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

This paper presents new Aqueye+ and NICER observations of the transitional millisecond pulsar PSR J1023+0038, revealing a parabolic increase in its orbital period consistent with non-conservative mass loss and confirming a common synchrotron origin for its optical and X-ray pulsations through a measured phase lag.

Original authors: Silvia Conforti, Luca Zampieri, Michele Fiori, Alessia Spolon, Giampiero Naletto, Aleksandr Burtovoi

Published 2026-04-22

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CC BY 4.0

Original authors: Silvia Conforti, Luca Zampieri, Michele Fiori, Alessia Spolon, Giampiero Naletto, Aleksandr Burtovoi

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a cosmic dance floor where two partners are locked in a tight, chaotic waltz. One partner is a Neutron Star—a city-sized ball of matter so dense that a teaspoon of it would weigh a billion tons. It spins incredibly fast, like a figure skater pulling in their arms, completing a rotation in just 1.7 milliseconds. The other partner is a Low-Mass Star, a much smaller, fluffier companion.

This specific pair, known as PSR J1023+0038, is a "transitional" dancer. Sometimes, the neutron star spins freely, blasting out radio waves like a lighthouse (a radio pulsar). Other times, it grabs onto the gas leaking from its partner, spinning up even faster and glowing brightly in X-rays (an accreting pulsar).

Astronomers have been watching this dance for years to understand two big mysteries:

How is the dance floor changing? (Is the distance between them growing or shrinking?)
What is the "light show" made of? (Why do they flash in both visible light and X-rays at almost the exact same time?)

Here is what the new study, using powerful "stopwatches" called Aqueye+ (an ultra-fast optical camera) and NICER (an X-ray telescope), has discovered.

1. The Dance Floor is Stretching Out

In a normal dance, if one partner loses weight, the other might drift away. But in this cosmic system, things are getting weird.

The astronomers measured the exact moment the neutron star passes a specific point in its orbit (like passing a specific tree in a park). They found that this moment is happening later and later every year.

The Analogy: Imagine a runner on a track. If the track suddenly gets longer, the runner takes more time to finish a lap.
The Finding: The "lap time" (orbital period) is getting longer by about 20 seconds every year. This means the two stars are slowly drifting apart.

Why is this happening?
The researchers propose a dramatic scenario: The neutron star isn't just quietly eating gas from its partner. It's blasting a powerful "wind" (a stream of high-energy particles) at the companion star.

The Metaphor: Think of the neutron star as a giant, high-pressure fire hose. It's spraying the companion star so hard that it's blowing away the star's atmosphere.
The Result: The companion star is losing mass at a rate thousands of times faster than the neutron star can actually eat it. Most of the gas is being blasted out of the system entirely. Because so much mass is being ejected, the gravitational grip between the two weakens, and they slowly drift apart, stretching the orbit like a rubber band.

2. The Light Show: A Synchronized Flash

The second mystery was about the "light show." This system flashes in visible light (what our eyes see) and X-rays (high-energy light). Scientists debated whether these flashes came from two different places or the same place.

The Analogy: Imagine two fireworks exploding. If they explode from the same spot, they happen at the same time. If one is on the ground and one is in the sky, there's a delay.
The Finding: The astronomers measured the time difference between the visible flash and the X-ray flash. They found the visible light arrives just 0.0001 seconds after the X-rays.
The Conclusion: This tiny delay proves that both flashes are coming from the exact same location. It's like two different colored lights on the same firework shell.

What is causing the flash?
The leading theory is the "Shock Wave" model.

The Metaphor: Imagine the neutron star's "fire hose" (pulsar wind) crashing into the gas leaking from the companion star. This collision creates a massive, glowing shockwave, like a sonic boom but made of light.
The Result: This shockwave acts like a cosmic neon sign, glowing in both X-rays and visible light simultaneously. The fact that the flashes are so perfectly synchronized confirms that the "shockwave" is the engine driving the light show.

The Big Picture

This paper tells us that PSR J1023+0038 is in a violent, evolving phase.

The neutron star is acting like a cosmic blowtorch, stripping its partner star of its mass.
This mass loss is pushing the two stars further apart, making their orbit wider every year.
The beautiful, synchronized flashes of light we see are the result of the neutron star's wind crashing into the stolen gas, creating a shockwave that glows in multiple colors.

It's a dramatic story of a cosmic dance where one partner is slowly being evaporated by the other, leaving behind a trail of expanding space and a dazzling, synchronized light show.

1. Problem Statement and Context

Transitional millisecond pulsars (tMSPs) are neutron stars that switch between a rotation-powered radio pulsar state and an accreting X-ray binary state. PSR J1023+0038 is the prototype of this class. A central debate in the field concerns the emission mechanism of its optical and X-ray pulsations.

The Debate: While some models suggest thermal emission from the neutron star surface, the prevailing "shock-driven" model (Veledina et al. 2019; Papitto et al. 2019) posits that both optical and X-ray pulsations arise from synchrotron emission generated by a shock where the pulsar wind interacts with the accretion disk.
Key Evidence Needed: This shock model predicts a very short phase lag (near zero) between optical and X-ray pulses and a common emission origin. Furthermore, the long-term evolution of the binary system (specifically the orbital period) is poorly understood, with previous data suggesting irregular variations.
Objective: The authors aim to (1) measure the precise phase lag between optical and X-ray pulses to test the common emission mechanism, and (2) analyze the long-term evolution of the time of passage at the ascending node ( $T_{asc}$ ) to constrain the binary's mass transfer and orbital evolution.

