arXiv subjects

B. F. Liu

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

53 records · Page 3Linked to original sources

arXiv2009

Investigating the Disk-Corona Relation in a Blue AGN Sample

We compile a blue AGN sample from SDSS and investigate the ratio of hard X-ray to bolometric luminosity in dependence on Eddington ratio and black hole mass. Our sample comprises 240 radio-quiet Seyfert 1 galaxies and QSOs. We find that the fraction of hard X-ray luminosity (log$(L_{\rm 2-10 kev}/L_{\rm bol})$) decreases with the increase of Eddington ratio. We also find that the fraction of hard X-ray luminosity is independent on the black hole mass for the radio-quiet AGNs. The relation of log$(L_{\rm 2-10 kev}/L_{\rm bol})$ decreasing with increasing Eddington ratio indicates that X-ray bolometric correction is not a constant, from a larger sample supporting the results of Vasudevan & Fabian (2007). We interpret our results by the disk corona evaporation/condensation model (Meyer et al. \cite{me200}; Liu et al. 2002a; Liu et al. 2007). In the frame of this model, the Compton cooling becomes efficient in cooling of the corona at high accretion rate (in units of Eddington rate), leading to condensation of corona gas to the disk. Consequently, the relative strength of corona to the disk becomes weaker at higher Eddington ratio. Therefore, the fraction of hard X-ray emission to disk emission and hence to the bolometric emission is smaller at higher Eddington ratio. The independence of the fraction of hard X-ray luminosity on the mass of the black hole can also be explained by the disk corona model since the corona structure and luminosity (in units of Eddington luminosity) are independent on the mass of black holes.

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arXiv2009

The Dependence of Spectral State Transition and Disk Truncation on Viscosity Parameter $α

A wealth of Galactic accreting X-ray binaries have been observed both in low/hard state and high/soft state. The transition between these two states was often detected. Observation shows that the transition luminosity between these two states is different for different sources, ranging from 1% to 4% of the Eddington luminosity. Even for the same source the transition luminosity at different outbursts is also different. The transition can occur from 0.0069 to 0.15 Eddington luminosity. To investigate the underlying physics, we study the influence of viscosity parameter $α$ on the transition luminosity on the basis of the disk-corona model for black holes. We calculate the mass evaporation rate for a wide range of viscosity parameter, $0.1\le α\le 0.9$. By fitting the numerical results, we obtain fitting formulae for both the transition accretion rate and the corresponding radius as a function of $α$. We find that the transition luminosity is very sensitive to the value of $α$, $L/L_{\rm Edd}\proptoα^{2.34}$. For $0.1\leα\le 0.6$, the transition luminosity varies by two orders of magnitude, from 0.001 to 0.2 Eddington luminosity. Comparing with observations we find that the transition luminosity can be fitted by adjusting the value of $α$, and the model determined values of $α$ are mostly in the range of observationally inferred value. Meanwhile we investigate the truncation of the disk in the low/hard state for some luminous sources. Our results are roughly in agreement with the observations.

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arXiv2008

On the Properties of Inner Cool Disks in the Hard State of Black Hole X-Ray Transient Systems

The formation of a cool disk in the innermost regions of black hole X-ray transient systems in the low hard state is investigated. Taking into account the combined cooling associated with the Compton and conductive energy transport processes in a corona, the radial structure of a disk is described for a range of mass accretion rates. The mass flow in an optically thick inner region can be maintained by the condensation of matter from a corona with the disk temperature and luminosity varying continuously as a function of the accretion rate. Although such a disk component can be present, the contribution of the optically thick disk component to the total luminosity can be small since the mass flow due to condensation in the optically thick disk underlying the corona can be significantly less than the mass flow rate in the corona. The model is applied to the observations of the low quiescent state of the black hole source GX 339-4 at luminosities of around $0.01 L_{Edd}$ and is able to explain the temperature of the thermal component at the observed luminosities. Since conductive cooling dominates Compton cooling at low mass accretion rates, the luminosity corresponding to the critical mass accretion rate above which a weak thermal disk component can be present in the low hard state is estimated to be as low as $0.001 L_{Edd}$.

