On Associating Fast Radio Bursts with Afterglows

A radio source that faded over six days, with a redshift of z ≈ 0.5 host, has been identified by Keane et al. as the transient afterglow to a fast radio burst (FRB 150418). We report follow-up radio and optical observations of the afterglow candidate and find a source that is consistent with an active galactic nucleus. If the afterglow candidate is nonetheless a prototypical FRB afterglow, existing slow-transient surveys limit the fraction of FRBs that produce afterglows to 0.25 for afterglows with fractional variation, m=2| {S}₁-{S}₂| /({S}₁+{S}₂)≥slant 0.7, and 0.07 for m ≥ 1, at 95% confidence. In anticipation of a barrage of bursts expected from future FRB surveys, we provide a simple framework for statistical association of FRBs with afterglows. Our framework properly accounts for statistical uncertainties, and ensures consistency with limits set by slow-transient surveys.