Unveiling the population of orphan γ-ray bursts

Gamma-ray bursts (GRBs) are detectable in the γ-ray band if their jets are oriented toward the observer. However, for each GRB with a typical θ<inf>jet</inf>, there should be ∼2/θ²<inf>jet</inf>2/θjet2 bursts whose emission cone is oriented elsewhere in space. These off-axis bursts can eventually be detected when, due to the deceleration of their relativistic jets, the beaming angle becomes comparable to the viewing angle. Orphan afterglows (OAs) should outnumber the current population of bursts detected in the γ-ray band even if they have not been conclusively observed so far at any frequency. We compute the expected flux of the population of orphan afterglows in the mm, optical, and X-ray bands through a population synthesis code of GRBs and the standard afterglow emission model. We estimate the detection rate of OAs with ongoing and forthcoming surveys. The average duration of OAs as transients above a given limiting flux is derived and described with analytical expressions: in general OAs should appear as daily transients in optical surveys and as monthly/yearly transients in the mm/radio band. We find that ∼2 OA? yr^-1 could already be detected by Gaia and up to 20 OA? yr^-1 could be observed by the ZTF survey. A larger number of 50 OA? yr^-1 should be detected by LSST in the optical band. For the X-ray band, ∼26 OA? yr^-1 could be detected by the eROSITA. For the large population of OA detectable by LSST, the X-ray and optical follow up of the light curve (for the brightest cases) and/or the extensive follow up of their emission in the mm and radio band could be the key to disentangling their GRB nature from other extragalactic transients of comparable flux density.