Standard Thin Disk Model Research Articles

Active Galactic Nuclei Continuum Reverberation Mapping Based on Zwicky Transient Facility Light Curves

We perform a systematic survey of active galactic nuclei (AGNs) continuum lags using ∼3 days cadence gri-band light curves from the Zwicky Transient Facility. We select a sample of 94 type 1 AGNs at z < 0.8 with significant and consistent inter-band lags based on the interpolated cross-correlation function method and the Bayesian method JAVELIN. Within the framework of the “lamp-post” reprocessing model, our findings are: (1) The continuum emission (CE) sizes inferred from the data are larger than the disk sizes predicted by the standard thin-disk model. (2) For a subset of the sample, the CE size exceeds the theoretical limit of the self-gravity radius (12 lt-days) for geometrically thin disks. (3) The CE size scales with continuum luminosity as R CE ∝ L 0.48±0.04 with a scatter of 0.2 dex, analogous to the well-known radius–luminosity relation of broad Hβ. These findings suggest a significant contribution of diffuse continuum emission from the broad-line region (BLR) to AGN continuum lags. We find that the R CE–L relation can be explained by a photoionization model that assumes ∼23% of the total flux comes from the diffuse BLR emission. In addition, the ratio of the CE size and model-predicted disk size anticorrelates with the continuum luminosity, which is indicative of a potential nondisk BLR lag contribution evolving with the luminosity. Finally, a robust positive correlation between the CE size and black hole mass is detected.

Density Profile of the Ambient Circumnuclear Medium in Seyfert 1 Galaxies

Abstract The shape of the ambient circumnuclear medium (ACM) density profile can probe the history of accretion onto the central supermassive black holes in galaxies and the circumnuclear environment. However, due to the limitations of instrument resolution, the density profiles of the ACM for most galaxies remain largely unknown. In this work, we propose a novel method to measure the ACM density profile of active galactic nuclei (AGNs) by the equilibrium between the radiation pressure on the warm absorbers (WAs, a type of AGN outflow) and the drag pressure from the ACM. We study the correlation between the outflow velocity and ionization parameter of WAs in each of the five Seyfert 1 galaxies (NGC 3227, NGC 3783, NGC 4051, NGC 4593, and NGC 5548), inferring that the density profile of the ACM is between n ∝ r −1.7 and n ∝ r −2.15 (n is number density and r is distance) from 0.01 pc to parsec scales in these five AGNs. Our results indicate that the ACM density profile in Seyfert 1 galaxies is steeper than the prediction by the spherically symmetric Bondi accretion model and the simulated results of the hot accretion flow, but more in line with the prediction by the standard thin-disk model.

An extreme ultraluminous X-ray source X-1 in NGC 5055

Aims. We analysed multi-epoch X-ray data of the ultraluminous X-ray source NGC 5055 X-1, with luminosity up to 2.32 × 1040 erg s−1, to constrain the physical parameters of the source. Methods. We performed a timing and spectral analysis of Chandra and XMM-Newton observations. We used spectral models that assume the emission is from an accreting black hole system. We fit the data with a multicolour disk combined with a powerlaw or a thermal Comptonization (NTHCOMP) component and compared those fits with a slim disk model. Results. The light curves of the source do not show significant variability. From the hardness ratios (3–10 keV/0.3–3 keV flux), we infer that the source is not spectrally variable. We found that the photon index is tightly, positively correlated with the unabsorbed 0.3–10 keV flux and the hydrogen column density. Furthermore, the temperature emissivity profile indicates a deviation from the standard sub-Eddington thin disk model. The source shows an inverse correlation between luminosity and inner disk temperature in all fitted models. Conclusions. Our analysis favours the source to be in an ultraluminous soft state. The positive correlations between the photon index and the flux as well as between the photon index and the hydrogen column density may suggest the source is accreting at high Eddington ratios and might indicate the presence of a wind. The inverse luminosity relation with the inner disk temperature for all spectral models may indicate that the emission is geometrically beamed by an optically thick outflow.

