Orphan afterglows of collimated gamma-ray bursts: Rate predictions and prospects for detection

We make a quantitative prediction for the detection rate of orphan gamma-ray burst (GRB) afterglows as a function of flux sensitivity in X-ray, optical, and radio wave bands, based on a recent model of collimated GRB afterglows. We find that the orphan afterglow rate strongly depends on the opening angle of the jet (roughly proportional totheta(jet)(-2)), as expected from simple geometrical consideration, if the total jet energy is kept constant as suggested by recent studies. The relative beaming factor b(rel), i.e., the ratio of all afterglow rates including orphans to those associated with observable prompt GRBs, could be as high as b(rel) greater than or similar to 100 for searches deeper than R 24, depending on afterglow parameters. To make the most plausible predictions, we average the model emission for 10 sets of afterglow parameters obtained through fits to 10 well-observed, collimated GRB jets, weighted by the sky coverage of each jet. Our model expectations are consistent with the results ( or constraints) obtained by all past searches. We estimate the number of orphan afterglows in the first 1500 deg(2) field of the Sloan Digital Sky Survey (SDSS) to be about 0.2. The relative beaming factor b(rel) is rapidly increasing with the search sensitivity: b(rel) similar to 3 for the SDSS sensitivity to transient objects in the northern sky (R similar to 19), similar to14 for the past high-z supernova searches (R similar to 23), and similar to50 for the sensitivity of the Subaru Suprime-Cam (R similar to 26). Predictions are made for the current facilities and future projects in X-ray, optical, and radio bands. Among them, the southern sky observation of the SDSS ( sensitive to transients down to R similar to 23) could detect similar to40 orphan afterglows during the 5 yr operation. The Allen Telescope Array would find about 200 afterglows in a radio band at similar to0.1-1 mJy with b(rel) similar to 15.