arXiv subjects

F. K. Liu

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

At least 37 records · Page 2Linked to original sources

arXiv2010

Estimating black hole masses of blazars

Estimating black hole masses of blazars is still a big challenge. Because of the contamination of jets, using the previously suggested size -- continuum luminosity relation can overestimate the broad line region (BLR) size and black hole mass for radio-loud AGNs, including blazars. We propose a new relation between the BLR size and $H_β$ emission line luminosity and present evidences for using it to get more accurate black hole masses of radio-loud AGNs. For extremely radio-loud AGNs such as blazars with weak/absent emission lines, we suggest to use the fundamental plane relation of their elliptical host galaxies to estimate the central velocity dispersions and black hole masses, if their velocity dispersions are not known but the host galaxies can be mapped. The black hole masses of some well-known blazars, such as OJ 287, AO 0235+164 and 3C 66B, are obtained using these two methods and the M - $σ$ relation. The implications of their black hole masses on other related studies are also discussed.

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arXiv2009

Interruption of Tidal Disruption Flares By Supermassive Black Hole Binaries

Supermassive black hole binaries (SMBHBs) are products of galaxy mergers, and are important in testing Lambda cold dark matter cosmology and locating gravitational-wave-radiation sources. A unique electromagnetic signature of SMBHBs in galactic nuclei is essential in identifying the binaries in observations from the IR band through optical to X-ray. Recently, the flares in optical, UV, and X-ray caused by supermassive black holes (SMBHs) tidally disrupting nearby stars have been successfully used to observationally probe single SMBHs in normal galaxies. In this Letter, we investigate the accretion of the gaseous debris of a tidally disrupted star by a SMBHB. Using both stability analysis of three-body systems and numerical scattering experiments, we show that the accretion of stellar debris gas, which initially decays with time $\propto t^{-5/3}$, would stop at a time $T_{\rm tr} \simeq ηT_{\rm b}$. Here, $η\sim0.25$ and $T_{\rm b}$ is the orbital period of the SMBHB. After a period of interruption, the accretion recurs discretely at time $T_{\rm r} \simeq ξT_b$, where $ξ\sim 1$. Both $η$ and $ξ$ sensitively depend on the orbital parameters of the tidally disrupted star at the tidal radius and the orbit eccentricity of SMBHB. The interrupted accretion of the stellar debris gas gives rise to an interrupted tidal flare, which could be used to identify SMBHBs in non-active galaxies in the upcoming transient surveys.

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arXiv2009

Enhanced tidal disruption rates from massive black hole binaries

"Hard" massive black hole (MBH) binaries embedded in steep stellar cusps can shrink via three-body slingshot interactions. We show that this process will inevitably be accompanied by a burst of stellar tidal disruptions, at a rate that can be several orders of magnitude larger than that appropriate for a single MBH. Our numerical scattering experiments reveal that: 1) a significant fraction of stars initially bound to the primary hole are scattered into its tidal disruption loss cone by gravitational interactions with the secondary hole, an enhancement effect that is more pronounced for very unequal-mass binaries; 2) about 25% (40%) of all strongly interacting stars are tidally disrupted by a MBH binary of mass ratio q=1/81 (q=1/243) and eccentricity 0.1; and 3) two mechanisms dominate the fueling of the tidal disruption loss cone, a Kozai non-resonant interaction that causes the secular evolution of the stellar angular momentum in the field of the binary, and the effect of close encounters with the secondary hole that change the stellar orbital parameters in a chaotic way. For a hard MBH binary of 10^7 solar masses and mass ratio 0.01, embedded in an isothermal stellar cusp of velocity dispersion sigma*=100 km/s, the tidal disruption rate can be as large as 1/yr. This is 4 orders of magnitude higher than estimated for a single MBH fed by two-body relaxation. When applied to the case of a putative intermediate-mass black hole inspiraling onto Sgr A*, our results predict tidal disruption rates ~0.05-0.1/yr.

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arXiv2008

Low heat conduction in white dwarf boundary layers?

