arXiv subjects

B. F. Liu

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

At least 37 records · Page 2Linked to original sources

arXiv2018

A systematic study of the condensation of the corona and the application for $Γ_{\rm 2-10keV}-L_{\rm bol}/L_{\rm Edd}$ correlation in luminous active galactic nuclei

In this paper, we explained the observed $Γ_{\rm 2-10keV}-L_{\rm bol}/L_{\rm Edd}$ correlation in luminous active galactic nuclei within the framework of the condensation of the corona around a supermassive black hole (Liu et al. 2015; Qiao & Liu 2017). Specifically, we systemically test the effects of black hole mass $M$, the viscosity parameter $α$, and the magnetic parameter $β$ (with magnetic pressure $p_{\rm m}=B^2/{8π}=(1-β)p_{\rm tot}$, $p_{\rm tot}=p_{\rm gas}+p_{\rm m}$) on the structure of the accretion disc and the corona, as well as the corresponding emergent spectra. It is found that the hard X-ray photon index $Γ_{\rm 2-10keV}$ nearly does not change with changing black hole mass $M$, or changing magnetic parameter $β$. Meanwhile, it is found that the geometry of the accretion flow, i.e., the relative configuration of the disc and corona, as well as the emergent spectra can be strongly affected by changing the value of $α$. By comparing with a sample composed of 29 luminous active galactic nuclei with well constrained X-ray spectra and Eddington ratios, it is found that the observed $Γ_{\rm 2-10keV}-L_{\rm bol}/L_{\rm Edd}$ correlation can be well matched with a relatively bigger value of $α$, i.e., $α\sim 1$, as previously also suggested by Narayan (1996) for luminous accreting black holes.

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arXiv2017

Interaction of the accretion flows in corona and disk near the black hole in AGN

Accretion flows toward black holes can be of a quite different nature, described as an optically thick cool gas flow in a disk for high accretion rates or as a hot coronal optically thin gas flow for low accretion rates, possibly affected by outflowing gas. The detection of broad iron emission lines in active galactic nuclei (AGN) indicates the coexistence of corona and disk. The appearance and relative strength of such flows essentially depends on their interaction. Liu et al. suggested that condensation of gas from the corona to the disk allows to understand accretion flows of comparable strength of emission. Matter inflow due to gravitational capture of gas is important for the condensation process. We discuss observational features predicted by the model. Data from simultaneous observations of AGN with {\it {Swift's}} X-ray and UV-optical telescopes are compared with the theoretical predictions. The frequent detection of broad iron K$α$ emission lines and the dependence of the emitted spectra on the Eddington ratio, described by the values of the photon index $Γ$ and the two-point spectral index $α_{\rm{ox}}$ are in approximate agreement with the predictions of the condensation model; the latter, however, with a large scatter. The model further yields a coronal emission concentrated in a narrow inner region as is also deduced from the analysis of emissivity profiles. The accretion flows in bright AGN could be described by the accretion of stellar wind or interstellar medium and its condensation into a thin disk.

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arXiv2017

Centrally Concentrated X-ray Radiation from an Extended Accreting Corona in Active Galactic Nuclei

The X-ray emission from bright active galactic nuclei (AGNs) is believed to originate in a hot corona lying above a cold, geometrically thin accretion disk. A highly concentrated corona located within $\sim10$ gravitational radii above the black hole is inferred from observations. Based on the accretion of interstellar medium/wind, a disk corona model has been proposed in which the corona is well coupled to the disk by radiation, thermal conduction, as well as by mass exchange \citep{Liu2015, Qiao2017}. Such a model avoids artificial energy input to the corona and has been used to interpret the spectral features observed in AGN. In this work, it is shown that the bulk emission size of the corona is very small for the extended accretion flow in our model. More than 80\% of the hard X-ray power is emitted from a small region confined within 10 Schwarzschild radii around a non-spinning black hole, which is expected to be even smaller accordingly for a spinning black hole. Here, the corona emission is more extended at higher Eddington ratios. The compactness parameter of the corona, $l={L\over R}{σ_{\rm T}\over m_{\rm e} c^3}$, is shown to be in the range of 1-33 for Eddington ratios of 0.02 - 0.1. Combined with the electron temperature in the corona, this indicates that electron--positron pair production is not dominant in this regime. A positive relation between the compactness parameter and photon index is also predicted. By comparing the above model predictions with observational features, we find that the model is in agreement with observations.

