Correlation between the isotropic equivalent luminosity L_iso and the bulk Lorentz factor Γ₀. Estimates of Γ₀ from the measured afterglow onset t_p for 68 long GRBs (red filled circles and green filled stars) and the short GRB 090510 (green filled square symbol). Lower limits (derived from upper limits on the onset time ) are shown by the rightward black arrows. Upper limits (derived assuming that the afterglow onset time is larger than the peak time of the prompt emission, that is, t_p ≥ T_p,γ) are shown by the grey (leftward) arrows. Upper limit on Γ₀ imposed by the requirement that the deceleration radius is larger than the transparency radius is shown by the grey shaded triangular region (for two values of the radius R₀ where the fireball is formed – see Eq. (16)). The solid red line shows the correlation obtained with Γ₀ solely (bisector method), while the black dot–dashed line is the correlation obtained through the Monte Carlo method which accounts for the reconstructed distribution of Γ₀. Left and right panels show the case of a homogeneous and wind medium, respectively.