. Comparison of the detailed morphology and ionization structure of the R-T fingers in the Crab with recent magnetohydrodynamical simulations which follow the development of magnetic R-T instabilities into the non-linear regime is used to establish a sequence of filament properties which are determined by the density of the shell of swept-up ejecta at the edge of the synchrotron nebula. When the density is below a critical value, the interface is stable. For somewhat higher densities R-T instabilities grow, but the field, which becomes aligned along the length of the R-T fingers, is strong enough to prevent the development of secondary KelvinHelmholtz (K-H) instabilities as the finger falls through the lighter medium. At higher densities these K-H instabilities develop, but the field is still strong enough to maintain a long streamer-like connection between the head of the filament and the shell. In a few cases, the density of the shell is high enough that the magnetic field is unable to prevent the fragmentation of R-T fingers, and the structure becomes more characteristic of a nonmagnetic R-T instability. The magnetic field is oriented along the length of an R-T finger, so material is free to "pour" into the finger from above. In equilibrium, gradients in thermal pressure and effective gravity must balance along field lines. As a result, loss of pressure support in the fingers due to cooling enhances the flow of material into the fingers, "siphoning" gas into the finger from above. If an extended remnant of ejecta surrounds the visible extent of the Crab, as has been suggested frequently, then the synchrotron nebula is expanding through this extended remnant, sweeping up ejecta as it goes. R-T instabilities channel this swept-up ejecta into the hierarchy of dense visible filaments. It seems likely that the current system of filaments originated as a result of R-T instabilities as the synchrotron nebula expanded out through more uniformly distributed ejecta. If an extended remnant remains today, then filament formation is an ongoing process. The ionization structure of filaments is also found to change in a systematic way as a function of the relative importance of the magnetic field and the mass density. Filaments which are dominated by the magnetic field are confined by the field and have sharp, well defined edges. Filaments in which the magnetic field is less dominant consist of high-density, low-ionization cores embedded within more extended high-ionization material. This confirms a previous suggestion that variations in magnetic confinement are an important caveat to published interpretations of spectra of Crab filaments.
All Science Journal Classification (ASJC) codes
- Astronomy and Astrophysics
- Space and Planetary Science
- ISM: Individual (Crab Nebula)
- ISM: Structure -radiation mechanisms: Nonthermal