Magnetohydrodynamic simulations of gamma-ray burst jets: Beyond the progenitor star

Abstract

Achromatic breaks in afterglow light curves of gamma-ray bursts (GRBs) arise naturally if the product of the jet’s Lorentz factor c and opening angle Hj satisfies cHj 1 at the onset of the afterglow phase, i.e., soon after the conclusion of the prompt emission. Magnetohydrodynamic (MHD) simulations of collimated GRB jets generally give cHj K1, suggesting that MHD models may be inconsistent with jet breaks. We work within the collapsar paradigm and use axisymmetric relativistic MHD simulations to explore the effect of a finite stellar envelope on the structure of the jet. Our idealized models treat the jet–envelope interface as a collimating rigid wall, which opens up outside the star to mimic loss of collimation. We find that the onset of deconfinement causes a burst of acceleration accompanied by a slight increase in the opening angle. In our fiducial model with a stellar radius equal to 104:5 times that of the central compact object, the jet achieves an asymptotic Lorentz factor c 500 far outside the star and an asymptotic opening angle Hj ’ 0:04 rad ’ 2 , giving cHj 20. These values are consistent with observations of typical long-duration GRBs, and explain the occurrence of jet breaks. We provide approximate analytic solutions that describe the numerical results well.