Preamble

Vol. 66 No. 4
July, 2025

Acta Astronomica Sinica
doi: 10.15940/j.cnki.0001-5245.2025.04.012

Progress in Observing Isolated Pulsars and Accreting Millisecond Pulsars with Insight-HXMT

GE Ming-yu¹† LI Zhao-sheng²‡
(1 Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049)
(2 School of Physics and Optoelectronics, Xiangtan University, Xiangtan 411105)

Abstract

The Insight-HXMT (Insight-Hard X-ray Modulation Telescope) is China's first space X-ray astronomical satellite. Its primary scientific objectives include studying compact objects such as black holes and neutron stars, as well as monitoring violent transient phenomena like gamma-ray bursts. Isolated X-ray pulsars and accreting millisecond X-ray pulsars constitute important observational targets for Insight-HXMT. To date, Insight-HXMT has observed seven isolated pulsars and five accreting millisecond pulsars. This paper first introduces the high-precision pulse profiles and broader energy-phase spectra obtained for the Crab pulsar through Insight-HXMT observations, revealing the evolution of X-ray spectral properties and spectral parameters with phase. We further investigate the delayed spin-up characteristics during glitches and whether these glitches cause changes in X-ray emission, while also conducting research on orbit determination algorithms using X-ray pulsars. Second, we present observations of five accreting millisecond pulsars with Insight-HXMT, during whose outbursts hard X-ray pulsed radiation was detected. Notably, MAXI J1816–195 showed spin-up behavior, which constrained the neutron star's magnetic field.

Keywords pulsars: isolated pulsar, pulsars: accreting millisecond pulsar, telescopes: Insight-HXMT
CLC number: P142 Document code: A

1 Introduction

In October 1967, Antony Hewish and Jocelyn Bell discovered regular pulsed signals while examining radio telescope data—signals with an extremely stable period of 1.337 seconds. Subsequent data analysis revealed several similar pulsed sources [1]. In 1968, Gold and Pacini identified these objects as rotating, strongly magnetized neutron stars [2–3]. Known as pulsars, these discoveries rank among the four major astronomical breakthroughs of the 1960s, alongside quasars, cosmic microwave background radiation, and interstellar organic molecules. Generally, neutron stars have masses of approximately 1.4 solar masses, radii of about 12 km, and core densities reaching several times nuclear density. Many extreme astrophysical phenomena are associated with neutron stars, including supernovae and gamma-ray bursts. From a stellar evolution perspective, when intermediate-mass stars reach their final evolutionary stages, core collapse triggers supernova explosions. The ejected material forms supernova remnants, leaving behind a rapidly rotating neutron star at the center [4]. With observational instruments spanning infrared to gamma-ray wavelengths, pulsars exhibit diverse pulsed radiation phenomena. Currently, several hundred pulsars have been detected in X-rays or gamma-rays, while only a handful show optical emission. High-energy pulsars are defined as sources exhibiting X-ray or gamma-ray pulsed radiation, characterized not only by high-energy photons but also by radiation mechanisms fundamentally different from radio pulsars.

To date, the known pulsar catalog includes over 4,000 sources (including discoveries from FAST [5–7]), displaying diverse characteristics and classifications. Based on their energy sources, pulsars can be divided into four categories: (1) rotation-powered pulsars, whose radiation energy derives from the star's rotational energy loss, exemplified by the Crab pulsar and Vela pulsar; (2) accretion-powered pulsars, which convert gravitational potential energy into electromagnetic radiation through mass accretion from companion stars, typical examples include high-mass X-ray binaries, low-mass X-ray binaries, and transients; (3) magnetars, believed to be powered by magnetic field energy [8]; and (4) X-ray dim isolated neutron stars, which can only radiate residual thermal energy after all possible energy sources have been exhausted [9].