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arXiv2007

The Existence of Inner Cool Disks in the Low Hard State of Accreting Black Holes

The condensation of matter from a corona to a cool, optically thick inner disk is investigated for black hole X-ray transient systems in the low hard state. A description of a simple model for the exchange of energy and mass between corona and disk originating from thermal conduction is presented, taking into account the effect of Compton cooling of the corona by photons from the underlying disk. It is found that a weak, condensation-fed inner disk can be present in the low hard state of black hole transient systems for a range of luminosities which depend on the magnitude of the viscosity parameter. For $α\sim 0.1-0.4$ an inner disk can exist for luminosities in the range $\sim 0.001- 0.02$ Eddington value. The model is applied to the X-ray observations of the black hole candidate sources GX 339-4 and Swift J1753.5-0127 in their low hard state. It is found that Compton cooling is important in the condensation process, leading to the maintenance of cool inner disks in both systems. As the results of the evaporation/condensation model are independent of the black hole mass, it is suggested that such inner cool disks may contribute to the optical and ultraviolet emission of low luminosity active galactic nuclei.

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arXiv2007

Disk-Evaporation Fed Corona: Structure and Evaporation Feature with Magnetic Field

The disk-corona evaporation model naturally interprets many observational phenomena in black hole X-ray binaries, such as the truncation of an accretion disk and the spectral state transitions. On the other hand, magnetic field is known to play an important role in transporting angular momentum and producing viscosity in accretion flows. In this work, we explicitly take the magnetic field in the accretion disk corona into account and numerically calculate the coronal structure on the basis of our two-temperature evaporation code. We show that the magnetic field influences the coronal structure by its contribution to the pressure, energy and radiative cooling in the corona and by decreasing the vertical heat conduction. We found that the maximal evaporation rate keeps more or less constant ($\sim 0.03$ Eddington rate) while the strength of magnetic fields changes, but that the radius corresponding to the maximal evaporation rate decreases with increasing magnetic field. This predicts that the spectral state transition always occurs at a few percent of Eddington accretion rate, while the inner edge of thin disk can be at $\sim 100 R_{\rm S} $ or even less in the hard state before the transition to the soft state. These results alleviate the problem that previous evaporation models predict too large a truncation radius, and are in better agreement with the observational results of several black hole X-ray binaries, though discrepancies remain.

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arXiv2006

Re-condensation from an ADAF into an inner disk - the intermediate state of black hole accretion?

Context: Accretion onto galactic and supermassive black holes occurs in different modes, which are documented in hard and soft spectral states, commonly attributed to an advection-dominated flow (ADAF) inside a truncated disk and standard disk accretion, respectively. At the times of spectral transition an intermediate state is observed, for which the accretion flow pattern is still unclear. Aims: We analyze the geometry of the accretion flow when the mass flow rate in the disk decreases (soft/hard transition) and evaporation of gas into the coronal flow leads to disk truncation. Methods: We evaluate the physics of an advection-dominated flow affected by thermal conduction to a cool accretion disk underneath. We find re-condensation of gas from the ADAF into the underlying inner disk at distances from the black hole and at rates, that depend on the properties of the hot ADAF and vary with the mass accretion rate. This sustains an inner disk for longer than a viscous decay time after the spectral transition occurred, in accordance with the spectra that indicate cool gas in the neighborhood of the accreting black hole. The model allows us to understand why Cyg X-1 does not show hysteresis in the spectral state transition luminosity that is commonly observed for X-ray transient sources. Conclusions: Our results shed new light on the complex mass flow pattern during spectral state transition.

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arXiv2006

An inner disk below the ADAF: the intermediate spectral state of black hole accretion

Aims: The hard and soft spectral states of black hole accretion are understood as connected with ADAF accretion (truncated disk) and standard disk accretion, respectively. However, observations indicate the existence of cool gas in the inner region at times when the disk is already truncated outside. We try to shed light on these not yet understood intermediate states. Methods: The disk-corona model allows to understand the spectral state transitions as caused by changes of the mass flow rate in the disk and provides a picture for the accretion geometry when disk truncation starts at the time of the soft/hard transition, the formation of a gap in the disk filled by an advection-dominated flow (ADAF) at the distance where the evaporation is maximal. We study the interaction of such an ADAF with an inner thin disk below. Results: We show that, when the accretion rate is not far below the transition rate, an inner disk could exist below an ADAF, leading to an intermediate state of black hole accretion.

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arXiv2005

Spectral state transitions in low-mass X-ray binaries - the effect of hard and soft irradiation

In neutron star and black hole X-ray binaries the transitions between the two spectral states, hard and soft, signals the change between accretion via a hot advection-dominated flow(ADAF) and disk accretion. In a few cases the hard/soft transition were observed during the rise to the nova outburst, mostly only the soft/hard transition during the luminosity decrease. Surprisingly the luminosities at the second transition is always lower by a factor of 3 to 5. A model for this hysteresis was presented in a preceding paper: It was shown that this switch in the accretion mode at different mass accretion rates and therefore different luminosities is caused by the different amount of Compton cooling or heating of the accretion disk corona as it is irradiated by hard or soft radiation from the central light source, respectively. We now give detailed results on the dependence on hardness of this radiation and on radiation efficiency. We further discuss the influence of the inclination and a possible warping of the disk on the observed hysteresis.

