A Common Central Engine for Long Gamma Ray Bursts and Type Ib/c Supernovae?
Long-duration, spectrally-soft Gamma-Ray Bursts (GRBs) are associated with Type Ic Core Collapse (CC) Supernovae (SNe), and thus arise from the death of massive stars. In the collapsar model, the jet launched by the central engine must bore its way out of the progenitor star before it can produce a GRB. Most of these jets do not break out, and are instead "choked" inside the star, as the central-engine activity time, $t_{\rm e}$, is not long enough. Modelling the long-soft GRB duration distribution assuming a power-law distribution for their central-engine activity times, $\propto t_{\rm e}^{-α}$ for $t_{\rm e}>t_{\rm b}$, we find a steep distribution ($α\sim4$) and a typical GRB jet breakout time of $t_{\rm b}\sim 60\text{ s}$ in the star's frame. The latter suggests the presence of a low-density, extended envelope surrounding the progenitor star, similar to that previously inferred for low-luminosity GRBs. Extrapolating the range of validity of this power law below what is directly observable, to $t_{\rm e}<t_{\rm b}$, by only a factor of $\sim$4-5 produces enough events to account for all Type Ib/c SNe. Such extrapolation is necessary to avoid fine-tuning the distribution of central engine activity times with the breakout time, which are presumably unrelated. We speculate that central engines launching relativistic jets may operate in all Type Ib/c SNe. In this case, the existence of a common central engine would imply that (i) the jet may significantly contribute to the energy of the SN; (ii) various observational signatures, like the asphericity of the explosion, could be directly related to jet's interaction with the star.