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 [114]. 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 [87]), GRB 980703 (z
= 0.966 [41]), and GRB 990123 (
[5
]), 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) [26
], 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 [71].
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., [144]).
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 [88
]. 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 [140
]. 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 [175] and as GRB 980425 was not extraordinarily bright,
GRB-supernovae are more than four orders of magnitude fainter (
erg for GRB 980425 [26]) 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 [140].
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 [119], collapsars [192,
101], and hypernovae [135]. 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
[151]. 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 [88]. 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 [160]. 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. [4]. Using a collapsar progenitor model of MacFadyen &
Woosley [101] 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 [3
]. 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 [101] are clearly inadequate.
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Numerical Hydrodynamics in Special Relativity
Jose Maria Martí and Ewald Müller http://www.livingreviews.org/lrr-1999-3 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |