Constraining External Reverse Shock Physics of GRBs from ROTSE-III Limits

TL;DR

This study uses early optical observations from ROTSE-III to constrain the initial Lorentz factor of GRB outflows by analyzing reverse shock models in different environments, providing limits on their physical parameters.

Contribution

It offers the first comprehensive constraints on the initial Lorentz factor for both relativistic and non-relativistic reverse shock models in GRBs using early optical data.

Findings

Relativistic reverse shock models are constrained with Lorentz factors from hundreds to thousands.

Non-relativistic reverse shock models are constrained with Lorentz factors from about 30 to 350.

Lower limits on Lorentz factors challenge previous correlations with gamma-ray energy.

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 $F_{\rm \nu}$ at the RS crossing time should be lower than the observed upper limit $F_{\rm \nu,limit}$. We consider the different spectral regimes that the observed optical frequency $\nu_{\rm opt}$ may locate in, which are divided by the orders for the minimum synchrotron frequency $\nu_{\rm m}$ and the cooling frequency $\nu_{\rm c}$. {\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 $E_{\rm \gamma, iso}$ released in prompt phase.