We model the observed radio through X-ray spectrum of the GRB 980329 afterglow, and its evolution through time, as follows. We take the intrinsic spectrum to be a thrice broken power law, motivated by the relativistic fireball model, in which spectral breaks may occur due to synchrotron self-absorption, the synchrotron peak, and electron cooling (see e.g., Sari et al. 1998). The spectrum that we fit is a generalization of the spectrum expected in this model, in the sense that we do not constrain the slopes of the four spectral segments, nor the (power-law) rates at which these segments fade, a priori.
We allow the intrinsic spectrum to be modified in the following ways. First, we allow this spectrum to be extincted by dust and absorbed by the Lyman limit at a single redshift, assumed to be the redshift of the burst and its host galaxy. We adopt the six parameter ultraviolet extinction curve of Fitzpatrick & Massa (1988) and the one parameter optical and near-infrared extinction curve of Cardelli et al. (1989). Finally, we redshift the modified spectrum to the observer's frame of reference, and model the Lyman- forest due to absorption by gas clouds along the line-of-sight between the burst and the observer.
|Figure 2: The radio through X-ray spectrum of the afterglow of GRB 980329. All measurements have been scaled to a common time, approximately three days after the GRB. The solid curve is the best fit spectrum for an isotropic fireball that expands into a homogeneous external medium, extincted by dust at a redshift of z = 3.5. The dotted curve is the un-extincted spectrum|
The afterglow of GRB 980329 is unique among afterglows observed to date in that enough measurements of it have been taken to determine all the parameters of our model. From the results of our fits, we draw six conclusions: (1) The inferred intrinsic spectrum of the afterglow is consistent with the predictions of the simplest relativistic fireball model, in which an isotropic fireball expands into a homogeneous external medium. (2) The intrinsic spectrum of the afterglow is extincted by dust (source frame mag). (3) The linear component of the extinction curve is flat, which is typical of young star-forming regions like the Orion Nebula but is not typical of older star-forming or starburst regions. (4) The 2 mag drop between the R and the I bands can be explained by the Ly- forest if the burst redshift is (Fruchter 1999), by the far-ultraviolet non-linear component of the extinction curve if , and by the 2175 Å bump if ; other redshifts are not consistent with these data, given this general model. Djorgovski et al. (1999) report that z < 3.9 based upon the non-detection of the Ly- forest in a Keck II spectrum of the host galaxy. (5) Assuming a redshift of z = 3.5 for illustrative purposes, using the observed breaks in the intrinsic spectrum, and solving for the physical properties of the fireball (see, e.g., Wijers & Galama 1998), we find that the energy of the fireball per unit solid angle is erg sr-1 if and . (6) Similarly, we find that the density of the external medium into which this fireball expands is 103 cm-3 if and . This density suggests that GRB 980329 occurred in a molecular cloud, which is consistent with the fact that the observed extinction features are characteristic of star-forming regions.
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