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 $\gamma {\Theta }_j?1$, 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 $\gamma ～500$ far outside the star and an asymptotic opening angle ${\Theta }_j?0.04\text{rad}?2°$, giving $\gamma {\Theta }_j～20$. 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.