Preamble

Vol. 66 No. 4

July 2025

Acta Astronomica Sinica

Transfer of Magnetic Field and Jets in Black Hole X-Ray Binaries

YANG Shuai-kang YOU Bei†
(School of Physics and Technology, Wuhan University, Wuhan 430072)

Abstract

Black hole X-ray binary (BHXRB) is a binary system composed of a central compact black hole and its companion star. Its outburst phase is always accompanied by multi-wavelength radiation. With the development of multi-messenger astronomy, a general picture of the physical processes and spectral energy distribution (SED) behind the multi-wavelength emission has emerged: the accretion disk and corona around the black hole dominate the X-ray emission; black hole X-ray binaries are always accompanied by jets, which are the main source of radio emission; the physical processes dominating the optical/near-infrared emission are more complex, generally believed to involve three processes: X-ray reprocessing, viscous thermal radiation from the outer accretion disk, and jet emission. Studies have found that there often exists a power-law correlation between the luminosities at different wavelengths, implying a connection between the underlying physical processes. However, the specific physical processes linking jets and accretion disks remain unclear. Research suggests that weak external magnetic fields in BHXRBs can be dragged inward through the accretion disk to form strong magnetic fields near the black hole. This process significantly amplifies the magnetic field within the accretion flow, providing a prerequisite for theoretical models of jet launching and acceleration such as the BZ (Blandford-Znajek) and BP (Blandford-Payne) models. Meanwhile, strong magnetic fields can also alter the structure of the inner accretion flow, potentially forming a magnetically arrested accretion disk (MAD) in regions near the black hole. Using broadband X-ray observations from the Insight-HXMT (Insight Hard X-ray Modulation Telescope), we can glimpse the high-energy radiation processes in such compact regions. Considering magnetic field transport in black hole binaries can partially explain the accretion disk-jet coupling relationship. We review recent research on magnetic field transport and jets in BHXRB accretion and introduce the latest advances in black hole accretion and magnetic field transport.

Keywords stars: black holes, X-rays: binaries, radiation mechanisms: general, accretion disks, relativistic processes

1 Introduction

Black hole X-ray binary (BHXRB) is a binary system consisting of a central compact black hole and its companion star. The black hole accretes matter from the companion star, forming an accretion disk structure near itself, where gravitational energy of the accreting flow is released through viscous dissipation \cite{1}. A hotter plasma gas cloud (corona) also exists around the black hole, whose structure and location remain uncertain. Current explanations place it near the black hole, at the base of the jet, or above the accretion disk, with its geometry still unclear \cite{2–4}. Decades of research have shown that black hole accretion is often accompanied by jet emission \cite{5–6}, producing multi-wavelength radiation from radio to X-ray bands. By detecting this multi-wavelength emission, we can study the physical mechanisms and behavior patterns of black hole X-ray binaries.

China launched its first X-ray space telescope, the Insight Hard X-ray Modulation Telescope (Insight-HXMT), in 2017. Insight-HXMT has played an important role in black hole X-ray binary research. Its broadband observing capability of 1–250 keV enables systematic detection of thermal radiation from black hole accretion disks, high-energy Comptonization components, and non-thermal radiation features related to jets. Additionally, Insight-HXMT's excellent time resolution allows study of rapid variability in different radiation components, helping to reveal physical processes in extreme gravitational environments near black holes.

Most black hole X-ray binaries remain in quiescence for extended periods, with very low levels of X-ray and radio emission, before undergoing one or several outburst cycles lasting months to years. During an outburst, X-ray luminosity rises by 2–3 orders of magnitude within days, remains at high levels for weeks to months, then gradually decays back to pre-outburst levels before returning to quiescence \cite{7}.

We use "low/hard state" to describe the initial outburst phase when the system is faint in X-rays with a power-law index of approximately 1.5 and a hard spectrum. Radio emission in this state shows characteristics of steady jet synchrotron radiation. During the initial rising hard state, both X-ray and radio luminosities increase while the X-ray spectrum remains hard, dominated by a power-law spectrum believed to result from inverse Compton scattering in a corona of hot electrons near the black hole \cite{8–9}. The weaker thermal component is generally attributed to a truncated, geometrically thick, optically thin accretion disk \cite{10}. As the outburst progresses, thermal radiation from the accretion disk rapidly strengthens until it dominates the X-ray emission, causing the X-ray spectrum to soften quickly. This disk-dominated state is called the "high/soft state," where the disk is believed to be geometrically thin and optically thick, with an effective surface temperature where $k$ is the Boltzmann constant and $T_{\rm bb}$ is the blackbody effective temperature. The disk's inner radius is considered to be the innermost stable circular orbit (ISCO). Between the low/hard and high/soft states exist two intermediate states—the hard-intermediate and soft-intermediate states—not all sources traverse both. Some remain in the low/hard state until returning to quiescence \cite{11–12}.

During the transition from low/hard to high/soft states, radio flares are observed in some systems \cite{13–14}. Regardless of whether such flares are observed (possibly due to lack of radio coverage during transition), radio emission is suppressed when reaching the high/soft state \cite{15}. As thermal disk radiation weakens in the soft state, non-thermal components gradually recover, and the system transitions back to the low/hard state at lower luminosities, with radio emission reappearing. The outburst essentially ends when the system returns to quiescence.

