A semi-coherent search for optical pulsations from Scorpius X-1

The emission of continuous gravitational waves (CWs) possibly explains why pulsars spinning with a period shorter than a millisecond have not been observed so far. Neutron stars accreting mass at the highest rates are the most promising targets for a search for CWs, because a strong emission of gravitational waves is required to balance the torque exerted by mass accretion onto the neutron star. Detecting coherent pulsations in the electromagnetic emission maximizes the search sensitivity, but has so far not been successful for most of the brightest accreting neutron stars. Here, we present the first search for pulsations in the optical band from the brightest accreting neutron star known, Sco X-1. To this end, we tailored semi-coherent search strategies to data obtained over four years, for a total of $\sim$$56$ ks, by the SiFAP2 fast photometer mounted at the Telescopio Nazionale Galileo (TNG). These searches are especially suited to analysing long observations of systems for which only limited knowledge on the orbital parameters is available, and involve joining coherent analyses on shorter segments without connecting the spin phase between them. The large count rates afforded by an optical telescope and the efficiency of the search strategy employed allowed us to set an upper limit of $9 \times 10^{-5}$ to the pulsed amplitude, which is lower by a factor of four with respect to previous searches in the X-ray band. We also show that the application of semi-coherent searches to SiFAP2 observations of the first detected optical millisecond pulsar, PSR J1023+0038, could have preceded its detection in the radio band. These results highlight the role played by high-time-resolution optical observations in performing deep searches of quickly rotating pulsars.