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We provided a comprehensive study of the properties of the black hole in the low-mass X-ray binary system 4U 1543-47, specifically focusing on the 2021 outburst (MJD 59380–59470). Using observations from the Insight - HXMT mission, we employed X-ray reflection fitting method and analysed spectral data to estimate key black hole parameters. Through our investigation redbased on 6 out of the 52 available observations, we estimated the spin parameter of the black hole to be |$0.902_{-0.053}^{+0.054}$| and the inclination angle of the accretion disc to be |$28.91_{-1.24}^{+1.82}$| ° (90 per cent confidence limits, statistical only), then we discussed the influence of high luminosity. Based on the relxill series models are not suitable for thick disc scenario, and in comparison with findings from other studies, we propose that our estimation of the spin value may be exaggerated. [ABSTRACT FROM AUTHOR]

It is commonly believed that accretion discs are truncated and their inner regions are described by advection dominated accretion flows (ADAFs) in the hard spectral state of black hole X-ray binaries. However, the increasing occurrence of a relativistically blurred Fe K α line together with a hard continuum points to the existence of a thin disc located near the innermost stable circular orbit (ISCO). Assuming the accretion in the hard state is via an ADAF extending to near 100 Schwarzschild radii, which is supplied by either a stellar wind from a companion star or resulting from an evaporated disc, we study the possible condensation of the hot gas during its accretion towards the black hole. It is found that a small fraction of the ADAF condenses into a cold disc as a consequence of efficient radiative cooling at small distances, forming a disc-corona configuration near the ISCO. This takes place for low accretion rates corresponding to luminosities ranging from ∼10−3 to a few per cent of the Eddington luminosity. The coexistence of the weak inner disc and the dominant hot accretion flow provides a natural explanation of the broad K α line in the hard state. Detailed computations demonstrate that such accretion flows produce a hard X-ray spectrum accompanied by a weak disc component with a negative correlation between the 2 and 10 keV photon index and the Eddington ratio. The predicted spectrum of Cygnus X-1 and the correlation between the photon index and the Eddington ratio are in good agreement with observations. [ABSTRACT FROM AUTHOR]

Observationally, two main spectral states, i.e. the low/hard state and the high/soft state, are identified in black hole X-ray binaries (BH-XRBs). Meanwhile, the transitions between the two states are often observed. In this paper, we re-investigate the transition luminosities in the framework of the self-similar solution of the advection-dominated accretion flow (ADAF). Specifically, we search for the critical mass accretion rate |$\dot{m}_{\rm crit}$| of ADAF for different radii r , respectively. It is found that |$\dot{m}_{\rm crit}$| decreases with decreasing r. By testing the effects of BH mass m , the magnetic parameter β and the viscosity parameter α, it is found that only α has significant effects on |$\dot{m}_{\rm crit}\text{--}r$| relation. We define the minimum |$\dot{m}_{\rm crit}$| (roughly at the innermost stable circular orbit) as the hard-to-soft transition rate |$\dot{m}_{\rm tr:H\text{--} S}$|⁠ , above which BH will gradually transit from the low/hard state to the high/soft state, and |$\dot{m}_{\rm crit}$| at 30 Schwarzschild radii as the soft-to-hard transition rate |$\dot{m}_{\rm tr:S\rightarrow H}$|⁠ , below which BH will gradually transit from the high/soft state to the low/hard state. We derive fitting formulae of |$\dot{m}_{\rm tr:H\rightarrow S}$| and |$\dot{m}_{\rm tr:S\rightarrow H}$| as functions of α, respectively. By comparing with observations, it is found that the mean value of α are α ∼ 0.85 and α ∼ 0.33 for the hard-to-soft transition and the soft-to-hard transition, respectively, which indicates that two classes of α are needed for explaining the hysteresis effect during the state transition. Finally, we argue that such a constrained α may provide valuable clues for further exploring the accretion physics in BH-XRBs. [ABSTRACT FROM AUTHOR]

