Preamble

Vol. 66 No. 4

July 2025

Acta Astronomica Sinica Vol. 66 No. 4 Jul., 2025 doi: 10.15940/j.cnki.0001-5245.2025.04.007

Research Progress on Quasi-Periodic Oscillation Phenomena Based on Insight-HXMT Observations*

ZHANG Liang†　QU Jin-lu　ZHANG Shu
(Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049)

Abstract

Quasi-Periodic Oscillations (QPOs) are commonly observed in the light curves of X-ray binaries. Since QPOs are generally believed to originate from the accretion flow very close to the compact object, they serve as important probes for testing general relativistic effects in strong gravitational fields and for studying the evolution of accretion geometry near compact objects. Before the launch of the Insight-HXMT satellite, QPO research was primarily limited to energies below 30 keV. With its exceptionally large effective area at high energies, Insight-HXMT has opened a new window for investigating the high-energy properties of QPOs. This paper summarizes the progress achieved by Insight-HXMT in QPO research, including the observational characteristics of high-energy QPOs, their physical origins, and the corresponding evolution of accretion geometry. We also discuss possible future breakthrough directions.

Keywords X-rays: binaries, accretion, accretion disks, black hole physics

1 Introduction

X-ray binaries are binary systems composed of a compact object (a stellar-mass black hole or neutron star) and a companion star. The compact object accretes matter from its companion, releasing enormous gravitational potential energy as the material falls inward, which is converted into radiation primarily in the X-ray band. These objects harbor extreme physical environments of gravity, magnetic fields, and density, providing an excellent laboratory for studying the states and dynamics of matter under extreme conditions. Based on the mass of the companion star, X-ray binaries can be broadly classified into low-mass X-ray binaries (LMXBs) and high-mass X-ray binaries (HMXBs). LMXBs include black hole X-ray binaries, neutron star X-ray binaries of Z and Atoll types, while HMXBs can be further divided into Be X-ray binaries and supergiant X-ray binaries according to the companion star type. The spatial scales of X-ray binary systems are extremely small and currently cannot be spatially resolved, but timing characteristics provide an indirect method for measuring the accretion geometry around compact objects. The most prominent features in the power spectra of X-ray binaries are narrow peaks known as Quasi-Periodic Oscillations (QPOs). Since QPOs are generally believed to originate from the accretion flow near the compact object, they serve as powerful probes for testing general relativistic effects in strong gravitational fields and for studying the evolution of accretion geometry around compact objects.

According to their centroid frequencies, QPOs in X-ray binary systems can be divided into three categories: millihertz QPOs (<0.01 Hz), low-frequency QPOs (~0.01–60 Hz), and high-frequency QPOs (>60 Hz). In black hole systems, low-frequency QPOs can be further classified into three types—C, B, and A—based on differences in their power spectral and cross-spectral properties (centroid frequency, full width at half maximum, amplitude, and time lag). C-type and B-type QPOs exhibit strong amplitudes and narrow widths, while A-type QPOs have weak amplitudes and broad widths. The centroid frequency of C-type QPOs (~0.1–30 Hz) increases as the energy spectrum softens, and the power spectrum shows strong broadband noise components and harmonic features of the QPO. B-type QPOs have centroid frequencies concentrated in the 4–6 Hz range, with strong broadband noise components and common secondary harmonic peaks. A-type QPOs have centroid frequencies mainly around 6–8 Hz, accompanied by very weak broadband noise and generally no harmonics. Different types of low-frequency QPOs appear in different spectral states: C-type QPOs primarily occur in the hard state and hard intermediate state, while B-type and A-type QPOs appear in the soft intermediate state and soft state, respectively.

Although many models have been proposed to explain low-frequency QPOs (for an introduction to QPO models see reference [1]), their physical origin remains controversial. Recent observational evidence suggests that the flux modulation of QPOs arises from geometric effects, with Lense-Thirring precession as predicted by general relativity being a possible generation mechanism. High-frequency QPOs in black hole systems are generally weak and have only been detected with significant signals in a few sources such as GRS 1915+105, GRO J1655–40, and XTE J1550–564.