Black hole X-ray binaries always exhibit multi-wavelength radiation during outbursts. The current picture describes: an accretion disk emitting blackbody radiation that contributes soft X-rays; a corona structure near the black hole where UV and soft X-ray photons from the disk undergo inverse Compton scattering, producing hard X-ray power-law spectra—these two processes dominate X-ray emission. Additionally, BHXRBs feature intermittent relativistic outflows (jets) detected primarily in radio, which constitute the main radio emission source. In the optical/near-infrared (OIR) band, the radiation origin is less clear compared to other bands. Optical observations of BHXRBs are often comprehensive, and extensive studies have examined OIR emission during both outburst and quiescence. OIR spectra and variability are complex, indicating multiple contributing physical processes \cite{16}, each depending on independent parameters, explaining the complexity.

In high-mass X-ray binaries (HMXB), OIR emission is largely dominated by the massive companion star \cite{17–18}, with minor contributions from processes like X-ray reprocessing. In low-mass black hole X-ray binaries, spectral and timing analyses of many sources suggest OIR emission results from X-ray reprocessing in the outer disk \cite{19–20}, though this is not universal—other processes can contribute or even dominate in some systems \cite{21}.

Viscous heating in the outer accretion disk produces thermal radiation extending from optical through UV to X-ray bands \cite{1,22}. OIR characteristics in BHXRBs indicate this process is important in some systems \cite{21,23–24}. Companion star thermal emission is also observed in quiescent low-mass X-ray binaries \cite{25–27}. Jet studies show that optically thick flat spectra extend from radio to optical bands \cite{28–31}. These three processes—X-ray reprocessing, viscous disk thermal radiation, and jet emission—have been most commonly used to explain optical emission over decades. Discrepant spectral and timing behaviors are attributed to processes like outer disk magnetic reconnection \cite{32}, magnetically dominated dense corona radiation \cite{33}, or advection-dominated region emission \cite{34}.

Power-law correlations between luminosities at different bands are frequently observed, expressed as $L_A/L_B \propto L_B^{\alpha}$, where $L_A$ and $L_B$ represent luminosities in two bands and $\alpha$ is the power-law index. Studying these correlations helps investigate binary radiation mechanisms, estimate mass accretion rates, constrain physical parameters, and limit jet power \cite{35}.

The OIR/X-ray power-law correlation can be derived from radiation processes. van Paradijs & McClintock \cite{16} proposed in 1995 that if OIR emission originates from X-ray reprocessing, $L_{\rm OIR} \propto L_X^{1/2}T^{-2}L^{0.5}$, where subscripts denote corresponding bands, $a$ is orbital separation, and $T$ is temperature. This correlation was indeed observed in low-mass X-ray binaries. If OIR emission originates from viscous disk thermal radiation, a similar correlation can be derived. For jet-origin OIR emission, OIR/X-ray correlation is also predicted. Steady compact jet models indicate a relationship between radio luminosity and total jet power \cite{36–39}. Migliari et al. \cite{40} showed that in the hard state of BHXRBs, jet power is proportional to the mass accretion rate. For radiation-efficient processes, X-ray luminosity satisfies $L_X \propto \dot{m}$, while for radiation-inefficient objects, $L_X \propto \dot{m}^2$. BHXRBs in the hard state have low radiative efficiency, with most gravitational energy dissipated viscously rather than radiated. Therefore, for hard-state BHXRBs:

$$
L_{\rm radio} \propto L_{\rm jet} \propto \dot{m} \propto L_X^{0.5}
$$

Corbel et al. \cite{9} observed this correlation in the BHXRB GX 339–4 in 2003. If the optically thick jet spectrum is indeed flat from radio to optical bands, then:

$$
L_{\rm OIR} \propto L_{\rm radio} \propto L_X^{0.5}
$$

Homan et al. \cite{21} observed a near-infrared-X-ray correlation $F_{\rm NIR} \propto F_X^{0.53\pm0.02}$ for GX 339–4 in the hard state in 2005, where $F_{\rm NIR}$ and $F_X$ are near-infrared and X-ray fluxes, respectively.

The radio-X-ray correlation in BHXRBs was first discovered in GX 339–4. [FIGURE:1] shows the radio-X-ray power-law correlation from 1997–2000 observations analyzed by Corbel et al. \cite{9} in 2003. Simultaneous correlation analysis of radio and X-ray luminosities in GX 339–4's low/hard state revealed this relationship extends over three orders of magnitude in X-ray luminosity down to quiescence. This radio-X-ray correlation was subsequently found in other black hole binaries and even in active galactic nuclei, following the form $L_{\rm radio} \propto L_X^{0.5-0.7}$. The strong correlation observed across multiple sources indicates a tight connection between the physical processes dominating radio emission (jets) and X-ray emission (accretion flow including disk and corona) in the hard state, pointing to accretion disk-jet coupling in BHXRBs. Fender et al. conducted detailed studies of this correlation in GRS 1915+105 and proposed a unified disk-jet coupling model based on existing observations. A primary goal of studying coupling between inflow (accretion) and outflow (jets) in BHXRBs is to link the evolution of radio emission (from jets) with X-ray emission (from the inner accretion flow or jet base) \cite{13}. This model was refined with higher-frequency, higher-resolution radio observations.

2 Accretion Disk and Large-Scale Magnetic Field

For low-mass black hole X-ray binaries, the truncated disk model well explains spectral and variability properties during state transitions, such as in the transient source V404 Cyg \cite{42–43}. In this model, a standard thin disk extends from the outer radius $R_{\rm out}$ inward to a truncation radius $R_{\rm in}$, where it transitions to an inner advection-dominated accretion flow (ADAF). Observations using this model show that the truncation radius from spectral fitting agrees well with that from quasi-periodic oscillations (QPOs). BHXRBs undergo state transitions during outburst evolution, which the truncated disk model can explain \cite{10}. In the hard state, X-ray spectra often show reflection components \cite{44}, which some studies suggest can be explained by the truncated disk model.