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arXiv2017

The condensation of the corona for the correlation between the hard X-ray photon index $Γ$ and the reflection scaling factor $\Re$ in active galactic nuclei

Observationally, it is found that there is a strong correlation between the hard X-ray photon index $Γ$ and the Compton reflection scaling factor $\Re$ in active galactic nuclei. In this paper, we propose that the $Γ-\Re$ correlation can be explained within the framework of the condensation of the hot corona onto the cold accretion disc around a supermassive black hole. In the model, it is presumed that, initially, a vertically extended hot gas (corona) is supplied to the central supermassive black hole by capturing the interstellar medium and stellar wind. In this scenario, when the initial mass accretion rate $\dot M/ \dot M_{\rm Edd} \gtrsim 0.01$, at a critical radius $r_{\rm d}$, part of the hot gas begins to condense onto the equatorial disc plane of the black hole, forming an inner cold accretion disc. Then the matter is accreted in the form of the disc-corona structure extending down to the innermost stable circular orbits of the black hole. The size of the inner disc is determined by the initial mass accretion rate. With the increase of the initial mass accretion rate, the size of the inner disc increases, which results in both the increase of the Compton reflection scaling factor $\Re$ and the increase of the hard X-ray photon index $Γ$. By comparing with a sample of Seyfert galaxies with well-fitted X-ray spectra, it is found that our model can roughly explain the observations. Finally, we discuss the possibility to apply our model to high mass X-ray binaries, which are believed to be fueled by the hot wind from the companion star.

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arXiv2016

Revisiting the structure and spectrum of the magnetic-reconnection-heated corona in luminous AGNs

It is believed that the hard X-ray emission in the luminous active galactic nuclei (AGNs) is from the hot corona above the cool accretion disk. However, the formation of the corona is still debated. Liu et al. investigated the spectrum of the corona heated by the reconnection of the magnetic field generated by dynamo action in the thin disk and emerging into the corona as a result of buoyancy instability. In the present paper, we improve this model to interpret the observed relation of the hard X-ray spectrum becoming softer at higher accretion rate in luminous AGNs. The magnetic field is characterized by $β_{\rm 0}$, i.e., the ratio of the sum of gas pressure and radiation pressure to magnetic pressure in the disk ($β_{\rm 0}=(P_{\rm g,d}+P_{\rm r,d})/P_{\rm B}$). Besides, both the intrinsic disk photons and reprocessed photons by the disk are included as the seed photons for inverse Compton scattering. These improvements are crucial for investigating the effect of magnetic field on the accretion disk-corona when it is not clear whether the radiation pressure or gas pressure dominates in thin disk. We change the value of $β_{\rm 0}$ in order to constrain the magnetic field in the accretion disk. We find that the energy fraction released in the corona ($f$) gradually increases with the decrease of $β_{\rm 0}$ for the same accretion rate. When $β_{\rm 0}$ decreases to less than 50, the structure and spectrum of the disk-corona is independent on accretion rate, which is similar to the hard spectrum found in Liu et al.(2003). Comparing with the observational results of the hard X-ray bolometric correction factor in a sample of luminous AGNs, we suggest that the value of $β_{\rm 0}$ is about 100-200 for $α=0.3$ and the energy fraction $f$ should be larger than $30\%$ for hard X-ray emission.

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arXiv2015

A Hybrid Two Component Accretion Flow Surrounding Supermassive Black Holes in AGN

It is commonly believed that the optical/UV and X-ray emissions in luminous AGN are produced in an accretion disk and an embedded hot corona respectively. The inverse Compton scattering of disk photons by hot electrons in the corona can effectively cool the coronal gas if the mass supply is predominantly via a cool disk like flow as in BHXRBs. Thus, the application of such a model to AGNs fails to produce their observed X-ray emission. As a consequence, a fraction of disk accretion energy is usually assumed to be transferred to the corona. To avoid this assumption, we propose that gas in a vertically extended distribution is supplied to a supermassive black hole by the gravitational capture of interstellar medium or stellar wind material. In this picture, the gas partially condenses to an underlying cool disk as it flows toward the black hole, releasing accretion energy as X-ray emission and supplying mass for the disk accretion. Detailed numerical calculations reveal that the X-ray luminosity can reach a few tens of percent of the bolometric luminosity. The value of $α_{\rm ox}$ varies from 0.9 to 1.2 for the mass supply rate ranging from 0.03 to 0.1 times the Eddington value. The corresponding photon index in the 2-10 keV energy band varies from 1.9 to 2.3. Such a picture provides a natural extension of the model for low luminosity AGN where condensation is absent at low mass accretion rates and no optically thick disk exists in the inner region.

