Failed gamma-ray bursts and orphan afterglows

It is believed that orphan afterglow searches can help to measure the beaming angle in gamma-ray bursts (GRBs). Great expectations have been put on this method. We point out that the method is in fact not as simple as we originally expected. As a result of the baryon-rich environment that is common to almost all popular progenitor models, there should be many failed gamma-ray bursts, i.e. fireballs with Lorentz factor much less than 100-1000, but still much larger than unity. In fact, the number of failed gamma-ray bursts may even be much larger than that of successful bursts. Owing to the existence of these failed gamma-ray bursts, there should be many orphan afterglows even if GRBs are due to isotropic fireballs, then the simple discovery of orphan afterglows never means that GRBs are collimated. Unfortunately, to distinguish between a failed-GRB orphan and a jetted but off-axis GRB orphan is not an easy task. The major problem is that the trigger time is unknown. Some possible solutions to the problem are suggested.