Searching for optical pulsations from spider millisecond pulsars with the fast photometer SiFAP2

Optical pulsations from millisecond pulsars (MSPs) have recently been detected in a transitional MSP and an accreting MSP. Evidence for optical pulsations has also been found for a rotation-powered redback MSP. Observations suggest that optical pulsed emission is produced by different mechanisms depending on whether an accretion disk is present in the system. We explored a sample of rotation-powered MSPs in close binaries (P orb<1, day; redbacks and black widows), searching for optical periodic signals with the SiFAP2 photometer mounted on the Telescopio,Nazionale, Galileo (TNG). We performed pulsation searches using the epoch-folding method with the most up-to-date (radio or gamma-ray) orbital solution for each system. These solutions were based either on previously published works or recent observations from Nançay, the Giant Metrewave Radio Telescope, the Parkes Observatory, and Fermi-LAT. We update or confirm radio and gamma-ray ephemerides for five of the presented systems. No optical pulsations were detected with a significance exceeding a 3σ confidence level in any of our searches, despite achieving sensitivities close to the instrument's limit. This places correspondingly stringent upper limits on the systems' optical pulsed magnitude and conversion efficiency. Our upper limits are consistent with the pulsed optical luminosity of optical pulsations from the redback PSR J2339-0533. Compared to accreting and transitional MSPs, redback and black widow systems show much lower efficiency in converting their spin-down power into pulsed optical emission. This supports the recent suggestion that the accretion disk around the neutron star plays a role in accelerating the particles responsible for producing bright optical pulsed emission.