We derive spectra and light curves of the afterglow emission from a highly collimated jet if the power-law index (p) of the electron 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-like, the light curve index above the characteristic frequency increases slowly for the ISM, and even decreases for the wind, as the spectral index of the emission increases. (3) Once the jet enters the spreading phase, the high-frequency emission flux decays as ∝ t −2 rather than ∝ t −p. All these results differ strongly from those in the case of p> 2. We compare our analytical results with the observations on GRB 010222, and conclude that the jet model turns out to be unable to explain the observed data of the afterglow. 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. Subject headings: gamma-rays: bursts — relativity — shock waves 1
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