Concerning the distance of GRB sources, major
progress has first 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 [188]. However, until 1997 no
counterparts (quiescent as well as transient) could be found, and
observations did not provide a direct measurement of their
distance. Then, in 1997, the detection and the rapid availability
of accurate coordinates ( arcminutes) of the fading
X-ray counterparts of GRBs by the Italian-Dutch BeppoSAX
spacecraft [61, 228] has allowed for
subsequent successful ground based observations of faint GRB
afterglows at optical [283], millimeter [36], and radio [94] wavelengths (for a
review see, e.g., [284]). In 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) [39, 4]. Updated information on GRBs which
have been localized within a few hours to days to less than
1 degree by various instruments and procedures can be obtained
from a web site maintained by Greiner [116
].
As of June 2002, the distances of about two dozen gamma-ray bursts have been determined from optical spectra of the GRB afterglows and/or of the GRB host galaxies (for an overview see [116]). The observed redshifts confirm that (probably most) GRBs occur at cosmological distances.
Assuming isotropic emission, the inferred total
energy of cosmological GRBs emitted in form of gamma-rays ranges
from to about
, the record
presently being held by GRB 990123 with
[29
, 95
]. The median
bolometric isotropic equivalent prompt energy release is
, with an rms scatter of
[29].
In April 1998, the pure cosmological origin of
GRBs was challenged by the detection of the Type Ib/c supernova
SN 1998bw [98, 99] within the
8 arcminute error box of GRB 980425 [263, 222
]. Its explosion time
is consistent with that of the GRB, and relativistic expansion
velocities are derived from radio observations of
SN 1998bw [149]. 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 [222]. As the host galaxy
ESO 184
82 of SN 1998bw is only at a
redshift of
[278], it was not difficult to
study and analyze this particular GRB/supernova.
Assuming isotropic emission the total energy
radiated by GRB 980425 in form of gamma-rays is only [44], i.e., more than four
orders of magnitude smaller than that of a typical cosmological
GRB. The optical spectra and light curve of the associated
supernova SN 1998bw can be modelled very well by an unusually
energetic explosion (kinetic energy of the ejecta
) of a massive star composed mainly of
carbon and oxygen, i.e., by a very energetic
SNe Ib/c [99, 131
, 302]. Thus, Iwamoto et
al. [131] called SN 1998bw a
hypernova, a name which was originally proposed by
PaczyĆski [217
] for very luminous
GRB/afterglow events.
As of June 2002, besides
SN 1998bw/GRB 980425 two other SN-GRB associations have
been discovered: SN 1997cy/GRB 970514 [101, 281] and
SN 2001ke/GRB 011121 [100, 31, 237]. In addition, several
other hypernovae have been observed (see, e.g., [186, 185]) where no associated GRB
has been detected, while several other GRBs show indirect evidence
for an association with a supernova like, e.g., a deviation from a
power-law decline of the afterglow light curve (see e.g., [30]) or the presence of
metal-enriched circumburst matter at high velocity () [239]. Hence, observational
data show evidence for an association (of at least a sub-class) of
GRBs with type Ib/Ic core collapse supernovae resulting from the
death of a massive star with a rich circumburst medium fed by the
mass-loss wind of the progenitor.
The redshift measurements of GRBs imply isotropic
gamma-ray energy releases approaching . To find an
astrophysical site producing such a huge amount of gamma-ray energy
within a few tenth of seconds or in an even shorter time poses a
severe problem for any theoretical GRB model. However, this problem
could be eased considerably, if the radiation from GRBs is strongly
beamed. And indeed, there exists observational evidence that the
gamma-ray and afterglow radiation of (some) GRBs is not emitted
isotropically, but may be beamed (for a review see, e.g., [73]). In particular, 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 conical flow or jet
after it slows down and spreads laterally [254].
