# Gamma ray bursts theory

Post-publication activity

Curator: Peter Mészáros

Gamma-Ray bursts (GRB) are sudden, intense flashes of gamma-rays, detected mainly in the MeV band, which for a few seconds completely overwhelm every other gamma-ray source in the sky, including the Sun. They are the brightest and most concentrated electromagnetic explosions in the Universe. Until 1997 they were undetected at any wavelengths other than gamma-rays, which are difficult to focus and hence provided poor directional information for identifying the sites of origin. The BATSE experiment on the Compton Gamma Ray Observatory (CGRO), launched in 1991, however, observed a high degree of isotropy of the GRB spatial distribution which indicated that they must be at cosmological distances. Then the Beppo-SAX satellite (1996) succeeded in discovering the previously predicted, longer duration afterglows of GRB, which appear at softer (X-ray, optical and radio) energies yielding accurate angular positions. With the latter it became possible to identify the host galaxies and to measure the cosmological redshift distances of GRB, a task later taken over by the HETE-2 satellite (2001). More recently, dramatic observational advances have been made with the Swift satellite, launched in late 2004, which has enabled fundamental new insights into the physics of GRB thanks to two new capabilities: first, the greater sensitivity of its Burst Alert Telescope (BAT; energy range 20--150 keV); and second, its ability to rapidly (within 100s) slew to the direction of the burst with its high angular resolution X-ray and UV-Optical detectors, yielding prompt and detailed multi-wavelength early afterglow spectra and light curves. The latest, far reaching insights are being obtained through the analysis of data from the recently launched (2008) Fermi satellite. For more details on the observations see Gamma Ray Bursts Observations and Gamma Ray Bursts Afterglows; for recent theoretical reviews see, e.g. Zhang, 2007; Mészáros, 2006.

From the observations, it has been clear for some time now that GRB are associated with cataclysmic stellar events. The short variability timescales $$t_{v,-3}=(t_v/10^{-3}{\rm s}) <1$$ of the prompt gamma-ray emission, together with a light travel time argument, $$r_{min} \leq c t_{v} \sim 10^7 t_{v,-3} {\rm cm}$$ indicates that the central engine dimensions are of order tens of kilometers, typical of stellar mass black holes or neutron stars. The observed fluxes and the cosmological distances (e.g. Van Paradijs, Kouveliotou and Wijers, 2000) imply an energy release of the order of a solar rest-mass, if isotropic, or about $$10^{-2}- 10^{-3}$$ solar rest mass energies when one takes into account quantitative evidence for a collimation of the early emission.

Independently of the details of the central engine, and based only on the release of the above large energies on timescales of tens of seconds or less, the observed emission of gamma-rays and the afterglow must occur via a highly relativistic, in most cases jet-like outflow. The enormous energy release in such short times in such compact regions must lead to the formation of an $$e^\pm ,\gamma$$ fireball, which will expand relativistically (Paczynski, 1986; Goodman, 1986). The fact that observed $$\epsilon_\gamma >10$$ GeV photons survive annihilation against MeV photons through $$\gamma\gamma \to e^\pm$$ constrains (Harding and Baring, 1994) the relative photon incidence angle $$\theta$$ via the threshold condition $$\epsilon_\gamma . \epsilon_t > 2 (m_e c^2)^2/(1-\cos\theta) \sim 4 (m_e c^2)^2/ \theta^2\ ,$$ and from the light cone (causality) condition, the bulk Lorentz factor $$\Gamma$$ must be $\Gamma \geq (1/\theta) \sim 10^2 [(\epsilon_\gamma /{\rm 10 GeV}) (\epsilon_t /{\rm MeV}) ]^{1/2},$ typical observed values being $$\Gamma_{2.5}=(\Gamma/300)\sim 1\ .$$ However, a smoothly expanding fireball (i.e., a laminar flow) would convert most of the explosion energy into kinetic energy of accelerated baryons, rather than into the (very high) observed photon energy, and would also produce a quasi-thermal spectrum (Shemi and Piran, 1990), whereas the usual observational description of GRB spectra is in terms of broken power laws suggesting a non-thermal origin. The most widely held view is that such non-thermal spectra arise from collisionless shocks which reconvert the expansion kinetic energy into non-thermal radiation, after the fireball has become optically thin. This is the fireball shock scenario (Rees and Mészáros, 1992; Mészáros and Rees, 1993a) The complicated light curves can be understood in terms of internal shocks (Rees and Mészáros, 1994; Sari and Piran, 1997) in the outflow itself, caused by velocity variations $$\Delta\Gamma\sim \Gamma$$ in the outflow from the central source, which occur at a radius $r_{dis} \sim 2 c t_{v} \Gamma^2 \sim 6\times 10^{12} t_{v,-3} \Gamma_{2.5}^2 ~ {\rm cm}.$ If the outflow is magnetically dominated, reconnection events leading to particle acceleration provide an alternative mechanism for the prompt emission (e.g. Lyutikov and Blandford, 2003). More recent evidence suggests that the characteristic spectral peak may be thermal in origin, possibly due to a jet photosphere, where the power law extensions may be due to shocks or multiple scattering (Thompson, Mészáros and Rees, 2007).

