  Gamma Ray Bursts are detectable in the gamma-ray band if their jets are
oriented towards the observer. However, for each GRB with a typical theta_jet,
there should be ~2/theta_jet^2 bursts whose emission cone is oriented elsewhere
in space. These off-axis bursts can be eventually detected when, due to the
deceleration of their relativistic jets, the beaming angle becomes comparable
to the viewing angle. Orphan Afterglows (OA) should outnumber the current
population of bursts detected in the gamma-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 OA by on-going and forthcoming surveys. The
average duration of OA as transients above a given limiting flux is derived and
described with analytical expressions: in general OA 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 disentangle their GRB nature from other
extragalactic transients of comparable flux density.