The most prominent features in the power spectra of Z and Atoll sources are pairs of kilohertz QPOs. Current theoretical models for explaining kilohertz QPOs include the beat-frequency model and the precession model. Compared to black hole systems, low-frequency QPO phenomena in neutron star systems are generally weaker. Depending on the evolutionary track branch, low-frequency QPOs in Z sources can be classified as Horizontal Branch Oscillation (HBO) QPOs, Normal Branch Oscillation (NBO) QPOs, and Flaring Branch Oscillation (FBO) QPOs, corresponding to C-type, B-type, and A-type QPOs in black hole systems, respectively. QPO phenomena similar to HBO and FBO in power spectral shape have also been observed in Atoll sources. It is generally believed that low-frequency QPOs in black hole and neutron star systems have similar physical origins. Additionally, millihertz QPO phenomena are also common in neutron star systems.

Before 2017, QPO observations primarily relied on the Rossi X-ray Timing Explorer (RXTE), which was decommissioned in 2012 after achieving fruitful results in QPO research. However, RXTE had a very small effective area at high energies (>30 keV), limiting previous studies. In 2017, China launched its first X-ray astronomy satellite, Insight-HXMT, which has a very large effective area at high energies and has opened a new window for studying the high-energy properties of QPOs. This paper will introduce the scientific achievements of Insight-HXMT in the study of QPO phenomena.

2.1.1 Observational Characteristics of High-Energy QPOs

During the RXTE era, the highest-energy QPOs detected through direct methods were around 40 keV. During its more than eight years of operation, Insight-HXMT has detected low-frequency QPOs above 50 keV in multiple black hole X-ray binaries [2–8], demonstrating that high-energy QPOs are a common phenomenon in these systems. Particularly noteworthy is the detection of a C-type QPO above 200 keV in the black hole X-ray binary MAXI J1820+070, which represents the highest-energy QPO phenomenon detected to date [3]. [FIGURE:1] shows the C-type QPOs observed by Insight-HXMT in MAXI J1820+070 at different energies, along with a schematic diagram of the jet precession model.

Over the 1–250 keV range, the centroid frequency of C-type QPOs remains essentially constant with energy. The observed variations in QPO frequency with energy in some observations [2, 8] may be caused by the simultaneous presence of two QPO components with different frequencies [9]. The typical amplitude spectrum of C-type QPOs can be approximately described by a broken power law: at low energies, the QPO amplitude increases with energy; above a certain break energy, the amplitude remains roughly constant or shows a slight decreasing trend [10]. [FIGURE:2] shows typical amplitude and lag spectra for different types of QPOs in black hole X-ray binaries. The break energy gradually increases as the energy spectrum softens, reaching ~10–20 keV in the intermediate state. The QPO amplitude at high energies (up to 20%) is much higher than at low energies, indicating that the QPO modulation primarily originates from the Comptonization process. The hot corona or jet base are possible generation regions, while the accretion disk component that dominates at low energies contributes little to the amplitude. In some cases, the reflection component also makes a significant contribution to the QPO flux modulation [12]. In terms of temporal evolution, as the energy spectrum softens and the QPO frequency increases, the amplitude of low-energy QPOs typically decreases while that of high-energy QPOs gradually increases [6, 13].

The evolution of QPO time lags with time and energy is more complex, and the calculation methods and physical interpretation of lags have long been controversial. The traditional method uses the average lag within half the full width at half maximum (FWHM/2) around the QPO frequency in the cross-spectrum as the QPO lag, but this approach does not account for the influence of broadband noise. Insight-HXMT has discovered that in the high-energy cross-spectrum, the phase lag within the low-frequency plateau noise range is large and approximately constant, while the structure corresponding to the QPO in the cross-spectrum is superimposed on the noise continuum. Therefore, calculating QPO lags requires consideration of broadband noise effects [3, 8, 14].

Ma et al. [3] proposed a new method for calculating QPO lags by subtracting the average phase lag within the low-frequency plateau noise range from the average phase lag within the QPO range, thereby obtaining the intrinsic phase lag of the QPO. Using this method, they obtained consistent QPO phase lag spectra across different observations of MAXI J1820+070, showing that both low-energy and high-energy photons arrive earlier than photons around 10 keV. The QPO lag spectrum obtained by extracting instantaneous QPO light curves using the Hilbert-Huang transform and calculating lags for different energy bands is essentially consistent with the intrinsic phase lag spectrum obtained by Ma et al. [15]. Similar QPO phase lag spectra have also been observed in the new source Swift J1727.8–1613 that erupted in 2023 [8]. QPO lags may arise from time delays due to different photon propagation paths or from phase differences between QPO waveforms at different energies. In MAXI J1820+070, the time delay between the highest-energy and low-energy bands reaches the order of seconds. If the lag were entirely due to time delay, the corresponding physical size would be about $10^4 R_g$, which is inconsistent with known physical pictures. Therefore, phase differences likely dominate the QPO lags.

