Constraining External Reverse Shock Physics of GRBs 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 ${\Gamma }_0$ 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 circum-burst environment, the constraints can be achieved by the fact that the peak flux $F_{\nu }$ at the RS crossing time should be lower than the observed upper limit $F_{\nu ,\mathrm{limit}}$. We consider the different spectral regimes that the observed optical frequency ${\nu }_{\mathrm{opt}}$ may locate in, which are divided by the orders for the minimum synchrotron frequency ${\nu }_{\mathrm{m}}$ and the cooling frequency ${\nu }_{\mathrm{c}}$. {\bf 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 ${\Gamma }_0$ 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 ${\Gamma }_0$ for 26 bursts ranging from $\sim 30$ to $\sim 350$.} The lower limits of ${\Gamma }_0$ achieved for the relativistic RS model is disfavored based on the previously discovered correlation between the initial Lorentz factor ${\Gamma }_0$ and the isotropic gamma-ray energy $E_{\gamma ,\mathrm{iso}}$ released in prompt phase.

11 pages, 5 tables, 4 figures, MNRAS in press

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