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Register a new userAdiabatic and Radiative Cooling of Relativistic Electrons Applied to Synchrotron Spectra and Light-Curves of Gamma-Ray Burst Pulses
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A. Panaitescu
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We investigate the adiabatic and radiative (synchrotron and inverse-Compton) cooling of relativistic electrons whose injected/initial distribution with energy is a power-law above a typical energy $gamma_i$. Analytical and numerical results are presented for the cooling-tail and the cooled-injected distribution that develop below and above the typical energy of injected electrons, for the evolution of the peak-energy $E_p$ of the synchrotron emission spectrum, and for the pulse shape resulting from an episode of electron injection. The synchrotron emission calculated numerically is compared with the spectrum and shape of Gamma-Ray Burst (GRB) pulses. Both adiabatic and radiative cooling processes lead to a softening of the pulse spectrum, and both types of cooling processes lead to pulses peaking earlier and lasting shorter at higher energy, quantitatively consistent with observations. For adiabatic-dominated electron cooling, a power-law injection rate $R_i$ suffices to explain the observed power-law GRB low-energy spectra. Synchrotron-dominated cooling leads to power-law cooling-tails that yield the synchrotron standard slope alpha = -3/2 provided that $R_i sim B^2$, which is exactly the expectation if the magnetic field is a constant fraction of the post-shock energy density. Increasing (decreasing) $R_i$ and decreasing (increasing) B(t) lead to slopes alpha harder (softer, respectively) than the standard value and to non--power-law (curved) cooling-tails. Inverse-Compton cooling yields four values for the slope alpha but, as for synchrotron, other $R_i$ or B histories yield a wider range of slopes and curved low-energy spectra. Feedback between the power-law segments that develop below and above the typical injected electron leads to a synchrotron spectrum with many breaks above and below the usual 10 keV-1 MeV observing range.
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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.
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