The Basic Scenarios for Gamma Ray Burst Emission 2431 GRB Emission Scenarios 24311 The Fireball

The basic scenario for the understanding of GRBs is the dissipative (shock) fireball model [59,60]. It assumes a very large energy deposition inside a very small volume (constrained by causality and the variability timescales of GRBs to be of order

Grb Fireball
Fig. 24.10 Sequence of 5780 s slices of the X-ray halo of GRB 031203 (0.7-2.5 keV) starting at 6 h after the GRB. The images are 10' on a side (from [95])

100 km or smaller), which leads to characteristic photon energy densities that produce an optically thick, highly super-Eddington ye± fireball. The fireball initially is thermal and converts most of its radiation energy into kinetic energy, i.e., bulk motion of a relativistically expanding blast wave. Lorentz factors r ~ 102~3 are required by theory to avoid degradation of the GeV photons by photon-photon interactions (note that GRBs involve the fastest bulk motions known so far in the universe). The kinetic energy is tapped by shocks as the most likely dissipation mechanism, and these shocks should probably occur after the fireball became optically thin, as suggested by the observed nonthermal GRB spectra. The internal shocks are generally at least mildly relativistic due to the large Lorentz factor difference between the colliding shells.

The later emission in X-ray to optical and radio wavelengths (so-called afterglow) is dominated by synchrotron emission, i.e., emission from relativistic electrons gyrating in magnetic fields [98, 99]. This synchrotron shock model is widely accepted as the major radiation mechanism in the external shock, and the macroscopic properties of such shocks are well understood. Under the implicit assumptions that the electrons are assumed to be "Fermi" accelerated and that they have a power-law distribution with an index p upon acceleration, their dynamics can be expressed in terms of the following main parameters: (1) the total internal energy in the shocked region as released in the explosion, (2) the density n (and its radial profile) of the surrounding medium, (3) the fraction of energy carried by the electrons £e since only a fraction of the total electrons associated with the ISM baryons are accelerated, (4) the fraction of energy density in the magnetic field £b. However, there are large uncertainties in their microphysics: How are the relativistic particles accelerated? How is the magnetic field in the shocked region generated? What is its structure? Why is the afterglow polarization only few percent [37,39], whereas synchrotron emission can be polarized up to 70%?

According to standard synchrotron emission theory, the radiation power of an electron with co-moving energy yemc2 is Pe = 4/3otcyI(B2/8n), so that high energy electrons cool more rapidly. For a continuous injection of electrons as is the case for ongoing plowing of the forward shock into the ISM, there is a break in the electron spectrum at ye = yc above which the electron energy spectrum is steepened due to cooling. This energy is time-dependent, so that this break moves to lower energies.

Besides this cooling frequency vc, there are two other important frequencies, namely the frequency vm corresponding to the electrons accelerated in the shock to a power-law distribution with minimum Lorentz factor, and the synchrotron self-absorption frequency va. The final GRB afterglow synchrotron spectrum is thus a four-segment broken power law [61, 84] separated by these frequencies va, vm, and vc. The order of vm and vc defines two types of spectra, namely the "slow cooling case" with vm < vc, and the "fast cooling case" vm > vc (Fig. 24.11).

24.3.1.2 Alternative Scenarios

Cannonball: In an alternative model to the fireball scenario, the cannonball model [19], long duration GRBs and their afterglows are produced in core-collapse supernovae by the ejection of bipolar jets of ordinary matter, hydrogenic plasma clouds ("cannonballs") with Lorentz factors of the order of 103. When the cannonball crosses circumburst shells with large velocity, its surface is heated up to keV temperatures and emits a single pulse, boosted by the cannonball motion towards y-ray energies. The typically observed multi-peaked light curves in GRBs are then explained by the acceleration of multiple cannonballs. The subsequent cooling of the cannonball will produce the fading afterglow.

Electromagnetic black holes: In the electromagnetic black hole theory [80] the energy is carried away by a plasma of electron-positron pairs with a temperature of 2MeV and total energy of a few times 1053 erg, created by the vacuum polarization process occurring during the gravitational collapse. Such an optically thick electron-positron plasma self-propels itself outward reaching ultrarelativistic velocities, interacts with the remnant of the progenitor star, and by further expansion becomes optically thin. The sub-structures in a long-duration GRB then originate in the collision between the accelerated (T ~ 300) baryonic matter pulse with inho-mogeneities in the interstellar medium [81], similar to the external shock producing the afterglow in the fireball scenario.

Poynting flux: Another hypothesis is that essentially all types of ultrarelativistic outflow (AGN jets, pulsar wind nebulae, and GRBs) are electromagnetic, rather than

Barcelo Raval

Fig. 24.11 Left: Synchrotron spectrum of a relativistic shock with a power-law distribution of electrons. (a) The case of fast cooling at early times (t < t0) in a GR afterglow. Self-absorption is important below va. The frequencies, vm, vc, and va, decrease with time as indicated; the scalings above the arrows correspond to an adiabatic evolution, and the scalings below, in square brackets, to a fully radiative evolution. (b) The case of slow cooling at late times (t > to). The evolution is always adiabatic. Right: Light curve due to synchrotron radiation from a spherical relativistic shock, ignoring the effect of self-absorption. (a) The high frequency case (v > v0). The four segments of the light curve are separated by the critical times, tc, tm, and t0. The labels, B, C, D, H, indicate the correspondence with spectral segments in the left panel. The observed flux varies with time as indicated; the scalings within square brackets are for radiative evolution (which is restricted to t < t0) and the other scalings are for adiabatic evolution. (b) The low frequency case (v < v0) (from [84])

Fig. 24.11 Left: Synchrotron spectrum of a relativistic shock with a power-law distribution of electrons. (a) The case of fast cooling at early times (t < t0) in a GR afterglow. Self-absorption is important below va. The frequencies, vm, vc, and va, decrease with time as indicated; the scalings above the arrows correspond to an adiabatic evolution, and the scalings below, in square brackets, to a fully radiative evolution. (b) The case of slow cooling at late times (t > to). The evolution is always adiabatic. Right: Light curve due to synchrotron radiation from a spherical relativistic shock, ignoring the effect of self-absorption. (a) The high frequency case (v > v0). The four segments of the light curve are separated by the critical times, tc, tm, and t0. The labels, B, C, D, H, indicate the correspondence with spectral segments in the left panel. The observed flux varies with time as indicated; the scalings within square brackets are for radiative evolution (which is restricted to t < t0) and the other scalings are for adiabatic evolution. (b) The low frequency case (v < v0) (from [84])

gas dynamical, phenomena [11,93]. Electromagnetic flows are naturally anisotropic and self-collimating so as to produce jet-like features. The generic concept is that of a source that ejects a magnetic bubble, which expands with Lorentz factor r ~ 30000. The magnetic field is mostly toroidal. The observed emission then traces out regions of high current density where global instabilities drive a turbulence spectrum that is ultimately responsible for the particle acceleration and the synchrotron, inverse Compton and synchro-Compton emission. The afterglow emission is created after the blast wave becomes free of its electromagnetic driver. In contrast to canonical models, an electromagnetically-driven blast wave creates an anisotropic explosion, remaining relativistic for the longest time closest to the symmetry axis.

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