  Unlike the ordinary supernovae (SNe) some of which are hydrogen and helium
deficient (called Type Ic SNe), broad-lined Type Ic SNe (SNe Ic-bl) are very
energetic events, and all SNe coincident with bona fide long duration gamma-ray
bursts (LGRBs) are of Type Ic-bl. Understanding the progenitors and the
mechanism driving SN Ic-bl explosions vs those of their SNe Ic cousins is key
to understanding the SN-GRB relationship and jet production in massive stars.
Here we present the largest set of host-galaxy spectra of 28 SNe Ic and 14 SN
Ic-bl, all discovered before 2013 by the same untargeted survey, namely the
Palomar Transient Factory (PTF). We carefully measure their gas-phase
metallicities, stellar masses (M*s) and star-formation rates (SFRs) by taking
into account recent progress in the metallicity field and propagating
uncertainties correctly. We further re-analyze the hosts of 10 literature
SN-GRBs using the same methods and compare them to our PTF SN hosts with the
goal of constraining their progenitors from their local environments by
conducting a thorough statistical comparison, including upper limits. We find
that the metallicities, SFRs and M*s of our PTF SN Ic-bl hosts are
statistically comparable to those of SN-GRBs, but significantly lower than
those of the PTF SNe Ic. The mass-metallicity relations as defined by the SNe
Ic-bl and SN-GRBs are not significantly different from the same relations as
defined by the SDSS galaxies, in contrast to claims by earlier works. Our
findings point towards low metallicity as a crucial ingredient for SN Ic-bl and
SN-GRB production since we are able to break the degeneracy between high SFR
and low metallicity. We suggest that the PTF SNe Ic-bl may have produced jets
that were choked inside the star or were able break out of the star as unseen
low-luminosity or off-axis GRBs.
