8 Afterglow models

The simple fireball model (i.e., a spherically symmetric relativistic external shock wave expanding into a homogeneous medium) has been "in and out of the hospital'' for months, but notices of its death appear to be premature. This amazes me, given the wealth of complexities one can easily imagine in the fireball itself and in its environment (Mészáros 1999). If the simple relativistic fireball model (or even more complex variants of it) suffice to explain burst afterglows (see Fig. 5), much can be learned, including the energy of the fireball per unit solid angle, the energy in the magnetic field, the energy in the relativistic electrons, and the density of the external medium into which the fireball expands (Wijers & Galama 1999; van Paradijs 1999; Lamb et al. 1999). It should be possible, in principle, to use the effects on the afterglow spectrum of extinction due to dust in the host galaxy and of absorption by the Lyman-${\alpha}$ forest to determine the redshift of the burst itself, but so far, this goal has eluded modelers (see, e.g., Lamb et al. 1999).

Currently, we are in the linear regime in terms of what we learn from each individual afterglow because, given the diversity of GRBs, GRB afterglows, and host galaxies, we have yet to sample the full "phase space'' of afterglow or host galaxy properties. Still less have we sampled the full "phase space'' of combinations of burst, afterglow, and host properties.

At the same time, we are in the strongly non-linear regime, in terms of what we learn from each individual observation of a burst afterglow. The value of each astronomer's observation is enhanced by the observations made by all other astronomers. As we have heard from several speakers at this workshop, the amount of information that can be gleaned from a given afterglow depends greatly on the number of measurements that exist both simultaneously in time and in wavelength, from the radio through the millimeter, sub-millimeter, near-infrared, optical, and X-ray bands. Furthermore, since the range of redshifts for the bursts (and therefore also their afterglows) is large, we cannot know in advance which bands will be crucial. Thus simultaneous or near-simultaneous multi-wavelength observations of burst afterglows are essential, and therefore observations by as many observers as possible must be encouraged. Finally, greater co-operation and co-ordination among observers is important, and should be facilitated, as has been done by setting up the invaluable service represented by the Gamma-Ray Burst Coordinate Network (GCN) (Barthelmy et al. 1999).