Lorentz Factor Constraint from the very early external shock of the gamma-ray burst ejecta

TL;DR

This paper constrains the initial Lorentz factors of gamma-ray burst ejecta by analyzing the absence of external shock emission during quiet periods, resulting in upper limits around hundreds.

Contribution

It introduces a novel method to set upper limits on Lorentz factors using quiet periods in GRB light curves, complementing existing lower limit estimates.

Findings

Upper limits on  for several GRBs are around hundreds.

Deep minima in light curves imply negligible external shock emission.

Results narrow down the possible range of initial Lorentz factors.

Abstract

While it is generally agreed that the emitting regions in Gamma-Ray Bursts (GRBs) move ultra relativistically towards the observer, different estimates of the initial Lorentz factors, $\Gamma_0$, lead to different, at times conflicting estimates. We show here that the quiet periods in which the signals goes down below the instrumental thresholds, put strong upper limits on the values of $\Gamma_0$. According to the standard internal-external shocks model an external shock should develop during the prompt stage. This external shock radiates in the hard X-rays to soft gamma-rays bands and this emission should be seen as a smooth background signal. The observed deep minima indicate that this contribution is negligible. This limits, in turn, $\Gamma_0$. We obtain upper limits on $\Gamma_0$ for several bursts with typical values around hundreds. We compare these values with those obtained by the other methods, which typically yield lower limits. The results are marginally consistent leaving only a narrow range of allowed values for $\Gamma_0$.