Orphan Afterglows (OA) are slow transients produced by Gamma Ray Bursts seen off–axis that become visible on timescales of days/years at optical/NIR and radio frequencies, when the prompt emission at high energies (X and γ rays) has already ceased. Given the typically estimated jet opening angle of GRBs θjet ~ 3°, for each burst pointing to the Earth there should be a factor ~ 700 more GRBs pointing in other directions. Despite this, no secure OAs have been detected so far. Through a population synthesis code we study the emission properties of the population of OA at radio frequencies. OAs reach their emission peak on year-timescales and they last for a comparable amount of time. The typical peak fluxes (which depend on the observing frequency) are of few μJy in the radio band with only a few OA reaching the mJy level. These values are consistent with the upper limits on the radio flux of SN Ib/c observed at late times. We find that the OA radio number count distribution has a typical slope − 1.7 at high fluxes and a flatter ( − 0.4) slope at low fluxes with a break at a frequency–dependent flux. Our predictions of the OA rates are consistent with the (upper) limits of recent radio surveys and archive searches for radio transients. Future radio surveys like VAST/ASKAP at 1.4 GHz should detect ~ 3 × 10− 3 OA deg− 2 yr− 1, MeerKAT and EVLA at 8.4 GHz should see ~ 3 × 10− 1 OA deg− 2 yr− 1. The SKA, reaching the μJy flux limit, could see up to ~ 0.2 − 1.5 OA deg− 2 yr− 1. These rates also depend on the duration of the OA above a certain flux limit and we discuss this effect with respect to the survey cadence.
