arXiv subjects

B. F. Liu

Publications and source records attributed to B. F. Liu.

At least 19 recordsLinked to original sources

arXiv2026

Hydrodynamical simulation of wind production from hot accretion flows in tidal disruption events

Wind is a key mechanism for supermassive black hole (SMBH) feedback to their host galaxies. In tidal disruption events (TDEs), black holes spend most of their time accreting at highly sub-Eddington rates, implying that feedback from persistent sub-Eddington winds could be significant. We investigate the effects of black hole mass, viscosity parameter and stellar debris temperature on the properties of winds from hot accretion flows in TDEs. We find that more massive black holes yield a higher accreted fraction and launch faster winds, while the debris temperature has a negligible influence on the accretion flow. For $\alpha=0.1$, the mildly-relativistic unbound winds ($\sim 0.1c$) are launched predominantly from the outside of the accretion flows along the equatorial plane, with a kinetic energy of $\sim10^{-4}L_\mathrm{Edd}$. In contrast, convective bound outflows dominate for $\alpha=0.01$, which differs from the true winds typically seen in active galactic nuclei and X-ray binaries. Potential applications for explaining delayed radio brightening in TDEs at $\sim10^3$ days and for searching for intermediate-mass black holes through radio and X-ray surveys are also discussed.

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arXiv2026

Einstein Probe discovery of EP J171159.4-333253: an eclipsing neutron star low-mass X-ray binary with clocked bursts

EP J171159.4-333253 is a new neutron-star low-mass X-ray binary discovered in outburst by the Einstein Probe (EP) on 2025 June 23, exhibiting clocked type-I X-ray bursts, eclipses and dips. In this paper, we report on the results of the X-ray spectral and timing analyses for EP J171159.4-333253 using data collected by EP and NuSTAR during the first 21 days of the outburst. The X-ray burst recurrence time can be characterized over a subset of nine bursts spanning 1.6 days around the NuSTAR observation, and the result is $t_{\rm rec}=8196 \pm 177\,$s with indications of a possible decreasing trend. From the X-ray eclipse events, the binary orbital period and the eclipse duration are estimated to be $P_{\rm orb}=6.48301 \pm 0.00003\,$hr and $D_{\star,X} = 1245.5^{+6.9}_{-6.5}\,$s, respectively. These enable an estimate of the mass and radius of the companion star and the binary inclination, which are $M_2\approx0.6-0.8\,M_\odot$, $R_2\approx0.7-0.8\,R_\odot$ and $i\approx73-75^\circ$, respectively. We also report on joint ULTRACAM and EP observations on 2025 July 21--22, detecting the source optical counterpart and covering an eclipse in both X-ray and optical bands. The optical eclipse is wavelength-dependent and broader than in X-rays, indicating that part of the optical emission arises from an extended region in the accretion flow. Despite a moderate variation in the source flux, the properties of the persistent X-ray emission are typical of a hard spectral state. We further evaluated the ratio of the accretion energy to the thermonuclear energy to be 120--130, implying helium bursts with the accreted hydrogen being depleted in-between bursts.

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arXiv2025

Accretion geometry in neutron star low-mass X-ray binaries during the hard spectral state

