Concerning the distance of GRB sources major progress has occurred through the observations by the BATSE detector on board the Compton Gamma-Ray Observatory (GRO), which have proven that GRBs are distributed isotropically over the sky . Even more important the detection and the rapid availability of accurate coordinates ( arc minutes) of the fading X-ray counterparts of GRBs by the BeppoSAX spacecraft beginning in 1997 [34, 146], has allowed for subsequent successful ground based observations of faint GRB afterglows at optical and radio wavelength. In the case of GRB 990123 the optical, X-ray and gamma-ray emission was detected for the first time almost simultaneously (optical observations began 22 seconds after the onset of the GRB) [22, 1]. From optical spectra thus obtained, redshifts of several gamma-ray bursts have been determined, e.g., GRB 970508 (z = 0.835 [116, 141]), GRB 971214 (z = 3.42 ), GRB 980703 (z = 0.966 ), and GRB 990123 ( ), which confirm that (at least some) GRBs occur at cosmological distances. Assuming isotropic emission the inferred total energy of cosmological GRBs emitted in form of gamma-rays ranges from several erg to erg (for GRB 971214) , and exceeds erg for GRB 990123 [5, 22]. Updated information on GRBs localized with BeppoSAX, BATSE / RXTE (PCA) or BATSE / RXTE (ASM) can be obtained from a web site maintained by Greiner .
The compact nature of the GRB source, the observed flux, and the cosmological distance taken together imply a large photon density. Such a source has a large optical depth for pair production. This is, however, inconsistent with the optically thin source indicated by the non-thermal gamma-ray spectrum, which extends well beyond the pair production threshold at 500 keV. This problem can be resolved by assuming an ultra-relativistic expansion of the emitting region, which eliminates the compactness constraint. The bulk Lorentz factors required are then W > 100 (see, e.g., ).
In April 1998 the pure cosmological origin of GRBs was challenged by the detection of the Type Ib/c supernova SN 1998bw [61, 62] within the 8 arc minute error box of GRB 980425 [165, 140]. Its explosion time is consistent with that of the GRB, and relativistic expansion velocities are derived from radio observations of SN 1998bw . BeppoSAX detected two fading X-ray sources within the error box, one being positionally consistent with the supernova and a fainter one not consistent with the position of SN 1998bw . Taken together these facts suggest a relationship between GRBs and SNe Ib/c, i.e., core collapse supernovae of massive stellar progenitors which have lost their hydrogen and helium envelopes [62, 78, 193]. As the host galaxy ESO 184-82 of SN 1998bw is only at a redshift of z = 0.0085  and as GRB 980425 was not extraordinarily bright, GRB-supernovae are more than four orders of magnitude fainter ( erg for GRB 980425 ) than a typical cosmological GRB. However, the observation of the second fading X-ray source within the error box of GRB 980425 and unrelated with SN 1998bw still causes some doubts on the GRB supernova connection, although the probability of chance coincidence of GRB 980425 and SN 1998bw is extremely low .
In order to explain the energies released in a GRB various catastrophic collapse events have been proposed including neutron-star/neutron-star mergers [134, 69, 47], neutron-star/black-hole mergers , collapsars [192, 101], and hypernovae . These models all rely on a common engine, namely a stellar mass black hole which accretes several solar masses of matter from a disk (formed during a merger or by a non-spherical collapse) at a rate of . A fraction of the gravitational binding energy released by accretion is converted into neutrino and anti-neutrino pairs, which in turn annihilate into electron-positron pairs. This creates a pair fireball, which will also include baryons present in the environment surrounding the black hole. Provided the baryon load of the fireball is not too large, the baryons are accelerated together with the e e pairs to ultra-relativistic speeds with Lorentz factors [27, 145, 144]. The existence of such relativistic flows is supported by radio observations of GRB 980425 . It has been further argued that the rapid temporal decay of several GRB afterglows is inconsistent with spherical (isotropic) blast wave models, and instead is more consistent with the evolution of a relativistic jet after it slows down and spreads laterally . Independent of the flow pattern the bulk kinetic energy of the fireball then is thought to be converted into gamma-rays via cyclotron radiation and/or inverse Compton processes (see, e.g., [115, 144]).
One-dimensional numerical simulations of spherically symmetric relativistic fireballs have been performed by several authors to model GRB sources [145, 137, 136]. Multi-dimensional modeling of ultra-relativistic jets in the context of GRBs has for the first time been attempted by Aloy et al. . Using a collapsar progenitor model of MacFadyen & Woosley  they have simulated the propagation of an axisymmetric jet through the mantle and envelope of a collapsing massive star () using the GENESIS special relativistic hydrodynamic code . The jet forms as a consequence of an assumed energy deposition of erg/sec within a 30 degree cone around the rotation axis. At break-out, i.e., when the jet reaches the surface of the stellar progenitor, the maximum Lorentz factor of the jet flow is about 20. The latter fact implies that Newtonian simulations of this phenomenon  are clearly inadequate.
|Numerical Hydrodynamics in Special Relativity
Jose Maria Martí and Ewald Müller
© Max-Planck-Gesellschaft. ISSN 1433-8351
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