“Orphan” afterglows in the Universal Structured Jet Model for γ-ray bursts

The paucity of reliable achromatic breaks in Gamma-Ray Burst afterglow light curves motivates independent measurements of the jet aperture. Orphan afterglow (OA) searches, 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 nearly isotropic afterglows to GRBs scales with the jet solid angle. Data could so far only loosely constrain the jet size. We consider, instead, an almost isotropic outflow with a luminosity that decreases across the emitting surface. The total GRB energy can be lower than for an isotropic top-hat jet, and the current lack of positive detections can be more easily explained. In particular, we adopt the universal structured jet (USJ) model, that reproduces the observed afterglow phenomenology to the same extent as the top-hat jet. However, the interpretation of the OA data is very different if GRBs are described by the USJ rather than the top-hat model. We compute, within the framework of the USJ, the number and rate of orphan 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. A comparison with the top-hat model is also performed. 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 and Pan-Starrs (in the optical band) will have excellent chances, not only to detect OAs, but also to put strong constraints on the jet models.