When neutron 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 exist 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 , b) 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 |$\epsilon \sim {\dot{M} GM\over R_{*}}/{\dot{M} c^2}\sim 0.2$| despite the existence of the hard surface. As a result, given an X-ray luminosity L 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 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 on to the surface of the NS forming the X-ray pulsation. [ABSTRACT FROM AUTHOR]

Observationally, an anticorrelation 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 0.5-10 keV, i.e. a softening of the X-ray spectrum with decreasing L 0.5-10 keV, is found in neutron star low-mass X-ray binaries (NS-LMXBs) in the range of |$L_{\rm 0.5\!-\!10\,keV}\sim 10^{34}\!-\!10^{36}\ \rm erg\ s^{-1}$|⁠. In this paper, we explain the observed anticorrelation between Γ and L 0.5–10 keV 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 anticorrelation between Γ and L 0.5–10 keV. In the ADAF model, there is a key parameter, f 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 th on the anticorrelation between Γ and L 0.5–10 keV. It is found that the value of f th can significantly affect the anticorrelation between Γ and L 0.5–10 keV. Specifically, the anticorrelation between Γ and L 0.5–10 keV becomes flatter with decreasing f th as taking f 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 0.5–10 keV, we find that indeed only a small value of 0.003 ≲ f th ≲ 0.1 is needed to match the observed anticorrelation between Γ and L 0.5–10 keV. Finally, we argue that the small value of f th ≲ 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 |$\epsilon \sim {\dot{M} GM\over R_{*}}/{\dot{M} c^2}\sim 0.2$|⁠. [ABSTRACT FROM AUTHOR]

We study the evolution of the temporal properties of MAXI J1820+070 during the 2018 outburst in its hard state from MJD 58,190 to 58,289 with Insight-HXMT in a broad energy band 1–150 keV. We find different behaviors of the hardness ratio, the fractional rms and time lag before and after MJD 58,257, suggesting a transition occurred around this point. The observed time lags between the soft photons in the 1–5 keV band and the hard photons in higher energy bands, up to 150 keV, are frequency-dependent: the time lags in the low-frequency range, 2–10 mHz, are both soft and hard lags with a timescale of dozens of seconds but without a clear trend along the outburst; the time lags in the high-frequency range, 1–10 Hz, are only hard lags with a timescale of tens of milliseconds; they first increase until around MJD 58,257 and decrease after this date. The high-frequency time lags are significantly correlated to the photon index derived from the fit to the quasi-simultaneous NICER spectrum in the 1–10 keV band. This result is qualitatively consistent with a model in which the high-frequency time lags are produced by Comptonization in a jet. [ABSTRACT FROM AUTHOR]

Observationally, the X-ray spectrum (0.5–10 keV) of low-level accreting neutron stars (NSs) (⁠|$L_{\rm 0.5{-}10\,\rm kev}\lesssim 10^{36}\ \rm erg \ s^{-1}$|⁠) 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 (⁠|$\eta \equiv L^{\rm power\ law}_{\rm 0.5{-}10\,\rm kev}/L_{\rm 0.5{-}10\,\rm kev}$|⁠) 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 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 (∼zero) with |$L_{\rm 0.5{-}10\,\rm kev}$| for different α with f th = 1, which is inconsistent with observations. Meanwhile, it is found that a change of f 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-low mass X-ray binaries probably dominated by low-level accretion on to NSs, it is found that a small value of f th ≲ 0.1 is needed to match the observed range of |$\eta \gtrsim 10{{\ \rm per\ cent}}$| in the diagram of η versus |$L_{\rm 0.5{-}10\,\rm kev}$|⁠. Finally, we argue that the small value of f th ≲ 0.1 implies that the radiative efficiency of NSs with an ADAF accretion may not be as high as the predicted result previously of |$\epsilon \sim {\dot{M} GM\over R_{*}}/{\dot{M} c^2}\sim 0.2$| despite the existence of the hard surface. [ABSTRACT FROM AUTHOR]