Rapidly rotating pulsars possess a co-rotating magnetosphere filled with charged particles. These particles are accelerated by strong electric fields and produce high-energy radiation through curvature radiation, synchrotron radiation, inverse Compton scattering, and other physical processes, thereby emitting X-ray and gamma-ray photons. Pulsar radiation models aim to investigate particle production sites, acceleration processes, acceleration regions, and radiation mechanisms [10]. Currently, mainstream radiation models include the polar cap model [11], outer gap model [12–14], slot gap model [15], and annular gap model [16]. Although these models differ significantly in the locations of acceleration and radiation zones, all place them within the light cylinder. In recent years, new magnetospheric models have been proposed, such as the FIDO (Force-free Inside and Dissipative Outside) model [17], various current sheet models [18], and kinetic/particle-in-cell simulations [19–20]. These new models and research results suggest that high-energy radiation originates from regions outside the light cylinder. While both classical dipole radiation models and the latest magnetospheric models can explain some current observational results—such as pulse profile shapes and phase-resolved spectra—no single model can account for all cases [10]. Therefore, studying pulsar radiation zone structures requires new models that can be tested and constrained through observations [10].

For rotation-powered pulsars, the spin period gradually increases, though occasional instabilities occur where the period changes abruptly, known as glitches [21–22]. Based on current observational samples, most glitches manifest as sudden spin-ups, some as gradual spin-ups, and a few even as spin-downs. Detailed observations reveal that glitches are often followed by one or several exponential recovery components, providing an excellent opportunity to understand neutron star interior structure. The current theoretical explanation posits that the neutron star crust and magnetosphere are coupled. As the magnetosphere radiates away rotational energy, the crust slows down. The superfluid beneath the crust couples weakly to it, so the neutron star interior maintains rapid rotation. As the crust continuously loses angular momentum, the rotational velocity difference between the interior and exterior increases. When this difference reaches a critical value, the coupling between the interior fluid and crust suddenly strengthens, rapidly transferring internal angular momentum to the crust [23].

Millisecond pulsars are an elderly class of pulsars with extremely rapid rotation; the fastest known pulsar has a period of 1.4 ms, and their spin-down rates are significantly lower than those of normal pulsars [24]. These millisecond pulsars are distributed not only in the Galactic disk but also in globular clusters, such as PSR B1821−24, the first isolated millisecond pulsar discovered in a globular cluster (M28) [25]. Millisecond pulsars exhibit X-ray and gamma-ray pulsed radiation. Additionally, some are accreting millisecond pulsars. The current consensus is that millisecond pulsars originate from the accretion-induced recycling of normal pulsars. The discovery of SAX J1808.4−3658, the first accreting millisecond pulsar, confirmed this hypothesis [26]; while direct observations of transitions between accretion and pulsar phases in PSR J1023+0038 and IGR J18245−2452 provided strong support for this view [27–28]. Furthermore, the Fermi telescope has discovered 127 gamma-ray millisecond pulsars [10]. Notably, pulsars exhibit stable spin evolution, particularly millisecond pulsars—a characteristic that makes them nature's most precise clocks, applicable for pulsar navigation, pulsar timing arrays, and low-frequency gravitational wave detection [29–30].

Pulsar radiation mechanisms and interior structure represent two fundamental questions in pulsar research. Despite rich observational phenomena across various wavelengths and numerous theoretical explanations, the origin of pulsar radiation and its specific conversion processes remain poorly understood, and the internal composition of neutron stars is even more enigmatic. Insight-HXMT observations of long-term pulsar evolution and short-timescale variations (such as glitches and state transitions) can probe the origins of pulsar radiation, while the evolutionary behavior during glitches can reveal secrets of neutron star interior structure. Accreting millisecond X-ray pulsars are also important observational targets for Insight-HXMT.

2 Insight-HXMT Observations

The "Insight" satellite, formally known as the Hard X-ray Modulation Telescope, is China's first X-ray astronomical satellite, launched on June 15, 2017, from the Jiuquan Satellite Launch Center [31]. Operating in a 550 km near-Earth circular orbit, it primarily observes black holes, neutron stars, and gamma-ray bursts. The satellite comprises three telescopes: the High Energy X-ray Telescope (HE, 20–250 keV, 5100 cm²) [32], the Medium Energy X-ray Telescope (ME, 8–35 keV, 952 cm²) [33], and the Low Energy X-ray Telescope (LE, 1–12 keV, 384 cm²) [34]. This configuration achieves the first-ever coverage of the 1–250 keV energy band, facilitating multi-band studies of X-ray source radiation mechanisms [32–35]. X-ray pulsars are important targets for Insight-HXMT, which has observed seven isolated pulsars and five accreting millisecond X-ray pulsars to date. This paper briefly introduces the observational results for both isolated pulsars and accreting millisecond pulsars.

