Force-free simulations of ultra-relativistic jets

We describe time-dependent axisymmetric numerical simulations of ultrarelativistic highly-magnetized, force-free jets. The simulations follow the jet from the central engine to beyond six orders of magnitude in radius. The simulated jets are confined by an external pressure which we take to vary as a power-law with distance along the jet. We find that the radial distance over which the jet is pressure supported determines the terminal Lorentz factor. For the collapsar model of GRBs, this distance is set by the size of the progenitor star and is very large. At this distance our fiducial model generates a Lorentz factor γ∼400 and a half-opening angle θ_j∼2°, consistent with observations of many long GRBs. Other models with slightly different parameters give γ in the range 100 to 5000 and θ_j from 0.1° to 10°, thus reproducing the range of properties inferred for GRB jets. A potentially observable feature of some of our solutions is that both γ and the Poynting flux S are concentrated in hollow cones, with the half-opening angle of the γ-cone θγ≪θ_j and the half-opening angle of the S-cone θ_s=θ_j. In the case of systems such as AGN, XRBs, and short GRBs, we expect the confining medium, viz., the disk wind, to act over a shorter range of distance. This would explain the lower terminal Lorentz factor of these systems compared to long GRBs.