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arXiv2004

Hysteresis in spectral state transitions - a challenge for theoretical modeling

Many low-mass X-ray binaries show both hard and soft spectral states. For several sources the transitions between these states have been observed, mostly from the soft to the hard state during a luminosity decrease. In a few cases also the transition from the hard to the soft state was observed, coincident with an increase of the luminosity. Surprisingly this luminosity was not the same as the one during a following change back to the hard state. The values differed by a factor of about 3 to 5. We present a model for this hysteresis in the light curves of low-mass X-ray binaries (sources with neutron stars or black holes). We show that the different amount of Compton cooling or heating acting on the accretion disk corona at the time of the transition causes this switch in the accretion mode at different mass accretion rates and therefore different luminosities. The inner disk during the soft state provides a certain amount of Compton cooling which is either not present or much less if the inner region is filled with a hot advection-dominated accretion flow (ADAF) that radiates a hard spectrum.

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arXiv2004

A cool disk in the Galactic Center?

We study the possibility of a cool disk existing in the Galactic Center in the framework of the disk-corona evaporation/condensation model. Assuming an inactive disk, a hot corona should form above the disk since there is a continuous supply of hot gas from stellar winds of the close-by massive stars. Whether the cool disk can survive depends on the mass exchange between the disk and corona. If the disk-corona interaction is dominated by evaporation and the rate is larger than the Bondi accretion rate in the Galactic Center, the disk will be depleted within a certain time period and no persistent disk will exist. On the other hand, if the interaction results in hot gas steadily condensing into the disk, an inactive cool disk might survive. For this case we further investigate the Bremsstrahlung radiation from the hot corona and compare it with the observed X-ray luminosity. Our model shows that, for standard viscosity in the corona (alpha=0.3), the mass evaporation rate is much higher than the Bondi accretion rate and the coronal density is much larger than that inferred from Chandra observations. An inactive disk can not survive such strong evaporation. For small viscosity (alpha<0.07) we find condensation solutions. But detailed computations show that in this case there is too much X-ray radiation from the corona to be in agreement with the observations. Therefore, we conclude that there should be no thin/inactive disk presently in the Galactic Center. However, we do not exclude that the alternative non-radiative model of Nayakshin (2004) might instead be realized in nature.

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arXiv2003

Spectra from a magnetic reconnection-heated corona in AGN

We investigate a corona coupled with underlying disk through magnetic field and radiation field, and present emergent spectra calculated from Monte Carlo simulations. The spectra are determined for given black-hole mass and accretion rate. We find two types of solutions corresponding for hard spectrum and soft spectrum. In the hard-spectrum solution, the accretion energy is dominantly dissipated in the corona, supporting a strong corona above a cool disk; The hard X-ray spectral indices are around 1.1, same for different accretion rates. In the soft-spectrum solution, the accretion energy is mainly dissipated in the disk. The coronal temperature and density are quite low. Consequently, the spectra are dominated by the disk radiation peaking at UV and soft X-rays. For low-luminosity systems, there exists only the solution of hard spectra; While for high-luminosity systems, there exist both solutions of hard and soft spectra. For middle-luminosity systems, besides the hard spectra, moderately soft spectra composed of an inner soft-spectrum solution and an outer hard-spectrum solution may occur, the softness of which increases with increasing luminosity. The hard spectra are close to the observed spectra in Seyfert galaxies and radio-quiet QSOs. The composite spectra may account for the diversity of broad band spectra observed in narrow-line Seyfert 1 galaxies.

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arXiv2002

A simple model for magnetic reconnection heated corona

We construct a simple model for a magnetic reconnection heated corona above a thin accretion disk in AGNs and Galactic black hole candidates(GBHCs). The basic assumptions are that (1) the magnetic reconnection heat is cooled down overwhelmingly by Compton scattering in the corona and that (2) thermal conduction is dominantly cooled by evaporation of the chromospheric plasma in the disk-corona interface before Compton cooling sets in. With these two basic equations as well as equi-partition of magnetic energy with gas energy in the disk, we can consistently determine the fraction of accretion energy dissipated in the corona without free parameters, and thus determine the temperature and all other quantities in both the corona and disk for given black hole mass and accretion rate. Then, we calculate the luminosity contributed from the disk and corona and the coronal flux weighted Compton $y$ parameter. It is found that, at a low luminosity (less than 0.1 Eddington luminosity) the spectrum is hard with energy spectral index of around 1, while at a high luminosity (larger than 0.1 Eddington luminosity) the spectrum can be either soft or hard. We also find that the situation is almost same for supermassive and stellar-mass black holes. These features are consistent with observations of AGNs and GBHCs.

