"Orphan" afterglows in the Universal Structured Jet Model for gamma-ray bursts

The paucity of reliable achromatic breaks in Gamma-Ray Burst afterglow light curves motivates independent measurements of the jet aperture. Serendipitous searches of afterglows, especially at radio wavelengths, have long been the classic alternative. These survey data have been interpreted assuming a uniformly emitting jet with sharp edges (``top-hat'' jet), in which case the ratio of weakly relativistically beamed afterglows to GRBs scales with the jet solid angle. In this paper, we consider, instead, a very wide outflow with a luminosity that decreases across the emitting surface. In particular, we adopt the universal structured jet (USJ) model, that is an alternative to the top-hat model for the structure of the jet. However, the interpretation of the survey data is very different: in the USJ model we only observe the emission within the jet aperture and the observed ratio of prompt emission rate to afterglow rate should solely depend on selection effects. We compute the number and rate of afterglows expected in all-sky snapshot observations as a function of the survey sensitivity. We find that the current (negative) results for OA searches are in agreement with our expectations. In radio and X-ray bands this was mainly due to the low sensitivity of the surveys, while in the optical band the sky-coverage was not sufficient. In general we find that X-ray surveys are poor tools for OA searches, if the jet is structured. On the other hand, the FIRST radio survey and future instruments like the Allen Telescope Array (in the radio band) and especially GAIA, Pan-Starrs and LSST (in the optical band) will have chances to detect afterglows.Comment: 10 pages, 8 figures. MNRAS accepted. Moderate revision