Preamble

Vol. 66 No. 4

July 2025

Acta Astronomica Sinica Vol. 66 No. 4 Jul., 2025 doi: 10.15940/j.cnki.0001-5245.2025.04.009

Insight-HXMT Studies of Cyclotron Resonant Scattering Features and Accretion Physics in Accreting X-ray Pulsars

JI Long (School of Physics and Astronomy, Sun Yat-Sen University, Zhuhai 519082)

Abstract

Since its launch in 2017, the Insight Hard X-ray Modulation Telescope (Insight-HXMT) has become one of the most important astronomical satellites in the field of accreting X-ray pulsar research, thanks to its wide energy band, large effective area, and high observational cadence. It has achieved significant progress in studies of cyclotron absorption lines and accretion physics, including the detection of high-energy cyclotron absorption lines, revealing the evolution of cyclotron line energies, and observing radiation-pressure-dominated accretion disks.

Keywords stars: neutron, accretion, X-rays: binaries, pulsars: general

1 Introduction

X-ray accreting pulsars are magnetized neutron stars in X-ray binary systems, typically with massive main-sequence companions. They possess extremely strong magnetic fields, reaching up to $10^{12}$–$10^{13}$ G, far exceeding anything achievable in Earth-based laboratories, making them natural laboratories for studying physics in extreme magnetic fields. Observational studies of accreting pulsars have continued for nearly 50 years since the 1970s, accumulating a vast amount of data. Based on companion type, these systems can be broadly classified as persistent sources or transients, with transients comprising the majority. The luminosity of accreting pulsars spans several orders of magnitude (from $\sim 10^{34}$ erg/s to $\sim 10^{40}$ erg/s). At low accretion rates, systems may enter a "propeller" state where accretion near the magnetosphere ceases due to centrifugal forces, while at high accretion rates they evolve into ultraluminous X-ray sources (ULXs). The strong magnetic field truncates the accretion flow near the magnetospheric radius. Inside this radius, matter falls along the pulsar's dipole field lines onto the polar caps, where gravitational potential energy is converted into X-ray radiation. Because the magnetic axis is typically misaligned with the rotation axis, we observe periodic modulation of the X-ray flux. Interested readers are referred to the review literature \cite{1}.

The spectra of accreting pulsars are dominated by non-thermal radiation, generally describable by phenomenological models such as a power law with a high-energy exponential cutoff (see review \cite{2} for mathematical forms). The spectra also exhibit narrow line features, including the 6.4 keV Fe fluorescence line and cyclotron resonant scattering features (CRSFs). The latter, commonly called "cyclotron lines," arise from the quantization of electron energy perpendicular to the magnetic field (Landau levels) in strong fields, appearing as broad absorption structures in the spectrum. The importance of cyclotron lines lies in their central energy $E_{\text{cyc}}$ being directly related to the local magnetic field strength: $E_{\text{cyc}} = n/(1+z) \times 11.6 \times B_{12}$ keV, where $n$ is the quantum number, $z$ is the gravitational redshift, and $B_{12}$ is the magnetic field in units of $10^{12}$ G. Thus, cyclotron lines provide the most direct means to measure magnetic fields in neutron star emission regions. These lines are not static; they typically vary with source luminosity, spin phase, orbital phase, superorbital phase, and different stages of outbursts. Crucially, these energy variations do not reflect changes in the neutron star's intrinsic magnetic field, but rather result from changes in the radiation structure or direction in the polar cap region. Therefore, studies of cyclotron lines, along with related timing and spectral analyses, represent the primary tools for investigating accretion and radiative transfer processes in polar cap regions.

In-depth studies of accreting pulsars require wide-band, large-effective-area instruments. Important previous missions include BeppoSAX, RXTE, NuSTAR, and INTEGRAL. In 2017, China's Insight-HXMT was successfully launched, featuring a broad energy band (1–250 keV) and large effective area in the hard X-ray band (see \cite{3}). Most importantly, its flexible observing strategy prioritizes exposure time during bright outbursts, obtaining unprecedented high-quality data for important transient sources such as Swift J0243.6+6124 and 1A 0535+262, making it one of the most important satellites in this research field. To date, researchers have published 36 papers on timing, spectral analysis, and theoretical modeling of accreting pulsars using HXMT data across 13 different sources. Due to space limitations, this review cannot cover all studies comprehensively and will instead focus on representative highlights.

2 A New Record for the Highest-Energy Cyclotron Absorption Line

Cyclotron lines typically have broad spectral features that can couple with the continuum, requiring wide energy coverage for accurate measurement. HXMT has detected cyclotron absorption lines in Her X-1, Vela X-1, Cen X-3, GRO J1008–57, Swift J0243.6+6124, and 1A 0535+262 \cite{4-10}, demonstrating its powerful detection capability, particularly at high energies. For example, in GRO J1008–57, the detection significance of the 90 keV cyclotron line was improved from the previous 2σ to 20σ \cite{7}. During the peak of the first Galactic ULX Swift J0243.6+6124, Kong et al. \cite{9} discovered a cyclotron absorption line at 120–146 keV through phase-resolved spectroscopy. The broadband spectrum and spectral fitting residuals for Swift J0243.6+6124 are shown in [FIGURE:1]. This represents a new record for the highest-energy cyclotron absorption line and the first measurement of a cyclotron line in a ULX. From this, the neutron star's surface magnetic field can be inferred to be $\sim 10^{13}$ G, significantly larger than previous estimates based on the "propeller" effect and accretion disk interactions \cite{11-12}. This suggests the presence of multipole fields on the pulsar surface, a phenomenon theoretically predicted but never before confirmed through cyclotron line measurements of neutron star surface fields. This result also has positive implications for understanding the relationship between ordinary X-ray pulsars and ULXs, indicating that some ULXs share similar radiation mechanisms with ordinary X-ray pulsars, with radiation dominated by "fan-beaming" patterns, and that their high luminosities are intrinsic rather than due to strong radiation collimation \cite{13-15}. On the other hand, based on spin evolution at low luminosities, Liu et al. \cite{16} observed that accretion flow properties may differ between different outburst states (strong and weak). At low luminosities, pulsars may not always enter the "propeller" state, challenging the use of the "propeller" effect to constrain neutron star dipole magnetic fields.

