2000ApJ...541L...9K

We calculate light curves for gamma-ray burst afterglows when material ejected in the explosion is confined to a jet that propagates in a medium with a power-law density profile. The observed light-curve decay steepens by a factor of Γ² when an observer sees the edge of the jet. In a uniform density medium, the increase in the power-law index (β) of the light curve as a result of this edge effect is ∼0.7 and is completed over one decade in observer time. For a preejected stellar wind (ρ∝r^–2), β increases by ∼0.4 over two decades in time as a result of the edge effect, and the steepening of the light curve as a result of the jet sideways expansion takes about four decades in time. Therefore, a break in the light curve for a jet in a wind model is unlikely to be detected even for a very narrow opening angle of a few degrees or less, a case where the lateral expansion occurs at early times when the afterglow is bright.

The light curve for the afterglow of GRB 990510, for which an increase in β of approximately 1.35 was observed on a timescale of 3 days, cannot be explained by only the sideways expansion and the edge effects in a jet in a uniform interstellar medium–the increase in β is too large and too rapid. However, the passage of the cooling or synchrotron peak frequencies through the observing band at about 0.1-1 day together with jet edge effect explains the observed data. The jet opening angle is found to be ∼5°, and the energy in the explosion to be about 10⁵¹ ergs.