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 the following: (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 proportional to t(-(p+6)/4) rather than proportional to 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.