Evolution of the transitional millisecond pulsar PSR J1023+0038 from Aqueye+ and NICER observations

Context. Transitional millisecond pulsars are old, rapidly rotating neutron stars spun up by accretion from a low-mass companion star. These objects can switch between two emission regimes: rotation-powered radio pulsars and accreting X-ray pulsars. The mechanism responsible for these pulsations remains debated, with one prominent model suggesting that optical and X-ray pulsations arise from synchrotron emission produced by a shock resulting from the interaction between the pulsar wind and the accretion disk. This scenario is supported by the minimal phase lag between optical and X-ray pulses in PSR J1023+0038, and by their detection in the high-mode (flaring state) of the system. Aims. We present a new measurement of the phase lag between optical and X-ray pulse profiles of PSR J1023+0038 and investigate the recent evolution of the binary system (until 2023), monitoring the variation in the time of passage at the ascending node ( T asc ). Methods. We performed a timing analysis of the optical observations of PSR J1023+0038 taken with Aqueye+ from 2021 through 2023 and NICER X-ray observations taken in 2023. We used the optical and X-ray data to derive new measurements for the variation in T asc and employed simultaneous Aqueye+ and NICER observations to measure the phase lag between optical and X-ray pulses. Results. We find the shift in T asc increases by ∼20 s each year, and in January 2023 we measured a phase lag between optical and X-ray data of 0.067 ± 0.018, or 112.3 ± 30.7 μs. Conclusions. After 2017, the variation in the time of passage at the ascending node follows a well-defined parabolic increasing trend, suggesting a corresponding increment in the orbital period and orbital separation of the system. This evolution is consistent with a scenario in which the binary system is evolving through nonconservative Roche lobe overflow and the donor is interacting with the pulsar wind, losing mass at a rate much higher than the inferred accretion rate. The measurement of the phase lag between optical and X-ray data confirms the common origin of such pulsations.