Late-time radio observations of 68 type IBc supernovae: Strong constraints on off-axis gamma-ray bursts

We present late-time radio observations of 68 local Type Ibc supernovae, including six events with broad optical absorption lines (hypernovae''). None of these objects exhibit radio emission attributable to off-axis gamma-ray burst jets spreading into our line of sight. Comparison with our afterglow models reveals the following conclusions. ( 1) Less than similar to 10% of Type Ibc supernovae are associated with typical gamma-ray bursts initially directed away from our line of sight; this places an empirical constraint on the GRB beaming factor of < f(b)(-1)> less than or similar to 10(4), corresponding to an average jet opening angle, theta(j) greater than or similar to 0.degrees 8. ( 2) This holds in particular for the broad-lined supernovae (SNe 1997dq, 1997ef, 1998ey, 2002ap, 2002bl, and 2003jd), which have been argued to host GRB jets. Our observations reveal no evidence for typical ( or even subenergetic) GRBs and rule out the scenario in which every broad-lined SN harbors a GRB at the 84% confidence level. Their large photospheric velocities and asymmetric ejecta ( inferred from spectropolarimetry and nebular spectroscopy) appear to be characteristic of the nonrelativistic SN explosion and do not necessarily imply the existence of associated GRB jets.