Zwicky Transient Facility constraints on the optical emission from the nearby repeating FRB 180916.J0158+65

The discovery rate of fast radio bursts (FRBs) is increasing dramatically thanks to new radio facilities. Meanwhile, wide-field instruments such as the 47 deg$^2$ Zwicky Transient Facility (ZTF) survey the optical sky to study transient and variable sources. We present serendipitous ZTF observations of the CHIME repeating source FRB 180916.J0158+65, that was localized to a spiral galaxy 149 Mpc away and is the first FRB suggesting periodic modulation in its activity. While 147 ZTF exposures corresponded to expected high-activity periods of this FRB, no single ZTF exposure was at the same time as a CHIME detection. No $>3\sigma$ optical source was found at the FRB location in 683 ZTF exposures, totalling 5.69 hours of integration time. We combined ZTF upper limits and expected repetitions from FRB 180916.J0158+65 in a statistical framework using a Weibull distribution, agnostic of periodic modulation priors. The analysis yielded a constraint on the ratio between the optical and radio fluences of $\eta \lesssim 200$, corresponding to an optical energy $E_{\rm opt} \lesssim 3 \times 10^{46}$ erg for a fiducial 10 Jy ms FRB (90% confidence). A deeper (but less statistically robust) constraint of $\eta \lesssim 3$ can be placed assuming a rate of $r(>5$ Jy ms)= hr$^{-1}$ and $1.2\pm 1.1$ FRB occurring during exposures taken in high-activity windows. The constraint can be improved with shorter per-image exposures and longer integration time, or observing FRBs at higher Galactic latitudes. This work demonstrated how current surveys can statistically constrain multi-wavelength counterparts to FRBs even without deliberately scheduled simultaneous radio observation.Comment: Accepted for publication in ApJL, 9 pages, 4 figures, 1 tabl