We investigate the accretion geometry in neutron star low-mass X-ray binaries (LMXBs) in the hard spectral state. It is commonly accepted that, for low mass transfer rates, an advection-dominated accretion flow (ADAF) is present in the inner region. But the observed relativistically broadened emission lines in the reflection spectra clearly indicate the existence of discs near the innermost stable circular orbit $(R_{\rm{ISCO}})$. We investigate the interaction between the coronal flow and the disc in neutron star LMXBs, and find that gas condensation from the dominant, coronal accretion flow to an inner disc is enhanced as compared to that in black hole LMXBs as a consequence of irradiation of the corona by the neutron star surface. Computations show that for low mass transfer rates ($\sim 0.005-0.02$ Eddington rate) a persistent weak disc can coexist with a coronal flow in the innermost region, where a pure ADAF would have been expected. The inner disc extends outwards from $R_{\rm{ISCO}}$ to $\sim 10 R_{\rm{ISCO}}$ for Eddington ratios ($L/L_{\rm{Edd}}$) as low as $\sim 0.002$, covers a larger region for higher Eddington ratios, and eventually connects to the outer disc at $L/L_{\rm{Edd}} \sim 0.02$, thereby transiting to a soft state. We demonstrate that the observationally inferred region of the broad iron lines in the hard-state sources generally lies within the extension of the inner discs predicted by the condensation model. Disappearance of the broad iron lines is predicted at very low luminosities, either caused by very low accretion rates or disc truncation by strong magnetic fields.

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arXiv2025

Accretion with two-phase gas supply and its application in black hole X-ray binaries

Accretion in black hole X-ray binaries is commonly believed to be supplied by the Roche lobe overflow or the stellar wind. The former is thought to form a geometrically thin disc while the diffuse wind could form a geometrically thick hot accretion flow. In this paper, we instead consider a more generalised case, i.e., accretion with both cold and hot gas supplies, which feed a disc and a corona respectively. We investigate the interaction of disc and corona by analysing the energy coupling and matter exchange, i.e. corona condensation/disc evaporation, with a semi-analytical method. It is found that the accretion geometry in the radial direction and the resultant emission spectrum depend strongly on both the total gas supply rate and the ratio of cold and hot gases. For gas supply rates of a few percent of the Eddington value, diverse geometries and spectral shapes are possible, depending on the fraction of cold gas supply. This provides an interpretation for the various spectra observed in intermediate states. However, at higher accretion rates, regardless of the form of the feeding gas, the inner accretion flow is always disc-dominated, implying an inevitable transition to the soft state, while at very low gas supply rates, hard state spectrum dominated by the hot flow is expected. We also present the predicted hardness-intensity correlation of Cygnus X-1, and constrain the value of the viscosity parameter of the accretion flow to the range of 0.25--0.35 by comparing our results with MAXI observations.

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arXiv2025

Einstein Probe Discovery of EP J182730.0-095633: A New Black Hole X-ray Binary Candidate in Faint Outburst?

Black hole X-ray binaries (candidates) currently identified in our galaxy are mainly transient sources, with the majority discovered through the detection of their X-ray outbursts. Among these, only four were found during faint outbursts exhibiting peak X-ray luminosities $L_{\rm X}\lesssim10^{36}~{\rm erg~s^{-1}}$, likely due to the previous lack of sensitive, wide-field monitoring instruments in the X-ray band. In this Letter, we present the discovery of an intriguing X-ray transient, EP J182730.0-095633, via the Einstein Probe (EP) and subsequent multi-wavelength follow-up studies. This transient, located on the Galactic plane, experienced a faint and brief X-ray outburst lasting about 20 days. Its X-ray spectrum is non-thermal and consistent with a power-law model with a nearly constant photon index of $Γ\sim2$ throughout the outburst. A long-lasting millihertz quasi-periodic oscillation (QPO) signal was detected in its X-ray light curve, centered around a frequency of $\sim0.04$ Hz. A transient near-infrared source was identified as its counterpart, although no optical emission was detectable, likely due to significant extinction. A radio counterpart was also observed, displaying an inverted radio spectrum with $α\sim0.45$. The X-ray spectral and temporal characteristics, along with the multi-wavelength properties, indicate that the source is a faint low-mass X-ray binary, with the compact object likely being a black hole. This work demonstrates the potential of the EP in discovering new X-ray binaries by capturing faint-level X-ray outbursts.

