From blast wave to observation

arXiv:0902.0233v1 [astro-ph.HE] 2 Feb 2009 From blast wave to observation H.J. van Eerten and R.A.M.J. Wijers Astronomical Institute ’Anton Pannekoek’, Kruislaan 403, 1098SJ Amsterdam, the Netherlands Abstract. Gamma-ray burst (GRB) afterglows are well described by synchrotron emission originating from the interaction between a relativistic blast wave and the external medium surrounding the GRB progenitor. We introduce a code to reconstruct spectra and light curves from arbitrary fluid configurations, making it especially suited to study the effects of fluid flows beyond those that can be described using analytical approximations. As a check and first application of our code we use it to fit the scaling coefficients of theoretical models of afterglow spectra. We extend earlier results of other authors to general circumburst density profiles. We rederive the physical parameters of GRB 970508 and compare with other authors. We also show the light curves resulting from a relativistic blast wave encountering a wind termination shock. From high resolution calculations we find that the observed transition from a stellar wind type light curve to an interstellar medium type light curve is smooth and without short-time transitory features. Keywords: gamma rays: bursts - gamma rays: theory - plasmas - radiation mechanisms: nonthermal - shock waves PACS: 98.62.Nx; 98.70.Rz; 95.30.Lz; 95.30.Gv INTRODUCTION In the fireball model, Gamma-Ray Burst (GRB) afterglows are thought to be the result of synchrotron radiation generated by electrons during the interaction of a strongly collimated relativistic jet from a compact source with its environment (for recent reviews, see [22, 18]). Initially the resulting spectra and light curves have been modelled using only the shock front of a spherical explosion and a simple power law approximation for the synchrotron radiation (e.g. [27, 17, 24]). One or more spectral and temporal breaks were used to connect regimes with different power law slopes. For the dynamics the self similar Blandford-McKee (BM) approximation of a relativistic explosion was used [1]. These models have been refined continuously. More details of the shock structure were included (e.g. [6, 10]), more accurate formulae for the synchrotron radiation were used (e.g. [26]) and efforts have been made to implement collimation using various analytical approximations to the jet structure and lateral spreading behavior (see [9] for an overview). On top of that, there have been studies focussing on arrival time effects (e.g. [12]) and some numerical simulations (e.g. [19, 7, 2]). In this paper we introduce a code to reconstruct spectra and light curves from AMRVAC, a high performance relativistic hydrodynamics code [15]. We verify our method by applying it to the analytically well understood BM solution. Because different authors have recently started using the circumstellar density structure as a fitting parameter when fitting the BM solution to afterglow data[25], we generalize existing scaling coefficient prescriptions from the literature [6] from insterstellar medium (ISM, for which the inverse radial slope of the density distribution k is zero) and stellar wind (k = 2) to general k. These scaling coefficients are tabulated in the appendix and can be directly used when fitting to afterglow data. We finish this part of the paper by comparing fit results to GRB 970508 using our prescription to those of other authors. Following this, we apply our radiation code to study the visible effect of the blast wave encountering a wind termination shock. Our simulations, done at high resolution to make sure we accurately probe the timescales at which the encounter is expected to take place, confirm the prediction of [19] of a smooth transition between two power law regimes in the observerd light curve. With the exception of the wind termination shock section, most of the work presented in this paper is also presented in [3]. DESCRIPTION OF THE RADIATION CODE The code takes as input a series of snapshots of relativistic hydrodynamicsconfigurations on a grid. The grids represent a spherically symmetric fluid configuration and all grid cells are assumed to emit a fraction of their energy as radiation. This fraction of course has to be small enough not to affect the dynamics, since the post-processing approach does not allow for feedback. For the time being we restrict ourselves to the optically thin case. In this section and the next we will use BM solution for adiabatic expansion of the blast wave to provide the content of the grid snapshots. The BM solution takes two input parameters: E52, the explosion energy in units of 1052 erg and n0, the circumburst number density at a characteristic distance of 1017 cm. Four ignorance parameters are provided to the code at runtime: p, ξN, εE and εB, denoting respectively the slope of the relativistic particle distribution, the fraction of particles accelerated to this relativistic distribution at any given time, t

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