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Register a new userBeaming, Baryon-Loading, and the Synchrotron Self-Compton Component in Gamma-Ray Burst Blast Waves Energized by External Shocks
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Authors
Charles D. Dermer
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We present detailed calculations of nonthermal synchrotron and synchrotron self-Compton (SSC) spectra radiated by blast waves that are energized by interactions with a uniform surrounding medium. Radio, optical, X-ray and gamma-ray light curves and spectral indices are calculated for a standard parameter set that yields hard GRB spectra during the prompt emission phase. Because no lateral spreading of the blast-wave is assumed, the calculated temporal breaks represent the sharpest breaks possible from collimated outflows in a uniform surrounding medium. Absence of SSC hardenings in observed GRB X-ray afterglows indicates magnetic field generation toward equipartition as the blast wave evolves. EGRET detections of 100 MeV-GeV photons observed promptly and 90 minutes after GRB 940217 are attributed to nonthermal synchrotron radiation and SSC emission from a decelerating blast wave, respectively. The SSC process will produce prompt TeV emission that could be observed from GRBs with redshifts $z lesssim 0.1$, provided $gamma$-$gamma$ opacity in the source is small. Measurements of the time dependence of the 100 MeV-GeV spectral indices with the planned {it GLAST} mission will chart the evolution of the SSC component and test the external shock scenario. Transient optical and X-ray emissions from misaligned GRBs are generally much weaker than on-axis emissions produced by dirty and clean fireballs that would themselves not trigger a GRB detector; thus detection of long wavelength transients not associated with GRBs will not unambiguously demonstrate GRB beaming.
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We point out that the already existing literature on relativistic collisionless MHD shocks show that the parameter sigma= upstream proper magnetic energy density/upstream rest mass energy density, plays an important role in determining the structure and accelerating properties of such shocks. By adopting a value of sigma= 0.002 which corresponds to the relativistic shock associated with the Crab nebula, and by using appropriate relativistic shock jump conditions, we obtain here a generous upper-limit on the value of (proper) the magnetic field, B ~ 1.5 10^{-3} eta n^{1/2} G, for gamma ray burst (GRB) blast wave. Here, eta= E/Mc^2, where E is the energy and M is the mass of the baryons entrained in the original fireball (FB), and n is the proper number density of the ambient medium. Further, we point out that, in realistic cases, the actual value B could be as low as 5 10^{-6} eta n^{1/2} G. for realistic cases.
We present a study of the intermediate regime between ultra-relativistic and nonrelativistic flow for gamma-ray burst afterglows. The hydrodynamics of spherically symmetric blast waves is numerically calculated using the AMRVAC adaptive mesh refinement code. Spectra and light curves are calculated using a separate radiation code that, for the first time, links a parametrisation of the microphysics of shock acceleration, synchrotron self-absorption and electron cooling to a high-performance hydrodynamics simulation.
We consider a relativistically moving blob consisting of an isotropic electron distribution that Compton-scatters photons from an external isotropic radiation field. We compute the resulting beaming pattern, i.e. the distribution of the scattered photons, in the blob frame as well as in the observers frame by using the full Klein-Nishina cross section and the exact incident photon distribution. In the Thomson regime the comparison of our approach with Dermer 1995 results in concurrent characteristics but different absolute number of the scattered photons by a factor of f_corr = 3.09. Additionally, our calculation yields a slightly lower boost factor which varies the more from the corresponding value in Dermer 1995 the higher the spectral index p of the electron distribution gets.
We show that the spectral shape of the low energy tails found for the time-integrated spectra of gamma-ray bursts, even in the absence of strong synchrotron cooling, can be significantly softer than the $ u F_ u propto u^{4/3}$ asymptote predicted by synchrotron shock models. As we have noted in a previous work, blast wave deceleration via interaction with ambient material causes the characteristic electron injection energy to decrease in proportion to the bulk Lorentz factor of the blast wave, and under certain conditions, this effect will at least partially account for the observed increase in pulse widths with decreasing energy. This spectral softening can also be reflected in the time-integrated pulse spectrum. Using a simple model for the blast wave interaction with a dense cloud of material, we show that just below the $ u F_ u$ spectral peak the integrated spectrum behaves as $ u F_ u sim u^{1/2}$ and rolls over to a $ u^{4/3}$ dependence at lower energies, thus a spectral shape arises which is similar to that predicted for the spectrum of a strongly synchrotron-cooled electron population. We discuss the implications of this work in the context of models of burst light curve variability which are based on blast wave/cloud interactions.
A wide range of mechanisms have been proposed to supply the energy for gamma-ray bursts (GRB) at cosmological distances. It is a common misconception that some of these, notably NS-NS mergers, cannot meet the energy requirements suggested by recent observations. We show here that GRB energies, even at the most distant redshifts detected, are compatible with current binary merger or collapse scenarios involving compact objects. This is especially so if, as expected, there is a moderate amount of beaming, since current observations constrain the energy per solid angle much more strongly and directly than the total energy. All plausible progenitors, ranging from NS-NS mergers to various hypernova-like scenarios, eventually lead to the formation of a black hole with a debris torus around it, so that the extractable energy is of the same order, 1E+54 ergs, in all cases. MHD conversion of gravitational into kinetic and radiation energy can significantly increase the probability of observing large photon fluxes, although significant collimation may achieve the same effect with neutrino annihilation in short bursts. The lifetime of the debris torus is dictated by a variety of physical processes, such as viscous accretion and various instabilities; these mechanisms dominate at different stages in the evolution of the torus and provide for a range of gamma-ray burst lifetimes.
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