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 deg² Zwicky Transient Facility (ZTF) survey the optical sky to study transient and variable sources. We present serendipitous ZTF observations of the Canadian Hydrogen Intensity Mapping Experiment (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 >3σ optical source was found at the FRB location in 683 ZTF exposures, totaling 5.69 hr 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 η ≲ 200, corresponding to an optical energy E_opt ≲ 3 × 10⁴⁶ erg for a fiducial 10 Jy ms FRB (90% confidence). A deeper (but less statistically robust) constraint of η ≲ 3 can be placed assuming a rate of $r(\gt 5\,\mathrm{Jy}\,\mathrm{ms})=1\,{\mathrm{hr}}^{-1}$ and 1.2 ± 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 multiwavelength counterparts to FRBs even without deliberately scheduled simultaneous radio observation.