3.1 Spin Evolution and Glitches

The Crab pulsar was born from the bright supernova explosion of 1054 AD (SN 1054) and was discovered in 1968 [36]. Pulsed radiation from the Crab pulsar has been observed across wavelengths from the lowest detectable radio band at 10 MHz to TeV gamma-rays, with pulse profiles showing a nearly double-peaked structure [37]. As a powerful central engine continuously injecting energy into the surrounding nebula and driving its rapid expansion, the Crab pulsar is not only a famous celestial object observed by various astronomical facilities but also a calibration source for Insight-HXMT's instrumental performance [38]. A dedicated 12.5 m radio telescope at Jodrell Bank monitors this pulsar [39]. Previous observations indicated that large glitches in the Crab pulsar exhibit a delayed spin-up component with a characteristic timescale of approximately one day, a feature crucial for studying pulsar structure [40–41].

In November 2017, the Crab pulsar experienced its largest observed glitch, which was monitored in detail by Insight-HXMT, as shown in [FIGURE:1]. Research revealed that this glitch also contained a delayed spin-up component with a characteristic timescale of two days (typically, glitch timescales are on the order of seconds, followed by exponential recovery) [42]. In July 2019, another glitch of similar magnitude occurred in the Crab pulsar, with timing results indicating a similar delayed spin-up component (as shown in [FIGURE:2]) [43]. The glitches of 2004 and 2011 also had large amplitudes. Timing analysis using historical observational data revealed delayed spin-up components in both events, as shown in [FIGURE:1]. Considering four known glitch events, six cases exhibit similar components. The presence of this component correlates with glitch amplitude: larger glitches show longer delayed spin-up timescales, as illustrated in [FIGURE:3]. Finally, statistical results shown in [FIGURE:4] indicate that samples with delayed spin-up components also represent cases with relatively large glitch amplitudes [42].

Detailed Insight-HXMT observations of the Crab pulsar's glitches enable quantitative studies of how glitches affect X-ray pulsed radiation properties. As shown in [FIGURE:5], the X-ray flux of the pulsar showed no significant change across the glitch, inconsistent with variations in spin-down energy loss (assuming constant conversion efficiency from spin-down energy to X-ray pulsed radiation). At current observational precision, this discrepancy suggests that the spin evolution during this glitch was dominated by internal processes without affecting the external pulsed radiation region. As shown in [FIGURE:6] and [FIGURE:7], the absence of significant differences in X-ray pulse shapes before and after the glitch indicates that the X-ray pulse profiles remained essentially unchanged during these two major glitches [43].

3.2 Braking Index Evolution

PSR B0540–69 in the Large Magellanic Cloud has a characteristic age of approximately 1670 years and a spin period of 50 ms, corresponding to a spin-down luminosity of 10³⁸ erg/s. These characteristics closely resemble those of the Crab pulsar, earning it the designation of the Crab pulsar's cousin or twin. In December 2011, the pulsar's spin-down rate suddenly increased by about 36% and remained stable, implying a sudden increase in spin-down energy loss rate of about 36% [44]. This change is termed a state transition. As shown in [FIGURE:8], the braking index became nearly zero after the state change. Further observations indicate a rapid recovery trend in the braking index, possibly suggesting a gradual increase in the pulsar's dipole magnetic field [45].