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arXiv2002

Two-temperature coronal flow above a thin disk

We extended the disk corona model (Meyer & Meyer-Hofmeister 1994; Meyer, Liu, & Meyer-Hofmeister 2000a) to the inner region of galactic nuclei by including different temperatures in ions and electrons as well as Compton cooling. We found that the mass evaporation rate and hence the fraction of accretion energy released in the corona depend strongly on the rate of incoming mass flow from outer edge of the disk, a larger rate leading to more Compton cooling, less efficient evaporation and a weaker corona. We also found a strong dependence on the viscosity, higher viscosity leading to an enhanced mass flow in the corona and therefore more evaporation of gas from the disk below. If we take accretion rates in units of the Eddington rate our results become independent on the mass of the central black hole. The model predicts weaker contributions to the hard X-rays for objects with higher accretion rate like narrow-line Seyfert 1 galaxies (NLS1s), in agreement with observations. For luminous active galactic nuclei (AGN) strong Compton cooling in the innermost corona is so efficient that a large amount of additional heating is required to maintain the corona above the thin disk.

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arXiv2000

Black hole X-ray binaries: A new view on soft-hard spectral transitions

The theory of coronal evaporation predicts the formation of an inner hole in the cool thin accretion disk for mass accretion rates below a certain value (~ 1/50 of the Eddington mass accretion rate) and the sudden disappearance of this hole when the mass accretion rate rises above that value. The inner edge of the standard thin disk then suddenly shifts inward from about a few hundred Schwarzschild radii to the last stable orbit. This appears to quantitatively account for the observed transitions between hard and soft spectral states at critical luminosities. Due to the evaporation process the matter accreting in the geometrically thin disk changes to a hot coronal flow which proceeds towards the black hole as an advection-dominated accretion flow (ADAF; for a review see Narayan et al. 1998).

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arXiv1999

Evaporation of accretion disks around black holes: the disk-corona transition and the connection to the advection-dominated accretion flow

We apply the disk-corona evaporation model (Meyer & Meyer-Hofmeister) originally derived for dwarf novae to black hole systems. This model describes the transition of a thin cool outer disk to a hot coronal flow. The mass accretion rate determines the location of this transition. For a number of well studied black hole binaries we take the mass flow rates derived from a fit of the ADAF model to the observed spectra (for a review see Narayan, Mahadevan, & Quataert) and determine where the transition of accretion via a cool disk to a coronal flow/ADAF would be located for these rates. We compare with the observed location of the inner disk edge, as estimated from the maximum velocity of the $\rm H_α$ emission line. We find that the transition caused by evaporation agrees with this in stellar disks. We also show that the ADAF and the ``thin outer disk + corona'' are compatible in terms of the physics in the transition region.

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arXiv1998

WZ Sagittae - an old dwarf nova

We model the evolution of the accretion disk of WZ Sagittae during the long quiescence. We find that the large amount of mass in the disk derived from the outburst luminosity is a severe constraint and demands values of $α_c$ $\approx$ 0.001 in contradiction to some recent suggestions. We include in our computations the formation of an inner disk hole and the growth of the disk due to redistribution of angular momentum. We find a new mode of disk evolution. The disk is quasi-stationary. Only about half of the mass transfered from the companion star flows through the disk, the other half is needed to build up the steadily growing outer disk. When the 3:1 resonance radius is reached the disk growth ends. From then on all transferred matter flows inward, the surface density increases, leading to an outburst within a few years. We predict superhumps at low luminosity during this last phase. We discuss X-rays expected, the white dwarf mass and distance to WZ Sagittae.

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arXiv1996

The long-term optical behavior of MRK421

All data available in B band for the BL Lac object MRK421 from 22 publications are used to construct a historical light curve, dating back to 1900. It is found that the light curve is very complicated and consists of a set of outbursts with very large duration. The brightness of MRK421 varies from 11.6 magnitude to more than 16 magnitude. Analyses with Jurkevich method of computing period of cyclic phenomena reveal in the light curve two kinds of behaviors. The first one is non-periodic with rapid, violent variations in intensity on time scales of hours to days. The second one is periodic with a possible period of $23.1\pm 1.1$ years. Another possible period of $15.3\pm 0.7$ years is not very significant. We have tested the robustness of the Jurkevich method. The period of about one year found in the light curves of MRK421 and of other objects is a spurious period due to the method and the observing window. We try to explain the period of $23.1 \pm1.1$ years under the thermal instability of a slim accretion disk around a massive black hole of mass of $2 *10^6 M_\odot$.

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