The Host Galaxies of Fast Radio Bursts Track a Combination of Stellar Mass and Star Formation, Similar to Type Ia Supernovae

We develop a new statistical framework for studying the host galaxies of astrophysical sources that accounts for both redshift evolution and the multi-variate nature of host-galaxy properties. These aspects are critical when dealing with sources that span a wide range of redshifts, and/or with unknown redshift-dependent selection effects. We apply our method to a sample of Fast Radio Burst (FRB) host-galaxies as a means of probing the uncertain progenitor(s) of these events. Using our method we are able to rule out that FRBs track star-formation rate (SFR), as would be expected if FRBs are associated exclusively with young neutron stars born via core-collapse supernovae (SNe). Furthermore, we rule out a recently proposed metallicity-dependent model whereby FRBs track SFR only above an oxygen abundance of 12+log(O/H) ~ 8. Motivated by the fact that at least one FRB has been localized to a globular cluster (GC), we also investigate the hypothesis that FRB sources track GC mass and explicitly rule out this scenario. Alternatively, we find that a `mixed' model whereby FRBs track a linear combination of both SFR and stellar-mass best explains the data. The preferred parameters of such a mixed model are similar to those inferred for Type Ia SNe, and implies a possible connection between the progenitors of these different transients.