3.3 X-ray Pulse Profiles and Phase-resolved Spectra

For the Crab pulsar, previous high-precision X-ray pulse profiles and phase-resolved spectra were limited to energies below 30 keV. Here, we performed joint phase-resolved spectral analysis across a broader energy band using ephemerides from NICER (Neutron star Interior Composition Explorer), Insight-HXMT, and the Jodrell Bank radio telescope. Unlike previous broad-band phase-resolved spectral analyses of the Crab pulsar, a broken power-law spectrum (bknpow) cannot adequately describe the spectral properties across the 2–250 keV band, particularly near the main and secondary peaks, requiring the introduction of a second break energy. When using a power-law model to fit the spectra, the overall behavior of the spectral index is remarkably similar across all phase intervals: the index clearly increases with energy, meaning higher energies correspond to larger spectral indices. Furthermore, we conducted quantitative analysis of pulse profiles across energy bands. As energy increases, the separation between the double peaks decreases, the full width at half maximum of both main and secondary peaks increases, and the flux ratio between the two peaks increases [46–47]. Compared with predictions from the outer gap model regarding the double-peak flux ratio and bridge-to-main-peak flux ratio, the observational results show significant discrepancies from the model's predicted trends [48], posing new challenges for high-energy radiation models. Meanwhile, the observed trend in spectral index evolution provides useful information for model improvements.

To further investigate the relative positions of the X-ray and radio emission regions in the Crab pulsar, we used simultaneous observations from Insight-HXMT and NICER to obtain more precise time delays. These time delays can be fitted linearly, as shown in [FIGURE:9].

Insight-HXMT also performed detailed pointed observations of the young pulsar PSR B1509–58, a typical soft gamma-ray pulsar [50]. Takata et al. systematically fitted the 0.5–200 keV band spectrum using data from Insight-HXMT and other telescopes, particularly the high-energy telescope observations [51]. The fitting results indicate that PSR B1509–58's spectrum requires a broken power-law description with a break energy at 5 keV. Phase-resolved spectra can also be described by the same model with a break energy near 5 keV [51]. Further analysis shows that the conversion efficiency of this class of soft gamma-ray pulsars is consistent with that of other gamma-ray pulsars, suggesting that their radiation characteristics are primarily determined by viewing geometry [51].

3.4 Progress in Pulsar Navigation

Pulsar navigation represents another important research objective for Insight-HXMT. The navigation principle is that observed pulsar signals are modulated by spacecraft motion—pulse arrival times depend on the spacecraft's spatial position. By analyzing the characteristics of pulsed signals received by detectors, the spacecraft's position and velocity in space can be determined. Since pulsars are extremely distant from Earth and unaffected by human factors, their navigation precision does not vary with spacecraft location, making them ideal for deep-space navigation and attracting significant attention. The European Space Agency and NASA have launched related research programs. In 2018, NASA announced the successful real-time orbital autonomous navigation experiment using the SEXTANT (Station Explorer for X-ray Timing and Navigation Technology) project on the International Space Station [52]. After 7.5 hours of pulsar observations, the autonomous navigation accuracy reached 5 km [52].

Meanwhile, China has conducted extensive theoretical and experimental research on pulsar navigation. For example, using observations of the Crab pulsar by the "Polar" gamma-ray burst polarimeter on Tiangong-2, China completed its first space-based pulsar navigation experiment [53]. China also launched the XPNAV-01 (X-ray Pulsar Navigation) test satellite for pulsar detection and related research [54]. As shown in [FIGURE:10], using five days of Crab pulsar observations and a "pulse profile significance versus satellite orbit correlation analysis" algorithm, the satellite positioning accuracy reached 10 km, equivalent to 3.3 km, meaning Insight-HXMT's navigation experiment precision is comparable to NICER/SEXTANT results [30].

