Linking Transients to their Host Galaxies: II. A Comparison of Host Galaxy Properties and Rate Dependencies across Supernova Types

We use the latest dataset of supernova (SN) host galaxies to investigate how the host properties -- stellar mass, star formation rate, metallicity, absolute magnitude, and colour -- differ across SN types, with redshift-driven selection effects controlled. SN Ib and Ic host galaxies, on average, are more massive, metal-rich, and redder than SN II hosts. For subtypes, SN Ibn and Ic-BL have bluer hosts than their normal SN Ib and Ic siblings; SN IIb has consistent host properties with SN Ib, while hosts of SN IIn are more metal-rich than those of SN II. Hydrogen-deficient superluminous supernovae feature bluer and lower luminosity hosts than most subtypes of core-collapse supernova (CC SN). Assuming simple proportionality of CC SN rates and host star formation rates (SFRs) does not recover the observed mean host properties; either a population of long-lived progenitors or a metallicity-dependent SN production efficiency better reproduces the observed host properties. Assuming the latter case, the rates of SN II are insensitive to host metallicity, but the rates of SN Ib and Ic are substantially enhanced in metal-rich hosts by a factor of ~10 per dex increase in metallicity. Hosts of SN Ia are diverse in their observed properties; subtypes including SN Ia-91T, Ia-02cx, and Ia-CSM prefer star-forming hosts, while subtypes like SN Ia-91bg and Ca-rich prefer quiescent hosts. The rates of SN Ia-91T, Ia-02cx, and Ia-CSM are closely dependent on, or even proportional to, their host SFRs, indicating relatively short-lived progenitors. Conversely, the rates of SN Ia-91bg and Ca-rich transients are proportional to the total stellar mass, favoring long-lived progenitors.