Using all GRB afterglows with known distances (as
of January 2001), Frail et al. [95] derived their conical
opening angles. These show a wide variation ( to
) reflecting the observed broad
distribution in fluence and luminosity for GRBs. Taking the
corrected emission geometry into account, Frail et al. find
that the gamma-ray energy release is narrowly clustered around
, i.e., the central engines of GRBs release energies
that are comparable to ordinary supernovae. A similar conclusion
can be derived by estimating the fireball energy based on X-ray
afterglow observations [96], and by modeling the
broadband emission of well-observed afterglows [218].
The compact nature of the GRB source, the
observed fluxes and the cosmological distance taken together imply
a very large photon density in the gamma-ray emitting fireball, and
hence 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 . 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
(for
reviews see, e.g., [224
, 226, 192
]).
In order to explain the existence of highly
relativistic outflow and the energies released in a GRB, various
catastrophic collapse events have been proposed including
neutron-star/neutron-star mergers [216, 111, 80], neutron-star/black-hole
mergers [197], and collapsars and
hypernovae [217, 301, 169, 170]. 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 core collapse) at a rate of
[235]. 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
pairs to ultra-relativistic speeds with Lorentz
factors
[46, 227
, 224].
Current observational facts and theoretical considerations suggest that GRBs involve three evolutionary stages (for reviews see e.g., [225, 192]):
One-dimensional numerical simulations of
spherically symmetric relativistic fireballs from GRB sources have
been performed by several authors [227, 219, 135
, 66
, 273
]. Panaitescu et
al. [219] modelled the interaction
between an expanding adiabatic fireball and a stationary external
medium whose density is either homogeneous or varies with distance
according to a power law. They used a hybrid code based on standard
Eulerian finite difference techniques in most of the computational
domain and a Glimm algorithm including an exact Riemann solver in
regions where discontinuities are present [295
]. They simulated the
evolution until most of the fireball’s kinetic energy was converted
into internal energy. Kobayashi et al. [135] studied the evolution of
an adiabatic relativistic fireball expanding into a cold uniform
medium using a relativistic Lagrangian code based on a second-order
Godunov method with an exact Riemann solver. They simulated the
initial free expansion and acceleration of the fireball, its
coasting, and deceleration to non-relativistic velocities. Daigne
and Mochkovitch [66] used a Lagrangian
hydrodynamics code based on relativistic PPM [60
, 181
] (extended by them
to spherical symmetry) to simulate the evolution of internal shocks
in a relativistic wind with a very inhomogeneous initial
distribution of the Lorentz factor. Tan et al. [273] investigated the
acceleration of shock waves to relativistic velocities in the outer
layers of exploding stars. By concentrating the energy of the
explosion in the outermost ejecta, such trans-relativistic blast
waves can serve as the progenitors of GRBs. For their study they
developed a relativistic 1D Lagrangian hydrodynamics code based on
an exact Riemann solver [181
].
Multi-dimensional modeling of ultra-relativistic
jets in the context of GRBs has for the first time been attempted
by Aloy et al. [7]. Using a collapsar
progenitor model of MacFadyen and Woosley [169
], they simulated the
propagation of an axisymmetric jet through the mantle and envelope
of a collapsing massive star (
) using the
GENESIS special relativistic hydrodynamics code [6
]. The jet forms as a
consequence of an assumed energy deposition of
within a 30 degree cone around the rotation
axis. At breakout, i.e., when the jets reach 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 [169] are inadequate. An MPEG
movie (Figure 21
) shows the evolution of the
Lorentz factor while the jet is propagating through the collapsar
progenitor.
Granot et al. [114, 115] performed 2D and 3D relativistic hydrodynamic simulations of the deceleration and lateral expansion of an adiabatic relativistic jet with an initial Lorentz factor of 23.7 as it expands into an ambient medium. The hydrodynamic calculations used an adaptive mesh refinement (AMR) code. They found that the sideways propagation is different than predicted by simple analytic models. The physical conditions at the sides of the jet are significantly different from those at the front of the jet, and most of the emission occurs within the initial opening angle of the jet assumed to be 0.2 radians.