4 Millisecond Pulsar Observational Progress

Accreting millisecond X-ray pulsars (AMXPs) are a special class of low-mass X-ray binaries containing neutron stars, where the compact object is a rapidly rotating, recycled pulsar and the companion is a low-mass main-sequence star or white dwarf. In 1998, Wijnands and van der Klis discovered coherent X-ray pulsations at approximately 401 Hz from SAX J1808.4–3658 [26]. Since the pulse frequency was modulated by binary orbital motion, they successfully measured the binary orbital parameters, marking the first confirmed AMXP. With the operation of RXTE (Rossi X-ray Timing Explorer), XMM-Newton (X-ray Multi-Mirror Mission), Chandra, INTEGRAL (International Gamma-Ray Astrophysics Laboratory), Swift, MAXI (Monitor of All-sky X-ray Image), NICER, and other high-energy telescopes, all-sky monitoring of X-ray source outbursts has been achieved. To date, 23 AMXPs have been discovered and identified, with this number continuing to grow [55–56]. These AMXPs were all detected during outbursts by X-ray telescopes, with orbital periods measured through timing analysis ranging from 40 minutes to 9 hours, and spin periods ranging from 1.9 to 10 ms. The outburst of IGR J00291+5934 lasted over a decade, representing the longest-duration AMXP outburst observed. AMXP outburst recurrence times are unpredictable, with most sources observed to outburst only once, implying recurrence periods of at least several decades. Only five AMXPs have shown repeated outbursts, with NGC 6440 X–2 having the shortest recurrence time of about one month, while SAX J1808.4–3658 has exhibited eight outbursts since its discovery, with an average recurrence interval of 2–4 years [55]. Studies have also found that broad-band X-ray pulse profiles during AMXP outbursts are closely related to key parameters including binary orbital inclination, magnetic inclination, accretion column height, and neutron star mass and radius [57].

The magnetic field decay timescale for isolated neutron stars is extremely long (over 10⁷ years), making direct observation of magnetic field evolution difficult. However, multi-wavelength observations of large neutron star samples can reveal magnetic field distributions across different subclasses (e.g., normal pulsars versus millisecond pulsars), allowing inference of overall evolutionary patterns. For AMXPs during outburst, magnetic field strength can be calculated based on accretion torque theory. For example, Mukherjee et al. (2015) calculated magnetic field ranges for 14 AMXPs using observed luminosity extrema [58]; Sanna et al. found that IGR J17591–2342 spun down during outburst and, after correcting the accretion rate and combining it with accretion torque theory, calculated a magnetic field strength of approximately 10⁸ Gs [59]. For quiescent AMXPs, dipole magnetic field strength can be estimated from the star's luminosity and spin-down rate [60–61], or based on standard accretion disk theory and optical observations during quiescence [26, 62–64]. For AMXPs with multiple outbursts, magnetic fields can also be calculated from spin-down between outbursts due to magnetic dipole radiation. Hartman et al. (2011) used this method to calculate a magnetic field of 10⁸ Gs for IGR J00291+5934 [65]; Sanna et al. (2018) similarly obtained a magnetic field range of 10⁸–10⁹ Gs for Swift J1756.9–2508 [66]. In summary, AMXP magnetic field calculations primarily depend on the star's spin frequency, frequency derivative, and luminosity, while also being affected by uncertainties in distance, mass, and radius parameters.

The transition of AMXPs from accretion states to radio emission states represents an important prediction of the pulsar recycling mechanism. AMXP IGR J18245–2452 was detected in radio pulsations two weeks after entering quiescence, confirming its transition from an accretion phase to a radio pulsar phase on short timescales and making it the only state-transitional millisecond pulsar observed to date [67]. Previously, Iacolina et al. searched for radio pulsations from XTE J0929–314, XTE J1751–305, and other sources in quiescence without success [68–69]. This indicates that detecting radio pulsed radiation from neutron stars in quiescent LMXBs depends on multiple factors, including whether the radio beam points toward the observer, telescope sensitivity, source distance, and free-free absorption by circumstellar medium. In the gamma-ray band, Fermi/LAT discovered that radio millisecond pulsars commonly exhibit high-energy pulsed radiation powered by a small fraction of the pulsar's spin-down energy loss [70]. Meanwhile, AMXP gamma-ray pulsed radiation is unaffected by free-free absorption. Therefore, searching for gamma-ray pulsed radiation can determine whether AMXPs have undergone state transitions, though no AMXP gamma-ray pulsed signals have been detected to date [71–72]. Future detection may become possible with precise AMXP orbital parameter measurements and accumulated gamma-ray observational data.

