  The peak time of optical afterglow may be used as a proxy to constrain the
Lorentz factor Gamma 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 Gamma. Combining all analyzed bursts in our sample, we find that the
previously reported correlation between Gamma and the burst luminosity L_gamma
does not hold. However, the data clearly shows a lower bound Gamma_min which
increases with L_gamma. We suggest an explanation for this feature: explosions
with large jet luminosities and Gamma < Gamma_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_gamma - Gamma 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.

High Energy Astrophysical Phenomena