Estimates for Lorentz factors of gamma-ray bursts from early optical afterglow observations

The peak time of optical afterglow may be used as a proxy to constrain the Lorentz factor Γ of the gamma-ray burst (GRB) ejecta. We revisit this method by including bursts with optical observations that started when the afterglow flux was already decaying; these bursts can provide useful lower limits on Γ. Combining all analyzed bursts in our sample, we find that the previously reported correlation between Γ and the burst luminosity L _γ does not hold. However, the data clearly show a lower bound Γ_min that increases with L _γ. We suggest an explanation for this feature: explosions with large jet luminosities and Γ < Γ_min suffer strong adiabatic cooling before their radiation is released at the photosphere; they produce weak bursts, barely detectable with present instruments. To test this explanation, we examine the effect of adiabatic cooling on the GRB location in the L _γ – Γ plane using a Monte Carlo simulation of the GRB population. Our results predict detectable on-axis 'orphan' afterglows. We also derive upper limits on the density of the ambient medium that decelerates the explosion ejecta. We find that the density in many cases is smaller than expected for stellar winds from normal Wolf-Rayet progenitors. The burst progenitors may be peculiar massive stars with weaker winds, or there might exist a mechanism that reduces the stellar wind a few years before the explosion.