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

Achromatic breaks in afterglow light curves of gamma-ray bursts (GRBs) arise naturally if the product of the jet's Lorentz factor gamma and opening angle Theta(j) satisfies gamma Theta(j) >> 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 gamma Theta(j) less than or similar to 1, 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 10(4.5) times that of the central compact object, the jet achieves an asymptotic Lorentz factor gamma similar to 500 far outside the star and an asymptotic opening angle Theta(j) similar or equal to 0.04 rad at similar or equal to 2 degrees, giving gamma Theta(j) similar to 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. (C) 2010 Elsevier B.V. All rights reserved.