7.2 Gamma-ray bursts (GRBs)

A second phenomenon which involves flows with velocities very close to the speed of light are gamma-ray bursts (GRBs). Although known observationally since over 30 years, their nature is still a matter of controversial debate. GRBs do not repeat except for a few soft gamma-ray repeaters. They are detected with a rate of about one event per day, and their duration varies from milliseconds to minutes. The duration of the shorter bursts and the temporal substructure of the longer bursts imply a geometrically small source (less than ∼ c 1 msec ∼ 100 km), which in turn points towards compact objects like neutron stars or black holes. The emitted gamma-rays have energies in the range 30 keV to 2 MeV, the spectra being non-thermal (for recent reviews see, e.g., [4573Jump To The Next Citation Point192Jump To The Next Citation Point225Jump To The Next Citation Point226Jump To The Next Citation Point227Jump To The Next Citation Point]).

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 [61229] 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) [394]. 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 [116Jump To The Next Citation Point].

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 5 × 1051 erg to about 1054 erg, the record presently being held by GRB 990123 with 1.44 × 1054 erg [29Jump To The Next Citation Point95Jump To The Next Citation Point]. The median bolometric isotropic equivalent prompt energy release is 2.2 × 1053 erg, with an rms scatter of 0.80 dex [29].

In April 1998, the pure cosmological origin of GRBs was challenged by the detection of the Type Ib/c supernova SN 1998bw [9899Jump To The Next Citation Point] within the 8 arcminute error box of GRB 980425 [264223Jump To The Next Citation Point]. 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 [223]. As the host galaxy ESO 184–82 of SN 1998bw is only at a redshift of z = 0.0085 [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 7 × 1047 erg [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 (2–5) × 1052 erg) of a massive star composed mainly of carbon and oxygen, i.e., by a very energetic SNe Ib/c [99131Jump To The Next Citation Point302]. Thus, Iwamoto et al. [131] called SN 1998bw a hypernova, a name which was originally proposed by Paczyński [218Jump To The Next Citation Point] 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 [101281] and SN 2001ke/GRB 011121 [10031238]. In addition, several other hypernovae have been observed (see, e.g., [186185]) 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 (∼ 0.1 c[240]. 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 ∼ 1054 erg. 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 [255].

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 (2∘ to 20∘) 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 5 × 1050 erg, 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 [219].

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 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 (for reviews see, e.g., [225Jump To The Next Citation Point227192Jump To The Next Citation Point]).

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 [21711180], neutron-star/black-hole mergers [197], and collapsars and hypernovae [218301169Jump To The Next Citation Point170]. 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 ∼ 1M ⊙ s− 1 [236]. 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 > 102 [46228Jump To The Next Citation Point225].

Current observational facts and theoretical considerations suggest that GRBs involve three evolutionary stages (for reviews see e.g., [226192]):

One-dimensional numerical simulations of spherically symmetric relativistic fireballs from GRB sources have been performed by several authors [228220Jump To The Next Citation Point135Jump To The Next Citation Point66Jump To The Next Citation Point273Jump To The Next Citation Point]. Panaitescu et al. [220] 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 [295Jump To The Next Citation Point]. 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 [60Jump To The Next Citation Point181Jump To The Next Citation Point] (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 [181Jump To The Next Citation Point].

Multi-dimensional modeling of ultra-relativistic jets in the context of GRBs has for the first time been attempted by Aloy et al. [7Jump To The Next Citation Point]. Using a collapsar progenitor model of MacFadyen and Woosley [169Jump To The Next Citation Point], they simulated the propagation of an axisymmetric jet through the mantle and envelope of a collapsing massive star (10 M ⊙) using the GENESIS special relativistic hydrodynamics code [6Jump To The Next Citation Point]. The jet forms as a consequence of an assumed energy deposition of 1051 erg s–1 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. A movie (Figure 21Watch/download Movie) shows the evolution of the Lorentz factor while the jet is propagating through the collapsar progenitor.

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Figure 21: mpg-Movie (14555 KB) The propagation of a relativistic jet from a collapsar, whose progenitor is a rotating He star with a radius of 3 × 1010 cm. All three panels show the rest mass density distribution. The left panel displays the computational domain up to the head of the jet (note the changing axis and color scales). The upper right panel shows the central region (scale fixed) where the jet forms due to a prescribed time-independent and spatially localized energy deposition rate (1050 erg s–1). One can recognize the central spherical region (black circle) of radius 2 × 107 cm which was excised from the computational domain. It contains a (rotating) black hole of initially three solar masses accreting matter through the inner grid boundary. The lower right panel provides a global view (scale fixed) of the computational domain up to the surface of the He star progenitor. (Movie courtesy of M.A. Aloy.)

Zhang, Woosley, and MacFadyen [308Jump To The Next Citation Point] performed a parameter study of the propagation of 2D relativistic jets through the stellar progenitor of a collapsar by varying the initial Lorentz factor, opening angle, power, and internal energy of the jet as well as the radius where it is introduced. They find, in agreement with Aloy et al. [7Jump To The Next Citation Point], that relativistic jets are collimated by their passage through the stellar mantle, and that the jet has a moderate Lorentz factor and very large internal energy when it emerges from the star. Zhang et al. [308] also simulated the evolution after the escape of the jet. During this phase, conversion of the internal energy leads to a further acceleration of the jet, thereby boosting its Lorentz factor to a terminal value of approximately 150 for the initial conditions chosen.

Granot et al. [114115] 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.

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