GRB 980923 was one of the brightest bursts observed by the Burst and Transient Source Experiment (BATSE). Previous studies have detected two distinct components in addition to the main prompt episode, which is well described by a Band function. The first of these is a tail with a duration of 400s, while the second is a high-energy component lasting 2s. After summarizing the observations, we present a model for this event and conclude that the tail can be understood as the early gamma-ray afterglow from forward shock synchrotron emission, while the high-energy component is described by the SSC emission from the reverse shock. The main assumption is that of a thick-shell case from highly magnetized ejecta. The calculated fluxes, break energies, starting times and spectral index are all consistent with the observed values.
The most successful theory to explain GRBs and their afterglows is the fireball model [1]. This model predicts an expanding ultrarelativistic shell that moves into the external medium. When the expanding shell collides with another shell (internal shocks) or surrounding interstellar media (external shocks) gives rise to radiation emission through the synchrotron and SSC processes. Besides when the expanding relativistic shell encounters the external medium involves two shocks: an outgoing shock (the forward shock) and other that propagates into the ejecta (the reverse shock). When the forward shock collides with ISM, electrons are accelerated up to relativistic energies. The reverse shock heats up the shell's matter and accelerates electrons when it crosses the shell. Now, although the contribution of the synchrotron emission of reverse shock to the X-ray band could be small, electrons in the reverse shock region can upscatter the synchrotron photons (SSC process) up to higher energies. In this work we extend the smooth tail work done by [2] and study synchrotron self-inverse Compton radiation from a thick shell of reverse shock fireball to explain the hard component of the GRB 980923.
GRB 980923 was observed by BATSE on 1998 September 23 at 20:10:52 UT for 32.02 s. It was localized to 2340 with respect to the pointing-axis direction of CGRO. In accordance to [3], the event consists of three components [4]. The first component is related to the typical prompt emission, the second one is related to the smooth tail which lasts 400s and the last one is related to the hard component which shows a high energy spectral component extending up to 150 MeV and the power index -1.44 ± 0.07. The smooth tail was well described by [2] as the evolution of a synchrotron cooling break in the slow-cooling regime at t 0 =32 seconds where the characteristic value of the power index was p= 2.4 ± 0.11. However, [3] point out that the tail could begin before or at least about 14s after the burst trigger and after of a short period of time occurred the transition between fast to slow cooling.
In a unified way between forward and reverse shock, we compute the energy range for synchrotron selfinverse Compton radiation from a thick shell of the reverse shock fireball to explain the hard component. The subscripts f and r refer throughout to the forward and reverse shock, respectively.
For the forward shock, we assume that electrons are accelerated in the shock to a power law distribution of Lorentz factor γ e with a minimum Lorentz factor γ m : N (γ e )dγ e ∝ γ -p e dγ e , γ e ≥ γ m and that constant fractions ǫ e,f and ǫ B,f of the shock energy go into the electrons and the magnetic field, respectively. Then
where we have used the value of p = 2.4 ± 0.11 as was obtained by [2]. Using the typical parameters given by [5], we compute the typical and cooling frequencies of the forward shock synchrotron emission [6] which are given by,
where the convention Q x = Q/10 x has been adopted in cgs units throughout this document unless otherwise specified. t tr,f is the transition time, when the spectrum changes from fast cooling to slow cooling, D is the luminosity distance, n f is the ISM density, t is the time of the evolution of the tail, E is the energy, and the term (1 + x f ) was introduced because a once-scattered synchrotron photon generally has energy larger than the electron mass in the rest frame of the second-scattering electrons. Multiple scattering of synchrotron photons can be ignored. x f is given by [22] as:
where η = (γ c,f /γ m,f ) 2-p for slow cooling and η = 1 for fast cooling. From eq. ( 2), we observe directly that ν m,f ≤ ν c,f , the break energy E c,f ∼ 124.1 keV and t tr,f ∼ 8.7, implying also that the transition from fast to slow cooling could take place on very short timescales, comparable to the duration of the burst.
For the reverse shock, it is possible to obtain a simple analytic solution in two limiting cases, thin and thick shell, [7] by using a critical Lorentz factor Γ c ,
T 90 32s
where T 90 is the time of the GRB, which is much larger that the peak time of the reverse shock emission, and n r is the thick shell density. We consider the thick shell case in which the reverse shock becomes relativistic during the propagation and the shell is significantly decelerated by the reverse shock. Hence, the Lorentz factor at the shock crossing time t c is given by γ d ∼ Γ c [8,9] and for σ = L pf /L kn ∼ 1 the crossing
where
) and R M = Γ 2 c /γ. The previous relations tell us that including the re-scaling there is a unified description between both shocks (forward and reverse). Such as the magnetic field where there are some central engine models [19][20][21] for which the fireball wind may be endowed with “primordial” magnetic fields. Also as the cooling Lorentz factor must be corrected, then R x is introduced as a correction factor for the IC cooling, where x r is obtained by [8] as,
Using equations ( 2
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