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 $\sim 10%$ 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 $<f_b^{-1}> \lesssim 10^4$ corresponding to an average jet opening angle, $\theta_j \gtrsim 0.8$ degrees. (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 sub-energetic) 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 non-relativistic supernova explosion and do not necessarily imply the existence of associated GRB jets.