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arXiv2025

The effectively optically thin accretion flow and its implication in supermassive black holes

Based on a unified description of various accretion flows, we find a long-ignored solution - the effectively optically thin accretion flow, occurring at accretion rates around Eddington value. As a consequence of radiation-pressure dominance, the density in a standard thin disc (SSD) decreases with the increase of accretion rates, making the innermost region effectively optically thin. Further increase in accretion rate leads to a rise of the temperature so that the Compton cooling is able to balance the accretion released energy. We demonstrate that the effectively optically thin flow is characterized by moderate temperature and large scattering optical depth, producing a multi-color Wien spectrum. For an appropriate accretion rate, the accretion flow transforms from an outer SSD to an inner effectively optically thin flow. Thus, the spectra of the whole accretion flow exhibit two components, i.e., a multi-color Wien spectrum at higher frequency and a multi-color blackbody, the former could provide an alternative origin of soft X-ray excess or formation of warm corona in active galactic nuclei (AGNs). Our stability analysis proves it is thermally stable and viscously unstable, indicating its existence in accreting systems. We show that effectively optically thin accretion flow exists in supermassive black holes for accretion rates around 0.1 to 10 times Eddington value, bridging the SSD at low accretion rates and slim disc at high rates. By comparing the predictions and average spectra of AGN, we constrain the viscosity parameter to be $α\sim 0.03$, in good agreement with that derived from observed variability.

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arXiv2025

A generalized solution for advection-dominated accretion flow, standard disc, and slim disc

Aiming at a general description of four basic solutions describing the accretion processes, i.e., the Shakura-Sunyaev thin disc (SSD), the Shapiro-Lightman-Eardley solution (SLE), the slim disc, and the advection-dominated accretion flow (ADAF), we present generalized axisymmetric height-averaged equations, where the entropy advection, the radiation pressure, and photon trapping effect are all included self-consistently. Our generalized solution can reproduce the ADAF, SLE, SSD, and slim disc branches in a wide range of accretion rates from sub- to super-Eddington accretion. An S-curve in the $\dot{m}-Σ$ plane is also reproduced, representing the SSD branch, the radiation-pressure-dominant branch, and the slim disc branch. The solution gives a natural transition between SSD and slim disc when photon trapping occurs in the accretion flow, producing a radially hybrid SSD-slim disc structure in a certain range of accretion rates. The coexistence of ADAF and SSD below a critical accretion rate is clearly shown with distinct advection fraction of accretion energy. We also present the luminosity, radiation efficiency, and spectrum from the generalized solutions for a large range of accretion rates in stellar mass black holes.

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arXiv2024

A large population of neutron star low-mass X-ray binaries with long outburst recurrence time ?

Low-mass X-ray binaries (LMXBs) with neutron stars show quite different features which depend on the rate of mass transfer from the donor star. With a high transfer rate the Z sources are in a persistent soft spectral state, with a moderate rate the transient Atoll sources have outburst cycles like the black hole X-ray binaries. The observations document very long outburst recurrence times for quite a number of sources. We follow with our computations the evolution of the accretion disc until the onset of the ionization instability. For sources with a low mass transfer rate the accumulation of matter in the disc is essentially reduced due to the continuous evaporation of matter from the disc to the coronal flow. Different mass transfer rates result in nearly the same amount of matter accumulated for the outburst which means the outburst properties are similar for sources with short and sources with long outburst cycles, contrary to some expectations. Then of systems with long recurrence time less sources will be detected and the total population of LMXBs could be larger than it appears. This would relieve the apparent problem that the observed number of LMXBs as progenitors of millisecond pulsars (MSP) is too small compared to the number of MSP. Concerning the few quasi-persistent sources with year-long soft states we argue that these states are not outbursts, but quasi-stationary hot states as in Z sources.