Observationally, for neutron star low-mass X-ray binaries, so far, the correlation between the radio luminosity L R and the X-ray luminosity L X, i.e. |$L_{\rm R}\propto L_{\rm X}^{\beta }$|⁠ , 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 ∼ 1.4 for 4U 1728-34, β ∼ 0.4 for Aql X-1, and β ∼ 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 flow (ADAF)-jet model, respectively. We calculate the emergent spectrum of the ADAF-jet model for L X and L R at different |$\dot{m}$| (⁠|$\dot{m}=\dot{M}/\dot{M}_{\rm Edd}$|⁠), adjusting η (⁠|$\eta \equiv \dot{M}_{\rm jet}/\dot{M}$|⁠ , describing the fraction of the accreted matter in the ADAF transferred 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. [ABSTRACT FROM AUTHOR]

The observed tight radio/X-ray correlation in the low spectral state of some black hole X-ray binaries implies the strong coupling of the accretion and jet. The correlation of Lr a LR ∝ Lx~0.5-0.7 was well explained by the coupling of a radiatively inefficient accretion flow and a jet. Recently, however, a growing number of sources show more complicated radio/X-ray correlations, e.g. LR ∝ Lx~1.4for LX/LEdd ≳ 10-3, which is suggested to be explained by the coupling of a radiatively efficient accretion flow and a jet. In this work, we interpret the deviation from the initial radio/X-ray correlation for LX/LEdd ≳ 10-3 with a detailed disc corona-jet model. In this model, the disc and corona are radiatively and dynamically coupled. Assuming a fraction of the matter in the accretion flow, η = Mjet/M, is ejected to form the jet, we can calculate the emergent spectrum of the disc corona-jet system. We calculate LR and LX at different M, adjusting η to fit the observed radio/X-ray correlation of the black hole X-ray transient H1743--322 for LX/LEdd > 10-3. It is found that always the X-ray emission is dominated by the disc corona and the radio emission is dominated by the jet. We noted that the value of η for the deviated radio/X-ray correlation for LX/LEdd > 10-3 is systematically less than that of the case for LX/LEdd < 10-3, which is consistent with the general idea that the jet is often relatively suppressed at the high-luminosity phase in black hole X-ray binaries. [ABSTRACT FROM AUTHOR]

Recent observations reveal that a cool disk may survive in the innermost stable circular orbit (ISCO) for some black hole X-ray binaries (BHXRBs) in the canonical low/hard state. The spectrum is characterized by a power law with a photon index Γ ~ 1.5-2.1 in the range of 2-10 keV and a weak disk component with a temperature of ~0.2 keV. In this work, we revisit the formation of such a cool, optically thick, geometrically thin disk in the innermost region of BHXRBs at the low/hard state within the context of disk accretion fed by condensation of the hot corona. By taking into account the cooling process associated with both Compton and conductive processes in a corona and the irradiation of the hot corona to the disk, we calculate the structure of the corona. For viscosity parameter α = 0.2, it is found that the inner disk can exist for an accretion rate ranging from M ~ 0.006 to 0.03 MEdd, over which the electron temperatures of the corona are in the range of 1-5 x 109 K producing the hard X-ray emission. We calculate the emergent spectra of the inner disk and corona for different mass accretion rates. The effect of viscosity parameter α and albedo a (a is defined as the energy ratio of reflected radiation from the surface of the thin disk to incident radiation upon it from the corona) on the emergent spectra is also presented. Our model is used to explain the recent observations of GX 339-4 and Cyg X-1, in which the thin disk may exist at the ISCO region in the low/hard state at a luminosity around a few percent of LEdd. It is found that the observed maximal effective temperature of the thermal component and the hard X-ray photon index Γ can be matched well by our model. [ABSTRACT FROM AUTHOR]