CONVECTIVE INSTABILITY OF HOLLOW SEDOV-TAYLOR BLAST WAVES

The self-similar solutions by Sedov and Taylor for a strong spherical shock in an ideal gas are evacuated at their centers if the preshock density falls as a high power of radius. These solutions could represent an idealized form of a supernova blast wave in the early phase when the shock moves through the stellar envelope. For astrophysically relevant values of the adiabatic index, the hollow solutions are unstable to global convective modes: that is, the compressible generalization of Rayleigh-Taylor modes. For very large spherical harmonic degrees l, the growth rate scales as l1/2 and the eigenfunction is concentrated within a distance proportional to 1/l of the inner edge of the fluid. A condition is also given for local convective instability, which may exist even when unstable global modes do not.