Abstract
The thin layer approximation applied to the expansion of a supernova remnant assumes that all the swept mass resides in a thin shell. The law of motion in the thin layer approximation is therefore found using the conservation of momentum. Here we instead introduce the conservation of energy in the framework of the thin layer approximation. The first case to be analysed is that of an interstellar medium with constant density and the second case is that of 7 profiles of decreasing density with respect to the centre of the explosion. The analytical and numerical results are applied to 4 supernova remnants: Tycho, Cas A, Cygnus loop, and SN 1006. The back reaction due to the radiative losses for the law of motion is evaluated in the case of constant density of the interstellar medium.
Highlights
The thin layer approximation assumes that the mass ejected in the explosion of a supernova (SN) resides in a thin layer
The thin layer approximation applied to the expansion of a supernova remnant assumes that all the swept mass resides in a thin shell
Can we model the energy conservation when the density of the interstellar medium (ISM) decreases with the distance from the point of the explosion? In order to answer the above questions, Section 2 reviews the standard laws of conservation, Section 3 introduces the conservation of energy and Section 4 applies the derived equations of motion to 4 supernova remnant (SNR)
Summary
The thin layer approximation assumes that the mass ejected in the explosion of a supernova (SN) resides in a thin layer. This approximation is usually applied in the late stage of the explosion in order to explain the supernova remnant (SNR), see [1] [2] [3]. Can we model the expansion of an SNR when the energy is conserved rather than the momentum?. Can we model the energy conservation when the density of the interstellar medium (ISM) decreases with the distance from the point of the explosion? In order to answer the above questions, Section 2 reviews the standard laws of conservation, Section 3 introduces the conservation of energy and Section 4 applies the derived equations of motion to 4 SNRs
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