Magnetar-energized supernova explosions and gamma-ray burst jets

In this paper, we report on the early evolution of a core-collapse supernova explosion following the birth of a magnetar with the dipolar magnetic field of B = 10¹⁵G and the rotational period of 2ms, which was studied by means of axisymmetric general relativistic magnetohydrodynamic simulations. In this study, we use realistic equation of state and take into account the cooling and heating associated with emission, absorption, annihilation, and scattering of neutrinos; the neutrino transport is treated in the optically-thin regime. The supernova explosion is initiated via introducing into the initial solution the `radiation bubble', whose total thermal energy is comparable with the typical energy of supernova ejecta. The numerical models exhibit highly collimated magnetically driven jets very early on. The jets are super-Alfvénic but remain subfast until the end of the simulations (t = 0.2s). The power released in the jets is about 3 × 10⁵⁰ergs^-1 which implies the spin-down time of ~=37s. The total rotational energy of the magnetar, E ~= 10⁵²erg, is sufficient to drive a hypernova but it is not clear as to how large a fraction of this energy can be transferred to the stellar ejecta. Given the observed propagation speed of the jets, v_p ~= 0.17c, they are expected to traverse the progenitor in few seconds and after this most of the released rotational energy would be simply carried away by these jets into the surrounding space. Three-dimensional effects such as the kink mode instability may reduce the jet propagation speed and increase the amount of energy transferred by the jets to the supernova ejecta. Our results provide the first more or less self-consistent numerical model of a central engine capable of producing, in the supernova setting and on a long-term basis, collimated jets with sufficient power to explain long-duration gamma-ray bursts (GRBs) and their afterglows. Although the flow speed of our jets is relatively low, only v_j ~= 0.5c, the cooling of protoneutron star will eventually result in much higher magnetization of its magnetosphere and ultrarelativistic asymptotic speeds of the jets. Given the relatively long cooling time-scale, we still expect the jets to be only weakly relativistic by the time of break-out. This leads to a model of GRB jets with a systematic longitudinal variation in the Lorentz factor which may have specific observational signatures both in the prompt and in the afterglow emission. The simulations also reveal quasi-periodic ejection of plasma clouds into the jet on a time-scale of 20ms related to the large-scale global oscillation of magnetar's magnetosphere caused by the opening-closing of the dead zone field lines. These kinds of central engine variability may be partly responsible for the internal shocks of GRB jets and the short-time variability of their gamma-ray emission.