Shock evolution in non-radiative supernova remnants

We present a new analytical approach to derive approximate solutions describing the shock evolution in non-radiative supernova remnants (SNRs). We focus on the study of the forward shock and contact discontinuity while application to the reverse shock is only discussed briefly. The spherical shock evolution of an SNR in both the interstellar medium with a constant density profile and a circumstellar medium with a wind density profile is investigated. We compared our new analytical solution with numerical simulations and found that a few per cent accuracy is achieved. For the evolution of the forward shock, we also compared our new solution to previous analytical models. In a uniform ambient medium, the accuracy of our analytical approximation is comparable to that in Truelove & McKee. In a wind density profile medium, our solution performs better than that in Micelotta, Dwek & Slavin, especially when the ejecta envelope has a steep density profile. The new solution is significantly simplified compared to previous analytical models, as it only depends on the asymptotic behaviours of the remnant during its evolution.