Evolution of Nonradiative Supernova Remnants

We conduct an analytic and numerical study of the dynamics of supernova remnant (SNR) evolution from the ejecta-dominated stage through the Sedov-Taylor (ST) stage, the stages that precede the onset of dynamically significant radiative losses and/or pressure confinement by the ambient medium. We assume spherical symmetry and focus on the evolution of ejecta described by a power-law density distribution expanding into a uniform ambient medium. We emphasize that all nonradiative remnants of a given power-law structure evolve according to a single unified solution, and we discuss this general property in detail. Use of dimensionless quantities constructed from the characteristic dimensional parameters of the problem—the ejecta energy, ejecta mass, and ambient density—makes the unified nature of the solution manifest. It is also possible to obtain a unified solution for the ST and radiative stages of evolution, and we place our work in the context of scaling laws for solutions for SNR evolution in those stages. We present numerical simulations of the flow and approximate analytic solutions for the motions of both the reverse shock and blast-wave shock. These solutions follow the shocks through the nonradiative stages of remnant evolution across periods of self-similar flow linked by non-self-similar behavior. We elucidate the dependence of the ejecta-dominated evolution on the ejecta power-law index n by developing a general trajectory for all n and explaining its relation to the solutions of Chevalier and Nadyozhin for n>5 and Hamilton & Sarazin for n=0. We demonstrate excellent agreement between our analytic solutions and numerical simulations. These solutions should be valuable in describing remnants such as SN 1006, Tycho, Kepler, Cassiopeia A, and other relatively young SNRs that are between the early ejecta-dominated stage and the late Sedov-Taylor stage. In appendices, we extend our results to power-law ambient media, and we describe an early period of the evolution in which the SNR is radiative and evolves according to a nonunified solution.