Fast-cooling synchrotron radiation in a decaying magnetic field and γ-ray burst emission mechanism

Abstract

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

Detection of Low-energy Breaks in Gamma-Ray Burst Prompt Emission Spectra

“…A marginally fast cooling regime (i.e. a situation where ν c ν m rather than ν c << ν m ) has been considered as a possible solution to the inconsistency between the expected and measured photon index (Derishev 2007;Daigne et al 2011;Beniamini & Piran 2013;Uhm & Zhang 2014). In the context of prompt emission, a theoretical prediction of the location of the cooling break frequency and of the ratio ν c /ν m is difficult to make, given the large uncertainties on the properties of the emitting region, such as dissipation radius, bulk Lorentz factor, magnetic field, and particle acceleration mechanism and efficiency.…”

“…Among the first class of models, we recall scenarios invoking Comptonization and/or thermal components Blinnikov et al 1999;Ghisellini & Celotti 1999;Lazzati et al 2000;Mészáros & Rees 2000;Stern & Poutanen 2004;Rees & Mészáros 2005;Ryde & Pe'er 2009;Guiriec et al 2011Guiriec et al , 2015aGuiriec et al ,b, 2016aGhirlanda et al 2013;Burgess et al 2014). For the second class of models (studies that consider synchrotron radiation) effects producing a hardening of the low-energy spectral index have been invoked, such as Klein-Nishina effects, marginally fast cooling regime, and anisotropic pitch angle distributions (Lloyd & Petrosian 2000;Derishev 2001Derishev , 2007Bosnjak et al 2009;Nakar et al 2009;Daigne et al 2011;Uhm & Zhang 2014). In spite of all theoretical efforts, there is still no consensus on the origin of the prompt emission.…”

Formation of very hard electron and gamma-ray spectra of flat-spectrum radio quasars in the fast-cooling regime

“…As a last remark, we note that very recently Uhm & Zhang (2014) and Zhao et al (2014) showed that a very hard electron spectrum with p ∼ 1 can be produced in the fast-cooling regime due to synchrotron radiation in a strongly decaying magnetic field. This can explain the γ-ray burst (GRB) prompt emission spectra whose low-energy photon spectral index has a value ∼ 1.…”

Time-resolved GRB spectra in the complex radiation of synchrotron and Compton processes

“…This suggests us that the thermal emission plus the geometry effect can create the observed GRB spectra. Another remarkable model which can solve the α ∼ −1 problem is the fast cooling synchrotron radiation in the decaying magnetic field (Uhm & Zhang 2014). The low energy spectral slope α is found to be related to the decaying slope of the magnetic filed by an analytic method.…”