Magnetic fields are ubiquitous in astrophysical objects. In BHXRB systems, magnetic fields exist around the central black hole, possibly dragged inward from weak fields in the outer disk region through the accretion process \cite{45–48}. In binary systems, the external weak magnetic field is generally believed to be provided by the companion star \cite{45–48}. The widely accepted view is that large-scale magnetic fields around black holes play a crucial role in accelerating and collimating jets or outflows \cite{49–51}. Theoretical studies of jet launching and acceleration, such as the BZ (Blandford-Znajek \cite{52}) and BP (Blandford-Payne \cite{53}) models, both require large-scale magnetic fields with open configurations. This section introduces large-scale magnetic fields in standard thin disks and ADAFs.

2.1 Standard Thin Disk and Large-Scale Magnetic Field

Research suggests that large-scale poloidal magnetic fields in the outer disk are dragged inward by accreting plasma while simultaneously diffusing outward. When inward advection balances outward diffusion, the magnetic field in the accretion disk reaches a stable configuration \cite{47}. This means the magnetic field structure is primarily determined by the disk's radial velocity and magnetic diffusivity. Since the disk's radial velocity is roughly proportional to the kinematic viscosity, the magnetic configuration is very sensitive to the magnetic Prandtl number $P_m = \eta/\nu$, where $\eta$ is magnetic diffusivity and $\nu$ is kinematic viscosity. The disk's radial velocity is approximately proportional to $\nu$. Parker argued that in isotropic turbulence, $P_m \sim 1$ \cite{54}, and many numerical simulations have since indicated the magnetic Prandtl number should be around 1 \cite{55–57}. An appropriate magnetic field configuration is crucial for jet launching from accretion disks. Specifically, launching jets from a Keplerian cold disk requires the angle between magnetic field lines and the disk plane to be less than $60^\circ$. For rapidly spinning black holes, this critical angle may exceed $60^\circ$ \cite{53,58}. Lubow et al. \cite{47} investigated the final stable magnetic field configuration when large-scale magnetic advection balances diffusion, finding that significant field dragging only occurs when $P_m \lesssim H/R$ (where $H$ is the disk height at radius $R$). This indicates that for geometrically thin standard disks, external magnetic field advection is always inefficient, with very small radial velocities.

Several models have been proposed to address the inefficient magnetic field advection in standard thin disks \cite{48,59–62}. Some studies suggest that a hot corona above the disk, moving inward relatively quickly, can effectively transport magnetic flux from the outer disk region inward \cite{63}. The hot gas above the standard thin disk can accrete faster than gas inside the disk, partially solving the low efficiency of magnetic flux transport. However, if the magnetic field required for jet launching is provided by the corona, the maximum jet power would be less than $0.05 L_{\rm Edd}$, inconsistent with strong jets observed in some binaries \cite{64}. Cao & Spruit \cite{62} argued that most angular momentum in standard thin disks can be removed by magnetically driven outflows, making the radial velocity significantly higher than in classical standard thin disks and allowing rapid gas accretion onto the black hole. Their calculations showed that even moderate-strength magnetic fields can cause sufficient angular momentum loss through magnetically driven outflows, accelerating inward magnetic advection to balance outward diffusion. Li & Cao \cite{65} numerically simulated the global structure of thin accretion disks driven by magnetic outflows in their 2019 work. [FIGURE:2] shows their main numerical simulation results. Panels (A)–(C) display the magnetic field configuration of a standard thin disk with outflows, showing that the magnetic field is transported inward, forming an open configuration penetrating the disk with field lines clearly inclined toward the disk—necessary for outflow launching. Panels (D)–(E) show the radial distribution of magnetic field strength formed by inward transport of external fields for different external field strengths. The magnetic field strength is significantly enhanced in the inner region of the standard thin disk. Without magnetic outflows, magnetic field transport is extremely inefficient, and no significant enhancement occurs in the inner disk. The enhancement amplitude in the inner disk is sensitive to the external field strength—a strong external field drives strong outflows, causing more angular momentum loss and rapid inward accretion, enabling efficient magnetic field transport. The stronger the external field, the stronger the final inner disk magnetic field.

Panels (F)–(G) show that outflows appear to have radial stratification, with velocity gradients along the radial direction of the disk surface where they are launched. Long-term studies of the active galactic nucleus PG 1211+143 found multiple blueshifted absorption lines in its X-ray spectrum corresponding to outflow velocities of $0.06c, 0.13c, 0.18c$, indicating that outflows likely have a multi-velocity radial stratification rather than moving at a single speed \cite{66–68}. In Li & Cao's \cite{65} work, gas flowing from the inner disk reaches speeds of $0.1c-0.3c$, decreasing with radius, while gas from the outer disk moves at $\sim 10^{-3}c-10^{-2}c$, consistent with observations of some high-luminosity quasars.

2.2 Advection-Dominated Accretion Flow (ADAF) and Large-Scale Magnetic Field

ADAF, a low-accretion-rate model where advective cooling dominates energy dissipation, is geometrically thick and optically thin, resulting in low density, low accretion rate, low radiative efficiency, and relatively large radial velocity. As mentioned, significant magnetic field inward transport occurs when $P_m \lesssim H/R$. For geometrically thick ADAFs with large radial velocities, external field transport efficiency is significantly higher than in standard thin disks. Cao \cite{69} studied the advection/diffusion problem of large-scale magnetic fields in ADAFs; [FIGURE:3] shows the main numerical simulation results. Panels (A)–(B) display the large-scale poloidal magnetic field configuration in ADAFs, clearly showing inward magnetic transport. Panels (C)–(E) illustrate how ADAF structure changes due to magnetic fields. Notably, the radial velocity of the accretion flow near the black hole is reduced by magnetic fields, indicating that if the external field is sufficiently strong, the accretion flow can be trapped by magnetic fields, forming a magnetically arrested accretion disk (MAD), confirming key assumptions of MAD qualitative analysis \cite{70}. In this case, plasma near the black hole horizon may accrete in the form of magnetically constrained gas blobs along field lines. Numerical simulations show that the magnetic field strength near the black hole horizon in ADAFs is mainly determined by the external field strength and ADAF outer radius. FIGURE:3 shows the radial distribution of large-scale magnetic field strength in ADAFs for different $P_m$ values and outer radii. Larger ADAFs starting accretion from greater radii produce stronger magnetic fields at the inner edge.