The external shock blast wave and its reverse shock, which occurs when the fireball ejecta unavoidably runs into the external interstellar medium or into the wind of the progenitor, results via synchrotron and inverse Compton radiation in a broad-band multi-wavelength spectrum (Mészáros and Rees, 1993b). As the fireball sweeps up more matter, the blast wave slows down and results in a subsequent, longer lasting and softer afterglow (Paczynski and Rhoads, 1994; Katz, 1994). For a burst of isotropic equivalent energy $$E_{53} = (E / {10^{53}{\rm erg}})$$ in an external medium of particle density $$n_{0}=(n/{1 \rm cm}^{-3})$$ the external shock emission reaches a maximum at a radius $r_{dec} \sim (3E/4\pi n_o m_p c^2 \Gamma^2)^{1/3} \sim 5\times 10^{16} E_{53}^{1/3} n_{0}^{-1/3} \Gamma_{2.5}^{-2/3} ~{\rm cm},$ and thereafter enters into a self-similar phase. The evolution of the external shock generates a prompt hard spectrum, which evolves as a power law in time into an optical and later a radio spectrum, while the reverse shock predicts a brief optical flash. This generic afterglow model (Mészáros and Rees, 1997) has been widely confirmed in its main features. There continue to remain, however, a number of interesting puzzles.

There are at least two distinct groups of GRB, the long ones with gamma-ray durations in excess of about 2 s, and the short ones with durations less than about 2 s. The long bursts are generally found in small star-forming galaxies, and in some cases long GRB are positionally and temporally associated with the onset of an anomalously broad-lined type Ic supernova ( SN ). Such SN result from the core collapse of stars initially more massive than about 25 solar masses, which lost most of its outer envelope (Wolf-Rayet stars). The stellar core mass is likely to exceed the Chandrasekhar limit, so it collapses either directly to a black hole (BH), or does so after a temporarily rotation-stabilized massive neutron star (NS) phase. The gravitational energy release from the subsequent accretion of gas onto the central BH or NS, or rotational energy of the compact object, is thought to provide the ultimate power for the burst (e.g. Woosley, 1993; MacFadyen and Woosley, 1999). The origin of the short bursts is less clear. There is good evidence that they are associated with old stellar populations, being found both in elliptical galaxies and in spirals or irregulars, and a likely guess (Paczynski, 1986; Eichler, Livio, Piran and Schramm, 1989) is that they result from NS-NS or NS-BH binary mergers (Ramirez-Ruiz, 2006; Lee and Ramirez-Ruiz, 2006), although other schemes involving old stars are not ruled out. The main energy source is likely to be again accretion of debris gas onto a compact central object, either a BH or a temporary massive NS which ultimately collapses to a BH, resulting from the merger or the collapse of a compact progenitor. In both long and short progenitors, accretion onto the central compact object, presumably a BH, is thought to feed the relativistic jet, which expands along the rotation axis. In the stellar collapse scenario the jet breaks through the stellar envelope, which helps to collimate it, while in the merger scenario it is expected to expand freely in a broader cone.