Quasar Microlensing Variability Studies Favor Shallow Accretion Disk Temperature Profiles

Abstract We compare the microlensing-based continuum emission region size measurements in a sample of 15 gravitationally lensed quasars with estimates of luminosity-based thin disk sizes to constrain the temperature profile of the quasar continuum accretion region. If we adopt the standard thin disk model, we find a significant discrepancy between sizes estimated using the luminosity and those measured by microlensing of log(r L /r μ ) = −0.57 ± 0.08 dex. If quasar continuum sources are simple, optically thick accretion disks with a generalized temperature profile T ( r ) ∝ r − β , the discrepancy between the microlensing measurements and the luminosity-based size estimates can be resolved by a temperature profile slope 0.37 &lt; β &lt; 0.56 at 1σ confidence. This is shallower than the standard thin disk model (β = 0.75) at 3σ significance. We consider alternate accretion disk models that could produce such a temperature profile and reproduce the empirical continuum size scaling with black hole mass, including disk winds or disks with nonblackbody atmospheres.

On the Relation between the Hard X-Ray Photon Index and Accretion Rate for Super-Eddington Accreting Quasars

Abstract We investigate whether the correlation between the hard X-ray photon index ( ) and accretion rate for super-Eddington accreting quasars is different from that for sub-Eddington accreting quasars. We construct a sample of 113 bright quasars from the Sloan Digital Sky Survey Data Release 14 quasar catalog, with 38 quasars as the super-Eddington subsample and 75 quasars as the sub-Eddington subsample. We derive black hole masses using a simple-epoch virial mass formula based on the lines, and we use the standard thin disk model to derive the dimensionless accretion rates ( ) for our sample. The X-ray data for these quasars are collected from the Chandra and XMM-Newton archives. We fit the hard X-ray spectra using a single power-law model to obtain values. We find a statistically significant ( , ) correlation between and for the super-Eddington subsample. The – correlation for the sub-Eddington subsample is also significant, but weaker ( , ). Linear regression analysis shows that and for the super- and sub-Eddington subsamples, respectively. The – correlations of the two subsamples are different, suggesting different disk–corona connections in these two types of systems. We propose one qualitative explanation of the steeper – correlation in the super-Eddington regime that involves larger seed photon fluxes received by the compact coronae from the thick disks in super-Eddington accreting quasars.

Quasar Accretion Disk Sizes from Continuum Reverberation Mapping in the DES Standard-star Fields

Abstract Measurements of the physical properties of accretion disks in active galactic nuclei are important for better understanding the growth and evolution of supermassive black holes. We present the accretion disk sizes of 22 quasars from continuum reverberation mapping with data from the Dark Energy Survey (DES) standard-star fields and the supernova C fields. We construct continuum light curves with the griz photometry that span five seasons of DES observations. These data sample the time variability of the quasars with a cadence as short as 1 day, which corresponds to a rest-frame cadence that is a factor of a few higher than most previous work. We derive time lags between bands with both JAVELIN and the interpolated cross-correlation function method and fit for accretion disk sizes using the JAVELIN thin-disk model. These new measurements include disks around black holes with masses as small as ∼107 M ⊙, which have equivalent sizes at 2500 Å as small as ∼0.1 lt-day in the rest frame. We find that most objects have accretion disk sizes consistent with the prediction of the standard thin-disk model when we take disk variability into account. We have also simulated the expected yield of accretion disk measurements under various observational scenarios for the Large Synoptic Survey Telescope Deep Drilling Fields. We find that the number of disk measurements would increase significantly if the default cadence is changed from 3 days to 2 days or 1 day.

Global Radiation Magnetohydrodynamic Simulations of sub-Eddington Accretion Disks around Supermassive Black Holes

