Constraining external reverse shock physics of gamma-ray bursts from ROTSE-III limits

Abstract

Assuming that the early optical emission is dominated by the external reverse shock (RS) in the standard model of gamma-ray bursts (GRBs), we intend to constrain RS models with the initial Lorentz factor Γ 0 of the outflows based on the ROTSE-III observations. We consider two cases of the RS behavior: the relativistic shock and the non-relativistic shock. For homogeneous interstellar medium (ISM) and wind circumburst environment, the constraints can be achieved by the fact that the peak flux F ν at the RS crossing time should be lower than the observed upper limit F ν,limit . We consider the different spectral regimes that the observed optical frequency ν opt may locate in, which are divided by the orders for the minimum synchrotron frequency ν m and the cooling frequency ν c . Considering the homogeneous and wind environment around GRBs, we find that the relativistic RS case can be constrained by the (upper and lower) limits of Γ 0 in a large range from about hundreds to thousands for 36 GRBs reported by ROTSE-III. The constraints on the non-relativistic RS case are achieved with limits of Γ 0 for 26 bursts ranging from ∼ 30 to ∼ 350. The lower limits of Γ 0 achieved for the relativistic RS model is disfavored based on the previously discovered correlation between the initial Lorentz factor Γ 0 and the isotropic gamma-ray energy E γ,iso released in prompt phase.