Due to magnetic pressure perpendicular to the disk plane, ADAF's gas pressure near the black hole increases significantly, while its vertical scale height decreases markedly. Compared to ADAF models without magnetic fields, the estimated magnetic field strength near the inner region is much higher.

3 Jet Observations and Theory

Relativistic outflows, or jets, are important and observationally prominent phenomena associated with accreting relativistic objects including X-ray binaries. Jets were first recognized in active galactic nuclei (AGN) as elongated structures connected to the nucleus. Soon they were identified as powerful energy and matter flows ejected from near black holes into intergalactic space, establishing jets as common phenomena in relativistic accretion systems \cite{71}. Subsequently, the connection between jets and stellar-mass black hole accretion was systematically studied.

Although jet electromagnetic radiation is believed to extend from radio to X-ray bands, radio remains the key observational band historically. Since the discovery of bright X-ray binary sources in the 1960s–70s, strong radio sources have been associated with these high-energy objects. However, X-ray binary jet research only truly began after high-resolution observations of the strong radio source associated with SS 433 \cite{5–6}. "Soft X-ray transient" outbursts are often associated with intermittent strong radio emission. In the 1990s, apparent superluminal motion was observed in the X-ray transient GRS 1915+105 \cite{72–74}, marking a new era in X-ray binary jet research. For the first time, it was realized that jets from X-ray binaries could exhibit the relativistic speeds (Lorentz factor $\Gamma \gtrsim 2$) seen in AGN jets. Since then, detailed studies of jets from X-ray binaries in radio and shorter wavelengths (e.g., optical) have provided clearer understanding of jet behavior and unique insights into the coupling between inflow and outflow in black hole X-ray binaries. However, deeper research reveals increasingly complex jet behavior, making this a rapidly developing field.

[FIGURE:4] shows radio images on arcsecond scales of jets in the black hole X-ray binary MAXI J1820+070.

3.1 Physical Properties of Jets

Observational evidence for jets in X-ray binaries—including "non-thermal" spectra, high radio brightness temperatures, and in some cases high linear polarization—indicates synchrotron radiation as the physical mechanism. [FIGURE:5] shows an observed radio flare event, generally interpreted as energy and particle injection into an expanding plasma cloud appearing as a jet \cite{76}. These radio flares feature optically thin spectra associated with X-ray transients or persistent flaring sources. The rise and decay phases are clearly defined. The "synchrotron bubble" model explains the rising phase behavior \cite{77–79}. Radio flares from X-ray transients show monotonic decay after several days, apparently caused by adiabatic expansion losses, characterized by consistent decay rates across all frequencies. Alternatively, significant energy loss through synchrotron radiation or inverse Compton scattering would cause faster decay at higher frequencies, steepening the spectrum.

Mirabel & Rodriguez \cite{73–75} first observed apparent superluminal motion in GRS 1915+105, allowing jet speed estimation after accounting for Doppler shifts. Direct measurements of steady jet speeds in BHXRB low/hard states are basically unavailable. However, clues suggest these jets may be mildly rather than highly relativistic. For intermittent jets in BHXRBs, such as the superluminal motions observed in GRS 1915+105, Lorentz factors $\Gamma \sim 2$ are generally considered appropriate—clearly relativistic but much less extreme than the most extreme AGN jets. However, Fender et al. \cite{15} suggest the Lorentz factor range may be much broader. With relatively precise distance estimates, jet Lorentz factors cannot be constrained by measuring radio component motions. Nevertheless, Fender & Kuulkers \cite{80} argue that the average Lorentz factor for BHXRB transients is likely $\Gamma \lesssim 5$; higher values would probably destroy the observed correlation between radio and X-ray peak fluxes.

Do jet speeds need to remain constant? In SS 433, they apparently do not—Eikenberry et al. \cite{81} showed variations exceeding 10%. Corbel et al. \cite{30} clearly observed jet deceleration in XTE J1550–564, likely resulting from interaction with the interstellar medium (ISM), a phenomenon that probably occurs to varying degrees in all X-ray binaries. In summary, steady jets in BHXRB low/hard states appear to be only mildly relativistic, while intermittent jets associated with X-ray transients almost certainly have much higher Lorentz factors that decrease over time through ISM interaction.

3.2 Steady Jets in the Low/Hard State

Low/hard state jets are characterized by "flat" spectra extending from radio to shorter wavelengths (spectral index $\alpha \sim 0$), linear polarization levels of 1%–3%, and power-law correlations between radio and X-ray flux evolution. These observational features, distinct from intermittent jets, are found in nearly every BHXRB in the low/hard state \cite{29}. By analogy with AGN, compact self-absorbed jets were proposed to explain these properties \cite{29,37,78,82}. Milliarcsecond imaging of Cyg X–1's low/hard state jet by Stirling et al. in 2001 confirmed this explanation \cite{83}. Low/hard state radio spectra appear "flat" or "inverted," extending to millimeter bands in Cyg X–1 and XTE J1118+480 \cite{29,84}. In most low/hard state sources, optical emission appears to lie on the flat extension of the radio spectrum \cite{85–86}. Jain et al. \cite{87} observed a secondary flare in XTE J1550–564's near-infrared light curve during its transition to the low/hard state, attributing it to self-absorbed synchrotron radiation from the jet. Rapid optical variability in XTE J1118+480 during the low/hard state can also be explained by self-absorbed synchrotron radiation. If the flat or inverted radio spectrum originates from self-absorbed synchrotron radiation in a conical jet, the spectrum should break at some frequency to an optically thin spectrum with spectral index $\alpha \sim 0.7$. Corbel et al. \cite{30} found such a break in GX 339–4's near-infrared band during the low/hard state.

