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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 γand opening angle Θ_j satisfies (γΘ_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 (γΘ_j) <~ 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 γ~ 500 far outside the star and an asymptotic opening angle Θ_j ~ 0.04 rad ~ 2 deg, giving (γΘ_j) ~ 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.