X-ray spectra of dwarf novae in quiescence observed by Chandra and XMM-Newton provide new information on the boundary layers of their accreting white dwarfs. Comparison of observations and models allows us to extract estimates for the thermal conductivity in the accretion layer and reach conclusions on the relevant physical processes. We calculate the structure of the dense thermal boundary layer that forms under gravity and cooling at the white dwarf surface on accretion of gas from a hot tenuous ADAF-type coronal inflow. The distribution of density and temperature obtained allows us to calculate the strength and spectrum of the emitted X-ray radiation. They depend strongly on the values of thermal conductivity and mass accretion rate. We apply our model to the dwarf nova system VW Hyi and compare the spectra predicted for different values of the thermal conductivity with the observed spectrum. We find a significant deviation for all values of thermal conductivity that are a sizable fraction of the Spitzer conductivity. A good fit arises however for a conductivity of about 1% of the Spitzer value. This also seems to hold for other dwarf nova systems in quiescence. We compare this result with thermal conduction in other astrophysical situations. The highly reduced thermal conductivity in the boundary layer requires magnetic fields perpendicular to the temperature gradient. Locating their origin in the accretion of magnetic fields from the hot ADAF-type coronal flow we find that dynamical effects of these fields will lead to a spatially intermittent, localized accretion geometry at the white dwarf surface.

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arXiv2007

Tidal Disruption of Stellar Objects by Hard Supermassive Black Hole Binaries

Supermassive black hole binaries (SMBHBs) are expected by the hierarchical galaxy formation model in $Λ$CDM cosmology. There is some evidence in the literature for SMBHBs in AGNs, but there are few observational constraints on the evolution of SMBHBs in inactive galaxies and gas-poor mergers. On the theoretical front, it is unclear how long is needed for a SMBHB in a typical galaxy to coalesce. In this paper we investigate the tidal interaction between stars and binary BHs and calculate the tidal disruption rates of stellar objects by the BH components of binary. We derive the interaction cross sections between SMBHBs and stars from intensive numerical scattering experiments with particle number $\sim10^7$ and calculate the tidal disruption rates by both single and binary BHs for a sample of realistic galaxy models, taking into account the general relativistic effect and the loss cone refilling because of two-body interaction. We estimate the frequency of tidal flares for different types of galaxies using the BH mass function in the literature. We find that because of the three-body slingshot effect, the tidal disruption rate in SMBHB system is more than one order of magnitude smaller than that in single SMBH system. The difference is more significant in less massive galaxies and does not depend on detailed stellar dynamical processes. Our calculations suggest that comparisons of the calculated tidal disruption rates for both single and binary BHs and the surveys of X-ray or UV flares at galactic centers could tell us whether most SMBHs in nearby galaxies are single and whether the SMBHBs formed in gas-poor galaxy mergers coalesce rapidly.

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arXiv2007

Evolution of Supermassive Black Hole Binary and Acceleration of Jet Precession in Galactic Nuclei

Supermassive black hole binary (SMBHB) is expected with the hierarchical galaxy formation model. Currently, physics processes dominating the evolution of a SMBHB are unclear. An interesting question is whether we could observationally determine the evolution of SMBHB and give constraints on the physical processes. Jet precession have been observed in many AGNs and generally attributed to disk precession. In this paper we calculate the time variation of jet precession and conclude that jet precession is accelerated in SMBHB systems but decelerated in others. The acceleration of jet precession $dP_{\rm pr} / dt$ is related to jet precession timescale $P_{\rm pr}$ and SMBHB evolution timescale $τ_{\rm a}$, ${dP_{\rm pr} \over dt} \simeq - Λ{P_{\rm pr} \over τ_{\rm a}}$. Our calculations based on the models for jet precession and SMBHB evolution show that $dP_{\rm pr} / dt$ can be as high as about $- 1.0$ with a typical value -0.2 and can be easily detected. We discussed the differential jet precession for NGC1275 observed in the literature. If the observed rapid acceleration of jet precession is true, the jet precession is due to the orbital motion of an unbound SMBHB with mass ratio $q\approx 0.76$. When jets precessed from the ancient bubbles to the currently active jets, the separation of SMBHB decrease from about $1.46 {\rm Kpc}$ to $0.80 {\rm Kpc}$ with an averaged decreasing velocity $da/dt \simeq - 1.54 \times 10^6 {\rm cm/s}$ and evolution timescale $τ_{\rm a} \approx 7.5\times 10^7 {\rm yr}$. However, if we assume a steady jet precession for many cycles, the observations implies a hard SMBHB with mass ratio $q\approx 0.21$ and separation $a\approx 0.29 {\rm pc}$.