After establishing that radio emission originates from steady self-absorbed synchrotron jets, the key is determining jet power. Estimates come from: (1) carefully measuring the synchrotron spectrum range; (2) introducing radiative efficiency to estimate total jet power:

$$
P_J = \frac{L_J}{\eta}F(\Gamma,i)
$$

where $L_J$ is total jet radiative luminosity (integrated from radio to the highest observed frequency), $\eta$ is radiative efficiency, and $F(\Gamma,i)$ is a correction factor for bulk relativistic motion with Lorentz factor $\Gamma$ and Doppler factor, where $i$ is the viewing angle \cite{29}.

A reasonable assumption is that all observed radio emission originates from synchrotron radiation \cite{71}, allowing investigation of how far the radio synchrotron spectrum extends to determine total synchrotron luminosity. For the transient XTE J1118+480, its low/hard state spectrum matches theoretical broadband predictions, showing clear excess in near-infrared and possibly optical bands, with radio spectrum smoothly connecting to 850 $\mu$m observations \cite{88}. Fender et al. \cite{29} argued that in this case, synchrotron luminosity exceeds observed X-ray luminosity by >10%. Estimating jet power then depends on radiative efficiency estimates. Fender & Pooley \cite{84} estimated $\eta \sim 0.1$ for GRS 1915+105's radio "oscillations." In Blandford & Konigl's original model \cite{36}, $\eta$ was likely $\lesssim 0.1$; in Markoff et al.'s model \cite{38}, $\eta \sim 0.15$; Celotti & Ghisellini \cite{89} estimated $\eta \sim 0.15$ for AGN samples. Theoretical studies of synchrotron processes in jets suggest $\eta > 0.2$ is unlikely and unsupported by observations. Therefore, for XTE J1118+480, jet power likely exceeds X-ray luminosity. Nearly all low/hard state BHXRBs show similar broadband spectral patterns; [FIGURE:6] shows broadband jet model fitting to GX 339–4's radio-X-ray spectrum in the low/hard state. It appears that almost all BHXRBs produce powerful steady jets in the low/hard state.

3.3 Jet Disappearance in the Soft State

The absence of radio compact jets in BHXRB soft X-ray states was first noted by Tananbaum et al. \cite{90} in 1972, who found Cyg X–1's radio flare associated with its transition from soft to hard state. Although radio variations were suspected to relate to X-ray properties, the specific pattern was unclear. In 1998, observations showing GX 339–4 remaining in the high/soft state for a year changed this situation. Prior to 1998, radio monitoring of GX 339–4 in the low/hard state had identified weak radio emission, but throughout the subsequent soft state, despite multiple observations, no radio emission was detected. The source then returned to the low/hard state, and weak radio emission reappeared \cite{8}. This provided strong evidence that radio emission is either absent or very weak in BHXRB soft states when the accretion disk dominates X-ray emission. High-cadence radio and X-ray observations of Cyg X–1 showed that radio emission is rapidly suppressed upon transition to the high/soft state, dropping to a few percent of Eddington luminosity \cite{91}. No counterexamples have been observed, leading to the conclusion that strong steady radio jets do not exist in BHXRB soft states. Klein-Wolt et al.'s \cite{92} long-term study of GRS 1915+105 also confirmed this, finding its soft states never associated with bright radio emission.

4 Studies on MAXI J1820+070

You et al. \cite{93} conducted a detailed study in 2021 of the 2018 outburst of the black hole X-ray binary MAXI J1820+070, revealing possible coronal configurations and behavior patterns in the hard state and providing new insights into accretion disk, corona, and jet behavior and disk-jet coupling. [FIGURE:7] shows MAXI J1820+070's light curves and hardness-intensity diagram (HID) from the 2018 outburst. The first outburst lasted from MJD 58200 to MJD 58286, with the source remaining in the hard state. Divided into rising and decaying phases based on X-ray luminosity, spectral fitting of X-ray spectra during this outburst showed that the reflection fraction rose sharply to ~0.5 during the rising phase, then slowly decreased to ~0.1 during the decay phase. The reflection fraction is defined as the ratio of coronal intensity illuminating the disk to that directly reaching the observer, meaning the proportion of coronal photons illuminating the disk increased during the rising phase and decreased during the decay phase.

Previous studies assumed a coronal geometry resembling a lighthouse-like point structure at a certain height above the black hole, where coronal height uniquely determines the reflection fraction for given model parameters. The relationship is: as the corona accelerates away from the black hole, beaming effects reduce disk illumination, decreasing the reflection fraction. Generally, the corona is believed to be located at the jet base \cite{95}, more complex than a lighthouse structure, characterized by two parameters—position and bulk velocity. You et al. \cite{93} studied the relationship between coronal parameters and reflection fraction, concluding that reflection fraction increases with decreasing coronal height, while increasing bulk velocity at a given height decreases reflection fraction. For MAXI J1820+070's decay phase, X-ray timing analysis indicated the corona contracted with decreasing height \cite{96}, which should increase reflection fraction. However, spectral fitting showed reflection fraction decreasing over time. To resolve this contradiction, You et al. \cite{93} proposed that as the corona contracted toward the black hole, the outflow velocity of coronal material increased significantly. In this scenario, the effect of coronal outflow on reflection fraction outweighs that of contraction toward the black hole, consistent with observations. [FIGURE:8] shows a schematic of their proposed coronal evolution.

