Steepening of Afterglow Decay for Jets Interacting with Stratified Media

Details Steepening of Afterglow Decay for Jets Interacting with Stratified Media Steepening of Afterglow Decay for Jets Interacting with Stratified Media

2000-03-17

arxiv.org/abs/astro-ph/0003264v1

Astronomy and Astrophysics

Astrophysics

6 pages including 3 figures, submitted to ApJ letter

Scientific paper

10.1086/312888

We calculate light-curves for Gamma-Ray Burst afterglows when material ejected in the explosion is confined to a jet which propagates in a medium with a power-law density profile. The observed light-curve decay steepens by a factor of $\Gamma^2$ when an observer sees the edge of the jet. In a uniform density medium the increase in the power-law index ($\beta$) of the light-curve as a result of this {\it edge effect} is $\sim0.7$ and is completed over one decade in observer time. For a pre-ejected stellar wind ($\rho \propto r^{-2}$) $\beta$ increases by $\sim0.4$ over two decades in time due to the edge effect and the steepening of the light-curve due to 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 very narrow jets of opening angle of a few degrees or less, in which case 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 $\beta$ of approximately 1.35 was observed on a time scale of 3 days, cannot be explained only by the sideways expansion and the edge effects in a jet in a uniform ISM -- the increase in $\beta$ 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 $\sim 5^o$ and the energy in the explosion to be less than about $10^{50}$ erg.

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