3 What we can learn from VLBI

Two weeks after the explosion the size of G970508, estimated from the observed scintillation (Frail et al. 1997b), was 0.003 mas. G970508 reached a peak of 0.7 mJy (with considerable variability) 60 days after the gamma-ray burst. At this time we can estimate a size of $\sim 0.02$ mas from equipartition arguments, unresolvable by VLBI observations (see Table 2). A similar GRB at a redshift of 0.2 would be $\sim$40 mJy, and have a size of 0.07 mas 60 days after the burst. With an easily achievable dynamic range image of 300:1, such a burst would be resolved by the VLBA. Unfortunately, if GRBs are homogeneously distributed out to z=4, or trace the star formation in the universe, then our chances of observing a GRB at z < 0.2 are less than 1 in 10⁴ (assuming $\Omega_0=0$). Belying that simple picture, one GRB, G980425, has already been found at z=0.0083. This has been explained as either a separate class of GRBs (Bloom et al. 1998), or the result of beaming such that only a small fraction of distant GRBs are detected (Wang & Wheeler 1998). By day 60 the predicted size of G980425 was 0.4 mas. Such an object in the northern sky would be easy to study with the VLBA.

Granot et al. (1998) have recently computed images of what the relativistically expanding fireball showing a disk-like, limb brightened geometry. If GRBs are substantially beamed (as is often invoked to reduce the energy requirements), then we expect substantial deviations from these predictions. Estimates of the rate of expansion also differ greatly (Waxman 1997 vs. Sari et al. 1998). By resolving the explosion the VLBA could play a crucial role in understanding the physics of these energetic events.

Combined VLA and VLBA observations can rule out significant gravitational lensing on scales of 10 mas - 300 arcsec in G970508 and G980703. This covers the range of lenses discussed in the literature, and rules out any substantial flux magnification of the gamma-ray burst by gravitational lensing.

The location of the GRB within the host galaxy is also a subject of interest. VLBA observations can pinpoint the location to within 1 mas (or a few parsecs at $z\sim 1$). Future optical or IR instruments capable of high resolution and absolute astrometry could use the VLBA position to shed light on the environment of the progenitor object.

  

Table 2: VLBI limits on expansion

Acknowledgements

The NRAO is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.