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arXiv2015

A disc corona-jet model for the radio/X-ray correlation in black hole X-ray binaries

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 $L_{\rm R} \propto L_{\rm X}^{\sim 0.5-0.7}$ 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., $L_{\rm R} \propto L_{\rm X}^{\sim 1.4}$ for $L_{\rm X}/L_{\rm Edd} \gtrsim 10^{-3}$, 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 $L_{\rm X}/L_{\rm Edd} \gtrsim 10^{-3}$ 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, $η\equiv \dot M_{\rm jet}/\dot M$, is ejected to form the jet, we can calculate the emergent spectrum of the disc corona-jet system. We calculate $L_{\rm R}$ and $L_{\rm X}$ at different $\dot M$, adjusting $η$ to fit the observed radio/X-ray correlation of the black hole X-ray transient H1743-322 for $L_{\rm X}/L_{\rm Edd}> 10^{-3}$. 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 $L_{\rm X}/L_{\rm Edd} > 10^{-3}$, is systematically less than that of the case for $L_{\rm X}/L_{\rm Edd} < 10^{-3}$, 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.

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arXiv2013

The disk evaporation model for the spectral features of low-luminosity active galactic nuclei

Observations show that the accretion flows in low-luminosity active galactic nuclei (LLAGNs) probably have a two-component structure with an inner ADAF and an outer truncated accretion disk. As shown by Taam et al. (2012), the truncation radius as a function of mass accretion rate is strongly affected by including the magnetic field within the framework of disk evaporation model, i.e., an increase of the magnetic field results in a smaller truncation radius of the accretion disk. In this work, we calculate the emergent spectrum of an inner ADAF + an outer truncated accretion disk around a supermassive black hole based on the prediction by Taam et al. (2012). It is found that an increase of the magnetic field from $β=0.8$ to $β=0.5$ (with magnetic pressure $p_{\rm m}=B^2/{8π}=(1-β)p_{\rm tot}$, $p_{\rm tot}=p_{\rm gas}+p_{\rm m}$) results in an increase of $\sim 8.7$ times of the luminosity from the truncated accretion disk. We found that the equipartition of gas pressure to magnetic pressure, i.e., $β=0.5$, failed to explain the observed anti-correlation between $L_{\rm 2-10 keV}/L_{\rm Edd}$ and the bolometric correction $κ_{\rm 2-10 keV}$ (with $κ_{\rm 2-10 keV} = L_{\rm bol}/L_{\rm 2-10 keV}$). The emergent spectra for larger value $β=0.8$ or $β=0.95$ can well explain the observed $L_{\rm 2-10 keV}/L_{\rm Edd}$-$κ_{\rm 2-10 keV}$ correlation. We argue that in the disk evaporation model, the electrons in the corona are assumed to be heated only by a transfer of energy from the ions to electrons via Coulomb collisions, which is reasonable for the accretion with a lower mass accretion rate. Coulomb heating is the dominated heating mechanism for the electrons only if the magnetic field is strongly sub-equipartition, which is roughly consistent with observations.

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arXiv2013

Constraints on the Viscosity and Magnetic Field in Hot Accretion Flows around Black Holes

