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Published November 2009 | Published
Journal Article Open

Composite self-similar solutions for relativistic shocks: The transition to cold fluid temperatures

Abstract

The flow resulting from a strong ultrarelativistic shock moving through a stellar envelope with a polytropelike density profile has been studied analytically and numerically at early times while the fluid temperature is relativistic—that is, just before and after the shock breaks out of the star. Such a flow should expand and accelerate as its internal energy is converted to bulk kinetic energy; at late enough times, the assumption of relativistic temperatures becomes invalid. Here we present a new self-similar solution for the postbreakout flow when the accelerating fluid has bulk kinetic Lorentz factors much larger than unity but is cooling through p/n of order unity to subrelativistic temperatures. This solution gives a relation between a fluid element's terminal Lorentz factor and that element's Lorentz factor just after it is shocked. Our numerical integrations agree well with the solution. While our solution assumes a planar flow, we show that corrections due to spherical geometry are important only for extremely fast ejecta originating in a region very close to the stellar surface. This region grows if the shock becomes relativistic deeper in the star.

Additional Information

© 2009 American Institute of Physics. Received 15 July 2009; accepted 25 August 2009; published 13 November 2009. This research was partially funded by an IRG grant, a NASA ATP grant, and NSF Grant No. PHY-0503584. M.P. thanks Frank and Peggy Taplin and the Association of Members of the Institute for Advanced Study for support. R.S. is a Packard Fellow and an Alfred P. Sloan Research Fellow.

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August 19, 2023
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