Abstract We conduct global three-dimensional radiation magnetohydrodynamic simulations of the inner regions of accretion flows around a 5 × 108 M ⊙ black hole, with mass accretion rates reaching 7% and 20% of the Eddington value. We choose initial field topologies that result in an inner disk supported by magnetic pressure, with surface density significantly smaller than the values predicted by the standard thin-disk model as well as a much larger disk scale height. The disks do not show any sign of thermal instability over many thermal timescales. More than half of the accretion is driven by radiation viscosity in the optically thin coronal region for the case of the lower accretion rate, while accretion in the optically thick part of the disk is driven by the Maxwell and Reynolds stresses from turbulence caused by magnetorotational instability. Optically thin plasma with gas temperatures ≳108 K is generated only in the inner ≈10 gravitational radii in both simulations, and is more compact in the case of the higher accretion rate. Such plasma does not form at larger radii because the surface density increases outward with radius, causing less dissipation outside the photosphere. In contrast to standard thin-disk models, the surface density in our simulations increases with increasing mass accretion rate at each radius. This causes a relatively weaker hot plasma component for the simulation with a higher accretion rate. We suggest that these results may provide a physical mechanism for understanding some of the observed properties of coronae and spectra of active galactic nuclei.

Accretion Disk Reverberation with Hubble Space Telescope Observations of NGC 4593: Evidence for Diffuse Continuum Lags

Abstract The Seyfert 1 galaxy NGC 4593 was monitored spectroscopically with the Hubble Space Telescope as part of a reverberation mapping campaign that also included Swift, Kepler, and ground-based photometric monitoring. During 2016 July 12–August 6, we obtained 26 spectra across a nearly continuous wavelength range of ∼1150–10000 Å. These were combined with Swift data to produce a UV/optical “lag spectrum,” which shows the interband lag relative to the Swift UVW2 band as a function of wavelength. The broad shape of the lag spectrum appears to follow the τ ∝ λ 4/3 relation seen previously in photometric interband lag measurements of other active galactic nuclei (AGNs). This shape is consistent with the standard thin disk model, but the magnitude of the lags implies a disk that is a factor of ∼3 larger than predicted, again consistent with what has been previously seen in other AGNs. In all cases these large disk sizes, which are also implied by independent gravitational microlensing of higher-mass AGNs, cannot be simply reconciled with the standard model. However, the most striking feature in this higher-resolution lag spectrum is a clear excess around the 3646 Å Balmer jump. This strongly suggests that diffuse emission from gas in the much larger broad-line region (BLR) must also contribute significantly to the interband lags. While the relative contributions of the disk and BLR cannot be uniquely determined in these initial measurements, it is clear that both will need to be considered to comprehensively model and understand AGN lag spectra.

Detection of Time Lags between Quasar Continuum Emission Bands Based On Pan-STARRS Light Curves

Abstract We study the time lags between the continuum emission of quasars at different wavelengths, based on more than four years of multi-band (g, r, i, z) light curves in the Pan-STARRS Medium Deep Fields. As photons from different bands emerge from different radial ranges in the accretion disk, the lags constrain the sizes of the accretion disks. We select 240 quasars with redshifts of z ≈ 1 or z ≈ 0.3 that are relatively emission-line free. The light curves are sampled from day to month timescales, which makes it possible to detect lags on the scale of the light crossing time of the accretion disks. With the code JAVELIN, we detect typical lags of several days in the rest frame between the g band and the riz bands. The detected lags are ∼2–3 times larger than the light crossing time estimated from the standard thin disk model, consistent with the recently measured lag in NGC 5548 and microlensing measurements of quasars. The lags in our sample are found to increase with increasing luminosity. Furthermore, the increase in lags going from g − r to g − i and then to g − z is slower than predicted in the thin disk model, particularly for high-luminosity quasars. The radial temperature profile in the disk must be different from what is assumed. We also find evidence that the lags decrease with increasing line ratios between ultraviolet Fe ii lines and Mg ii, which may point to changes in the accretion disk structure at higher metallicity.

OBSERVATIONS OF THE LENSED QUASAR Q2237+0305 WITH CANARICAM AT GTC

ABSTRACT We present new mid-IR observations of the quadruply lensed quasar Q2237+0305 taken with CanariCam on the Gran Telescopio Canarias. Mid-IR emission by hot dust, unlike the optical and near-IR emission from the accretion disk, is unaffected by the interstellar medium (extinction/scattering) or stellar microlensing. We compare these “true” ratios to the (stellar) microlensed flux ratios observed in the optical/near-IR to constrain the structure of the quasar accretion disk. We find a half-light radius of lt-day at and an exponent for the temperature profile of , where for a standard thin-disk model. If we assume that the differences in the mid-IR flux ratios measured over the years are due to microlensing variability, we find a lower limit for the size of the mid-IR-emitting region of lt-day. We also test for the presence of substructure/satellites by comparing the observed mid-IR flux ratios with those predicted from smooth lens models. We can explain the differences if the surface density fraction in satellites near the lensed images is for a singular isothermal ellipsoid plus external shear mass model or for a mass model combining ellipsoidal NFW and de Vaucouleurs profiles in an external shear.