2.1.2 Relationship Between C-Type QPO and Noise

Fitting the power spectra of black hole X-ray binaries typically employs multiple Lorentzian functions, which assume that QPO and broadband noise components are additive in the time domain, i.e., $f_{tot}(t) = n(t) + q(t)$, where $n(t)$ and $q(t)$ represent the light curves of the noise and QPO components, respectively. This model further assumes that QPO and noise are uncorrelated, so that in the frequency domain the total power spectrum is the sum of their individual powers. However, bispectrum studies reveal strong phase coupling between QPO and noise, which cannot be produced under the additive relationship [16].

Ma et al. [3] found a linear relationship between the phase lags of different power spectral components and the total component phase lags, suggesting that the intrinsic phase lag of QPOs can be obtained through linear correction. The traditional additive model between QPO and broadband noise is therefore unsuitable for linear extraction of intrinsic QPO phase lags. Zhou et al. [14] proposed a model where QPO and broadband noise have a convolution relationship in the time domain, i.e., $f_{tot}(t) = n(t) \otimes q(t)$, and mathematically demonstrated that intrinsic QPO phase lags can be extracted under this model. According to the convolution theorem, power spectra should be fitted using a multiplicative model under this framework. Compared with the traditional additive model, the multiplicative model yields similar QPO centroid frequencies and widths but slightly smaller QPO amplitudes. This work provides a new perspective for studying the coupling relationship between QPO and broadband noise components.

2.1.3 Physical Origin of C-Type QPO

Statistical analysis based on RXTE data revealed a strong correlation between C-type QPO amplitude and inclination angle, with high-inclination systems showing significantly higher QPO amplitudes than low-inclination systems [17]. Using phase-resolved spectroscopy analysis of Insight-HXMT observations, Shui et al. [18] found that the parameters of the Comptonization and reflection components are strongly modulated with QPO phase, while accretion disk parameters show little modulation. [FIGURE:3] shows the variation of different spectral parameters with QPO phase. The modulation of the reflection component and iron line centroid energy can be well explained by geometric effects. The most commonly used theoretical model for explaining QPO phenomena with geometric effects is the Lense-Thirring precession model [1], where the precessing region could be either the hot inner flow or the base of a small-scale jet. The hot inner flow precession model is based on the truncated disk assumption, where precession of the hot inner flow between the accretion disk and central compact object produces the observed QPO, while variations in the truncation radius lead to the evolution of QPO properties (frequency, amplitude, and lag) during outbursts. However, rapid QPO frequency variations were found in MAXI J1820+070 without significant changes in the inner boundary of the accretion disk [19], indicating that the hot inner flow precession model cannot explain the QPO phenomenon in this source, at least.

Based on Insight-HXMT results for MAXI J1820+070, Ma et al. [3] proposed a jet precession model (schematic shown in [FIGURE:1]), which suggests that QPOs originate from the precession of a small-scale jet. Doppler and solid-angle effects during precession produce flux modulation, with QPO amplitude primarily determined by jet velocity. QPOs at different energies originate from different regions of the jet: high-energy photons are produced at the jet base, while low-energy photons are produced at the jet top. Since the jet is curved, different regions of the jet face the observer at different QPO phases (producing maximum flux), resulting in phase differences between low-energy photons from the jet top and high-energy photons from the jet base. This model can well explain the QPO amplitude and lag spectra observed by Insight-HXMT. Additionally, QPOs have been detected simultaneously in the optical band with the same frequency as those in X-rays [20–21]. The rapid optical variability likely originates from the jet, supporting the jet precession model.

Furthermore, wavelet analysis results based on Insight-HXMT data [22–24] show that QPOs exhibit significant intensity variations on short timescales. In MAXI J1820+070, QPOs typically remain significantly detectable for timescales of about five QPO cycles, with this duration correlating with the QPO quality factor. No significant spectral differences are found between periods when QPOs are strong and when they are weak. The short-term intensity variations of QPOs may be caused by variations in jet velocity, which can also produce broadband noise components.