The magnitude of the viscosity and magnetic field parameters in hot accretion flows is investigated in low luminosity active galactic nuclei (LLAGNs). Theoretical studies show that a geometrically thin, optically thick disk is truncated at mass accretion rates less than a critical value by mass evaporated vertically from the disk to the corona, with the truncated region replaced by an advection dominated accretion flow (ADAF). The critical accretion rate for such a truncation is a function of the viscosity and magnetic field. Observations of X-ray photon indices and spectral fits of a number of LLAGNs published in the literature provide an estimate of the critical rate of mass accretion and the truncation radius respectively. By comparing the observational results with theoretical predictions, the viscosity and magnetic field parameters in the hot accretion flow region are estimated. Specifically, the mass accretion rates inferred in different sources constrain the viscosity parameter, whereas the truncation radii of the disk, as inferred from spectral fits, further constrain the magnetic field parameter. It is found that the value of the viscosity parameter in the corona/ADAF ranges from 0.17 to 0.5, with values clustered about 0.2-0.3. Magnetic pressure is required by the relatively small truncation radii for some LLAGNs and is found to be as high as its equipartition value with the gas pressure. The inferred values of the viscosity parameter are in agreement with those obtained from the observations of non-stationary accretion in stellar mass black hole X-ray transients. This consistency provides support for the paradigm that a geometrically thin disk is truncated by means of a mass evaporation process from the disk to the corona at low mass accretion rates.

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arXiv2012

A Model for the Correlation of Hard X-ray Index with Eddington Ratio in Black Hole X-ray Binaries

Observations show that there is a positive correlation between Eddington ratio $λ$ and hard X-ray index $Γ$ for $λ\gtrsim 0.01$, and there is an anti-correlation between $λ$ and $Γ$ for $λ\lesssim 0.01$ in black hole X-ray binaries (with $λ=L_{\rm bol}/L_{\rm Edd}$). In this work, we theoretically investigate the correlation between $Γ$ and $λ$ within the framework of disk-corona model. We improve the model by taking into account all cooling processes including synchrotron and self-Compton radiations in the corona, Comptonization of the soft photons from the underlying accretion disk, and the Bremsstrahlung radiations. Presuming that the coronal flow above the disk can reach up to 0.1 Eddington rate at the outer region, we calculate the structure of the two-phase accretion flows and the emergent spectra for accretion rates from 0.003 to 0.1. It is found that at accretion rates larger than $\backsim 0.01$ Eddington rate a fraction of coronal gas condenses into the disk and an inner disk can be sustained by condensation. In this case, the X-ray emission is dominated by the scattering the soft photon from the underlying disk in the corona. The emission from the inner disk and corona can produce the positive correlation between $λ$ and $Γ$. While at accretion rates lower than $\backsim 0.01$ Eddington accretion rate, the inner disk vanishes completely by evaporation, the accretion is dominated by ADAF, in which the X-ray emission is produced by the Comptonization of the synchrotron and bremsstrahlung photons of ADAF itself. The emission from ADAF can produce the anti-correlation between $λ$ and $Γ$.

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arXiv2012

Disk corona interaction: mechanism for the disk truncation and spectrum change in low luminosity AGN

The truncation of an optically thick, geometrically thin accretion disk is investigated in the context of low luminosity AGN (LLAGN). We generalize the disk evaporation model used in the interpretative framework of black hole X-ray binaries by including the effect of a magnetic field in accretion disks surrounding supermassive black holes. The critical transition mass accretion rate for which the disk is truncated is found to be insensitive to magnetic effects, but its inclusion leads to a smaller truncation radius in comparison to a model without its consideration. That is, a thin viscous disk is truncated for LLAGN at an Eddington ratio less than 0.03 for a standard viscosity parameter ($α= 0.3$). An increase of the viscosity parameter results in a higher critical transition mass accretion rate and a correspondingly smaller truncation distance, the latter accentuated by greater magnetic energy densities in the disk. Based on these results, the truncation radii inferred from spectral fits of LLAGN published in the literature are consistent with the disk evaporation model. The infrared emission arising from the truncated geometrically thin accretion disks may be responsible for the red bump seen in such LLAGN.

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arXiv2012

Coronae above accretion disks around black holes: The effect of Compton cooling

The geometry of the accretion flow around stellar mass and supermassive black holes depends on the accretion rate. Broad iron emission lines originating from the irradiation of cool matter can indicate that there is an inner disk below a hot coronal flow.These emission lines have been detected in X-ray binaries. Observations with the Chandra X-ray Observatory, XMM Newton and Suzaku have confirmed the presence of these emission lines also in a large fraction of Seyfert-1 active galactic nuclei (AGN). We investigate the accretion flow geometry for which broad iron emission lines can arise in hard and soft spectral state. We study an ADAF-type coronal flow, where the ions are viscously heated and electrons receive their heat only by collisions from the ions and are Compton cooled by photons from an underlying cool disk. For a strong mass flow in the disk and the resulting strong Compton cooling only a very weak coronal flow is possible. This limitation allows the formation of ADAF-type coronae above weak inner disks in the hard state, but almost rules them out in the soft state. The observed hard X-ray luminosity in the soft state, of up to 10% or more of the total flux, indicates that there is a heating process that directly accelerates the electrons. This might point to the action of magnetic flares of disk magnetic fields reaching into the corona. Such flares have also been proposed by observations of the spectra of X-ray black hole binaries without a thermal cut-off around 200 keV.