New insights on the burst and afterglow physics have been forthcoming from detailed X-ray light curves from Swift starting about 100 seconds after the trigger. Three of the features characterized by Swift have given rise in particular to much speculation. One of these is an initial very steep temporal decay $$F_X \propto t^{-\alpha_1}$$ with $$3 \leq \alpha_1 \leq 5\ ,$$ and an energy spectrum $$F_\nu \propto \nu^{-\beta_1}$$ with $$1 \leq \beta_1 \leq 2\ ,$$ extending up to times $$300 {\rm s} \leq t_1 \leq 500 {\rm s}\ .$$ The most widely considered explanation for this fast decay (Kumar and Panaitescu, 2000) is that it is due to off-axis emission, at $$\theta > \Gamma^{-1}\ ,$$ which due to Doppler suppression arrives after the line of sight gamma-rays have ceased, being weaker and softer than the latter. This steep X-ray decay is often followed, in Swift observations, by a flatter decay $$F_X \propto t^{-\alpha_2}$$ with $$0.2 \leq \alpha_2 \leq 0.8$$ and $$0.7 \leq \beta_2 \leq 1.2\ ,$$ at $$10^3 {\rm s} \leq t_2 \leq 10^4 {\rm s}\ .$$ Possible explanations include refreshed shocks or a continued energy input into the afterglow (Zhang et al, 2006; Nousek et al, 2006; Granot et al, 2006), varying shock parameters (Ioka et al, 2006), circumstellar gas or dust, etc. In addition, in many afterglows one or more steep X-ray flares appear superposed on the power law decay, typically between 100 s and sometimes as late as $$10^5$$ s, whose energy is $$\leq 0.01-1$$ of the prompt emission. In the case of a single flare reprocessing by a binary companion (MacFadyen, Ramirez-Ruiz and Zhang, 2006) may be a possibility. However, the rise and decay time index can be as steep as $$\pm 3$$ to 6, and especially for multiple flares, this is very hard to explain with any mechanism other than continued internal shocks or sudden dissipation (Zhang et al, 2006; Nousek et al, 2006; Krimm et al, 2007), implying a central engine activity which extends into much later times than usually expected from numerical simulations or analytical estimates.

An area of significant progress has been the connection between SN and long GRB, several of which have been discovered by Swift. Most notable has been the detection of the unusually long ($$\sim 2000$$ s), soft burst, GRB 060218 (Campana et al, 2006), associated with the nearby (z=0.033) SN2006aj, a type Ic supernova. It has been argued that the extremely long, soft power law emission may be caused by a neutron star, rather than a black hole central engine resulting from the core collapse. In any case, this was the first GRB/SN event which was was observed from the first $$\sim$$100~s in X-rays and UV/optical. The early X-ray spectrum is initially dominated by a power-law component, with an increasing black-body component which dominates after $$\approx$$3000~s. This black-body component may be due to the emergence of the SN shock through the optically thick wind of the progenitor (Waxman, Mészáros and Campana, 2007). From other GRB/SN coincidences, a trend that appears to be emerging is that in such cases the GRB is under-energetic, while the SNIc is hyper-energetic (a hypernova), or at any rate has a faster expansion rate than normal SNIc. Such GRB-related hypernovae may be significant contributors to cosmic rays in the $$10^{17}-10^{19}$$ eV range, while (long) GRB in general may accelerate, in the relativistic jet shocks, cosmic rays extending up to $$10^{20}$$ eV energies (Wang, et al, 2007; Budnik et al, 2007), and may also produce TeV-PeV energy neutrinos.

The successful launch of the Fermi Gamma-ray Space Telescope in 2008 has provided a new and powerful window into the very high energy behavior of GRBs. Roughly one GRB per week is detected with the Gamma-ray Burst Monitor (GBM, 8 keV-30 MeV), and roughly one a month is detected with the Large Area Telescope (LAT, 20 MeV-300 GeV). More than a dozen bursts have been detected by the LAT at energies above 1 GeV, including several short bursts. Among the earliest long bursts, much excitement was caused by GRB 080916C, which had 14 events ranging from 1 GeV to 13.6 GeV, and over 200 events above 100 MeV (Abdo, et al, 2009). The burst showed an interesting soft to hard to soft behavior, with a first peak in the MeV range only, but a second peak 3.5 s later with strong GeV emission. The MeV emission subsides after 55 s, but the GeV emission continues until 1400 s after the trigger. The spectra are of the Band-function (broken power law) type, with initially a hardening and then a softening of the peak energy and the high energy slope. The lack of a clearly separate second spectral component suggests a single emission emission mechanism, possibly with varying emission parameters. The presence of photons with up to 13.6 GeV coupled with a measured redshift z= 4.3 gives an estimate for the bulk Lorentz factor of $$\Gamma \geq 800\ .$$ The time lag of 3.6 s between the first GeV pulse and the first MeV pulse implies a lower limit for the quantum gravity (or Lorentz invariance violation) energy scale of $$E_{QG} \geq 1.5 \times 10^{18}$$ GeV for the first order, or $$9.4 \times 10^9$$ GeV for the second order terms (Abdo et al, 2009a).

