Hyperaccreting black hole as gamma-ray burst central engine. II. Temporal evolution of the central engine parameters during the prompt and afterglow phases

A hyperaccreting stellar-mass black hole (BH) has been proposed as the candidate central engine of gamma-ray bursts (GRBs). The rich observations of GRBs by Fermi and Swift make it possible to constrain the central engine model by comparing the model predictions against data. This paper is dedicated to studying the temporal evolution of the central engine parameters for both the prompt emission and afterglow phases. We consider two jet-launching mechanisms, i.e., nn-annihilations and the Blandford-Znajek (BZ) process, and obtain analytical solutions to these two models. We then investigate the BH central engine parameters, such as the jet power, the dimensionless entropy ?, and the central engine parameter μ0 = ? (1 + s0) (where s0 is the initial magnetization of the engine) at the base of the jet. The BH may be spun up by accretion or spun down by the BZ process, leaving imprints in the GRB light curves. Usually, a BZ jet is more powerful and is likely responsible for the late-time central engine activities. However, an initially non-spinning BH central engine may first launch a thermal "fireball" via neutrino annihilations, and then launch a Poynting-flux-dominated jet via the BZ process. Multiple flares, giant bumps, and plateaus in GRB afterglows can be produced as the result of late-time accretion onto the BH.