Self-similar solutions for the interaction of stellar ejecta with an external medium

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Abstract
The interaction of a uniformly expanding gas with a stationary ambient medium is studied in the case where the expanding matter has a power-law density profile (ρ ∝ r-n), as well as the ambient medium (ρ ∝ r-s). Self-similar solutions for the structure of the interaction region can be found provided that s5. Models for Type I supernovae indicate that a ρ ∝ r-7 profile may occur in the outer part of the expanding star. The n = 7, s = 0 solution is applied to the remnant of Tycho's supernova, and it is found to reproduce the basic dynamical and morphological properties of the remnant. The model may also explain the lack of strong Fe line emission in the X-ray spectrum. The solutions with s = 2 are applicable to Type II supernovae because the expanding supernova envelopes probably interact with regions of presupernova mass loss. The properties of the interactions region are important for the X-ray emission from Type II supernovae.

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