Interaction of Type Ia supernovae with their surroundings: The exponential profile in two dimensions

The evolution of Type Ia supernovae in the surrounding medium is studied using two-dimensional numerical hydrodynamic simulations. The ejecta are assumed to be described by an exponential density profile, following the work of Dwarkadas & Chevalier. The case of a circumstellar region formed by mass loss from the progenitor or a companion star is also considered. The decelerating contact discontinuity is found to be Rayleigh-Taylor (R-T) unstable, as expected, and the nature of the instability is studied in detail for two cases: (1) a constant density ambient medium, and (2) a circumstellar medium whose density scales as r(-2). The nature of the instability is found to be different in each case. In the case of a circumstellar medium the instability is much better resolved, and a fractal-like structure is seen. In the case of a constant density medium the extent of growth is less, and the R-T fingers are found to be limited by the presence of Kelvin-Helmholtz mushroom caps at the tips of the fingers. The unstable region is far enough away from the reverse shock that the latter is not affected by the mixing taking place in the interaction region. In contrast, the reverse shock in the case of a circumstellar medium is found to be rippled due to the formation of instabilities. In neither case is the outer shock front affected. These results are consistent with similar studies of power-law ejecta profiles conducted by Chevalier, Blondin, & Emmering. Our results are then applied to Tycho's supernova remnant. We conclude that it is unlikely that the instabilities seen in recent radio images of the remnant are similar to these studied herein, although we do not discount the possibility of initial conditions different from those studied herein leading to a much larger growth than we see in our simulations. We suggest that such instabilities may be better observed at X-ray wavelengths which probe the high-density shocked ejecta region.