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- W4386841403 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, $rho_{ej} propto t^{-3}gamma_{e}(R,t)^{-alpha}$, where $rho_{ej}$ is the medium proper density, $gamma_{e}$ is its Lorentz factor, $alpha>0$ is constant and $t$, $R$ are the time and radius from the center. We find that the shocks behavior can be characterized by their proper velocity, $U'=Gamma_s'beta_s'$, where $Gamma_s'$ is the shock Lorentz factor as measured in the immediate upstream frame and $beta_s'$ is the corresponding 3-velocity. While generally, we do not expect the shock evolution to be self-similar, for every $alpha>0$ we find a critical value $U'_c$ for which a self-similar solution with constant $U'$ exists. We then use numerical simulations to investigate the behavior of general shocks. We find that shocks with $U'>U'_c$ have a monotonously growing $U'$, while those with $U'<U'_c$ 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 ultra-relativistic." @default.
- W4386841403 created "2023-09-19" @default.
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- W4386841403 date "2023-09-15" @default.
- W4386841403 modified "2023-09-27" @default.
- W4386841403 title "Relativistic Spherical Shocks in Expanding Media" @default.
- W4386841403 doi "https://doi.org/10.48550/arxiv.2309.08309" @default.
- W4386841403 hasPublicationYear "2023" @default.
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