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 jets if the power-law index ($p$) of the electron energy distribution is above 1 but below 2. We find (1) below the characteristic synchrotron frequency, the light curve index depends generally on $p$. (2) As long as the jet expansion is spherical, the light curve index above the characteristic frequency increases slowly as the spectral index of the emission increases. (3) Once the jet enters the spreading phase, the high-frequency emission flux decays as $\propto t^{-(p+6)/4}$ rather than $\propto t^{-p}$. All these results differ from those in the case of $p>2$. We compare our analytical results with the observations on the GRB 010222 afterglow, and conclude that the jet model may be unable to explain the observed data. Thus, a more promising explanation for this afterglow seems to be the expansion of a relativistic fireball or a mildly collimated jet in a dense medium.