The Case for Anisotropic Afterglow Efficiency within Gamma-Ray Burst Jets

Early X-ray afterglows recently detected by {\it Swift} frequently show aphase of very shallow flux decay lasting from $\sim 10^{2.5} $s up to $\sim10^4 $s, followed by a steeper, more familiar decay. We suggest that the flatearly part of the light curve may be a combination of the decaying tail of theprompt emission and the delayed onset of the afterglow emission observed fromviewing angles slightly outside the edge of the region within the jet withprominent afterglow emission, as predicted previously. This would imply that asignificant fraction of viewers get very little external shock energy alongtheir line of sight, and, therefore, see a very high $\gamma$-ray to kineticenergy ratio at early times. The early flat phase in the afterglow light curveimplies, in a rather robust and model independent manner, a very large$\gamma$-ray efficiency, typically $\gtrsim 90%$, which is very difficult toextract from baryons by internal shocks.Comment: Revised version, submitted to Ap