Moreover, QPOs can serve as probes for studying the evolution of accretion geometry. By simultaneously fitting the time-averaged spectrum, QPO amplitude spectrum, and lag spectrum, Zhang et al. [25] found evidence in the intermediate state of MAXI J1535–571 for the gradual evolution of an extended hot corona into a radial jet, corresponding to the transition of the radio jet from a steady to a transient state.

2.2.1 Observational Characteristics of High-Energy QPOs

Insight-HXMT has observed B-type QPOs in sources such as MAXI J1348–630 and GX 339–4, with centroid frequencies concentrated in the 4–6 Hz range. The properties of B-type QPOs appearing in a single outburst are very similar. Notably, in MAXI J1348–630, B-type QPOs have been detected above 100 keV, representing the highest-energy B-type QPO phenomenon observed to date [5, 26]. The centroid frequency of B-type QPOs does not vary with energy. The amplitude spectrum is similar to that of C-type QPOs in the hard intermediate state before the spectral state transition: below ~10 keV, the QPO amplitude increases with energy; above ~10 keV, the amplitude remains essentially constant with energy, reaching up to 15% at high energies [5]. The lag spectrum of B-type QPOs typically shows a "V" shape, with photons at low energies (<2 keV) and high energies (>3 keV) both lagging behind photons around 2–3 keV; at high energies around 7 keV, the lag spectrum shows a clear break (see [FIGURE:2]).

2.2.2 Transient Nature of B-Type QPOs

A characteristic feature of B-type QPOs is their sudden disappearance/reappearance, with this transition occurring on very short timescales, typically within tens of seconds. Insight-HXMT has observed multiple instances of sudden QPO disappearance/reappearance in MAXI J1348–630. Broad-band spectral comparisons show clear differences between the spectra during QPO-present and QPO-absent periods [5, 26]. During QPO periods, the flux of the high-energy Comptonization component increases significantly, while the low-energy accretion disk component becomes substantially weaker.

Yang et al. [26] conducted a systematic study of the transient phenomenon of B-type QPOs in three sources, finding an obvious anti-correlation between the flux changes of the accretion disk component and the Comptonization component in the 0.5–10 keV range during the transition. This suggests that the essence of the QPO transient phenomenon is the reallocation of accretion energy between the accretion disk and the Comptonization region: QPOs appear when more accretion energy is injected into the Comptonization region, and disappear when more energy is injected into the accretion disk. The study also found that B-type QPOs only appear when the fraction of Comptonization flux (Comptonization component flux/total flux) exceeds a certain critical value, which varies among different sources. The factors determining this critical value require further investigation. [FIGURE:4] shows the ratio of spectra with and without B-type QPOs, and the relationship between flux changes of the Comptonization and disk components during the transition.

2.2.3 Physical Origin of B-Type QPOs

The first appearance of B-type QPOs during an outburst occurs very close to the time of large-scale transient jet ejection, leading to the belief that B-type QPO generation is related to large-scale jets [27]. By fitting the QPO amplitude and lag spectra, García et al. [28] found that the QPO variability spectrum requires two physically related Comptonization regions: a small-scale region (size ~25 $R_g$) with strong feedback to the accretion disk, likely corresponding to an extended hot corona; and a large-scale region (size ~1500 $R_g$) with weak feedback to the disk, likely corresponding to a radial jet. Yang et al. [26] proposed that B-type QPOs may originate from the joint precession of an extended hot corona and jet, while the sudden disappearance of QPOs may be caused by the Bardeen-Petterson effect aligning the inner accretion flow normal with the black hole spin axis, preventing precession.

2.3 Millihertz QPO Phenomena

Millihertz QPOs are extremely rare in black hole systems, typically appearing in spectrally hard accretion states. During the RXTE era, simultaneous observations of millihertz QPOs and C-type low-frequency QPOs suggested different physical origins [29]. Insight-HXMT observed a 60 mHz QPO during the rising phase of the 2021 outburst of the black hole candidate 4U 1630–47. Leveraging Insight-HXMT's high-energy, large-effective-area capabilities, Yang et al. [11] extended studies of black hole millihertz QPOs to 100 keV for the first time. The study found that the QPO amplitude increases with energy, indicating that the QPO modulation originates from the hot corona. Additionally, the observations show that soft photons lag behind hard photons, with the lag timescale increasing with energy (see [FIGURE:2]). Spectral analysis indicates that the optical depth of the hot corona decreases during millihertz QPO periods, possibly due to an increase in coronal size. The increased coronal size would enhance its coupling with the accretion disk. The observed millihertz QPO may arise from an instability process triggered by the coupling between the hot corona and accretion disk. Insight-HXMT only observed millihertz QPOs within a specific luminosity range, suggesting that the generation of this instability is related to changes in the accretion rate.

