A study of the afterglows of four gamma-ray bursts: Constraining the explosion and fireball model

We employ a fireball model of the gamma-ray burst (GRB) explosion to constrain intrinsic and environmental parameters of four events with good broadband afterglow data: GRB 970508, GRB 980329, GRB 980703, and GRB 000926. Using the standard assumptions of constant circumburst density and no evolution of the fraction of the explosion energy in the postshock magnetic field, we investigate the uniformity of the derived explosion and shock physics parameters among these events. We find a variety of parameters: densities that range from those of the interstellar mediumto diffuse clouds, energies comparable to the total GRB gamma-ray energy, collimations from near-isotropy to 0.04 radians, substantial electron energy fractions of 10%-30% with energy distribution indices of 2.1-2.9, and magnetic energy fractions from 0.2% to 25%. We also investigate the level to which the data constrain the standard model assumptions, such as the magnetic field evolution, and the allowed density profiles of the medium. Fits generally improve slightly with an increasing magnetic energy fraction ε_B. Good fits can be produced with magnetic energy accumulating or decaying with the shock strength over the afterglow as ε_B ∝ γ^x (-2 ≤ x ≤ +1). The data are not very sensitive to increasing density profiles, allowing good fits even with density ∝r¹⁰. Some parameter values change by up to an order of magnitude under such altered assumptions; the parameters of even good fits cannot be taken at face value. The data are sensitive to decreasing densities: r^-2 profiles may produce reasonable fits, but steeper profiles, even r^-2.5, will not fit the data.