Spectra of broad-lined Type Ic supernovae (SN Ic-BL), the only kind of SN observed at the locations of long-duration gamma-ray bursts (LGRBs), exhibit wide features indicative of high ejecta velocities (~0.1c). We study the host galaxies of a sample of 245 low-redshift (z<0.2) core-collapse SN, including 17 SN Ic-BL, discovered by galaxy-untargeted searches, and 15 optically luminous and dust-obscured z<1.2 LGRBs. We show that, in comparison with SDSS galaxies having similar stellar masses, the hosts of low-redshift SN Ic-BL and z<1.2 LGRBs have high stellar-mass and star-formation-rate densities. Core-collapse SN having typical ejecta velocities, in contrast, show no preference for such galaxies. Moreover, we find that the hosts of SN Ic-BL, unlike those of SN Ib/Ic and SN II, exhibit high gas velocity dispersions for their stellar masses. The patterns likely reflect variations among star-forming environments, and suggest that LGRBs can be used as probes of conditions in high-redshift galaxies. They may be caused by efficient formation of massive binary progenitors systems in densely star-forming regions, or, less probably, a higher fraction of stars created with the initial masses required for a SN Ic-BL or LGRB. Finally, we show that the preference of SN Ic-BL and LGRBs for galaxies with high stellar-mass and star-formation-rate densities cannot be attributed to a preference for low metal abundances but must reflect the influence of a separate environmental factor.
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