1 Introduction

 

Modern cosmological models for GRBs are of two varieties: 1) those that attempt to explain the burst itself and its "afterglows", given the prior existence of a highly relativistic jet or fireball having special properties, and 2) models for making that jet. This paper concerns the second kind of model.

Models for the "jet engine" must satisfy a number of constraints. First, the brightest bursts require $f_{\Omega} \, f_{\gamma}^{-1}$ erg where $f_{\Omega}$ is the beaming factor which, for gamma-rays, is probably not much less than 0.01 (half-opening angle 5 - 10 degrees), and $f_{\gamma}$ is the efficiency for converting total jet energy into gamma-rays of 10 keV to a few MeV, perhaps $\sim\!0.2$. Second, the jet must have a high $\Gamma$, so that relativistic beaming can keep the duration of the burst short even though the gamma-rays are made in a very large volume. Values of $\Gamma$ of are needed to explain most BATSE GRBs. However, as we will discuss later (Sect. 4), smaller $\Gamma \sim 5$ may explain faint events like GRB 980425. If $\Gamma \sim 300$, the corresponding mass is . That the requisite mass be this small is referred to as the "baryon loading problem". Finally, the events must occur at a reasonable rate. The exact value depends on the median red shift and is unknown, but $10^{-7}/f_{\Omega}$ per year per L_* galaxy is reasonable. At least some fraction of these, perhaps all events lasting long enough to trigger Beppo-Sax ( s), occur in star forming regions. The location of shorter bursts is unknown.

GRBs may also have diverse origins. The association of GRB 980425 with SN 1998bw remains controversial to some, but at 38 Mpc, the GRB energy was only about $10^{48} f_{\Omega}$ erg, less than 10^-5 the energy of GRB 971214. Collapsars have difficulty explaining short (mean duration 0.3 s) hard bursts, but merging neutron stars have difficulty explaining long (mean duration 20 s), complex ones. And, as has been remarked frequently, the range of GRB light curve shapes is very diverse.

Setting aside for now what one might term "exotic models" - supermassive stars, cosmic strings, physics beyond the standard model, and the like - the requisite conditions described above are best met by a class of models based upon hyperaccreting, stellar mass black holes. These can be realized in several ways (see Popham et al. 1998 for a summary), but have in common a black hole of several solar masses accreting matter from a disk at a rate 0.001 to $10\,M\hbox{$\odot$}\ {\rm s}^{-1}$. The models vary in disk mass, accretion rate, black hole mass and Kerr parameter, and the manner in which accretion energy is channeled into directed relativistic motion, but they have in common that the GRB they produce always signals either the birth or sudden appreciable growth of a black hole.