8.1. Long GRB hosts and progenitors
Out of the ~ 90 long bursts (t 2 s) detected by Swift up to the end of 2005, in all cases where a host galaxy was identified this was of an early type, usually a blue star-forming galaxy [52, 444, 456]. This was also the case for the thirty-some cases measured by Beppo-SAX (e.g. ) in the previous seven years. More recent observational studies have indicated also that the long GRB host galaxy metallicity is generally lower than that of the average massive star forming galaxies [262, 263, 456]. This has implications for the expected redshift distribution of GRB  (c.f. ), indicating that ~ 40% of long GRB may be at z 4. Long GRB may, in principle, be detectable up to z 25-30 [252, 68, 169].
The preponderance of short-lived massive star formation in such young galaxies, as well as the identification of a SN Ib/c light curve peaking weeks after the burst in few cases, has provided strong support for a massive stellar collapse origin of long GRBs, as argued by [514, 346, 513]. The relatively long duration of the gamma-ray emission stage in these bursts (2 s t 103 s) is generally ascribed to a correspondingly long duration for the accretion of the debris [283, 380] falling into the central black hole which must form as the core of a massive star collapses. (For initial stellar masses in excess of about 28-30 M, the core is expected to collapse to a BH, e.g. , while for smaller initial masses 10 M M* 28 M the collapsing core mass is below the Chandrasekhar mass and is expected to lead to a neutron star). This accretion onto the black hole feeds a relativistic jet, which breaks through the infalling core and the stellar envelope along the direction of the rotation axis.
A related massive core collapse mechanism has been considered by [476, 477] taking into account MHD effects in the disk and BH, in which the basic accretion time is short enough to be identified with short bursts, but magnetic tension can result in suspended accretion leading to long bursts. A mechanism based on the shorting of a charge separation built up around newly formed black holes has been discussed by [421, 422]. Other mechanism invoked include collapse of a neutron star to a strange star (e.g. [65, 33, 101]. The most widely adopted scenario, from this list, is the first one, in which the long GRB derive their energy from either the gravitational energy liberated by the torus of debris accreting onto the central BH formed by the massive core collapse, or by the extraction of the rotational energy of the BH, mediated by the presence of the debris torus, whose accretion lifetime in both cases is identified with the duration of the "prompt" gamma-ray emitting phase of the burst.
8.2. Supernova connection
In the year following the launch of Swift no supernovae were identified in association with GRB. In fact, there are some upper limits on possible supernovae, the most notable ones being on the short bursts GRB 050509b  and GRB 050709 . However, from the previous eight year period there are two well documented cases of supernovae associated with long bursts, and several more weaker cases, were the evidence suggests a long GRB-SN connection. The first evidence for a long GRB-supernova association was discovered in GRB 980425, which appeared associated with SN 1998bw [150, 241]. This was a peculiar, more energetic than usual Type Ib/c supernova, where the apparently associated GRBs properties seemed the same as usual, except for the redshift being extremely small (z ~ 0.0085). This implied the lowest ever long GRB isotropic equivalent energy E ~ 1048 erg, which resulted in the association being treated cautiously. However, using SN 1998bw as a template, other possible associations were soon claimed through detection of reddened bumps in the optical afterglow light-curves after a time delay compatible with a supernova brightness rise-time, e.g. in GRB 980326 , GRB 970228 [401, 151], GRB 000911 , GRB 991208 , a href="/cgi-bin/objsearch?objname=GRB+990712&extend=no&out_csys=Equatorial&out_equinox=J2000.0&obj_sort=RA+or+Longitude&of=pre_text&zv_breaker=30000.0&list_limit=5&img_stamp=YES" target="ads_dw">GRB 990712 , GRB 011121 , and GRB 020405 .
The first unambiguous GRB-SN association was identified in GRB 030329, at a redshift z = 0.169, through both a supernova light-curve reddened bump and, more convincingly, by measuring in it a supernova spectrum of type Ib/c (i.e. the same type as in 1998bw) [455, 196]. As a corollary, this observation rules out the "supra-nova" model , in which a core collapse to neutron star and a supernova was assumed to occur months before a second collapse of the NS into a BH and a GRB; the delay between GRB 030329 and SN 2003dh is less than two days, and is compatible with both events being simultaneous . For pre-Swift GRB-SN associations, see, e.g. [519, 518].
More recently, Swift observed with all three instruments, BAT, XRT and UVOT, an unusually long (~ 2000 s), soft burst, GRB 060218 , which was found to be associated with SN 2006aj, a very nearby (z = 0.033) type Ic supernova [287, 373, 317, 316, 454, 69]. This supernova light curve peaked earlier than most known supernovae, and its time origin can also be constrained to be within less than a day from the GRB trigger. This is the first time that a connected GRB and supernova event has been observed starting in the first ~ 100 s in X-rays and UV/Optical light, and the results are of great interest. The early X-ray light curve shows a slow rise and plateau followed by a drop after ~ 103 s, with a power law spectrum and an increasing black-body like component which dominates at the end. The most interesting interpretation involves shock break-out of a semi-relativistic component in a WR progenitor wind  (c.f. [114, 461]). After this a more conventional X-ray power law decay follows, and a UV component peak at a later time can be interpreted as due to the slower supernova envelope shock. Another GRB/SN detection based on Swift afterglow observations is that associated with GRB 050525A .
