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Relativistic dynamics: expansion and shock waves interactions
Relativistic outflows are extremely common in many different astronomical objects. Thus, accurate calculation of the dynamics of expanding - and interacting plasmas, including shock waves, is of high interest in studying many objects. One good example is GRBs: the progenitor of (long) GRBs is believed to be a a Wolf-Rayet, massive star. This star is expected to eject supersonic wind before exploding as a GRB. This ejected wind interacts with the surrounding ISM, to produce a "wind bubble" profile, characterized by two (forward and reverse) shock waves. When the star eventually explodes, the relativistic blast wave thus interacts with the wind termination (reverse) shock wave. The consequences of this scenario were studied in collaboration with Wijers.
As the blast wave propagates through the ISM, it collects matter and deccelerates. While this problem was treated a long time ago, recently I showed that a simple, yet accurate solution can be found for both the adiabatic and radiative regimes. The solution I find, which is correct in both the ultra-relativistic as well as Newtonian regime, accounts for both the energy and pressure behind the shock wave, and therefore corrects a common error in the literature.
Pe'er, A., & Wijers, R.A.M.J. (2006), "The Signature of a Wind Reverse Shock in Gamma-Ray Burst Afterglows" Ap.J. 643, 1036 8013018
Pe'er, A. (2012), "Dynamical Model of an Expanding Shell" Ap.J. (Lett) 752, L8