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.
Bibliographical noteFunding Information:
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.