Revisiting the evolution of nonradiative supernova remnants: A hydrodynamical-informed parameterization of the shock positions

Understanding the evolution of a supernova remnant shell in time is fundamental. Such understanding is critical to build reliable models of the dynamics of the supernova remnant shell interaction with any pulsar wind nebula it might contain. Here, we perform a large study of the parameter space for the one-dimensional spherically symmetric evolution of a supernova remnant, accompanying it by analytical analysis. Assuming, as is usual, an ejecta density profile with a power-law core and an envelope, and a uniform ambient medium, we provide a set of highly-accurate approximations for the evolution of the main structural features of supernova remnants, such as the reverse and forward shocks and the contact discontinuity. We compare our results with previously adopted approximations, showing that existing simplified prescriptions can easily lead to large errors. In particular, in the context of pulsar wind nebulae modelling, an accurate description for the supernova remnant reverse shock is required. We also study in depth the self-similar solutions for the initial phase of evolution, when the reverse shock propagates through the envelope of the ejecta. Since these self-similar solutions are exact, but not fully analytical, we here provide highly-accurate approximations as well.