IRON OPACITY BUMP CHANGES THE STABILITY AND STRUCTURE OF ACCRETION DISKS IN ACTIVE GALACTIC NUCLEI

ABSTRACT Accretion disks around supermassive black holes have regions where the Rosseland mean opacity can be larger than the electron scattering opacity due to the large number of bound–bound transitions in iron. We study the effects of this iron opacity “bump” on the thermal stability and vertical structure of radiation-pressure-dominated accretion disks, utilizing three-dimensional radiation magnetohydrodynamic (MHD) simulations in the local shearing box approximation. The simulations self-consistently calculate the heating due to MHD turbulence caused by magneto-rotational instability and radiative cooling by using the radiative transfer module based on a variable Eddington tensor in Athena. For a 5 × 108 solar mass black hole with ∼3% of the Eddington luminosity, a model including the iron opacity bump maintains its structure for more than 10 thermal times without showing significant signs of thermal runaway. In contrast, if only electron scattering and free–free opacity are included as in the standard thin disk model, the disk collapses on the thermal timescale. The difference is caused by a combination of (1) an anti-correlation between the total optical depth and the midplane pressure, and (2) enhanced vertical advective energy transport. These results suggest that the iron opacity bump may have a strong impact on the stability and structure of active galactic nucleus (AGN) accretion disks, and may contribute to a dependence of AGN properties on metallicity. Since this opacity is relevant primarily in UV emitting regions of the flow, it may help to explain discrepancies between observation and theory that are unique to AGNs.

THE LUMINOSITY DEPENDENCE OF QUASAR UV CONTINUUM SLOPE: DUST EXTINCTION SCENARIO

ABSTRACT We investigate the UV continuum slope α of a large quasar sample from SDSS DR7. By using specific continuum windows, we build two samples at lower ( ) and higher ( ) redshifts, which correspond to the continuum slopes at longer (near-UV) and shorter (far-UV) rest wavelength ranges, respectively. Overall, the average continuum slopes are −0.36 and −0.51 for and with similar dispersions . For both samples, we confirm the luminosity dependence of the continuum slope, i.e., fainter quasars have redder spectra. We further find that both and have a common upper limit ( ), which is almost independent of the quasar luminosity . This finding implies that the intrinsic quasar continuum (or the bluest quasar), at any luminosity, obeys the standard thin-disk model. We propose that the other quasars with redder α are caused by the reddening from the dust locally. With this assumption, we employ the dust extinction scenario to model the observed relation. We find that a typical value of (depending on the types of extinction curve) of the quasar local dust is enough to explain the discrepancy of α between the observation ( ) and the standard accretion disk model prediction ( ).

A GLOBAL THREE-DIMENSIONAL RADIATION MAGNETO-HYDRODYNAMIC SIMULATION OF SUPER-EDDINGTON ACCRETION DISKS

We study super-Eddington accretion flows onto black holes using a global three dimensional radiation magneto-hydrodynamical simulation. We solve the time dependent radiative transfer equation for the specific intensities to accurately calculate the angular distribution of the emitted radiation. Turbulence generated by the magneto-rotational instability provides self-consistent angular momentum transfer. The simulation reaches inflow equilibrium with an accretion rate ~220L_edd/c^2 and forms a radiation driven outflow along the rotation axis. The mechanical energy flux carried by the outflow is ~20% of the radiative energy flux. The total mass flux lost in the outflow is about 29% of the net accretion rate. The radiative luminosity of this flow is ~10L_edd. This yields a radiative efficiency ~4.5%, which is comparable to the value in a standard thin disk model. In our simulation, vertical advection of radiation caused by magnetic buoyancy transports energy faster than photon diffusion, allowing a significant fraction of the photons to escape from the surface of the disk before being advected into the black hole. We contrast our results with the lower radiative efficiencies inferred in most models, such as the slim disk model, which neglect vertical advection. Our inferred radiative efficiencies also exceed published results from previous global numerical simulations, which did not attribute a significant role to vertical advection. We briefly discuss the implications for the growth of supermassive black holes in the early universe and describe how these results provided a basis for explaining the spectrum and population statistics of ultraluminous X-ray sources.

