Constrains on optical emission of FAST-detected FRB 20181130B with GWAC synchronized observations

Multi-wavelength simultaneous observations are essential to the constraints on the origin of fast radio bursts (FRBs). However, it is a significant observational challenge due to the nature of FRBs as transients with a radio millisecond duration, which occur randomly in the sky regardless of time and position. Here, we report the search for short-time fast optical bursts in the GWAC archived data associated with FRB 20181130B, which were detected by the Five Hundred Meter Spherical Radio Telescope (FAST) and recently reported. No new credible sources were detected in all single GWAC images with an exposure time of 10 s, including image with coverage of the expected arrival time in optical wavelength by taking the high dispersion measurements into account. Our results provide a limiting magnitude of 15.43$\pm0.04$ mag in R band, corresponding to a flux density of 1.66 Jy or 8.35 mag in AB system by assuming that the duration of the optical band is similar to that of the radio band of about 10 ms. This limiting magnitude makes the spectral index of $\alpha<0.367$ from optical to radio wavelength. The possible existence of longer duration optical emission was also investigated with an upper limits of 0.33 Jy (10.10 mag), 1.74 mJy (15.80 mag) and 0.16 mJy (18.39 mag) for the duration of 50 ms, 10 s and 6060 s, respectively. This undetected scenario could be partially attributed to the shallow detection capability, as well as the high inferred distance of FRB 20181130B and the low fluence in radio wavelength. The future detectability of optical flashes associated with nearby and bright FRBs are also discussed in this paper.