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 $\pm$90 s around the burst. Correcting for interstellar extinction ($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 corrected upper limits to the fluence (specific fluence) are $3.1 \times 10^{-10}$ erg cm$^{-2}$ (0.35 Jy s), $4.2 \times 10^{-11}$ erg cm$^{-2}$ (4.8 Jy $\cdot$ 10 ms), and $1.6 \times 10^{-11}$ 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.