Applying an accurate spherical model to gamma-ray burst afterglow observations

We present results of model fits to afterglow data sets of GRB970508, GRB980703 and GRB070125, characterized by long and broadband coverage. The model assumes synchrotron radiation (including self-absorption) from a spherical adiabatic blast wave and consists of analytic flux prescriptions based on numerical results. For the first time it combines the accuracy of hydrodynamic simulations through different stages of the outflow dynamics with the flexibility of simple heuristic formulas. The prescriptions are especially geared towards accurate description of the dynamical transition of the outflow from relativistic to Newtonian velocities in an arbitrary power-law density environment. We show that the spherical model can accurately describe the data only in the case of GRB970508, for which we find a circumburst medium density consistent with a stellar wind. We investigate in detail the implied spectra and physical parameters of that burst. For the microphysics we show evidence for equipartition between the fraction of energy density carried by relativistic electrons and magnetic field. We also find that for the blast wave to be adiabatic, the fraction of electrons accelerated at the shock has to be smaller than 1. We present best-fit parameters for the afterglows of all three bursts, including uncertainties in the parameters of GRB970508, and compare the inferred values to those obtained by different authors.

Practical flux-prescriptions for gamma-ray burst afterglows, from early to late times

We present analytic flux prescriptions for broadband spectra of self-absorbed and optically thin synchrotron radiation from gamma-ray burst afterglows, based on one-dimensional relativistic hydrodynamic simulations. By treating the evolution of critical spectrum parameters as a power-law break between the ultrarelativistic and non-relativistic asymptotic solutions, we generalize the prescriptions to any observer time. Our aim is to provide a set of formulas that constitutes a useful tool for accurate fitting of model-parameters to observational data, regardless of the dynamical phase of the outflow. The applicability range is not confined to gamma-ray burst afterglows, but includes all spherical outflows (also jets before the jet-break) that produce synchrotron radiation as they adiabatically decelerate in a cold, power-law medium. We test the accuracy of the prescriptions and show that numerical evidence suggests that typical relative errors in the derivation of physical quantities are about 10 per cent. A software implementation of the presented flux prescriptions combined with a fitting code is freely available on request and on-line. Together they can be used in order to directly fit model parameters to data.