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Gamma-ray bursts (GRB) are brief events occurring at an average rate of a few per day throughout the universe, which for a brief period of seconds completely flood with their radiation an otherwise almost dark gamma-ray sky. While they are on, they outshine every other source of gamma-rays in the sky, including the Sun. In fact, they are the most concentrated and brightest electromagnetic explosions in the Universe. Until recently, they were undetected at any wavelengths other than gamma-rays, which provided poor directional information and hence no direct clues about their site of origin.

This changed in early 1997 when the Beppo-SAX satellite succeeded in detecting them in X-rays, which after a delay of some hours yielded sufficiently accurate positions for large ground-based telescope follow-up observations. These proved that they were at cosmological distances, comparable to those of the most distant galaxies and quasars known in the Universe. Since even at these extreme distances (up to Gigaparsecs, or ~ 1028 cm) they outshine galaxies and quasars by a very large factor, albeit briefly, their energy needs must be far greater. Their electromagnetic energy output during tens of seconds is comparable to that of the Sun over ~ few × 1010 years, the approximate age of the universe, or to that of our entire Milky Way over a few years. The current interpretation of how this prodigious energy release is produced is that a correspondingly large amount of gravitational energy (roughly a solar rest mass) is released in a very short time (seconds or less) in a very small region (tens of kilometers or so) by a cataclysmic stellar event (the collapse of the core of a massive star, or the subsequent mergers of two remnant compact cores). Most of the energy would escape in the first few seconds as thermal neutrinos, while another substantial fraction may be emitted as gravitational waves. This sudden energy liberation would result in a very high temperature fireball expanding at highly relativistic speeds, which undergoes internal dissipation leading to gamma-rays, and it would later develop into a blast wave as it decelerates against the external medium, producing an afterglow which gets progressively weaker. The resulting electromagnetic energy emitted appears to be of the order of a percent or less of the total energy output, but even this photon output (in gamma-rays) is comparable to the total kinetic energy output leading to optical photons by a supernova over weeks. The remarkable thing about this theoretical scenario is that it successfully predicts many of the observed properties of the bursts. This fireball shock scenario and the blast wave model of the ensuing afterglow have been extensively tested against observations, and have become the leading paradigms for the current understanding of GRB.

Historically, GRBs were first discovered in 1967 by the Vela satellites, although they were not publicly announced until 1973 [224]. These spacecraft, carrying omnidirectional gamma-ray detectors, were flown by the U.S. Department of Defense to monitor for nuclear explosions which might violate the Nuclear Test Ban Treaty. When these mysterious gamma-ray flashes were first detected, and it was determined that they did not come from the Earth's direction, the first suspicion (quickly abandoned) was that they might be the product of an advanced extraterrestrial civilization. Soon, however, it was realized that this was a new and extremely puzzling cosmic phenomenon [224]. For the next 25 years, only these brief gamma-ray flashes were observed, which could be only roughly localized, and which vanished too soon, leaving no traces, or so it seemed. Gamma-rays are notoriously hard to focus, so no sharp gamma-ray "images" exist to this day: they are just diffuse pin-pricks of gamma-ray light. This mysterious phenomenon led to a huge interest and to numerous conferences and publications on the subject, as well as to a proliferation of theories. In one famous review article at the 1975 Texas Symposium on Relativistic Astrophysics, no fewer than 100 different possible theoretical models of GRB were listed [417], most of which could not be ruled out by the observations then available.

The first significant steps in understanding GRBs started with the 1991 launch of the Compton Gamma-Ray Observatory, whose results were summarized in [127]. The all-sky survey from the BATSE instrument showed that bursts were isotropically distributed, strongly suggesting a cosmological, or possibly an extended galactic halo distribution, with essentially zero dipole and quadrupole components [119]. At cosmological distances the observed GRB fluxes imply enormous energies, which, from the fast time variability, must arise in a small volume in a very short time. This must lead to the formation of an e± - gamma; fireball [343, 167, 446], which will expand relativistically. The main difficulty with this scenario was that a smoothly expanding fireball would convert most of its energy into kinetic energy of accelerated baryons (rather than into photon energy), and would produce a quasi-thermal spectrum, while the typical timescales would not explain events much longer than milliseconds. This difficulty was addressed by the "fireball shock scenario" [403, 301], based on the realization that shocks are likely to arise, e.g. when the fireball ejecta runs into the external medium, after the fireball has become optically thin, thus reconverting the expansion kinetic energy into non-thermal radiation. The complicated light curves can also be understood, e.g. in terms of internal shocks [404, 439, 227] in the outflow itself, before it runs into the external medium, caused by velocity variations in the outflow from the source.

