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.
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