Deep upper limit on the optical emission during a hard X-ray burst from the magnetar SGR J1935+2154

In September 2021 the magnetar SGR J1935+2154 entered a stage of burst/flaring activity in the hard X-ray band. On September 10, 2021 we observed SGR J1935+2154 with the fiber-fed fast optical photon counter IFI+Iqueye, mounted at the 1.22 m Galileo telescope in Asiago. During one of the IFI+Iqueye observing windows a hard X-ray burst was detected with the Fermi Gamma-ray Burst Monitor. We performed a search for any significant increase in the count rate on the 1-s, 10-ms and 1-ms binned IFI+Iqueye light curves around the time of the Fermi burst. No significant peak was detected with a significance above 3 sigma in an interval of +- 90 s around the burst. Correcting for interstellar extinction ($A_V simeq 5.8$ mag), the IFI+Iqueye upper limits to any possible optical burst from SGR J1935+2154 are V=10.1 mag, V=7.2 mag and V=5.8 mag for the 1-s, 10-ms and 1-ms binned light curves, respectively. The corresponding extinction orrected upper limits to the fluence (specific fluence) are 3.1x10^(-10) erg cm^(-2) (0.35 Jy s), 4.2x10^(-11) erg cm^(-2) (4.8 Jy 10 ms), and 1.6x10^(-11) erg cm^(-2) (17.9 Jy ms), orders of magnitude deeper than any previous simultaneous optical limit on a magnetar burst. The IFI+Iqueye measurement can also place a more stringent constraint to the spectral index of the optical to hard X-ray fluence of SGR J1935+2154, implying a spectrum steeper than nu^0.64. Fast optical timing observations of bursts associated with radio emission have then the potential to yield a detection.