Affiliation:
1. School of Physics and Astronomy, Tel Aviv University , Tel Aviv 6997801 , Israel
Abstract
ABSTRACT
We investigate the propagation of spherically symmetric shocks in relativistic homologously expanding media with density distributions following a power-law profile in their Lorentz factor. That is, $\rho _{_{\rm {ej}}} \propto t^{-3}\gamma _{_{\rm {ej}}}(r,t)^{-\alpha }$, where $\rho _{_{\rm {ej}}}$ is the medium proper density, $\gamma _{_{\rm {ej}}}$ is its Lorentz factor, α > 0 is constant, and t, r are the time and radius from the centre. We find that the shocks behaviour can be characterized by their proper velocity, $U^{\prime }=\Gamma _s^{\prime }\beta _s^{\prime }$, where $\Gamma _s^{\prime }$ is the shock Lorentz factor as measured in the immediate upstream frame and $\beta _s^{\prime }$ is the corresponding three velocity. While generally, we do not expect the shock evolution to be self-similar, for every α > 0 we find a critical value $U^{\prime }_c$ for which a self-similar solution with constant U′ exists. We then use numerical simulations to investigate the behaviour of general shocks. We find that shocks with $U^{\prime }\gt U^{\prime }_c$ have a monotonously growing U′, while those with $U^{\prime }\lt U^{\prime }_c$ have a decreasing U′ and will eventually die out. Finally, we present an analytic approximation, based on our numerical results, for the evolution of general shocks in the regime where U′ is ultrarelativistic.
Publisher
Oxford University Press (OUP)
Subject
Space and Planetary Science,Astronomy and Astrophysics