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arXiv2007

Weighing black holes in radio-loud AGNs

Because of the contamination of jets, using the size -- continuum luminosity relation can overestimate the broad line region (BLR) size and black hole mass for radio-loud AGNs. We propose a new relation between the BLR size and $H_β$ emission line luminosity and present evidences for using it to get more accurate black hole masses of radio-loud AGNs. For extremely radio-loud AGNs such as blazars with weak/absent emission lines, we suggest to use the fundamental plane relation of their elliptical host galaxies to estimate the central velocity dispersions and black hole masses, if their host galaxies can be mapped.

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arXiv2006

Harmonic QPOs and Thick Accretion Disk Oscillations in BL Lac Object AO 0235+164

Periodic outbursts are observed in many AGNs and usually explained with a supermassive black hole binary (SMBHB) scenario. However, multiple periods are observed in some AGNs and cannot be explained with it. Here we analyze the periodicity of the radio light curves of AO 0235+164 at multi-frequencies and report the discovery of six QPOs in integer ratio 1:2:3:4:5:6 of QPO frequencies, of which the second with period $P_2 = (5.46 \pm 0.47) {\rm yr}$ is the strongest. We fit the radio light curves and show that the initial phases of six QPOs have zero or $π$ differences relative to each other. We suggest a harmonic relationship of QPOs. The centroid frequency, relative strength, harmonic relationship and relative initial phases of QPOs are independent of radio frequency. The harmonic QPOs are likely due to the quasi-periodic injection of plasma from an oscillating accretion disk into the jet. We estimate the supermassive black hole mass $M_{\rm BH} \simeq (4.72\pm 2.04) \times 10^8 M_\odot$ and the accretion rate $\dot{m}\simeq 0.007$. With the knowledge of accretion disk, it implies that the inner region of accretion disk of AO 0235+164 is a radiatively inefficient accretion flow. The oscillation accretion is due to the p-mode oscillation of the thick disk probably excited by a SMBHB. The theoretical predications of fundamental oscillation frequency and the harmonics are well consistent with the observations. Harmonic QPOs would be absent when the thick disk becomes geometrically thin due to the increase of accretion rate. We discuss the observations of AO 0235+164 basing on the SMBHB-thick disk oscillation scenario.

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arXiv2006

The non-constant slope of the CIV Baldwin effect in NGC 4151

The relationship between the emission-line equivalent width and the continuum luminosity, so called the Baldwin effect, plays an important role in studying the physics of the broad line region of AGNs. Using the archived ultraviolet spectra obtained by IUE, HST, and HUT in 1978-2002, we investigated the intrinsic CIV Baldwin effect of a well-studied Seyfert 1 galaxy NGC 4151. Both its continuum flux and CIV emission-line flux varied about two orders of magnitude in more than two decades, making it one of the best targets for studying the slope variation of the Baldwin effect. We fitted the CIV line profile of the 490 archived UV spectra of NGC 4151 with the same model consisting of a few Gaussian components, and derived the slope in the log-log plot for the total flux of CIV emission line against the UV continuum flux in different observation epochs.We found that the slope is not constant for NGC 4151, as it varies from 0.58 in the highest flux epoch to 0.83 in the lowest flux epoch. The slope evidently decreases as the continuum flux increases, which reinforces the previous findings of the non-constant slope in the H_beta Baldwin effect of NGC 5548 and the CIV Baldwin effect of Fairall 9. Our result suggests that such a non-constant slope may not be unusual for AGNs. Its physical origin is probably related to the different non-linear responses of the emission line to the variable ionizing continuum caused by the different accretion modes at different luminosity levels. We briefly discuss the effects of various absorption components in the CIV line profile of NGC 4151 and argue that the slope variation is not driven mainly by the absorption effect. Intensive, long-term and high resolution spectral observations of strongly variable AGNs are needed in the future to confirm our result.

