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The peak time of optical afterglow may be used as a proxy to constrain theLorentz factor Gamma of the gamma-ray burst (GRB) ejecta. We revisit thismethod by including bursts with optical observations that started when theafterglow flux was already decaying; these bursts can provide useful lowerlimits on Gamma. Combining all analyzed bursts in our sample, we find that thepreviously reported correlation between Gamma and the burst luminosity L_gammadoes not hold. However, the data clearly shows a lower bound Gamma_min whichincreases with L_gamma. We suggest an explanation for this feature: explosionswith large jet luminosities and Gamma < Gamma_min suffer strong adiabaticcooling before their radiation is released at the photosphere; they produceweak bursts, barely detectable with present instruments. To test thisexplanation we examine the effect of adiabatic cooling on the GRB location inthe L_gamma - Gamma plane using a Monte Carlo simulation of the GRB population.Our results predict detectable on-axis "orphan" afterglows. We also deriveupper limits on the density of the ambient medium that decelerates theexplosion ejecta. We find that the density in many cases is smaller thanexpected for stellar winds from normal Wolf-Rayet progenitors. The burstprogenitors may be peculiar massive stars with weaker winds or there mightexist a mechanism that reduces the stellar wind a few years before theexplosion.

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