The Difference Between the Amati and Ghirlanda Relations

It is pointed out that the beaming correction commonly inferred from the achromatic breaks in the afterglow light curve is biased in situations where the isotropic equivalent energy is affected by factors other than the spread in opening angles. In particular, it underestimates the beaming factor of sources observed off-axis. Here we show that both the slopes and scatters in the Amati and Ghirlanda relations, and the difference between them, are quantitatively consistent with a model proposed recently, in which the $E_{iso}-{\nu }_{peak}$ relation, as originally derived by Amati et al., is due to viewing angle effects. The quantitative difference between them confirms the relations between opening angle and break time suggested by Frail et al.