Since its operation, Insight-HXMT has observed five AMXPs: Swift J1756.9–2508, MAXI J1816–195, SAX J1808.4–3658, IGR J17498–2921, and SRGA J144459.2–604207. Swift J1756.9–2508 was discovered by Swift/BAT during its 2007 outburst, with coherent X-ray pulsations at 182 Hz confirming its AMXP nature. Subsequent Swift and RXTE observations measured an orbital period of 54.7 minutes, revealing a highly evolved white dwarf companion with mass between 0.0067 and 0.03 solar masses [73]. Swift J1756.9–2508 experienced three additional outbursts in 2009, 2018, and 2019. Insight-HXMT observed the 2018 outburst for 20 ks, achieving a signal-to-noise ratio of about 5 in the 5–45 keV pulse profile (see [FIGURE:11]), with pulse profile shapes consistent with other telescopes, demonstrating Insight-HXMT's accurate timing measurements for rapidly rotating pulsars. The pulsed fraction increased from 4% to 7.5% in the 1–5 keV band and saturated at higher energies. No significant spin frequency variations were detected. Comparing observed ascending node times with predicted values revealed no significant orbital period evolution in this binary system since its first outburst in 2007.

On June 7, 2022, MAXI's gas slit camera detected an X-ray outburst from the new transient MAXI J1816–195 [74]. Follow-up NICER observations detected pulsations and Type I X-ray bursts, confirming it as a 528 Hz AMXP with an orbital period of 4.83 hours and a projected semi-major axis of 0.26 light-seconds [75–78], with a companion mass between 0.10 and 0.55 solar masses [75]. Simultaneously, Insight-HXMT detected X-ray pulsations from MAXI J1816–195 in the hard X-ray/soft gamma-ray band [79]. Bult et al. proposed a flux bias model accounting for accretion torque at the neutron star surface and/or hot spot wandering to explain timing residuals throughout the outburst [75]. Chen et al. reported Insight-HXMT's detection of 73 Type I X-ray bursts from MAXI J1816–195, yielding a distance upper limit of 6.3 kpc [80]. Using Insight-HXMT/ME and HE telescopes, NICER, and NuSTAR data, we systematically studied the 0.8–210 keV X-ray timing and spectral behavior during MAXI J1816–195's 2022 outburst. Timing analysis using Insight-HXMT/HE data revealed complex residual behavior, confirmed by Insight-HXMT/ME and NICER observations, particularly during the outburst rise and decay phases. We therefore divided the outburst into a noisy rise phase (MJD 59737.0–59741.9, lasting about 5 days) and a decay phase (MJD 59741.9–59760.6, lasting 19 days). The decay phase timing could be fitted with a timing model including frequency ν and frequency derivative ν̇, with ν̇ = (9.0±2.1)×10⁻¹⁴ Hz/s, indicating the pulsar was in a spin-up state. We found that Bult et al.'s model cannot fully explain our observational data [75]. Furthermore, we detected hard X-ray pulsed radiation up to 95–210 keV in Insight-HXMT/HE data, with significant pulse profiles persisting in the 95–210 keV band, as shown in [FIGURE:12]. Such high-energy pulsed radiation suggests a non-thermal origin. Finally, pulse profiles remained stable throughout the outburst and could be well described by truncated Fourier series with two harmonics (fundamental and harmonic), with both components consistent across the 0.8–64 keV range. Based on these observations, we estimated MAXI J1816–195's magnetic field range as 10⁸–10⁹ Gs, consistent with most other AMXPs. Additionally, during IGR J17498–2921's 2023 outburst, Insight-HXMT and NICER conducted joint observations, detecting significant pulsed signals across 0.5–150 keV, with pulsed fraction increasing from about 2% at 1 keV to about 13% at 66 keV [81].

Insight-HXMT also detected pulsed radiation from SAX J1808.4–3658 and SRGA J144459.2–604207, with related results to be published.

5 Summary and Outlook

Insight-HXMT has accumulated rich observational data on pulsars, requiring further mining of existing datasets. For accreting millisecond X-ray pulsars, higher-energy pulsed signals provide important constraints on accretion pulsar emission regions. Additionally, Insight-HXMT's high-energy telescope CsI detectors cover the MeV band, offering potential for observing pulsar MeV radiation. Utilizing these observations to study MeV radiation characteristics will further reveal the geometric structure of pulsar high-energy emission zones. China's Einstein Probe satellite and the China-France SVOM satellite have also been launched, expanding X-ray observational capabilities. Joint observations with Insight-HXMT and these X-ray telescopes will enhance pulsar observational capacity and open new discovery space.

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