You et al. \cite{97} revisited MAXI J1820+070's 2018 outburst in 2023, focusing on the transition from soft to hard state at the outburst's end and investigating multi-wavelength behavior and correlations from radio to X-ray bands. This study provided the first observational evidence for MAD formation around black holes. Specifically, during the decaying hard state, MAXI J1820+070 transitioned from soft to hard state after MJD 58380. Multi-wavelength light curve analysis revealed that radio emission lagged X-ray emission by 8 days, and optical emission lagged X-ray by 17 days. Such day-scale time lags between different wavelength emissions had never been observed in BHXRBs before. You et al. \cite{97} interpreted this as reflecting the MAD formation process.

Numerous observations support a basic structure of coexisting inner hot corona and outer cold thin disk. Interaction between corona and thin disk creates a truncated disk structure. In low-mass BHXRBs, matter from the companion first enters the thin disk. In inner disk regions, gas evaporates from the disk plane into the corona. In ADAF-structured coronae, when the accretion rate exceeds the critical rate where ion-electron equilibrium timescale equals accretion timescale, the corona condenses into a disk \cite{98}. When companion mass supply is insufficient to replenish evaporated gas, the accretion disk shows a truncated structure; otherwise it is non-truncated \cite{99}. Generally, low-mass X-ray binaries have non-truncated disks in the soft state, with an optically thick disk extending inward to the ISCO, as in MAXI J1820+070. At the moment the source left the soft state and entered the intermediate state (MJD 58381), the thin disk likely extended to the ISCO. However, after entering the intermediate state, enhanced hard X-ray radiation was clearly observed, indicating increased inverse Compton scattering, generally believed to originate from the jet base or ADAF. More interestingly, You et al. \cite{97} found radio emission lagged hard X-ray emission by about 8 days, far exceeding predictions from light travel time.

To explain the day-scale radio-X-ray lag, You et al. \cite{97} proposed that MAXI J1820+070's disk behavior could be explained by the truncated disk model \cite{100}. As described earlier, this model's basic structure is a standard thin disk truncated at radius $R_{\rm tr}$, with an inner ADAF extending to the ISCO. For MAXI J1820+070, the 8-day radio lag ruled out hard X-ray emission from a jet-base corona, suggesting hard X-rays likely originated from ADAF, with the inner ADAF region being the primary source. After MAXI J1820+070 left the soft state, spectral fitting indicated the truncation radius continued to increase while the accretion rate decreased. In this case, the total gravitational dissipation power of the ADAF increased with $R_{\rm tr}$, while the innermost region's radiative power decreased with accretion rate. These two mechanisms compete: initially $R_{\rm tr}$ effects dominate, causing hard X-ray flux to rise; when their effects become comparable, hard X-ray flux peaks around $t_1$ = MJD 58389; subsequently, accretion rate effects dominate, causing hard X-ray flux to decline. How does this disk structural evolution lead to observed day-scale radio delays? Magnetic fields must be considered. As discussed, ADAF's high radial velocity can drag and amplify weak external magnetic fields. Larger ADAFs are expected to drag and amplify external fields more efficiently. Although hard X-ray flux peaked at $t_1$ = MJD 58389, ADAF's magnetic field dragging continued to strengthen. The magnetic field at the ISCO didn't saturate and begin decreasing until $t_2$ = MJD 58397. Jet power increases with magnetic field strength near the black hole, so radio emission increases until peaking at $t_2$ = MJD 58397. This explains the observed 8-day radio lag behind hard X-rays.

Assuming substantial magnetic flux near the black hole, gravitational pressure from continuous matter accretion prevents magnetic field escape. Thus, magnetic fields accumulate within the magnetospheric radius $R_m$, interfering with the original accretion flow. Note that $R_m$ exceeds the horizon radius, indicating a region where the accretion flow is significantly affected by magnetic fields. When $r \geq R_m$, the accretion flow behaves like a standard ADAF. When $r < R_m$, the large-scale accretion flow breaks into small gas blobs or streams that must penetrate magnetic field layers to finally fall into the black hole, making the radial velocity in this region much slower than in the external accretion flow. This region is called a magnetically arrested accretion disk (MAD) \cite{70}. Observationally, MAD contributions to the spectrum are not clearly distinguishable from standard and normal evolution (SANE) accretion flows \cite{101}. Therefore, although MAD formation was predicted in BHXRBs, it had never been observed in black hole sources before. This study \cite{97} provides the first observational evidence for MAD formation around black holes. Based on the above accretion flow evolution model, during MAXI J1820+070's transition from soft to hard state, the magnetic field in the ADAF inner region continuously strengthened. This increasingly strong magnetic field in turn affected the ADAF structure itself, as magnetic pressure opposes gravitational pressure. Calculations show that after the hard X-ray peak, the magnetic field in the expanding ADAF's innermost region continued to be amplified, eventually dominating at the inner edge. When radio emission peaked (MJD 58397), the magnetic field strength near the black hole reached levels required for MAD formation, creating a magnetically arrested accretion disk in the ADAF's innermost region. [FIGURE:9] shows this overall scenario.

5 Summary and Outlook

Throughout their outburst cycles, black hole X-ray binaries experience several different accretion modes, from low/hard to high/soft states. The behavior of accretion disks, jets, and internal magnetic fields differs significantly among these modes. Multi-wavelength observations from radio through X-ray to gamma-ray bands are crucial for studying accretion processes, jet mechanisms, and ultimately understanding black holes \cite{35,102}.

