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Physical parameters of GRB 970508 and GRB 971214 from their afterglow synchrotron emission

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 Added by Ralph Wijers
 Publication date 1998
  fields Physics
and research's language is English




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We have calculated synchrotron spectra of relativistic blast waves, and find predicted characteristic frequencies that are more than an order of magnitude different from previous calculations. For the case of an adiabatically expanding blast wave, which is applicable to observed gamma-ray burst (GRB) afterglows at late times, we give expressions to infer the physical properties of the afterglow from the measured spectral features. We show that enough data exist for GRB970508 to compute unambiguously the ambient density, n=0.03/cm**3, and the blast wave energy per unit solid angle, E=3E52 erg/4pi sr. We also compute the energy density in electrons and magnetic field. We find that they are 12% and 9%, respectively, of the nucleon energy density and thus confirm for the first time that both are close to but below equipartition. For GRB971214, we discuss the break found in its spectrum by Ramaprakash et al. (1998). It can be interpreted either as the peak frequency or as the cooling frequency; both interpretations have some problems, but on balance the break is more likely to be the cooling frequency. Even when we assume this, our ignorance of the self-absorption frequency and presence or absence of beaming make it impossible to constrain the physical parameters of GRB971214 very well.



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We report on the results of optical follow-up observations of the counterpart of GRB 970508, starting 7 hours after the event. Multi-color U, B, V, R$_{c}$ and I$_{c}$ band observations were obtained during the first three consecutive nights. The counterpart was monitored regularly in R$_{c}$ until $sim$ 4 months after the burst. The light curve after the maximum follows a decline that can be fitted with a power law with exponent $alpha$ = --1.141 $pm$ 0.014. Deviations from a smooth power law decay are moderate (r.m.s. = 0.15 magnitude). We find no flattening of the light curve at late times. The optical afterglow fluence is a significant fraction, $sim$ 5%, of the GRB fluence. The optical energy distribution can be well represented by a power law, the slope of which changed at the time of the maximum (the spectrum became redder).
149 - A. M. Beloborodov 2010
The curvature of a relativistic blast wave implies that its emission arrives to observers with a spread in time. This effect is believed to wash out fast variability in the lightcurves of GRB afterglows. We note that the spreading effect is reduced if emission is anisotropic in the rest-frame of the blast wave (i.e. if emission is limb-brightened or limb-darkened). In particular, synchrotron emission is almost certainly anisotropic, and may be strongly anisotropic, depending on details of electron acceleration in the blast wave. Anisotropic afterglows can display fast and strong variability at high frequencies (above the fast-cooling frequency). This may explain the existence of bizarre features in the X-ray afterglows of GRBs, such as sudden drops and flares. We also note that a moderate anisotropy can significantly delay the jet break in the lightcurve, which makes it harder to detect.
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The afterglow of GRB 170817A has been detected for more than three years, but the origin of the multi-band afterglow light curves remains under debate. A classical top-hat jet model is faced with difficulties in producing a shallow rise of the afterglow light curves as observed $(F_{ u} propto T^{0.8})$. Here we reconsider the model of stratified ejecta with energy profile of $E(>Gamma beta)=E_0(Gamma beta)^{-k}$ as the origin of the afterglow light curves of the burst, where $Gamma$ and $beta$ are the Lorentz factor and speed of the ejecta, respectively. $k$ is the power-law slope of the energy profile. We consider the ejecta are collimated into jets. Two kinds of jet evolutions are investigated, including a lateral-spreading jet and a non-lateral-spreading jet. We fit the multi-band afterglow light curves, including the X-ray data at one thousand days post-burst, and find that both the models of the spreading and non-spreading jets can fit the light curves well, but the observed angular size of the source and the apparent velocity of the flux centroid for the spreading jet model are beyond the observation limits, while the non-spreading jet model meets the observation limits. Some of the best-fit parameters for the non-spreading jet model, such as the number density of the circumburst medium $sim10^{-2}$ cm$^{-3}$ and the total jet kinetic energy $E sim 4.8times 10^{51}$ erg, also appear plausible. The best-fit slope of the jet energy profile is $k sim 7.1$. Our results suggest that the afterglow of GRB 170817A may arise from the stratified jet and that the lateral spreading of the jet is not significant.
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