2017ApJ...849..162E

The first precise localization of a fast radio burst (FRB) sheds light on the nature of these mysterious bursts and the physical mechanisms that power them. Increasing the sample of FRBs with robust host galaxy associations is the key impetus behind ongoing and upcoming searches and facilities. Here, we quantify the robustness of FRB host galaxy associations as a function of localization area and galaxy apparent magnitude. We also explore the use of FRB dispersion measures to constrain the source redshift, thereby reducing the number of candidate hosts. We use these results to demonstrate that even in the absence of a unique association, a constraint can be placed on the maximum luminosity of a host galaxy as a function of localization and dispersion measure (DM). We find that localizations of 0.5'' are required for a chance coincidence probability of 1 % for dwarf galaxies at z 0.1; if some hosts have luminosities of ∼L^*^, then localizations of up to ~5^′′ may suffice at z∼0.1. Constraints on the redshift from the DM only marginally improve the association probability unless the DM is low, 400 pc cm^–3. This approach also relies on the determination of galaxy redshifts, which is challenging at z 0.5 if the hosts are dwarf galaxies. Finally, interesting limits on the maximum host luminosity require localizations of 5^′′ at z 0.1. Even a few such localizations will explain the nature of FRB progenitors, their possible diversity, and their use as cosmological tools.