Prompt optical emission and synchrotron self-absorption constraints on emission site of GRBs

We constrain the distance of the gamma-ray burst (GRB) prompt emission site from the explosion centre R, by determining the location of the electron's self-absorption frequency in the GRB prompt optical-to-X/gamma-ray spectral energy distribution, assuming that the optical and the gamma-ray emissions are among the same synchrotron radiation continuum of a group of hot electrons. All possible spectral regimes are considered in our analysis. The method has only two assumed parameters, namely the bulk Lorentz factor of the emitting source Gamma and the magnetic field strength B in the emission region (with a weak dependence). We identify a small sample of four bursts that satisfy the following three criteria: (1) they all have simultaneous optical and gamma-ray detections in multiple observational time intervals, (2) they all show temporal correlations between the optical and gamma-ray light curves and (3) the optical emission is consistent with belonging to the same spectral component as the gamma-ray emission. For all the time intervals of these four bursts, it is inferred that R >= 1014 (Gamma/300)3/4 (B/105 G)1/4 cm. For a small fraction of the sample, the constraint can be pinned down to R approximate to 1014-1015 cm for Gamma similar to 300. For a second sample of bursts with prompt optical non-detections, only upper limits on R can be obtained. We find no inconsistency between the R-constraints for this non-detection sample and those for the detection sample.