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arXiv2012

The Structure and Spectral Features of a Thin Disk and Evaporation-Fed Corona in High-Luminosity AGNs

We investigate the accretion process in high-luminosity AGNs (HLAGNs) in the scenario of the disk evaporation model. Based on this model, the thin disk can extend down to the innermost stable circular orbit (ISCO) at accretion rates higher than $0.02\dot{M}_{\rm Edd}$; while the corona is weak since part of the coronal gas is cooled by strong inverse Compton scattering of the disk photons. This implies that the corona cannot produce as strong X-ray radiation as observed in HLAGNs with large Eddington ratio. In addition to the viscous heating, other heating to the corona is necessary to interpret HLAGN. In this paper, we assume that a part of accretion energy released in the disk is transported into the corona, heating up the electrons and thereby radiated away. We for the first time, compute the corona structure with additional heating, taking fully into account the mass supply to the corona and find that the corona could indeed survive at higher accretion rates and its radiation power increases. The spectra composed of bremsstrahlung and Compton radiation are also calculated. Our calculations show that the Compton dominated spectrum becomes harder with the increase of energy fraction ($f$) liberating in the corona, and the photon index for hard X-ray($2-10 \rm keV$) is $2.2 < Γ< 2.7 $. We discuss possible heating mechanisms for the corona. Combining the energy fraction transported to the corona with the accretion rate by magnetic heating, we find that the hard X-ray spectrum becomes steeper at larger accretion rate and the bolometric correction factor ($L_{\rm bol}/L_{\rm 2-10keV}$) increases with increasing accretion rate for $f<8/35$, which is roughly consistent with the observational results.

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arXiv2011

The Emission from Inner Disk and Corona in the Low and Intermediate Spectral States of Black Hole X-ray Binaries

Recent observations reveal that a cool disk may survive in the innermost stable circular orbit (ISCO) for some black hole X-ray binaries in the canonical low/hard state. The spectrum is characterized by a power law with a photon index $Γ\sim 1.5-2.1$ in the range of 2-10 keV and a weak disk component with temperature of $\sim 0.2$ keV. In this work, We revisit the formation of such a cool, optically thick, geometrically thin disk in the most inner region of black hole X-ray binaries at the low/hard state within the context of disk accretion fed by condensation of 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's found that the inner disk can exist for accretion rate ranging from $\dot M \sim 0.006-0.03 \dot M_{\rm Edd}$, over which the electron temperatures of the corona are in the range of $1-5\times 10^9\ \rm K$ 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) to the emergent spectra are 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 ISCO region in the low/hard state at luminosity around a few percent of $L_{\rm Edd}$. It's 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.

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arXiv2010

The effect of coronal radiation on a residual inner disk in the low/hard spectral state of black hole X-ray binary systems

Thermal conduction between a cool accretion disk and a hot inner corona can result in either evaporation of the disk or condensation of the hot corona. At low mass accretion rates, evaporation dominates and can completely remove the inner disk. At higher mass accretion rates, condensation becomes more efficient in the very inner regions, so that part of the mass accretes via a weak (initially formed) inner disk which is separated from the outer disk by a fully evaporated region at mid radii. At still higher mass accretion rates, condensation dominates everywhere, so there is a continuous cool disk extending to the innermost stable circular orbit. We extend these calculations by including the effect of irradiation by the hot corona on the disk structure. The flux which is not reflected is reprocessed in the disk, adding to the intrinsic thermal emission from gravitational energy release. This increases the seed photons for Compton cooling of the hot corona, enhancing condensation of the hot flow and re-inforcing the residual inner disk rather than evaporating it. Our calculations confirm that a residual inner disk can co-exist with a hard, coronally dominated, spectrum over a range of $0.006<\dot m<0.016$ (for $α=0.2$). This provides an explanation for the weak thermal component seen recently in the low/hard state of black hole X-ray binary systems.

