Deep Synoptic Array science I: discovery of the host galaxy of FRB 20220912A

We report the detection and interferometric localization of the repeating fast radio burst (FRB) source FRB 20220912A during commissioning observations with the Deep Synoptic Array (DSA-110). Two bursts were detected from FRB 20220912A, one each on 2022 October 18 and 2022 October 25. The best-fit position is (R.A. J2000, decl. J2000) = (23:09:04.9, +48:42:25.4), with a 90% confidence error ellipse of $\pm2$ arcsec and $\pm1$ arcsec in right ascension and declination respectively. The two bursts have disparate polarization properties and temporal profiles. We find a Faraday rotation measure that is consistent with the low value of $+0.6$ rad m$^{-2}$ reported by CHIME/FRB. The DSA-110 localization overlaps with the galaxy PSO J347.2702+48.7066 at a redshift $z=0.0771$, which we identify as the likely host. PSO J347.2702$+$48.7066 has a stellar mass of approximately $10^{10}M_{\odot}$, modest internal dust extinction, and a star-formation rate likely in excess of $0.1\,M_{\odot}$ yr$^{-1}$. The host-galaxy contribution to the dispersion measure is likely $\lesssim50$ pc cm$^{-3}$. The FRB 20220912A source is therefore likely viewed along a tenuous plasma column through the host galaxy.