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 $112.3 \pm 30.7,μ$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.

💡 Research Summary

This paper presents a comprehensive timing study of the transitional millisecond pulsar (tMSP) PSR J1023+0038, using optical data from the fast photon counter Aqueye+ (2021–2023) and X‑ray data from NICER (2023). The authors aim to (i) track the long‑term evolution of the time of passage at the ascending node (Tasc), and (ii) measure the phase lag between simultaneous optical and X‑ray pulsations.

The optical observations consist of five runs (January 2021, January–February 2022, January 2023, and January and December 2023) obtained with Aqueye+ on the 1.8 m Copernicus telescope. Photon arrival times were barycentered with TEMPO2 (JPL DE405) and corrected for binary motion using the orbital parameters from Archibald et al. (2013): projected semi‑major axis a sin i = 0.343356 s and orbital period P_orb = 0.1980963155 d. For each epoch, an epoch‑folding search was performed while varying only Tasc; the χ² maximum was fitted with a Gaussian to obtain the best offset and its uncertainty. The resulting Tasc offsets are 44.35 ± 0.17 s (2021), 81.05 ± 1.23 s (Jan 2023), and 97.33 ± 1.39 s (Dec 2023) relative to the reference value of Ambrosino et al. (2017). This corresponds to an increase of roughly 20 s per year.

Compiling all published Tasc measurements from 2017 onward, the authors fit the evolution with a quadratic function ΔTasc(T) = A + B T + ½ C T². The curvature term C = (1.5 ± 0.1) × 10⁻⁵ s MJD⁻² translates to a derivative of the orbital period dP_orb/dt ≈ 3.5 × 10⁻¹¹ s s⁻¹, indicating a secular increase in the orbital period and binary separation. The authors interpret this as evidence for non‑conservative Roche‑lobe overflow: the donor star loses mass at a rate far exceeding the accretion rate onto the neutron star, likely driven by interaction with the pulsar wind. The resulting loss of angular momentum expands the orbit, producing the observed parabolic Tasc trend.

Simultaneous optical and X‑ray observations were obtained in January 2023 (NICER and Aqueye+ on 21 January). NICER data (0.5–12 keV) were processed with the standard NICER pipeline, barycentered, and corrected for the same binary parameters. The X‑ray Tasc offset was measured as 80.25 ± 0.89 s, consistent with the optical value. Both data sets were folded using the same reference epoch (t₀ = 59965.0 MJD) and the spin period extrapolated from the long‑term timing solution of Burtovoi et al. (2020) (P ≈ 1.687987447 ms). Pulse profiles were modeled with a sum of two harmonically related sinusoids plus a constant. By comparing the phase of the second harmonic in the optical and X‑ray profiles, the authors find that the optical pulses lag the X‑ray pulses by 112.3 ± 30.7 µs, corresponding to a phase lag of 0.067 ± 0.018. This small lag, well within the range 0–0.15 reported in earlier works, supports the hypothesis that both emissions arise from the same physical region – a shock formed where the pulsar wind collides with the inner accretion flow – and are produced by synchrotron radiation from relativistic particles accelerated in that shock.

In the discussion, the authors contrast the earlier irregular Tasc behavior (post‑2000 transition) with the newly observed smooth, quadratic increase, arguing that the system has entered a phase where the orbital expansion dominates. They present a simple angular‑momentum conservation model for non‑conservative mass loss, showing that the observed dP_orb/dt is compatible with a donor mass‑loss rate an order of magnitude larger than the accretion rate inferred from X‑ray luminosity.

Overall, the paper delivers three key results: (1) a precise, multi‑year measurement of Tasc showing a secular increase of ~20 s yr⁻¹ and a well‑defined quadratic trend, (2) a high‑precision determination of the optical‑X‑ray phase lag (112 µs), reinforcing the common‑origin shock‑synchrotron model, and (3) an evolutionary interpretation linking the orbital expansion to non‑conservative Roche‑lobe overflow and strong pulsar‑wind driven mass loss. These findings advance our understanding of the dynamical evolution of transitional millisecond pulsars and the mechanisms powering their multi‑wavelength pulsations.