2009MNRAS.398.1936S

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/γ-ray spectral energy distribution, assuming that the optical and the γ-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 Γ 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 γ-ray detections in multiple observational time intervals, (2) they all show temporal correlations between the optical and γ-ray light curves and (3) the optical emission is consistent with belonging to the same spectral component as the γ-ray emission. For all the time intervals of these four bursts, it is inferred that R ≥ 10¹⁴(Γ/300)^3/4 (B/10⁵G)^1/4 cm. For a small fraction of the sample, the constraint can be pinned down to R ~ 10¹⁴-10¹⁵ cm for Γ ∼ 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.