8.3. Jet dynamics, cocoons and progenitors
For both long and short bursts, the most widely discussed central engine invokes a central black hole and a surrounding torus, either produced by a massive stellar core collapse (long bursts) or the merger of NS-NS or NS-BH binaries (short bursts). The latter mechanism is observationally on a less firm footing than the first, and in both collapse and merger cases the black hole could be preceded by a temporary massive, highly magnetized neutron star. There are two ultimate energy sources: the gravitational binding energy of the torus and the spin energy of the black hole. A possible third is the magnetic energy stored during the collapse, which derives its energy from the other two. Two main ways have been discussed for extracting the accretion energy and black hole spin energy, namely a neutrino-driven wind [105, 419, 420, 283, 145, 260], and the Blandford-Znajek  mechanism. Both mechanisms lead to an optically thick e± jet or fireball, but the second is dynamically Poynting-dominated, i.e. dominated by strong magnetic fields threading the black hole [306, 278, 474, 266]. Needless to say, identification of the content of the fireball and the mechanism of GRB prompt emission would shed light on the mechanism that powers the central engine. Hence the excitement following claims of a very large gamma-ray polarization in GRB 021206  suggesting a strongly magnetized central engine. This observation has been challenged [423, 511]. A strong gamma-ray polarization could in principle be expected from a pure Poynting-flux dominated jet , or in a baryonic hydrodynamic jet with a globally organized magnetic field configuration [499, 179, 177]. A strong but less extreme magnetization of the jet is inferred from a combined reverse-forward shock emission analysis of GRB 990123 [521, 110].
In all models, an e±, fireball is expected as a result of the dissipation associated with the transient core collapse or merger event. The initial chaotic motions and shears also are expected to lead to build up significant magnetic stresses . A combination of the relativistic lepton (e±) and MHD fields up to ~ 1015 Gauss can provide the driving stresses leading to a highly relativistic expansion with j >> 1. The fireball is very likely also to involve some fraction of baryons, and uncertainties in this "baryon pollution"  remain difficult to quantify until 3D MHD calculations capable of addressing baryon entrainment become available. If the progenitor is a massive star, the expectation is that the fireball will likely be substantially collimated, due to the transverse containing pressure of the stellar envelope, which, if fast-rotating, provides a natural fireball escape route along the centrifugally lightened rotation axis.
The development of a jet and its Lorentz factor in a collapsar has been discussed analytically in [311, 504, 288, 256]. The essence of the dynamics of the jet in a burst from a massive star is that as long as the central BH accretes, it injects along the rotation axis a relativistic jet, whose dimensionless entropy must be comparable to or larger than the final bulk Lorentz factor of the jet once it has emerged from the star, = (L / c2) j 100. Even though such a jet is highly relativistic as it is injected, the overburden of the stellar core and envelope slow the jet head down to a sub-relativistic speed of advance, which gradually increases as the jet moves down the density gradient of the star. The difference between the injection and advance speed causes gas and energy spill-over into a transrelativistic cocoon of waste heat [311, 288, 256] surrounding the jet, which may be detectable [392, 368]. By the time it reaches the boundary of the He core (RHe ~ 1011 cm) the jet head has reached a speed vj ~ c. This takes, in the star's frame, ~ 10 s, hence the central engine must continue injecting energy and momentum into the jet for at least this long. A very sharp drop in density is predicted by stellar models at this radius, beyond which a tenuous hydrogen envelope extends as a power law. In going down this sharp gradient, the jet head Lorentz factor shoots up to a value comparable to its final value, j 100 ([311, 504]). Once the jet head is relativistic, it becomes ballistic, and it is no longer affected by whether the central engine energy injection continues or not. A constraint on the mass of the envelope is that the mass overburden within the jet solid angle must be less than the jet total energy divided by j c2 (). If the star has lost is H envelope, this condition is guaranteed, e.g. as in Wolf-Rayet type stars, where a stellar wind phase leads to envelope loss previous to the core collapse phase. WR stars are, in fact, thought to be the progenitors of type Ib/c supernovae, which is the only type so far seen in a few cases associated with GRB. A modest envelope, however, should still be compatible with a high Lorentz factor, which could be tested through detection of weak H lines in a GRB associated supernova (and may also be tested through TeV neutrino observations, ).
The 2D development of a relativistic jet making its way out through a star have been calculated numerically by, e.g. [5, 529], while magnetically dominated jets are discussed by [508, 102, 385]. Jets in compact mergers have calculated numerically by [214, 6]. The relativistic numerical calculations of GRB jets are, so far, mainly hydrodynamic, and involve approximations about the energy and momentum injection at the lower boundary, the numerical difficulties in covering the entire dynamical range being extreme. The results  show that a jet of j ~ 100 can escape a star of radius comparable to a WR (R* ~ 1011 cm). The angular structure of the jet is, as expected, one where the Lorentz factor and energy per solid angle tapers off towards the edges, where instabilities cause mixing with and drag by the stellar envelope walls. An analytical argument  shows that this tapering off can result in an energy profile Ej() -2. Such a jet profile is a possible interpretation [414, 524] of the observational correlation between the isotropic equivalent jet energy and the jet break time derived from a sample of burst afterglows [135, 352].