The local stability of accretion disk models with considering the role of various viscosity and cooling mechanisms

The standard thin accretion disk model can explain the soft X-ray spectra of Galactic black hole systems and AGN successfully. However, there are still a few observational documents for Radiation pressure theory in X-ray novae in black hole binary systems and AGN. The luminosity in accretion onto black holes is corresponds to L>0.01L E . According to standard thin disk model, when the accretion rate is over a small fraction of the Eddington rate, L>0.01L E , the inner region of the disk is radiation-pressure-dominated and thermally unstable. However, observations of the high/soft state of black hole X-ray binaries with luminosity within (0.01L E <L<0.5L E ) show that the disk is quite stable. Thus, this contradiction shows the objection of this model and maybe it is essential to change the standard viscosity law or one of the other basic assumptions in order to get a stable disk models. In this paper, we revisit and recalculate the thermal instability with a different models of viscosity and cooling functions and show that the choosing of an arbitrary cooling and viscosity functions can affect on the stability of a general disk model and hence maybe answer to a this problem in accretion disk theory. We choose an arbitrary functions of surface density Σ and half thickness of disk H for cooling and viscosity. Also, we discuss a general disk with thermal conduction, radial force and advection. Then, we solve the equations numerically. We obtain a fourth degree dispersions relation and discuss solutions and instability modes. This analysis shows the great sensitivity of stability of disk to the form of viscosity, so there are various effective factors to stabilize the disk. For example the exist of advection and thermal conduction can effect to stability of disks also.

A GENERAL RELATIVISTIC MODEL OF ACCRETION DISKS WITH CORONAE SURROUNDING KERR BLACK HOLES

We calculate the structure of a standard accretion disk with corona surrounding a massive Kerr black hole in general relativistic frame, in which the corona is assumed to be heated by the reconnection of the strongly buoyant magnetic fields generated in the cold accretion disk. The emergent spectra of the accretion disk-corona systems are calculated by using the relativistic ray-tracing method. We propose a new method to calculate the emergent Comptonized spectra from the coronae. The spectra of the disk-corona systems with a modified $\alpha$-magnetic stress show that both the hard X-ray spectral index and the hard X-ray bolometric correction factor $L_{\rm bol}/L_{\rm X,2-10keV}$ increase with the dimensionless mass accretion rate, which are qualitatively consistent with the observations of active galactic nuclei (AGNs). The fraction of the power dissipated in the corona decreases with increasing black hole spin parameter $a$, which leads to lower electron temperatures of the coronas for rapidly spinning black holes. The X-ray emission from the coronas surrounding rapidly spinning black holes becomes weak and soft. The ratio of the X-ray luminosity to the optical/UV luminosity increases with the viewing angle, while the spectral shape in the X-ray band is insensitive with the viewing angle. We find that the spectral index in the infrared waveband depends on the mass accretion rate and the black hole spin $a$, which deviates from $f_\nu\propto\nu^{1/3}$ expected by the standard thin disk model.

RADIATION PRESSURE-SUPPORTED ACCRETION DISKS: VERTICAL STRUCTURE, ENERGY ADVECTION, AND CONVECTIVE STABILITY

By taking into account the local energy balance per unit volume between the viscous heating and the advective cooling plus the radiative cooling, we investigate the vertical structure of radiation pressure-supported accretion disks in spherical coordinates. Our solutions show that the photosphere of the disk is close to the polar axis and therefore the disk seems to be extremely thick. However, the profile of density implies that most of the accreted matter exists in a moderate range around the equatorial plane. We show that the well-known polytropic relation between the pressure and the density is unsuitable for describing the vertical structure of radiation pressure-supported disks. More importantly, we find that the energy advection is significant even for slightly sub-Eddington accretion disks. We argue that the non-negligible advection may help to understand why the standard thin disk model is likely to be inaccurate above \sim 0.3 Eddington luminosity, which was found by some works on the black hole spin measurement. Furthermore, the solutions satisfy the Solberg-Hoiland conditions, which indicates the disk to be convectively stable. In addition, we discuss the possible link between our disk model and ultraluminous X-ray sources.