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arXiv2006

Black hole mass and accretion rate of Active Galactic Nuclei

The determination of the central black hole mass is crucial to the understanding of AGN physics. In this paper we briefly review some methods that are currently used to estimate the black hole mass of AGNs. Particularly we demonstrate the importance of two correlations: one between the black hole mass and the stellar velocity dispersion and another one between the broad line region (BLR) size and the optical continuum luminosity. Besides applying these relations in deriving black hole masses of various types of AGNs, we also employed the fundamental plane of elliptical galaxies to estimate the central velocity dispersions of AGN host galaxies, and then the black hole masses of AGNs including BL Lac objects. In addition, we derived another empirical relation between the BLR size and H_beta emission line luminosity from AGNs with the BLR size measured by reverberation mapping studies, and argued that more accurate black hole masses of extremely radio-loud AGNs could be obtained with it than using the usual R-L_{5100Å} relation because of the jet contribution to the optical continuum. Finally we pointed out that black hole mass estimation is very much helpful to determine the accretion rate and understand the accretion process in AGNs.

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arXiv2005

XMM-Newton view of PKS 2155-304: hardness ratio and cross-correlation analysis of EPIC pn observations

With currently available XMM-Newton EPIC pn observations spanned over about 3 years, we present a detailed spectral and temporal variability of the 0.2--10 keV X-ray emission from the X-ray bright BL Lac object PKS 2155-304. The spectral variability is examined with a model independent hardness ratio method. We find that the spectral evolution of the source follows the light curves well, indicating that the spectra harden when the fluxes increase. The plots of hardness ratios versus count rates show that the spectral changes are particularly significant during flares. The cross-correlation functions (CCFs) show that the light curves in the different energy bands are well correlated at different time lags. The CCF peaks (i.e., the maximum correlation coefficients) tend to become smaller with larger energy differences, and the variability in the different energy bands are more correlated for the flares than for the other cases. In most cases the higher energy band variations lead the lower energy band, but in two cases we observed the opposite behavior that the lower energy variability possibly leads the higher energy variability. The time lags increase with the energy differences between the two cross-correlated light curves. The maximum lag is found to be up to about one hour, in support with the findings obtained with previous low Earth orbit X-ray missions. We discuss our results in the context of the particle acceleration, cooling and light crossing timescales.

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arXiv2004

Black hole mass and accretion rate of active galactic nuclei with double-peaked broad emission lines

(Abridged) Using an empirical relation between the broad line region size and optical continuum luminosity, we estimated the black hole mass and accretion rate for 135 AGNs with double-peaked broad emission lines in two samples. With black hole masses from $3\times 10^7M_\odot$ to $5\times 10^9M_\odot$, these AGNs have the dimensionless accretion rates (Eddington ratios) between 0.001 and 0.1, and the bolometric luminosity between $10^{43}erg/s$ and $10^{46}erg/s$, both being significantly larger than those of several previously known low-luminosity double-peaked AGNs. The optical-X-ray spectra indices, $α_{OX}$, of these high-luminosity double-peaked AGNs is between 1 and 1.9. Modest correlations of the $α_{OX}$ value with the Eddington ratio and bolometric luminosity indicate that double-peaked AGNs with higher Eddington ratio or higher luminosity tend to have larger $α_{OX}$ value. Therefore we suggested that the accretion process in some high-luminosity double-peaked AGNs is probably different from that of low-luminosity objects where an ADAF-like accretion flow was thought to exist. This is also supported by the presence of possible big blue bumps in the spectra of some double-peaked AGNs with higher Eddington ratios. We noticed that the prototype double-peaked emission line AGN, Arp 102B, may be an ``intermediate'' object between the high and low luminosity double-peaked AGNs. In addition, we found an apparent strong anti-correlation between the peak separation of double-peaked profile and Eddington ratio. If it is real, it may provide us a clue to understand why double-peaked broad emission lines were hardly found in luminous AGNs with Eddington ratio larger than 0.1.

