Modeling Gamma-Ray Burst X-Ray Flares Within the Internal Shock Model

Abstract

X-ray afterglow light curves have been collected for over 400 Swift gamma-ray bursts (GRBs) with nearly half of them having X-ray flares superimposed on the regular afterglow decay. Evidence suggests that gamma-ray prompt emission and X-ray flares share a common origin and that at least some flares can only be explained by long-lasting central engine activity. We have developed a shell model code to address the question of how X-ray flares are produced within the framework of the internal shock model. The shell model creates randomized GRB explosions from a central engine with multiple shells and follows those shells as they collide, merge, and spread, producing prompt emission and X-ray flares. We pay special attention to the time history of central engine activity, internal shocks, and observed flares, but do not calculate the shock dynamics and radiation processes in detail. Using the empirical E p -E iso (Amati) relation with an assumed Band function spectrum for each collision and an empirical flare temporal profile, we calculate the gamma-ray (Swift/BAT band) and X-ray (Swift/XRT band) lightcurves for arbitrary central engine activity and compare the model results with the observational data. We show that the observed X-ray flare phenomenology can be explained within the internal shock model. The number, width, and occurring time of flares are then used to diagnose the central engine activity, putting constraints on the energy, ejection time, width, and number of ejected shells. We find that the observed X-ray flare time history generally reflects the time history of the central engine, which reactivates multiple times after the prompt emission phase with progressively reduced energy. The same shell model predicts an external shock X-ray afterglow component, which has a shallow decay phase due to the initial pile-up of shells onto the blast wave. However, the predicted X-ray afterglow is too bright as compared with the observed flux level, unless e is as low as 10 −3 .

Open questions in GRB physics

“…The morphology is essentially impossible to be interpreted within the framework of the external shock model [256]. One therefore needs to appeal to late central engine activities to interpret them [253,125,257,258,259]. The most convincing evidence of such an interpretation is the reset of the clock for each episode of engine activity, as is suggested from the data: in order to interpret the decay following an X-ray flare as the high latitude emission effect, the required T0 is usually right before the rise of the flare [175].…”

The History of GRB Outflows: Ejection Lorentz Factor and Radiation Location of X-Ray Flares

“…With promptly slewing capacity, the X-ray telescope (XRT) onboard the Swift mission observed erratic flares during the prompt gamma-ray phase and even up to several days post the GRB trigger (e.g., Burrows et al 2005;Zhang et al 2006;Nousek et al 2006;O'Brien et al 2006;Falcone et al 2006;Falcone et al 2007;Chincarini et al 2007;Chincarini et al 2010). These flares are found to be internal origin and they sinal the restart of the GRB central engine after the prompt gamma-rays (e.g., Burrows et al 2005;Fan & Wei 2005;Zhang et al 2006;Dai et al 2006;Proga & Zhang 2006;Perna et al 2006;Romano et al 2006;Liang et al 2006;Wu et al 2006 ;Margutti et al 2010;Maxham & Zhang 2009) 1 . Taking these flares into account, the duration of the GRB central engines are much longer than the duration of the prompt gamma-rays (Qin et al 2013;Virgili et al 2013;Levan et al 2014;Zhang et al 2014).…”

“…One may estimate Γ X by assuming that the flares follow the same Γ γ − L iso relation. Further more, it is believed that the steep decay observed in the X-ray flares is due to the curvature effect (Fan & Wei 2005;Dyks et al 2005;Liang et al 2006;Zhang et al 2006;Panaitescu et al 2006;Wu et al 2006;Zhang et al 2007;Zhang et al 2009;Qin 2008;c.f., Hascoët et al 2015). This paper dedicates to study Γ X and R X of X-ray flares based the Γ γ − L γ,iso relation and the curvature effect on the X-ray flare tails.…”

Photospheric emission in gamma-ray bursts

“…However, a well known problem is the very low efficiency in energy conversion, typically no more than a few %. [43][44][45][46][47][48][49][50] A second theoretical problem that arises from fitting the data is that the required values of the magnetic field needed to produce the sub MeV peak are close to equipartition, while fits of the afterglow show that the magnetic field produces at shock fronts is typically two orders of magnitude below equipartition, and in many cases less. 33,51 A third problem is the fact that the energy of the peak is very sensitive to the model parameters (bulk Lorentz factor, Γ, electron's temperature, θ e and magnetic field, B): E peak ∝ Γθ 2 e B.…”