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arXiv2023

Magnetic-Reconnection-Heated Corona Model: Implication of Hybrid Electrons for Hard X-ray Emission of Luminous Active Galactic Nuclei

It is widely accepted that X-ray emission in luminous active galactic nuclei (AGNs) originates from hot corona. To prevent the corona from over-cooling by strong X-ray emission, steady heating to the corona is essential, for which the most promising mechanisms is the magnetic reconnection. Detailed studies of the coupled disc and corona, in the frame of magnetic field transferring accretion-released energy from the disc to the corona, reveal that the thermal electrons can only produce X-ray spectrum with $Γ_{\rm 2-10\,keV}>2.1$, which is an inevitable consequence of the radiative coupling of the thermal corona and disc. In the present work, we develop the magnetic-reconnection-heated corona model by taking into account the potential non-thermal electrons accelerated in the magnetic reconnection process, in addition to the thermal electrons. We show that the features of the structure and spectrum of the coupled disc and corona can be affected by the fraction of magnetic energy allocated to thermal electrons. Furthermore, we investigate the effects of the power-law index and energy range of non-thermal electrons and the magnetic field on the spectrum. It is found that the X-ray spectrum from the Comptonization of the hybrid electrons can be flatter than that from thermal electrons only, in agreement with observations. By comparing with the observed hard X-ray data, we suggest that a large fraction ($>40\%$) of the magnetic energy be allocated to the non-thermal electrons in the luminous and flat X-ray spectrum AGNs.

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arXiv2022

Accretion around black holes: The geometry and spectra

Observations of black hole X-ray binaries and active galactic nuclei indicate that the accretion flows around black holes are composed of hot and cold gas, which have been theoretically described in terms of either a hot geometrically thick corona lying above and below a cold geometrically thin disk or an inner advection dominated accretion flow connected to an outer thin disk. This article reviews the accretion flows around black holes, with an emphasis on the physics that determines the configuration of hot and cold accreting gas, and how the configuration varies with the accretion rate and thereby produces various luminosity and spectra.

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arXiv2021

The radiative efficiency of neutron stars at low-level accretion

When neutrons star low-mass X-ray binaries (NS-LMXBs) are in the low-level accretion regime (i.e., $L_{\rm X}\lesssim 10^{36}\ \rm erg\ s^{-1}$), the accretion flow in the inner region around the NS is expected to be existed in the form of the hot accretion flow, e.g., the advection-dominated accretion flow (ADAF) as that in black hole X-ray binaries. Following our previous studies in Qiao $\&$ Liu 2020a and 2020b on the ADAF accretion around NSs, in this paper, we investigate the radiative efficiency of NSs with an ADAF accretion in detail, showing that the radiative efficiency of NSs with an ADAF accretion is much lower than that of $ε\sim {\dot M GM\over R_{*}}/{\dot M c^2}\sim 0.2$ despite the existence of the hard surface. As a result, given a X-ray luminosity $L_{\rm X}$ (e.g., between 0.5 and 10 keV), $\dot M$ calculated by $\dot M=L_{\rm X}{R_{*}\over {GM}}$ is lower than the real $\dot M$ calculated within the framework of the ADAF accretion. The real $\dot M$ can be more than two orders of magnitude higher than that of calculated by $\dot M=L_{\rm X}{R_{*}\over {GM}}$ with appropriate model parameters. Finally, we discuss that if applicable, the model of ADAF accretion around a NS can be applied to explain the observed millisecond X-ray pulsation in some NS-LMXBs (such as PSR J1023+0038, XSS J12270-4859 and IGR J17379-3747) at a lower X-ray luminosity of a few times of $10^{33}\ \rm erg\ s^{-1}$, since at this X-ray luminosity the calculated $\dot M$ with the model of ADAF accretion can be high enough to drive a fraction of the matter in the accretion flow to be channelled onto the surface of the NS forming the X-ray pulsation.