Previous studies widely used SED fitting and correlation analysis to investigate the origins of multi-wavelength radiation and related physical processes \cite{8,103–104}. In recent years, increasing research combines timing and spectral analysis to explore multi-wavelength variability of accretion disks and jets in BHXRBs on different timescales \cite{93,105–106}. These studies have confirmed correlations between X-ray, optical, and radio emissions in BHXRBs and discovered minute-scale time delays between optical, X-ray, and radio bands. These results effectively constrain jet composition and geometry \cite{106}. You et al. \cite{97} discovered day-scale radio delays in MAXI J1820+070, far exceeding previous theoretical predictions. Considering magnetic field variations around black holes, combined with disk-jet coupling and truncated disk models, this observation can be quantitatively explained. Thus, magnetic field variations in BHXRBs have gained further attention, and we have for the first time observed the formation process of a MAD around a black hole.

Coordinated multi-wavelength observations are crucial for BHXRB research. Over the past 20 years, the number of X-ray space telescopes has increased, including RXTE (Rossi X-ray Timing Explorer), MAXI (Monitor of All-sky X-ray Image), and NuSTAR (Nuclear Spectroscopic Telescope Array). In 2017, China launched its first X-ray space telescope, Insight-HXMT. Its unique broadband X-ray observing capability, particularly its large effective area in the hard X-ray band, enables systematic study of various radiation processes from accretion disks to jets in BHXRBs, making it one of the few satellites worldwide capable of continuous observations across such a wide energy range. On January 9, 2024, China's first wide-field X-ray survey satellite, the "Einstein Probe" (EP), was successfully launched and continues operating. EP offers significant advantages in real-time survey capability and detection sensitivity, completing half the sky in half a day with sensitivity more than an order of magnitude higher than similar instruments. With increasing observational resources, joint observations between multiple detectors are becoming more frequent, greatly compensating for previous shortages of simultaneous data. More observational samples will enable more comprehensive and systematic studies of accretion flow dynamics and jet formation. Improved observational capabilities also make it possible to study BHXRBs during the very early and late stages of outbursts. It is foreseeable that our understanding of physical processes in these binary systems will greatly expand in the future.

