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James Chiang
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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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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.
Multi-wave band synchrotron linear polarization of gamma-ray burst (GRB) afterglows is studied under the assumption of an anisotropic turbulent magnetic field with a coherence length of the plasma skin-depth scale in the downstream of forward shocks. We find that for typical GRBs, in comparison to the optical polarization, the degree of radio polarization shows a similar temporal evolution but a significantly smaller peak value. This results from differences in observed intensity image shapes between the radio and optical bands. We also show that the degree of the polarization spectrum undergoes a gradual variation from the low- to the high-polarization regime above the intensity of the spectral peak frequency, and that the difference in polarization angles in the two regimes is zero or 90 degrees. Thus, simultaneous multi-wave band polarimetric observations of GRB afterglows would be a new determinative test of the plasma-scale magnetic field model. We also discuss theoretical implications from the recent detection of radio linear polarization in GRB 171205A with ALMA and other models of magnetic field configuration.
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 performed a time-resolved spectral analysis of 53 bright gamma-ray bursts (GRBs) observed by textit{Fermi}/GBM. Our sample consists of 908 individual spectra extracted from the finest time slices in each GRB. We fitted them with the synchrotron radiation model by considering the electron distributions in five different cases: mono-energetic, single power-law, Maxwellian, traditional fast cooling, and broken power-law. Our results were further qualified through Bayesian Information Criterion (BIC) by comparing with the fit by empirical models, namely the so-called Band function and cut-off power-law models. Our study showed that the synchrotron models, except for the fast-cooling case, can successfully fit most observed spectra, with the single power-law case being the most preferred. We also found that the electron distribution indices for the single power-law synchrotron fit in more than half of our spectra exhibits flux-tracking behavior, i.e., the index increases/decreases with the flux increasing/decreasing, implying that the distribution of the radiating electrons is increasingly narrower with time before the flux peaks and becomes more spreading afterward. Our results indicate that the synchrotron radiation is still feasible as a radiation mechanism of the GRB prompt emission phase.
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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