Afterglow Emission from Highly Collimated Jets with Flat Electron Spectra: Application to the GRB 010222 Case?

We derive light curves of the afterglow emission from highly collimated jetsif the power-law index ($p$) of the electron energy distribution is above 1 butbelow 2. We find (1) below the characteristic synchrotron frequency, the lightcurve index depends generally on $p$. (2) As long as the jet expansion isspherical, the light curve index above the characteristic frequency increasesslowly as the spectral index of the emission increases. (3) Once the jet entersthe spreading phase, the high-frequency emission flux decays as $\proptot^{-(p+6)/4}$ rather than $\propto t^{-p}$. All these results differ from thosein the case of $p>2$. We compare our analytical results with the observationson the GRB 010222 afterglow, and conclude that the jet model may be unable toexplain the observed data. Thus, a more promising explanation for thisafterglow seems to be the expansion of a relativistic fireball or a mildlycollimated jet in a dense medium.Comment: shortened version accepted for publication in ApJ Letter