The next major developments came after 1997, when the Italian-Dutch satellite Beppo-SAX succeeded in detecting fading X-ray images which, after a delay of 4-6 hours for processing, led to positions [74], allowing follow-ups at optical and other wavelengths, e.g. [472]. This paved the way for the measurement of redshift distances, the identification of candidate host galaxies, and the confirmation that they were indeed at cosmological distances [295, 100, 240, 243]. The detection of other GRB afterglows followed in rapid succession, sometimes extending to radio [132, 134] and over timescales of many months [471], and in a number of cases resulted in the identification of candidate host galaxies, e.g. [430, 48, 341], etc. The study of afterglows has provided strong confirmation for the generic fireball shock model of GRB. This model led to a correct prediction [305], in advance of the observations, of the quantitative nature of afterglows at wavelengths longer than gamma-rays, which were in substantial agreement with the data [483, 463, 495, 400, 515].

A consolidation of the progress made by Beppo-SAX was made possible through the HETE-2 satellite [195], after the demise of CGRO and Beppo-SAX. It provided a continuing stream of comparable quality afterglow positions, after typical delays of hours, and contributed to the characterization of a new class of sources called X-ray flashes or XRF [194] resembling softer GRBs, which had been earlier identified with Beppo-SAX. It also localized GRB 030329, which resulted in the first unambiguous association with a supernova (SN 2003dh) [455, 196].

The third wave of significant advances in the field is due to the Swift multi-wavelength afterglow satellite, launched in November 2004, which achieved the long-awaited goal of accurately localized afterglows starting a minute or so after the burst trigger, at gamma-ray, X-ray and optical wavelenghts [460, 156]. This revealed the hitherto unexplored afterglow behavior between minutes to hours, enabling a study of the transition from the prompt emission and the subsequent long term afterglow, and revealing a rich range of X-ray early behavior. It also achieved the long-awaited discovery of the afterglows of "short" gamma-ray bursts (whose hard gamma-ray emission is briefer than 2 s). It furthermore broke through the symbolic redshift z = 6 barrier, beyond which very few objects of any kind have been measured.

On the theoretical side, a major issue raised by the large redshifts, e.g. [240, 244], is that the measured gamma-ray fluences (the flux integrated over time) imply a total energy of order a solar rest mass, Modot c2 ~ 2× 1054 ergs, if it is emitted isotropically. By contrast, the total radiant (and the associated kinetic expansion energy) of supernovae (SN), which is detected over timescales of weeks to months, is of the order of a thousandth of a solar rest mass, 1051 ergs. A GRB emission which is concentrated in a jet, rather than isotropically, alleviates significantly the energy requirements. There is now extensive observational evidence for such collimated emission from GRBs, provided by breaks in the optical/IR light curves of their afterglows [244, 140, 62]. The inferred total amount of radiant and kinetic energy involved in the explosion is in this case comparable to that of supernovae (except that in GRBs the energy is mostly emitted in a jet in gamma-rays over tens of seconds, whereas in supernovae it is emitted isotropically in the optical over weeks). While the luminous (electromagnetic) energy output of a GRB is thus "only" of the same order of magnitude as that of supernovae, the explosion is much more concentrated, both in time and in direction, so its specific brightness for an observer aligned with the jet is many orders of magnitude more intense, and appears at much higher characteristic photon energies. Including the collimation correction, the GRB electromagnetic emission is energetically quite compatible with an origin in, say, either compact mergers of neutron star-neutron star (NS-NS) or black hole-neutron star (BH-NS) binaries [343, 105, 331, 299], or with a core collapse (hypernova or collapsar) model of a massive stellar progenitor [514, 346, 380, 283, 513], which would be related to but much rarer than core-collapse supernovae. While in both cases the outcome could be, at least temporarily, a massive fast-rotating ultra-high magnetic field neutron star (a magnetar), the high mass involved is expected to lead inevitably to the formation of a central black hole, fed through a brief accretion episode from the surrounding disrupted core stellar matter, which provides the energy source for the ejection of relativistic matter responsible for the radiation.

A stellar origin of GRB leads to two predictions which are similar to those for core-collapse supernovae, albeit in so far unobserved aspects. In both GRB (whether from compact mergers or from collapsar scenarios) and in core-collapse SN, the central material is compressed to nuclear densities and heated to virial temperatures characteristically in the multi-MeV range, leading to 5-30 MeV thermal neutrinos. And in both cases, the merging or collapsing core material acquires a time-varying quadrupole mass moment (which may be smaller in SN not related to GRB), which leads to gravitational wave emission. In both GRB and supernovae, the total neutrino emission is of the order of a fraction of a solar rest mass, ~ several × 1053 ergs. The gravitational wave emission is of the same order for compact mergers, probably less than that for collapsars, and much less in normal core collapse SNe. Experiments currently planned or under construction will be able to probe these new channels.

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