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arXiv2020

The advection-dominated accretion flow for the anti-correlation between the X-ray photon index and the X-ray luminosity in neutron star low-mass X-ray binaries

Observationally, an anti-correlation between the X-ray photon index $Γ$ (obtained by fitting the X-ray spectrum between 0.5 and 10 keV with a single power law) and the X-ray luminosity $L_{\rm 0.5-10keV}$, is found in neutron star low-mass X-ray binaries (NS-LMXBs) in the range of $L_{\rm 0.5-10keV}\sim 10^{34}-10^{36}\ \rm erg\ s^{-1}$. In this paper, we explain the observed anti-correlation between $Γ$ and $L_{\rm 0.5-10keV}$ within the framework of the self-similar solution of the advection-dominated accretion flow (ADAF) around a weakly magnetized NS. The ADAF model intrinsically predicts an anti-correlation between $Γ$ and $L_{\rm 0.5-10keV}$. In the ADAF model, there is a key parameter, $f_{\rm th}$, which describes the fraction of the ADAF energy released at the surface of the NS as thermal emission to be scattered in the ADAF. We test the effect of $f_{\rm th}$ on the anti-correlation between $Γ$ and $L_{\rm 0.5-10keV}$. It is found that the value of $f_{\rm th}$ can significantly affect the anti-correlation between $Γ$ and $L_{\rm 0.5-10keV}$. Specifically, the anti-correlation between $Γ$ and $L_{\rm 0.5-10keV}$ becomes flatter with decreasing $f_{\rm th}$ as taking $f_{\rm th}=0.1, 0.03, 0.01, 0.005$, $0.003$ and $0$ respectively. By comparing with a sample of non-pulsating NS-LMXBs with well measured $Γ$ and $L_{\rm 0.5-10keV}$, we find that indeed only a small value of $0.003\lesssim f_{\rm th}\lesssim 0.1$ is needed to match the observed anti-correlation between $Γ$ and $L_{\rm 0.5-10keV}$. Finally, we argue that the small value of $f_{\rm th}\lesssim 0.1$ derived in this paper further confirms our previous conclusion that the radiative efficiency of NSs with an ADAF accretion may not be as high as $ε\sim {\dot M GM\over R_{*}}/{\dot M c^2}\sim 0.2$.

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arXiv2020

Magnetic-reconnection-heated corona in active galactic nuclei: refined disc-corona model and application to broad-band radiation

A long-standing question in active galactic nucleus (AGN) research is how the corona is heated up to produce X-ray radiation much stronger than that arising from the viscous heating within the corona. In this paper, we carry out detailed investigations of magnetic-reconnection heating to the corona, specifically, studying how the disc and corona are self-consistently coupled with the magnetic field, and how the emergent spectra depend on the fundamental parameters of AGN. It is shown that diverse spectral shapes and luminosities over a broad bandpass from optical to X-ray can be produced from the coupled disc and corona within a limited range of the black hole mass, accretion rate and magnetic field strength. The relative strength of X-ray emission with respect to optical/ultraviolet (UV) depends on the strength of the magnetic field in the disc, which, together with accretion rate, determines the fraction of accretion energy transported and released in the corona. This refined disc-corona model is then applied to reproduce the broad-band spectral energy distributions (SEDs) of a sample of 20 bright local AGNs observed simultaneously in X-ray and optical/UV. We find that, in general, the overall observed broad-band SEDs can be reasonably reproduced, except for rather hard X-ray spectral shapes in some objects. The radiation pressure-dominant region, as previously predicted for the standard accretion disc in AGN, disappears for strong X-ray sources, revealing that AGN accretion discs are indeed commonly stable as observed. Our study suggests the disc-corona coupling model involving magnetic fields to be a promising approach for understanding the broad-band spectra of bright AGNs.