3.1 QPO Phenomena in Neutron Star Low-Mass X-Ray Binaries

Insight-HXMT conducted high-cadence monitoring of the Z source Sco X-1, obtaining a complete evolution track and observing low-frequency QPOs on different branches as well as kilohertz QPOs [30]. NBO (~6 Hz) and FBO (~16 Hz) appear at the end of the normal branch and the beginning of the flaring branch, respectively, when the energy spectrum is soft. These QPOs are only detected in LE and ME data, with no significant QPO signals in HE data. In contrast, HBO (~40 Hz) and kilohertz QPOs (~800 Hz) appear simultaneously on the horizontal branch when the spectrum is hard, with QPOs being significant only in ME and HE bands. For all types of QPOs, the centroid frequency does not vary with energy, while the QPO amplitude increases with energy, indicating that QPO modulation more likely originates from the Comptonization process. Particularly noteworthy is that Insight-HXMT observed kilohertz QPOs from Sco X-1 above 20 keV for the first time. The mainstream model for kilohertz QPOs suggests they originate from the inner edge of the accretion disk and are dominated by thermal radiation, making it difficult to reach such high energies. The Insight-HXMT observations challenge mainstream kilohertz QPO models. By comparing time-averaged spectra with QPO amplitude spectra, Jia et al. [31] localized the generation region of kilohertz QPOs to the inner region of the transition layer.

3.2 QPO Phenomena in Accreting Pulsars

Insight-HXMT discovered millihertz QPO phenomena during the 2020 outburst of the high-mass X-ray pulsar 1A 0535+262, with QPO centroid frequencies varying in the 35–95 mHz range and showing positive correlation with source flux [32–33]. The QPOs were significantly detected only in the 25–120 keV range, with the highest significance in the 50–65 keV band. Notably, this is the first time astronomers have detected millihertz QPOs above 80 keV in a neutron star system. The study found that the QPO amplitude first increases and then decreases with energy, reaching a maximum at 50–65 keV. Additionally, during the outburst peak, the millihertz QPO exhibited a twin-peak structure, with a constant frequency difference of about 0.02 Hz between the two peaks, which is twice the neutron star's spin frequency in this system. Previous theoretical models for explaining millihertz QPO phenomena in neutron star systems, such as the Beat Frequency model, Keplerian Frequency model, and neutron star precession model, cannot explain the energy evolution of the QPO amplitude in 1A 0535+262. Insight-HXMT results suggest that the origin of millihertz QPOs may be related to variations in non-thermal radiation, with resonance between the accretion column and the accretion disk or neutron star being a possible mechanism.

Millihertz QPOs have also been detected in the X-ray pulsar Cen X-3, with a frequency around 40 mHz [34]. Unlike in 1A 0535+262, the QPO frequency in Cen X-3 is not correlated with X-ray flux but varies with orbital phase. The QPOs appear below 20 keV, and their amplitude gradually decreases with increasing energy. Similarly, beat-frequency and Keplerian frequency models cannot explain the evolution of this millihertz QPO's frequency and amplitude. The QPO may originate from an instability process when the accretion disk is truncated at the corotation radius.

RX J0440.9+4431 is a high-mass X-ray pulsar with a 205 s period. This source experienced its brightest recorded outburst at the end of 2022, with a peak flux exceeding 2 Crab. In the supercritical accretion state, short-timescale strong flares frequently appeared at the peaks of the high-energy pulse profile. Insight-HXMT discovered quasi-periodic modulations in flares at five pulse profile peaks [35]. The QPO frequencies varied among different pulses, ranging from 0.2–0.5 Hz and showing no correlation with source flux. QPOs appeared in the 10–130 keV energy range and were not significant below 10 keV. Furthermore, QPO amplitude increased with energy. Insight-HXMT observations suggest that QPOs in pulse flares may be related to instabilities in the accretion flow.

