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

Transitional millisecond pulsars (tMSPs) are old neutron stars spun up by accretion from a low-mass companion. These objects can switch between two emission regimes: rotation-powered radio pulsar and accreting X-ray pulsar. The origin of their optical and X-ray pulsations is still debated, although one model attributes them to synchrotron emission produced in a shock between the pulsar wind and the accretion flow. The small phase lag observed between optical and X-ray pulses in PSR J1023+0038 supports a common origin. We present a new measurement of the phase lag between optical and X-ray pulse profiles of PSR J1023+0038 and investigate the evolution of the time of passage at the ascending node ($T_{\rm{asc}}$) up to 2023. We performed a timing analysis of optical observations obtained with Aqueye+ between 2021 and 2023 and of X-ray data from NICER in 2023. We derive updated values of $T_{\rm{asc}}$ and measure the optical - X-ray phase lag from simultaneous observations. We find that $T_{\rm{asc}}$ increases by about 20 s per year. In January 2023, we measure a phase lag of $0.067 \pm 0.018$, corresponding to $112.3 \pm 30.7\,\mu$s. Since 2017, the evolution of $T_{\rm{asc}}$ follows a parabolic trend, indicating an increase in the orbital period and orbital separation of the system. This behaviour is consistent with non-conservative Roche-lobe overflow, with the donor losing mass at a rate much higher than the accretion rate. The phase lag measurement further supports a common origin of the optical and X-ray pulsations.