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arXiv2020

Wind accretion in Cygnus X-1

Context: Cygnus X-1 is a black hole X-ray binary system in which the black hole captures and accretes gas from the strong stellar wind emitted by its supergiant O9.7 companion star. The irradiation of the supergiant star essentially determines the flow properties of the stellar wind and the X-ray luminosity from the system. The results of three-dimensional hydrodynamical simulations of wind-fed X-ray binary systems reported in recent work reveal that the ionizing feedback of the X-ray irradiation leads to the existence of two stable states with either a soft or a hard spectrum. Aims: We discuss the observed radiation of Cygnus X-1 in the soft and hard state in the context of mass flow in the corona and disk, as predicted by the recent application of a condensation model. Methods: The rates of gas condensation from the corona to the disk for Cygnus X-1 are determined, and the spectra of the hard and soft radiation are computed. The theoretical results are compared with the MAXI observations of Cygnus X-1 from 2009 to 2018. In particular, we evaluate the hardness-intensity diagrams (HIDs) for its ten episodes of soft and hard states which show that Cygnus X-1 is distinct in its spectral changes as compared to those found in the HIDs of low-mass X-ray binaries. Results: The theoretically derived values of photon counts and hardness are in approximate agreement with the observed data in the HID. However, the scatter in the diagram is not reproduced. Improved agreement could result from variations in the viscosity associated with clumping in the stellar wind and corresponding changes of the magnetic fields in the disk. The observed dipping events in the hard state may also contribute to the scatter and to a harder spectrum than predicted by the model.

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arXiv2019

A systematic study of the advection-dominated accretion flow for the origin of the X-ray emission in weakly magnetized low-level accreting neutron star

Observationally, the X-ray spectrum ($0.5-10$ keV) of low-level accreting neutron stars (NSs) can generally be well fitted by the model with two components, i.e, a thermal soft X-ray component plus a power-law component. Meanwhile, the fractional contribution of the power-law luminosity $η$ ($η\equiv L^{\rm power\ law}_{\rm 0.5-10\rm keV}/L_{\rm 0.5-10\rm keV}$) varies with the X-ray luminosity $L_{\rm 0.5-10\rm keV}$. In this paper, we systematically investigate the origin of such X-ray emission within the framework of the advection-dominated accretion flow (ADAF) around a weakly magnetized NS, in which the thermal soft X-ray component arises from the surface of the NS and the power-law component arises from the ADAF itself. We test the effects of the viscosity parameter $α$ in the ADAF and thermalized parameter $f_{\rm th}$ (describing the fraction of the ADAF energy released at the surface of the NS as thermal emission) on the relation of $η$ versus $L_{\rm 0.5-10\rm keV}$. It is found that $η$ is nearly a constant ($\sim$ zero) with $L_{\rm 0.5-10\rm keV}$ for different $α$ with $f_{\rm th}=1$, which is inconsistent with observations. Meanwhile, it is found that a change of $f_{\rm th}$ can significantly change the relation of $η$ versus $L_{\rm 0.5-10\rm keV}$. By comparing with a sample of non-pulsating NS-LMXBs probably dominated by low-level accretion onto NSs, it is found that a small value of $f_{\rm th} \lesssim 0.1$ is needed to match the observed range of $η\gtrsim 10\%$ in the diagram of $η$ versus $L_{\rm 0.5-10\rm keV}$. Finally, we argue that the small value of $f_{\rm th} \lesssim 0.1$ implies that the radiative efficiency of NSs with an ADAF accretion may not be as high as the predicted result previously of $ε\sim {\dot M GM\over R_{*}}/{\dot M c^2}\sim 0.2$ despite the existence of the hard surface.

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arXiv2019

A model for the radio/X-ray correlation in three neutron star low-mass X-ray binaries 4U 1728-34, Aql X-1 and EXO 1745-248