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arXiv2004

Black hole mass estimation with a relation between the BLR size and emission line luminosity of AGN

An empirical relation between the broad line region (BLR) size and optical continuum luminosity is often adopted to estimate the BLR size and then the black hole mass of AGNs. However, optical luminosity may not be a good indicator of photoionizing luminosity for extremely radio-loud AGNs because the jets usually contribute significantly to the optical continuum. Therefore, the black hole masses derived for blazar-type AGNs with this method are probably overestimated. Here we first derived a tight empirical relation between the BLR size and the H$_β$ emission line luminosity, $R(\rm{light-days})= 24.05(L_{H_β}/10^{42} ergs s^{-1})^{0.68}$, from a sample of 34 AGNs with the BLR size estimated with the reverberation mapping technique. Then we applied this relation to estimate the black hole masses of some AGNs and found that for many extremely radio-loud AGNs the black hole masses obtained with the $R-L_{H_β}$ relation are systematically lower than those derived previously with the $R-L_{5100Å}$ relation, while for radio-quiet and slightly radio-loud AGNs the results obtained with these two methods are almost the same. The difference of black hole masses estimated with these two relations increases with the radio-loudness for extremely radio-loud AGNs, which is consistent with the fact that their equivalent widths of H$_β$ emission line become smaller at higher radio-loudness. If the small H$_β$ equivalent widths of extremely radio-loud AGNs are indeed caused by the beaming effect, we argue that the optical emission line luminosity may be a better tracer of ionizing luminosity for blazar-type AGNs and the black hole mass derived with the $R-L_{H_β}$ relation are probably more accurate.

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arXiv2003

X-shaped radio galaxies as observational evidence for the interaction of supermassive binary black holes and accretion disk at pc scale

A supermassive black hole binary may form during galaxy mergering. we investigate the interaction of the supermassive binary black holes (SMBBHs) and an accretion disk and show that the detected X-shaped structure in some FRII radio galaxies may be due to the interaction-realignment of inclined binary and accretion disk occurred within the pc scale of the galaxy center. We compare in detail the model and observations and show that the configuration is consistent very well with the observations of X-shaped radio sources. X-shaped radio feature form only in FRII radio sources due to the strong interaction between the binary and a standard disk, while the absence of X-shaped FRI radio galaxies is due to that the interaction between the binary and the radiatively inefficient accretion flow in FRI radio sources is negligible. It is suggested that the binary would keep misaligned with the outer disk for most of the life time of FRII radio galaxies and the orientation of jet in most FRII radio galaxies distributes randomly, while the jets in most FRI radio galaxies is expected to be vertical to the accretion disk and thus the major axis of host galaxy. We discuss the relationship of X-shaped and double-double radio galaxies (DDRGs). The model is applied in paticular to two X-shaped radio sources 4C+01.30 and 3C293 and one DDRG source J0116-473 and show that the SMBBHs in the three objects have black hole mass ratios $q \sim 0.1 - 0.3$.

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arXiv2003

Double-double radio galaxies: remnants of merger of supermassive binary black holes

