We calculate the time evolution of the flux, apparent size, and image centroid motion of gamma-ray burst (GRB) radio jets and show that they can be resolved by the Very Long Baseline Array (VLBA) at distances of hundreds of megaparsecs. We find that GRB 030329, which showed spectroscopic evidence for an associated Type Ic supernova (SN) at a distance of ≈800 Mpc, might just be resolvable by VLBA after several months. The prospects are much better for jets that are oriented sideways in similar SNe with no GRB counterpart; in particular, the motion of the flux centroid in such jets can be detected by the VLBA up to z ∼ 1, even when the jet cannot be resolved. If most GRBs are accompanied by a Type Ib/c SN, then there should be a few SN/GRB jets per year within a distance ≲200 Mpc, and most of them would be oriented sideways with no gamma-ray or X-ray precursor. Detection of these jets can be used to calibrate the fraction of all core-collapse SNe that produce relativistic outflows and determine the local GRB rate. Overall, the rate of Type Ib/c SNe that do not produce a GRB at all, but rather make relativistic radio jets with an initial Lorentz factor of a few, may be larger by up to 2 orders of magnitude than the rate of those that produce GRBs.
ملاحظة ببليوغرافيةFunding Information:
We thank Josh Winn, Mark Reid, and Re’em Sari for useful discussions. This work was supported in part by the Institute for Advanced Study (IAS), funds for natural sciences (J. G.), and NSF grants AST 00-71019 and AST 02-04514 and NASA grant NAG5-13292 (A. L.). A. L. acknowledges support from the IAS at Princeton and the J. S. Guggenheim Memorial Fellowship.