How limiting is optical follow-up for fast radio burst applications? Forecasts for radio and optical surveys

Fast radio bursts (FRBs) are the first cosmological radio sources that vary on millisecond timescales, which makes them a unique probe of the Universe. Many proposed applications of FRBs require associated redshifts. These can only be obtained by localizing FRBs to their host galaxies and subsequently measuring their redshifts. Upcoming FRB surveys will provide arcsecond localization for many FRBs, not all of which can be followed up with dedicated optical observations. We aim to estimate the fraction of FRB hosts that will be catalogued with redshifts by existing and future optical surveys. We use the population synthesis code frbpoppy to simulate several FRB surveys, and the semi-analytical galaxy formation code GALFORM to simulate their host galaxies. We obtain redshift distributions for the simulated FRBs and the fraction with host galaxies in a survey. Depending on whether FRBs follow the cosmic star formation rate or stellar mass, 20 to 40 per cent of CHIME FRB hosts will be observed in an SDSS-like survey, all at \(z