3 Evolution of Cyclotron Line Energy

Cyclotron line energy typically varies with changes in the polar cap accretion structure. For example, in the well-observed Her X-1, a positive correlation between cyclotron line energy and luminosity has been found, along with long-term evolution on decadal timescales \cite{17-20}. Since HXMT's launch, multiple observations of Her X-1 have confirmed this long-term evolutionary trend \cite{5, 20}, with continued monitoring planned to capture any sudden changes in cyclotron line energy.

In many sources, cyclotron line energy correlates with pulsar luminosity: most show a positive correlation, while only a few show an inverse correlation at high luminosities \cite{2, 21}. Theory suggests that at high accretion rates (supercritical state; subcritical otherwise), high luminosity in the polar caps creates strong radiation pressure that hinders matter from reaching the neutron star surface. This leads to the formation of an accretion column whose height increases with accretion rate, with the luminosity at which the column forms called the critical luminosity \cite{21-24}. When luminosity exceeds this critical value, the main emission region moves slightly away from the polar caps \cite{23, 25}, causing the local magnetic field strength to decrease and producing an inverse luminosity-cyclotron energy relationship. This inverse correlation was previously observed only in V0332+53 \cite{26-27}. At the end of 2020, HXMT observations of the outburst state of 1A 0535+262 broke this solitary case. In this source, the cyclotron line energy was positively correlated with luminosity at low luminosities but inversely correlated at high luminosities \cite{10}, strongly supporting theoretical models. [FIGURE:2] shows the relationship between cyclotron absorption line energy and luminosity at different outburst stages. Subsequent pulse-to-pulse analysis by Shui et al. \cite{28} provided more detailed investigation of this relationship, extending to even lower luminosities and offering observational guidance for theoretical modeling.

Another interesting issue is that, as shown in [FIGURE:2], the evolution of cyclotron line energy differs between the rising and fading phases of outbursts. Meanwhile, pulse profile studies reveal distinct differences between these phases even at the same luminosity \cite{29-30}. This suggests that accretion rate is not the only factor affecting polar cap accretion structure, and further investigation is needed.

4 Radiation-Pressure-Dominated Accretion Disks

While the observed radiation originates directly from the polar caps near the neutron star, the properties of accretion flows on larger scales (outside the magnetosphere) also significantly affect the timing and spectral characteristics of accreting pulsars. This occurs for two main reasons: (1) the geometric scale of the polar caps is believed to be related to the thickness of the accretion disk, so changes in disk thickness affect the local accretion rate in the polar caps; and (2) variability in the accretion flow propagates to the polar caps, causing non-periodic flux variations primarily reflected in the power spectrum \cite{31}. Classic Shakura-Sunyaev accretion disk theory posits that at low accretion rates, the disk is geometrically thin and optically thick, with pressure dominated by gas pressure, while at high accretion rates, radiation pressure gradually dominates, affecting the vertical structure and creating a radiation-pressure-dominated thick disk \cite{32}. However, this picture had never been observationally confirmed in accreting pulsars before.

Doroshenko et al. \cite{12} studied the evolution of pulse profiles and power spectra in Swift J0243.6+6124 in detail, with the long-term outburst evolution and associated timing changes shown in [FIGURE:3]. They found two sudden changes in pulse profile morphology with luminosity evolution: one explained by the formation of an accretion column, and another possibly due to the transition of the accretion disk from a gas-pressure-dominated thin disk to a radiation-pressure-dominated thick disk, accompanied by significant changes in power spectral shape. Kong et al. \cite{33} analyzed the contemporaneous spectral data and found clear spectral evolution near the pulse profile transitions, supporting the physical picture of radiation-pressure-dominated disks at high luminosities. Wang et al. \cite{34} and Liu et al. \cite{35-36} conducted detailed analyses of Swift J0243.6+6124 using pulse fraction and torque models, with high-luminosity results also consistent with radiation-pressure-dominated disk models. Another interesting phenomenon is that Liu et al. \cite{35} found the "luminosity-frequency derivative" relation deviates from radiation-pressure-dominated disk predictions at higher luminosities ($\sim 10^{39}$ erg/s). This may be because radiation from the accretion column irradiates the disk, driving a disk wind that removes some angular momentum. Additionally, based on pulse profile and power spectrum evolution, radiation-pressure-dominated disks have been observed in other sources \cite{37-38}, though significant differences exist between sources, requiring further observational study.

5 Summary and Outlook

Over the past seven years, by leveraging its advantages of wide energy band, high statistics, and high observational cadence, Insight-HXMT has become one of the most important satellites for accreting pulsar research, yielding fruitful results. Particularly for bright outbursts of transient sources, HXMT has provided unprecedented high-quality observations that directly test and advance models of polar cap accretion physics. In the future, HXMT will continue its previous observing strategy, aiming for breakthroughs in several areas: (1) using pulse-to-pulse techniques to analyze existing data or capture new outburst data to search for evidence of cyclotron lines at even higher energies; (2) continuing long-term monitoring of cyclotron line evolution in persistent sources like Her X-1; (3) expanding the source sample for the luminosity-cyclotron energy relationship to confirm previously observed anomalous cases \cite{8}; and (4) combining timing and spectral evolution to search for observational evidence of radiation-pressure-dominated disks in more sources.

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