Spectra of broad-lined Type Ic supernovae (SNe 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 SNe, including 17 SNe Ic-BL, discovered by galaxy-untargeted searches, and 15 optically luminous and dust-obscured z 1.2 LGRBs. We show that, in comparison with Sloan Digital Sky Survey galaxies having similar stellar masses, the hosts of low-redshift SNe Ic-BL and z 1.2 LGRBs have high stellar mass and star formation rate densities. Core-collapse SNe having typical ejecta velocities, in contrast, show no preference for such galaxies. Moreover, we find that the hosts of SNe Ic-BL, unlike those of SNe Ib/Ic and SNe 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 progenitor systems in densely star-forming regions, or, less probably, a higher fraction of stars created with the initial masses required for an SN Ic-BL or LGRB. Finally, we show that the preference of SNe 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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