4 Summary and Outlook

This paper summarizes the important achievements of Insight-HXMT in QPO research over the past eight years. Insight-HXMT has discovered QPO phenomena above 100 keV in multiple black hole X-ray binaries, with the amplitude and lag properties at high energies suggesting they may originate from the precession of small-scale jets. Leveraging Insight-HXMT's large effective area, detailed spectral and timing analyses of short-timescale QPO variability reveal that QPO transient phenomena are likely related to the reallocation of accretion energy. Additionally, Insight-HXMT observations of QPO phenomena in neutron stars pose stricter challenges to existing models. These results highlight the advantages of Insight-HXMT in studying high-energy radiation from accretion systems.

Although Insight-HXMT observations have provided crucial constraints on existing QPO models and facilitated the development of new theoretical models, many questions regarding the physical origin of QPOs remain unresolved. For example, does the precession model apply to all types of QPOs? What is the relationship between QPOs and noise? How are harmonic and subharmonic components generated?

Future next-generation X-ray astronomy satellites, such as the enhanced X-ray Timing and Polarimetry mission (eXTP), will have larger effective areas and higher energy and time resolution, allowing more precise tests of existing theoretical models. On the other hand, polarization measurements will impose stricter constraints on QPO physical models. For instance, precession models predict clear modulation of polarization angle and degree with QPO phase, but recent results based on data from the Imaging X-ray Polarimetry Explorer (IXPE) have not found such modulation [36], challenging the precession model. Additionally, the introduction of unconventional methods (such as wavelet transform and Hilbert-Huang transform) has greatly helped our understanding of QPO properties, particularly their short-timescale characteristics.

References

Ingram A, Motta S E. NewAR, 2019, 85: 101524
Huang Y, Qu J L, Zhang S N, et al. ApJ, 2018, 866:
Ma X, Tao L, Zhang S N, et al. NatAs, 2021, 5: 94
Bu Q C, Zhang S N, Santangelo A, et al. ApJ, 2021, 919: 92
Liu H X, Huang Y, Bu Q C, et al. ApJ, 2022, 938: 108
Zhu H F, Chen X, Wang W, et al. MNRAS, 2023, 523:
Jin Y J, Wang W, Chen X, et al. ApJ, 2023, 953: 33
Yu W, Bu Q C, Zhang S N, et al. MNRAS, 2024, 529:
Méndez M, Peirano V, García F, et al. MNRAS, 2024, 527: 9405
Ma X, Zhang L, Tao L, et al. ApJ, 2023, 948: 116
Zhang P, Soria R, Zhang S, et al. A&A, 2023, 677:
Yang Z X, Zhang L, Huang Y, et al. ApJ, 2022, 937: 33
Gao C X, Yan Z, Yu W F. MNRAS, 2023, 520: 5544
Zhang Y X, Méndez M, García F, et al. MNRAS, 2022,
Kong L D, Zhang S, Chen Y P, et al. JHEAp, 2020, 25:
Yang Z X, Zhang L, Zhang S N, et al. MNRAS, 2023,
Zhou D K, Zhang S N, Song L M, et al. MNRAS, 2022, 521: 3570
Yu W, Bu Q C, Yang Z X, et al. ApJ, 2023, 951: 130
Ding Q, Ji L, Bu Q C, et al. RAA, 2023, 23: 085024
Motta S E, Casella P, Henze M, et al. MNRAS, 2015, 447: 2059
Shui Q C, Zhang S, Zhang S N, et al. ApJ, 2023, 957:
Kara E, Steiner J F, Fabian A C, et al. Nature, 2019, 565: 198
Thomas J K, Buckley D A H, Charles P A, et al.
Homan J, Bright J, Motta S E, et al. ApJ, 2020, 891:
García F, Méndez M, Karpouzas K, et al. MNRAS, 2021, 501: 3173
Trudolyubov S P, Borozdin K N, Priedhorsky W C. MNRAS, 2001, 322: 309
Jia S M, Bu Q C, Qu J L, et al. JHEAp, 2020, 25: 1
Jia S M, Qu J L, Lu F J, et al. ApJ, 2021, 913: 119
Ma R C, Tao L, Zhang S N, et al. MNRAS, 2022, 517:
Reig P, Ma R C, Tao L, et al. A&A, 2022, 659: A187
Liu Q, Wang W, Chen X, et al. MNRAS, 2022, 516:
Chen X, Wang W, You B, et al. MNRAS, 2022, 513:
Li P P, Tao L, Ma R C, et al. MNRAS, 2024, 529: 1187
Chen X, Wang W, Tian P F, et al. MNRAS, 2022, 517:
Zhao Q C, Tao L, Li H C, et al. ApJ, 2024, 961: L42