2. Methodology

The study utilizes high-precision timing analysis of multi-wavelength data collected between 2021 and 2023.

Optical Observations:
- Instrument: Aqueye+ fast photon counter mounted on the 1.82m Copernicus telescope (Asiago, Italy).
- Data: Five observing runs spanning January 2021, January–February 2022, and January/December 2023.
- Processing: Photon arrival times were barycentered using TEMPO2 (JPL DE405 ephemerides). The time series were corrected for orbital motion using known orbital parameters ( $a \sin i$ , $P_{orb}$ ).
X-ray Observations:
- Instrument: NICER (Neutron star Interior Composition Explorer) on the ISS.
- Data: Simultaneous observations with Aqueye+ in January and December 2023.
- Processing: Standard HEASoft processing (v.6.34), selecting the 0.5–12 keV energy range. Data were barycentered using barycorr.
Timing Analysis Techniques:
- Epoch Folding: Used to determine the precise time of passage at the ascending node ( $T_{asc}$ ) and spin period ( $P_{spin}$ ) for each run.
- Profile Fitting: Pulse profiles were fitted with a model consisting of a constant plus two harmonically related sinusoids (Eq. 2) to extract phase information.
- Phase Lag Measurement: Simultaneous optical and X-ray light curves were folded and fitted to measure the time delay between the peaks of the second harmonic (which has higher signal-to-noise).
- Orbital Evolution Modeling: The evolution of $T_{asc}$ was fitted with a second-order polynomial to derive the orbital period derivative ( $\dot{P}_{orb}$ ). This was compared against theoretical models of conservative vs. non-conservative Roche lobe overflow (RLOF).

3. Key Contributions and Results

A. Orbital Evolution ( $T_{asc}$ )

Parabolic Trend: The authors found that since 2017, the variation in $T_{asc}$ follows a well-defined parabolic increasing trend, rather than the previously observed irregular oscillations.
Quantitative Shift: The shift in $T_{asc}$ increases by approximately 20 seconds per year.
Orbital Period Derivative: Fitting the data yielded a second derivative of the orbital period $C' = (3.52 \pm 0.23) \times 10^{-11}$ s/s. This indicates a steady increase in the orbital period and, consequently, the orbital separation.
Evolutionary Scenario: The authors rule out conservative mass transfer (where mass lost by the donor is fully accreted by the pulsar), as it would predict a decreasing orbital period. Instead, they propose a non-conservative Roche lobe overflow scenario. In this model, the donor star interacts with the pulsar wind, losing mass at a rate ( $\sim 10^{18}$ g/s) orders of magnitude higher than the inferred accretion rate. The excess mass is likely shocked by the pulsar wind and ejected from the system, driving the orbital expansion.

B. Phase Lag Measurement

Simultaneous Measurement: Using simultaneous Aqueye+ and NICER data from January 21, 2023, the authors measured the time delay between optical and X-ray pulses.
Result: The optical pulses are delayed relative to the X-ray pulses by $112.3 \pm 30.7$ µs, corresponding to a phase lag of $0.067 \pm 0.018$ .
Consistency: This result is consistent with previous measurements (Illiano et al. 2023) and confirms that the lag is extremely small (between 0 and 0.15 phase).
Note on Summary Discrepancy: While Section 3.3 and Figure 4 report a lag of $112.3 \pm 30.7$ µs ($0.067$ phase), the Summary (Section 5) and Discussion (Section 4.2) mention a value of $0.036 \pm 0.016$ ($60.7$ µs). The detailed results in Section 3.3 ($112$ µs) are the primary finding derived from the specific simultaneous fit described, though the authors note consistency with the broader range of previous findings.

C. Timing Solution

A new timing solution was derived for the January 2021 run, providing a precise spin period of $P_{spin} \approx 1.687987447$ ms.
For 2023, the spin period was extrapolated from long-term solutions, showing a negligible change ( $\sim 4.4 \times 10^{-13}$ s) compared to 2018.

4. Significance and Conclusions

Confirmation of Emission Mechanism: The detection of a minimal phase lag ( $<0.1$ ) and the similar morphology of optical and X-ray pulse profiles strongly support the shock-driven synchrotron emission model. This confirms that both bands originate from the same region: the interaction zone between the pulsar wind and the accretion disk (the "striped wind" scenario).
Binary Evolution Insight: The discovery of a steady, parabolic increase in $T_{asc}$ provides strong evidence that PSR J1023+0038 is evolving through non-conservative mass loss. The donor star is being stripped of mass by the pulsar wind at a rate far exceeding the accretion rate, leading to a widening orbit. This resolves previous ambiguities regarding the system's irregular behavior.
Future Outlook: The study establishes a robust baseline for monitoring the system's long-term rotational and orbital history, suggesting that continued timing observations are crucial to fully understand the physics of the pulsar-donor interaction.

In summary, this paper provides critical observational evidence linking the micro-physics of the pulsar wind-disk shock (via phase lag) to the macro-physics of binary evolution (via orbital period expansion), solidifying the theoretical framework for transitional millisecond pulsars.