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Register a new userConstraining the Magnetic Field in Gamma Ray Burst Blast Waves
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Publication date
1998
fields
Physics
and research's language is
English
Authors
Abhas Mitra
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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.
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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.
In the internal shock model for gamma-ray bursts (GRBs), the synchrotron spectrum from the fast cooling electrons in a homogeneous downstream magnetic field (MF) is too soft to produce the low-energy slope of GRB spectra. However the magnetic field may decay downstream with distance from the shock front. Here we show that the synchrotron spectrum becomes harder if electrons undergo synchrotron and inverse-Compton cooling in a decaying MF. To reconcile this with the typical GRB spectrum with low energy slope $ u F_ upropto u$, it is required that the postshock MF decay time is comparable to the cooling time of the bulk electrons (corresponding to a MF decaying length typically of $sim10^5$ skin depths); that the inverse-Compton cooling should dominate synchrotron cooling after the MF decay time; and/or that the MF decays with comoving time roughly as $Bpropto t^{-1.5}$. An internal shock synchrotron model with a decaying MF can account for the majority of GRBs with low energy slopes not harder than $ u^{4/3}$.
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.
We demonstrate that gamma-ray burst afterglow spectra and light curves can be calculated for arbitrary explosion and radiation parameters by scaling the peak flux and the critical frequencies connecting different spectral regimes. Only one baseline calculation needs to be done for each jet opening angle and observer angle. These calculations are done numerically using high-resolution relativistic hydrodynamical afterglow blast wave simulations which include the two-dimensional dynamical features of expanding and decelerating afterglow blast waves. Any light curve can then be generated by applying scaling relations to the baseline calculations. As a result, it is now possible to fully fit for the shape of the jet break, e.g. at early time X-ray and optical frequencies. In addition, late-time radio calorimetry can be improved since the general shape of the transition into the Sedov-Taylor regime is now known for arbitrary explosion parameters so the exact moment when the Sedov-Taylor asymptote is reached in the light curve is no longer relevant. When calculating the baselines, we find that the synchrotron critical frequency and the cooling break frequency are strongly affected by the jet break. The synchrotron break temporal slope quickly drops to the steep late time Sedov-Taylor slope, while the cooling break first steepens then rises to meet the level of its shallow late time asymptote.
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.
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