A ROBUST DETERMINATION OF THE SIZE OF QUASAR ACCRETION DISKS USING GRAVITATIONAL MICROLENSING

Using microlensing measurements from a sample of 27 image-pairs of 19 lensed quasars we determine a maximum likelihood estimate for the accretion disk size of an {{\em}average} quasar of $r_s=4.0^{+2.4}_{-3.1} $ light days at rest frame $<\lambda>=1736$\AA\ for microlenses with a mean mass of $<M>=0.3M_\odot$. This value, in good agreement with previous results from smaller samples, is roughly a factor of 5 greater than the predictions of the standard thin disk model. The individual size estimates for the 19 quasars in our sample are also in excellent agreement with the results of the joint maximum likelihood analysis.

Effects of Toroidal Magnetic Fields on the Thermal Instability of Thin Accretion Disks

The standard thin disk model predicts that when the accretion rate is moderately high, the disk is radiation–pressure-dominated and thermally unstable. However, observations indicate the opposite, namely the disk is quite stable. We present an explanation in this work by taking into account the role of the magnetic field which was ignored in the previous analysis.

REVISITING THE THERMAL STABILITY OF RADIATION-DOMINATED THIN DISKS

The standard thin disk model predicts that when the accretion rate is over a small fraction of the Eddington rate, which corresponds to $L \ga 0.06 L_{Edd}$, the inner region of the disk is radiation-pressure-dominated and thermally unstable. However, observations of the high/soft state of black hole X-ray binaries with luminosity well within this regime ($0.01L_{Edd} \la L \la 0.5L_{Edd}$) indicate that the disk has very little variability, i.e., quite stable. Recent radiation magnetohydrodynamic simulations of a vertically stratified shearing box have confirmed the absence of the thermal instability. In this paper, we revisit the thermal stability by linear analysis, taking into account the role of magnetic field in the accretion flow. By assuming that the field responses negatively to a positive temperature perturbation, we find that the threshold of accretion rate above which the disk becomes thermally unstable increases significantly compared with the case of not considering the role of magnetic field. This accounts for the stability of the observed sources with high luminosities. Our model also presents a possible explanation as to why only GRS 1915+105 seems to show thermally unstable behavior. This peculiar source holds the highest accretion rate (or luminosity) among the known high state sources, which is well above the accretion rate threshold of the instability.

THE QUASAR ACCRETION DISK SIZE-BLACK HOLE MASS RELATION

We use the microlensing variability observed for 11 gravitationally lensed quasars to show that the accretion disk size at a rest-frame wavelength of 2500 Å is related to the black hole mass by log(R2500/cm) = (15.78 ± 0.12) + (0.80 ± 0.17)log(MBH/109 M☉). This scaling is consistent with the expectation from thin-disk theory (R ∝ M2/3BH), but when interpreted in terms of the standard thin-disk model (T ∝ R−3/4), it implies that black holes radiate with very low efficiency, log(η) = −1.77 ± 0.29 + log(L/LE), where . Only by making the maximum reasonable shifts in the average inclination, Eddington factors, and black hole masses can we raise the efficiency estimate to be marginally consistent with typical efficiency estimates (η ≈ 10%). With one exception, these sizes are larger by a factor of ∼4 than the size needed to produce the observed 0.8 μm quasar flux by thermal radiation from a thin disk with the same T ∝ R−3/4 temperature profile. While scattering a significant fraction of the disk emission on large scales or including a large fraction of contaminating line emission can reduce the size discrepancy, resolving it also appears to require that accretion disks have flatter temperature/surface brightness profiles.