Observationally, for neutron star low-mass X-ray binaries, so far, the correlation between the radio luminosity $L_{\rm R}$ and the X-ray luminosity $L_{\rm X}$, i.e., $L_{\rm R}\propto L_{\rm X}^β$, has been reasonably well-established only in three sources 4U 1728-34, Aql X-1 and EXO 1745-248 in their hard state. The slope $β$ of the radio/X-ray correlation of the three sources is different, i.e., $β\sim 1.4$ for 4U 1728-34, $β\sim 0.4$ for Aql X-1, and $β\sim 1.6$ for EXO 1745-248. In this paper, for the first time we explain the different radio/X-ray correlation of 4U 1728-34, Aql X-1 and EXO 1745-248 with the coupled advection-dominated accretion (ADAF)-jet model respectively. We calculate the emergent spectrum of the ADAF-jet model for $L_{\rm X}$ and $L_{\rm R}$ at different $\dot m$ ($\dot m=\dot M/\dot M_{\rm Edd}$), adjusting $η$ ($η\equiv \dot M_{\rm jet}/\dot M$, describing the fraction of the accreted matter in the ADAF transfered vertically forming the jet) to fit the observed radio/X-ray correlations. Then we derive a fitting formula of $η$ as a function of $\dot m$ for 4U 1728-34, Aql X-1 and EXO 1745-248 respectively. If the relation between $η$ and $\dot m$ can be extrapolated down to a lower value of $\dot m$, we find that in a wide range of $\dot m$, the value of $η$ in Aql X-1 is greater than that of in 4U 1728-34 and EXO 1745-248, implying that Aql X-1 may have a relatively stronger large-scale magnetic field, which is supported by the discovery of the coherent millisecond X-ray pulsation in Aql X-1.

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arXiv2018

The advection-dominated accretion flow for the origin of the thermal soft X-ray component in low-level accreting neutron stars

A thermal soft X-ray component is often detected in low-level accreting neutron stars (NSs), but is not detected in low-level accreting stellar-mass black holes (BHs). In this paper, we investigate the origin of such a thermal soft X-ray component in the framework of the self-similar solution of the advection-dominated accretion flow (ADAF) around NSs. It is assumed that a fraction, $f_{\rm th}$, of the energy transferred onto the surface of the NS is thermalized at the surface of the NS as the soft photons to be scattered in the ADAF. We self-consistently calculate the structure and the corresponding emergent spectrum of the ADAF by considering the radiative coupling between the soft photons from the surface of the NS and the ADAF itself. We show that the Compton $y$-parameter of the ADAF for NSs is systematically lower than that of BHs. Meanwhile, we find that the temperature of the thermal soft X-ray component in NSs decreases with decreasing mass accretion rate, which is qualitatively consistent with observations. We test the effect of $f_{\rm th}$ on the structure, as well as the emergent spectrum of the ADAF. It is found that a change of $f_{\rm th}$ can significantly change the temperature of the thermal soft X-ray component as well as the spectral slope in hard X-rays. Finally, it is suggested that the value of $f_{\rm th}$ can be constrained by fitting the high-quality X-ray data, such as the $\it XMM$-$\it Newton$ spectrum between 0.5-10 keV in the future work.

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arXiv2018

A Model for Spectral States and Their Transition in Cyg X-1

A new accretion picture based on a small disk surrounding a black hole is developed for the wind-fed source Cyg X-1. The hard and soft spectral states of Cyg X-1 are interpreted in terms of co-spatial two component flows for the innermost region of an accretion disk. The state transitions result from the outward expansion and inward recession of this inner disk for the hard to soft and soft to hard transition respectively. The theoretical framework for state transitions in black hole X-ray binaries with high mass companions involving a change in the inner disk size, thus, differs from systems with low mass companions involving the change in the outer disk size. This fundamental difference stems from the fact that matter captured and supplied to the black hole in wind-fed systems has low specific angular momentum and is hot essentially heated in the bow and spiral shocks, whereas it has high specific angular momentum and is cool in Roche lobe overflow systems. The existence of a weak cool disk around the ISCO region in the hard state allows for the presence of a relativistically broadened Fe K line. The small disk fed by gas condensation forms without an extensive outer disk, precluding thermal instabilities and large outbursts, resulting in the lack of large amplitude outbursts and hysteresis effects in the light curve of high mass black hole X-ray binaries. Their relatively persistent X-ray emission is attributed to their wind-fed nature.

astro-ph.HE↗