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

TL;DR

This study analyzes PSR J1023+0038 with Aqueye+ optical timing (2021–2023) and NICER X-ray data (2023) to trace the evolution of the ascending node time $T_{ m asc}$ and to measure the optical–X-ray phase lag. The authors find a clear parabolic trend in $T_{ m asc}$ since 2017, implying an increasing orbital period and separation, consistent with non-conservative Roche-lobe overflow and donor wind loss. They measure a small but significant optical–X-ray phase lag in January 2023 ($0.067 \\pm \\ 0.018$ in phase, ≈$112.3 \\pm \\ 30.7 \\mu$s) from simultaneous observations, and a related lag of $0.036 \\pm \\ 0.016$ (≈$60.7 \\pm \\ 27.7 \\mu$s) from another January 2023 analysis, supporting a common origin for the pulses. Collectively, the results favor a shock-driven synchrotron emission scenario in which the pulsar wind interacts with the accretion environment, with mass loss from the donor dominating the long-term orbital evolution.

Abstract

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 $112.3 \pm 30.7\,μ$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.

Figures (4)

• Figure 1: Variation of the time of passage at the ascending node, $T_{\rm{asc}}$ , concerning the reference value measured in radio reported in jaodand2016timing. The dotted black line represents the fit of the data with the equation (\ref{['fit_tasc_evolution']}).
• Figure 2: Optical pulse profile of the PSR J1023+0038 obtained with Aqueye+ from January 12th to January 16th, 2021. The (red) solid line is the fit with eq. (\ref{['two_harmonically_related_sinusoid']}).
• Figure 3: Optical pulse profile of the PSR J1023+0038 obtained with Aqueye+ from December 12th and 15th, 2023. The (red) solid line is the fit with eq. (\ref{['two_harmonically_related_sinusoid']}).
• Figure 4: Pulse profiles of PSR J1023+0038 in the optical (Aqueye+) and the X-ray (NICER) energy bands. The two panels show the pulse profile of January 21st, 2023, in X-ray (top panel, green dots) and optical (bottom panel, blue dots). Both profiles are fitted with the same model (see equation (\ref{['two_harmonically_related_sinusoid']})) (yellow and red solid lines), folded with the same spin period (see Table \ref{['tab:tab_tasc_values']}), and with the same $t_0$ =59965.0 MJD. The navy dashed lines in both panels represent the phase of the second harmonic ($x_2$), used to measure the phase lag, while the light blue shaded bands indicate the corresponding uncertainties.