The activity of active galaxy may be triggered by the merge of galaxies and present-day galaxies are probably the product of successive minor mergers. The frequent galactic merges at high redshift imply that active galaxy harbors supermassive unequal-mass binary black holes in its center at least once during its life time. In this paper, we showed that the recently discovered double-lobed FR II radio galaxies are the remnants of such supermassive binary black holes. The inspiraling secondary black hole opens a gap in the accretion disk and removes the inner accretion disk when it merges into the primary black hole, leaving a big hole of about several hundreds of Schwarzschild radius in the vicinity of the post-merged supermassive black hole and leading to an interruption of jet formation. When the outer accretion disk slowly refills the big hole on a viscous time scale, the jet formation restarts and the interaction of the recurrent jets and the inter-galactic medium forms a secondary pair of lobes. We applied the model to a particular double-lobed radio source B1834+620 and showed that the orbit of the secondary is elliptical with a typical eccentricity $e \simeq 0.68$ and the mass ratio $q$ of the secondary and the primary is $0.01 \la q \la 0.4$. The accretion disk is a standard $α$-disk with $0.01 \la α\la 0.04$ and the ratio of disk half height $H$ and radius $r$ is $δ\simeq 0.01$. The model predicates that double-lobed radio structure forms only in FR II radio galaxies.

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arXiv2002

A new list of extra-galactic radio jets

A catalogue of extra-galactic jets is very useful both in observational and theoretical studies of active galaxies. With the use of new powerful radio instruments, the detailed structures of very compact or weak radio sources are investigated observationally and many new radio jets are detected. In this paper, we give a list of 661 radio sources with detected radio jets known to us prior to the end of December 2000. All references are collected for the observations of jets in radio, IR, optical, UV and X-ray wave-bands.

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arXiv2002

Black hole mass and binary model for BL Lac object OJ 287

Recent intensive observations of the BL Lac object OJ 287 raise a lot of questions on the models of binary black holes, processing jets, rotating helical jets and thermal instability of slim accretion disks. After carefully analyzing their radio flux and polarization data, Valtaoja et al. (\cite{valtaoja00}) propose a new binary model. Based on the black hole mass of $4 \times 10^8 {\rm M_\odot}$ estimated with the tight correlations of the black hole masses and the bulge luminosity or central velocity dispersion of host galaxies, we computed the physical parameters of the new binary scenario. The impact of the secondary on the accretion disk around the primary black hole causes strong shocks propagating inwards and outwards, whose arrival at the jet roots is identified with the rapid increase of optical polarization and the large change of polarization angle at about 0.30 yr after the first main optical flare. An increase of optical polarization, a large rotation of positional angle and a small synchrotron flare at 2007.05 between the optical outbursts at 2006.75 and 2007.89 are expected by the model. With the estimated parameters, we predicated an increase of $γ$-ray flux appearing about 5 days after the first optical/IR peak, which is consistent with the EGRET observations.

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arXiv2002

Supermassive Black Hole Masses of AGNs with Elliptical Hosts

The recently discovered tight correlation between supermassive black hole mass and central velocity dispersion suggests a possibility to estimate the SMBH mass from the measured central velocity dispersion. However, for most AGNs it is difficult to measure the central velocity dispersions of their host galaxies directly. In this paper we adopt the fundamental plane for ellipticals to estimate the central velocity dispersion and SMBH mass for a number of AGNs with morphology parameters of their elliptical host galaxies obtained by the HST imaging observations. The estimated SMBH masses of 63 BL Lac objects, 10 radio galaxies, 10 radio-loud quasars and 9 radio-quiet quasars are mostly in the range of $10^{7.5} M_\odot$ to $10^{9} M_\odot$. No significant difference in black hole mass is found for high-frequency peaked BL Lacs and low-frequency peaked BL Lacs, as well as for radio galaxies and radio-loud quasars. The Eddington ratios of radio galaxies are substantially smaller than those of quasars. This suggests that the different observational features of radio-loud AGNs may be mainly dominated by accretion rate rather than by the black hole mass, which is in agreement with some evolutionary scenarios recently proposed for radio-loud AGNs. Different from some previous claims, we found that the derived mean SMBH mass for radio-loud quasars is only slightly larger than that of radio-quiet quasars. Though their SMBH mass distributions are statistically different, their Eddington ratio distributions are probably from the same population. In addition, we noted that the relation between black hole mass and host galaxy luminosity obtained using the fundamental plane provides further arguments for a nonlinear scaling law between SMBH and galactic bulge mass.

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