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arXiv2010

The Spectral Features of Disk and Corona with Mass Evaporation in the Low/Hard State

We investigate the spectral features of accretion flows composed of an outer cool, optically thick disk and inner hot, optically thin, advection dominated accretion flows (ADAF) within the framework of disk and corona with mass evaporation (Liu et al. 2002a). In this work, both the magnetic field and Compton scattering of soft photons from the disk by electrons in the corona are included to calculate the evaporation rates at different distances. The disk is truncated at the distance where the evaporation rate equals to the accretion rate ($\dot m_{\rm evap}(r_{\rm tr})=\dot m$). For a series of accretion rates, the corresponding truncation radii are calculated out, with which we are able to calculate the emergent spectra from the inner ADAF + outer disk + corona. At very low accretion rates, the spectra are similar to that of a pure ADAF because the disk is truncated at large distances. The disk component becomes important at high accretion rates since the truncation occurs at small distances. An anti-correlation between the Eddington ratio $ξ\equiv L_{\rm 0.5-25 \,keV}/L_{\rm Edd}$ and the hard X-ray photon index $Γ_{\rm 3-25 \,keV}$ at low/hard states is predicted by the model. Comparing the theoretical results with observations, we find that our model can reproduce the anti-correlation between the Eddington ratio $ξ$ and the hard X-ray photon index observed for the X-ray binary XTE J1118+480.

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arXiv2009

The hard to soft spectral transition in LMXBs - affected by recondensation of gas into an inner disk

Soft and hard spectral states of X-ray transient sources reflect two modes of accretion, accretion via a geometrically thin, optically thick disk or an advection-dominated accretion flow (ADAF). The luminosity at transition between these two states seems to vary from source to source, or even for the same source during different outbursts, as observed for GX 339-4. We investigate how the existence of an inner weak disk in the hard state affects the transition luminosity. We evaluate the structure of the corona above an outer truncated disk and the resulting disk evaporation rate for different irradiation. In some cases, recent observations of X-ray transients indicate the presence of an inner cool disk during the hard state. Such a disk can remain during quiescence after the last outburst as long as the luminosity does not drop to very low values (10^-4 to 10^-3 of the Eddington luminosity). Consequently, as part of the matter accretes via the inner disk, the hard irradiation is reduced. The hard irradiation is further reduced, occulted and partly reflected by the inner disk. This leads to a hard-soft transition at a lower luminosity if an inner disk exists below the ADAF. This seems to be supported by observations for GX 339-4.

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arXiv2009

Application of the Disk Evaporation Model to AGNs

The disk corona evaporation model extensively developed for the interpretation of observational features of black hole X-ray binaries (BHXRBs) is applied to AGNs. Since the evaporation of gas in the disk can lead to its truncation for accretion rates less than a maximal evaporation rate, the model can naturally account for the soft spectrum in high luminosity AGNs and the hard spectrum in low luminosity AGNs. The existence of two different luminosity levels describing transitions from the soft to hard state and from the hard to soft state in BHXRBs, when applied to AGNs, suggests that AGNs can be in either spectral state within a range of luminosities. For example, at a viscosity parameter, α, equal to 0.3, the Eddington ratio from the hard to soft transition and from the soft to hard transition occurs at 0.027 and 0.005 respectively. When the Eddington ratio of the AGN lies below the critical value corresponding to its evolutionary state, the disk is truncated. With decreasing Eddington ratios, the inner edge of the disk increases to greater distances from the black hole with a concomitant increase in the inner radius of the broad line region, $R_{BLR}$. The absence of an optically thick inner disk at low luminosities gives rise to region in the size of borad line-luminosity plane for which the relation $R_{BLR} \propto L^{1/2}$ inferred at high luminosities is excluded. As a result, a lower limit to the accretion rate is predicted for the observability of broad emission lines, if the broad line region is associated with an optically thick accretion disk. Thus, true Seyfert 2 galaxies may exist at very low accretion rates/luminosities. The differences between BHXRBs and AGNs in the framework of the disk corona model are discussed and possible modifications to the model are briefly suggested.

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