Even more exciting were the results of the analysis of GRB 090510 (Abdo, et al, 2009b), for three completely different reasons. First, it was the first short GRB to be clearly detected in the LAT, up to 31 GeV, a record at the time of measurement. This required an even larger lower limit for the bulk Lorentz factor, $$\Gamma \geq 1200\ .$$ Second, this burst, in contrast to a number of previous ones, also showed for the first time a clear second spectral component, in addition to the usual Band-type simple broken power law . However, it is as yet unclear whether this is of leptonic or hadronic origin. Third, this burst also showed a time lag between the high and low energy emission, allowing an even stricter limit on the quantum gravity energy scale. The experimental lower limit for the first order term in this burst exceeds the Planck energy by a factor of 4, so the first order term can be ruled out. Only second order term in an effective field theory expansion can be present. This imposes restrictions on certain classes of quantum gravity theories. It is remarkable that these unimaginably high energies around the Planck scale, which are completely out of reach of even the highest energy particle accelerators such as the LHC at CERN, can nonetheless be probed with GRB observations of photons in the tens of GeV range, which give a set of robust experimental lower limits on this fundamental energy scale.

The relativistic jets of GRB are thought to be capable of accelerating cosmic rays up to GZK energies, $$E_p \sim 10^{20}$$ eV, leading to a flux at Earth comparable (Waxman, 1995; Vietri, 1995) to that observed with large extended air shower arrays such as the Pierre AUGER observatory. Both leptonic, e.g. synchrotron and inverse Compton (Sari and Esin, 2001), as well as hadronic processes (Dermer, 2002) can lead to GeV-TeV gamma-rays measurable by Fermi Gamma-ray Space Telescope, AGILE, or air Cherenkov telescopes such as HESS and VERITAS, providing useful probes of the burst physics and model parameters. Photo-meson interactions also produce neutrinos at energies ranging from sub-TeV to EeV (e.g. Waxman, 2006) which is being or will be probed with experiments such as ICECUBE, KM3NeT and ANITA. This would provide information about the fundamental interaction physics, the acceleration mechanism, the nature of the sources and their environment. Another type of non-photonic emission may be gravitational waves, especially from short GRB if these are compact (NS-NS or NS-BH) mergers (e.g. Kobayashi and Mészáros, 2002; Nakar, Gal-Yam and Fox, 2006). Such signals are being actively sought with the LIGO and VIRGO gravitational wave observatories.

Long bursts are being increasingly found at redshift distances z>5. For example, GRB 080913 had a redshift z= 6.7, comparable to the distance of the most remote galaxies and quasars, being observed at a time when the Universe was less than six percent of its present age. This burst was extremely bright, its X-ray flux exceeding for a whole day that of the most distant X-ray quasar by a factor of up to $$10^5\ .$$ Another burst, GRB 080913 was detected at a redshift z=6.7, and GRB 090423 was detected at z=8.3 (Tanvir et al, 2009). The latter is the highest confirmed spectroscopic redshift of any objects so far (July 2009), whether quasar, galaxy or GRB.

The prospect of using such high z GRB for determining cosmological parameters is tempting (Firmani, et al, 2007), but difficult, due to problems in calibrating their absolute luminosities as a yardstick. On the other hand, their intense X-ray beams are excellent for absorption spectroscopic analyses of the intervening intergalactic medium, observed at redshifts when the Universe was being re-ionized by the first stars and galaxies. They can also provide a unique means of tracing star formation rates at very high redshifts.

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