References

Shakura N I, Sunyaev R A. A&A, 1973, 24: 337
Laor A. ApJ, 1991, 376: 90
Martocchia A, Karas V, Matt G. MNRAS, 2000, 312:
Haardt F, Maraschi L, Ghisellini G. ApJ, 1994, 432:
Spencer R E. Nature, 1979, 282: 483
Hjellming R M, Johnston K J. Nature, 1981, 290: 100
McClintock J E, Remillard R A. Black Hole Binaries // Lewin W H G, van der Klis M. Compact Stellar X-ray Sources. Cambridge: Cambridge University Press, 2006: 157
Corbel S, Fender R P, Tzioumis A K, et al. A&A, 2000, 359: 251
Corbel S, Nowak M A, Fender R P, et al. A&A, 2003, 400: 1007
Lasota J P, Narayan R, Yi I. A&A, 1996, 314: 813
Brocksopp C, Bandyopadhyay R M, Fender R P. NewA, 2004, 9: 249
Capitanio F, Belloni T M, Del Santo M, et al. MNRAS, 2009, 398: 1194
Fender R P, Belloni T M, Gallo E. MNRAS, 2004, 355: 1105
Fender R P, Homan J, Belloni T M. MNRAS, 2009, 396: 1370
Fender R, Corbel S, Tzioumis T. ApJ, 1999, 519: L165
van Paradijs J, McClintock J E. Optical and Ultraviolet Observations of X-ray Binaries // Lewin W H G, van Paradijs J, van der Heuvel E P J. X-ray Binaries. Cambridge: Cambridge University Press, 1995: 58
van den Heuvel E P J, Heise J. NPhS, 1972, 239: 67
Treves A. ApJ, 1980, 242: 1114
Cunningham C. ApJ, 1976, 208: 534
Vrtilek S D, Raymond J C, Garcia M R, et al. A&A, 1990, 235: 162
Homan J, Belloni T M. Ap&SS, 2005, 300: 107
Frank J, King A, Raine D J. Accretion Power in Astrophysics. 3rd ed. Cambridge: Cambridge University Press, 2002: 80
Kuulkers E. NewA, 1998, 42: 1
Soria R, Wu K, Johnston H M. MNRAS, 1999, 310: 71
Bailyn C D. ApJ, 1992, 391: 298
Greene J, Bailyn C D, Orosz J A. ApJ, 2001, 554:
Mikolajewska J, Rutkowski A, Goncalves D R, et al. MNRAS, 2005, 362: L13
Lovelace R V E, Rothstein D M, Bisnovatyi-Kogan G S. ApJ, 2009, 701: 885
Fender R P. MNRAS, 2001, 322: 31
Corbel S, Fender R P. ApJ, 2002, 573: L35
Markoff S, Nowak M, Corbel S. A&A, 2003, 397: 645
Zurita C, Casares J, Shahbaz T. ApJ, 2003, 582: 369
Merloni A, DiMatteo T, Fabian A C. MNRAS, 2000, 318: L15
Shahbaz T, Dhillon V S, Marsh T R, et al. MNRAS, 2003, 346: 1116
Guilet J, Ogilvie G I. MNRAS, 2012, 424: 2097
Guilet J, Ogilvie G I. MNRAS, 2013, 430: 822
Cao X W, Spruit H C. ApJ, 2013, 765: 149
Beckwith K, Hawley J F, Krolik J H. ApJ, 2009, 707:
Cao X W. MNRAS, 2018, 473: 4268
Li J W, Cao X W. ApJ, 2019, 872: 149
Pounds K A, Reeves J N, King A R, et al. MNRAS, 2003, 345: 705
Russell D M, Fender R P, Hynes R I, et al. MNRAS, 2006, 371: 1334
Pounds K, Lobban A, Reeves J, et al. MNRAS, 2016, 457: 2951
Blandford R D, Konigl A. ApJ, 1979, 232: 34
Falcke H, Biermann P L. A&A, 1996, 308: 321
Pounds K A, Lobban A, Reeves J N, et al. MNRAS, 2016, 459: 4389
Heinz S, Sunyaev R A. MNRAS, 2003, 343: L59
Migliari S, Fender R P. MNRAS, 2006, 366: 79
Cao X. ApJ, 2011, 737: 94
Narayan R, Igumenshchev I V, Abramowicz M A. PASJ, 2003, 55: L69
Narayan R. ApJ, 1996, 462: 136
Fender R. Jets from X-ray Binaries // Lewin W H G, van der Klis M. Compact Stellar X-ray Sources, 2006, 39: 381
Esin A A, McClintock J E, Narayan R. ApJ, 1997, 489: 865
Zdziarski A A, Lubinski P, Gilfanov M, et al. MNRAS, 2003, 342: 355
Bisnovatyi-Kogan G S, Ruzmaikin A A. Ap&SS, 1974, 28: 45
Mirabel I F, Rodriguez L F. Nature, 1994, 371: 46
Mirabel I F, Rodriguez L F. ARA&A, 1999, 37: 409
Rodriguez L F, Mirabel I F. ApJ, 1999, 511: 398
Bright J S, Fender R P, Motta S E. et al. NatAs, 2020, 4: 697
Bisnovatyi-Kogan G S, Ruzmaikin A A. Ap&SS, 1976, 42: 401
Longair M S. High Energy Astrophysics. Stars, the Galaxy and the Interstellar Medium. Cambridge: Cambridge University Press, 1994, 2: 331
Lubow S H, Papaloizou J C B, Pringle J E. MNRAS, 1994, 267: 235
Spruit H C, Uzdensky D A. ApJ, 2005, 629: 960
Konigl A, Pudritz R E. Disk Winds and the Accretion-Outflow Connection // Mannings V, Boss A P, Russell S S. Protostars and Planets IV. Tucson: University of Arizona Press, 2000: 759
Pudritz R E, Ouyed R, Fendt C, et al. Disk Winds, Jets, and Outflows: Theoretical and Computational Foundations // Reipurth B, Jewitt D, Keil K. Protostars and Planets V. Tucson: University of Arizona Press, 2007: 277
Spruit H C. Theory of Magnetically Powered Jets // Wolf B, Jurgen E, Klaus H. Lecture Notes in Physics. Berlin: Springer Verlag, 2010: 233
Blandford R D, Znajek R L. MNRAS, 1977, 179: 433
Blandford R D, Payne D G. MNRAS, 1982, 199: 883
Parker E N. Cosmical Magnetic Fields: Their Origin and Their Activity. Oxford: Clarendon Press, 1979:
Fender R P, Kuulkers E. MNRAS, 2001, 324: 923
Eikenberry S S, Matthews K, Muno M, et al. ApJ, 2002, 523: L33
Falcke H, Biermann P L. A&A, 1999, 342: 49
Stirling A M, Spencer R E, de la Force C J, et al. MNRAS, 2001, 327: 1273
Fender R P, Pooley G G. MNRAS, 2000, 318: L1
Brocksopp C, Jonker P G, Fender R P, et al. MNRAS, 2001, 323: 517
Corbel S. ApJ, 2001, 554: 43
Jain R K, Bailyn C D, Orosz J A, et al. ApJ, 2001, 554: L181
Hynes R I, Mauche C W, Haswell C A, et al. ApJ, 2000, 539: L37
Yousef T A, Brandenburg A, Rudiger G. A&A, 2003, 411: 321
Fromang S, Stone J M. A&A, 2009, 507: 19
Celotti A, Ghisellini G. MNRAS, 2008, 385: 283
Tananbaum H, Gursky H, Kellogg E, et al. ApJ, 1972, 177: L5
Guan X, Gammie C F. ApJ, 2009, 697: 1901
Cao X W, Spruit H C. A&A, 1994, 287: 80
Gallo E, Fender R P, Pooley G G. MNRAS, 2003, 344:
Klein-Wolt M, Fender R P, Pooley G G, et al. MNRAS, 2002, 331: 745
Yuan F, Narayan R. ARA&A, 2014, 52: 529
Xie F G, Zdziarski A A. ApJ, 2019, 887: 167
Homan J, Buxton M, Markoff S, et al. ApJ, 2005, 624:
You B, Tuo Y, Li C, et al. NatCo, 2021, 12: 1025
Dauser T, Garcia J, Walton D J, et al. A&A, 2016, 590: A76
Marino A, Barnier S, Petrucci P O, et al. A&A, 2021, 656: A63
Henri G, Pelletier G. ApJ, 1991, 383: L7
Coriat M, Corbel S, Prat L, et al. MNRAS, 2011, 414:
Kara E, Steiner J F, Fabian A C, et al. Nature, 2019, 565: 198
Tetarenko A J, Casella P, Miller-Jones J C A, et al. MNRAS, 2019, 484: 2987
Cao X W, You B, Yan Z. A&A, 2021, 654: A81
Tetarenko A J, Casella P, Miller-Jones J C A, et al. MNRAS, 2021, 504: 3862
Liu B F, Qiao E. Science, 2022, 25: 103544