Associating Fast Radio Bursts with Their Host Galaxies

The first precise localization of a fast radio burst (FRB), leading to an association with a low metallicity dwarf galaxy at $z=0.193$, has began to shed 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 on-going 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 further use these results to demonstrate that even in the absence of a robust unique association, a constraint can be placed on the maximum luminosity of a host galaxy as a function of localization area and DM. We examine these results in the context of existing and future FRB facilities. We find that localizations of $\lesssim 0.5''$ are required for a chance coincidence probability of $\lesssim 1\%$ for dwarf galaxies at $z\gtrsim 0.1$; if some hosts have luminosities of $\sim L^*$, then localizations of up to $\approx 3''$ may suffice at $z\sim 0.1$ (but $\lesssim 1''$ at $z\approx 1$). Constraints on the redshift from the DM only marginally improve the association probability, unless the DM is low, $\lesssim 400$ pc cm$^{-3}$ ($z\lesssim 0.5$). This approach also relies on the determination of galaxy redshifts, which is challenging at $z\gtrsim 0.5$ if the hosts are generally dwarf galaxies. Finally, interesting limits on the maximum host luminosity (for example, sufficient to demonstrate that the hosts are generally dwarf galaxies) require localizations of $\lesssim 5''$ at $z\gtrsim 0.1$. Even a few such localizations will shed light on the nature of FRB progenitors, their possible diversity, and their use as cosmological tools.