Classical and relativistic laws of motion for spherical supernovas

Abstract

We derive some first order differential equations which model the classical and the relativistic thin layer approximations. The circumstellar medium is assumed to follow a density profile which can be exponential, Gaussian, Plummer-like, self-gravitating of Lane--Emden ($n=5$) type, or power law. The first order differential equations are solved analytically, or numerically, or by a series expansion, or by recursion, or by Padé approximation. The initial conditions are chosen in order to model the temporal evolution of SN 1993J over ten years. The Padé approximated equations of motion are applied to four SNRs: Tycho, Cas A, Cygnus loop, and SN~1006.

35 Pages and 17 low quality figures. arXiv admin note: substantial text overlap with arXiv:1410.5193

References in corpus (3)

• High-Velocity Features in Type Ia Supernova Spectra
• SN 1993J VLBI (IV): A Geometric Determination of the Distance to M81 with the Expanding Shock Front Method
• Padé approximant for the equation of motion of a supernova remnant