Magnetar as Central Engine of Gamma-Ray Bursts: Quasi-universal Jet, Event Rate, and X-Ray Luminosity Function of Dipole Radiations

Abstract

Early shallow-decaying X-ray afterglows of gamma-ray bursts (GRBs) may be attributed to the dipole radiations of newly born magnetars. Assuming that the GRB jets powered by magnetars are quasi-universal, we find that the jet structure can be parameterized as a uniform jet with a luminosity of (1 σ ) and an opening angle (50% confidence level), surrounding by a power-law decay component with an index of (1 σ ). The inferred local GRB rate is ρ  = 9.6 Gpc −3 yr −1 by including both the typical GRBs and LL-GRBs as the same population. The typical viewing angle is 3.3°, and may be 20° ∼ 30° for LL-GRBs. The X-ray luminosity function of the dipole radiation wind can be empirically described by a broken power-law function with indices and broken at . In the case where the wind outflow is collimated and coaxial with the GRB jet, we find that the wind structure is similar to the GRB jet, i.e., , , and . The observed correlation between the prompt gamma-ray luminosity and X-ray luminosity of the wind may result from the viewing angle effect in such a jet–wind system. A discussion on surveys using the X-ray instruments on board the Einstein Probe mission in the soft X-ray band for the jet and wind emission is also presented.