Synchrotron radiation of relativistic electrons is an important radiation mechanism in many astrophysical sources. In the sources where the synchrotron cooling timescale is shorter than the dynamical timescale, electrons are cooled down below the minimum injection energy. It has been believed that such 'fast cooling' electrons have a power-law distribution in energy with an index −2, and their synchrotron radiation has a photon spectral index 1 −1.5. On the other hand, in a transient expanding astrophysical source, such as a γ-ray burst (GRB), the magnetic field strength in the emission region continuously decreases with radius. Here we study such a system, and find that in a certain parameter regime, the fast-cooling electrons can have a harder energy spectrum. We apply this new physical regime to GRBs, and suggest that the GRB prompt emission spectra whose low-energy photon spectral index has a typical value 2-5 −1 could be due to synchrotron radiation in this moderately fast-cooling regime. The radiation mechanism of γ-ray bursts (GMBs), the most luminous explosions in the Universe, remains unidentified after 45 years since their discovery in the late 1960s. A typical GRB prompt emission spectrum is a smoothly connected broken power law called the Band function 2 , whose typical low-and high-energy photon spectral indices (in the convention of dN /dE γ ∝ E α or ∝ E β) are α ∼ −1 and β ∼ −2.2. Synchrotron radiation of electrons accelerated in relativistic shocks has been suggested as the leading mechanism 6,7. However, for nominal parameters, the magnetic field strength in the GRB emission region is strong enough that the electrons are in the fast-cooling regime; that is, the cooling timescale t c is shorter than the dynamical time scale t dyn. In this regime, it has been believed that the photon index should be −1.5 (corresponding to a spectral density distribution F ν ∝ ν −1/2 ; ref. 1). As a result, a fast-cooling synchrotron mechanism has been disfavoured 8. Proposed solutions include introducing a spatially decaying magnetic field behind the internal shock front 9-11 , or slow heating from a turbulent downstream region of the shock 12. Applying a synchrotron model to directly fit the GRB data has recently been carried out 13,14. However, the electron cooling is not tracked to calculate a time-dependent photon spectrum in their modelling. This well-known index α = −1.5 can be derived from a simple argument. Let us consider a continuity equation of electrons in energy space (∂/∂t)(dN e /dγ e) + (∂/∂γ e) [γ e (dN e /dγ e)] = Q(γ e , t), where dN e /dγ e is the instantaneous electron spectrum of the system at the epoch t, and Q(γ e , t) is the source function above a minimum injection Lorentz factor γ m of the electrons. For synchrotron radiation, the electron energy loss rate iṡ
The standard model of afterglow production by the forward shock wave is not supported by recent observations. We propose a model in which the forward shock is invisible and afterglow is emitted by a long-lived reverse shock in the burst ejecta. It explains observed optical and X-ray light curves, including the plateau at 10^3-10^4 s with a peculiar chromatic break, and the second break that was previously associated with a beaming angle of the explosion. The plateau forms following a temporary drop of the reverse-shock pressure much below the forward-shock pressure. A simplest formalism that can describe such blast waves is the ``mechanical'' model (Beloborodov, Uhm 2006); we use it in our calculations.Comment: 11 pages, 3 figures, accepted to ApJ Letter
We perform a time-resolved spectral analysis of GRB 130606B within the framework of a fast-cooling synchrotron radiation model with magnetic field strength in the emission region decaying with time, as proposed by Uhm & Zhang. The data from all time intervals can be successfully fit by the model. The same data can be equally well fit by the empirical Band function with typical parameter values. Our results, which involve only minimal physical assumptions, offer one natural solution to the origin of the observed GRB spectra and imply that, at least some, if not all, Band-like GRB spectra with typical Band parameter values can indeed be explained by synchrotron radiation.
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