Abstract
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. Therefore, the jet launched by their 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 chocked inside the star as the
central-engine activity time, \$t\_e\$, is not long enough. Such events do
not lead to typical GRBs, and instead possibly result in low-luminosity GRBs.
Modelling the long-soft GRB duration distribution, we find a typical GRB jet
breakout time of \$t\_b60 s\$ (in the star's frame), which
suggests the presence of a low-density, extended envelope surrounding the
progenitor star. The envelope properties are similar to those previously
inferred for low-luminosity GRBs, pointing towards a common progenitor for both
low-luminosity GRBs and long-soft GRBs. Moreover, the distribution of central
engine activity times is consistent with a steep power law \$t\_\rm
e^-\alpha\$, with \$\alpha4\$ for \$t\_e>t\_min\$. The
extrapolation of \$t\_e\$ to values only \$4-5\$ times below \$t\_b\$
produces enough events to account for all Type Ib/c SNe, corresponding to an
interesting lower limit, \$t\_min\gtrsim13\;\$s. This suggests 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.
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