Investigating the origin of optical and X-ray pulsations of the transitional millisecond pulsar PSR J1023+0038

PSR J1023+0038 is the first millisecond pulsar that was ever observed as an optical and UV pulsar. So far, it only transitional The rotation- accretion-powered emission mechanisms hardly individually explain characteristics of pulsations. A synergistic model, combining these standard processes, proposed to origin X-ray/UV/optical We study phase lag between pulses in X-ray bands gain insight into physical cause it. performed a detailed timing analysis simultaneous or quasi-simultaneous observations band, acquired with XMM-Newton NICER satellites, fast photometers SiFAP2 (mounted at 3.6 m Telescopio Nazionale Galileo) Aqueye+ 1.8 Copernicus Telescope). estimated time pulsation respect X-rays by modeling folded pulse profiles two harmonic components. Optical $\sim$ 150 $\mu$s instruments (NICER Aqueye+) whose absolute uncertainty much smaller than measured lag. also show pulsations lies limited range values, $\delta \phi \in$ (0 $-$ 0.15), which maintained over timescales about five years. This indicates both originate from same region, supports hypothesis common mechanism. Our results are interpreted shock-driven mini nebula scenario. scenario suggests produced synchrotron shock formed within few light cylinder radii away ($\sim$ 100 km) pulsar, where its striped wind encounters accretion disk inflow.