Slim Accretion Disks Research Articles

Slim-disk modeling reveals an accreting intermediate-mass black hole in the luminous fast blue optical transient AT2018cow

The origin of the most luminous subclass of the fast blue optical transients (LFBOTs) is still unknown. We present an X-ray spectral analysis of AT2018cow – the LFBOT archetype – using NuSTAR, Swift, and XMM-Newton data. The source spectrum can be explained by the presence of a slim accretion disk, and we find that the mass accretion rate decreases to sub–Eddington levels ≳200 days after the source’s discovery. Applying our slim-disk model to data obtained at multiple observational epochs, we constrain the mass of the central compact object in AT2018cow to be log(M•/M⊙) = 2.4−0.1+0.6 at the 68% confidence level. Our mass measurement is independent from, but consistent with, the results from previously employed methods. The mass constraint is consistent with both the tidal disruption and the black hole–star merger scenarios, if the latter model can be extrapolated to the measured black hole mass. Our work provides evidence for an accreting intermediate–mass black hole (102 − 106 M⊙) as the central engine in AT2018cow, and, by extension, in LFBOT sources similar to AT2018cow.

A Two-zone Accretion Disk in the Changing-look Active Galactic Nucleus 1ES 1927+654: Physical Implications for Tidal Disruption Events and Super-Eddington Accretion

The properties of slim accretion disks, while crucial for our understanding of black hole growth, have yet to be studied extensively observationally. We analyze the multiepoch broadband spectral energy distribution of the changing-look active galactic nucleus 1ES 1927+654 to derive the properties of its complex, time-dependent accretion flow. The accretion rate decays as Ṁ∝t−1.53 , consistent with the tidal disruption of a 1.1 M ⊙ star. Three components contribute to the spectral energy distribution: a central overheated zone resembling a slim disk, an outer truncated thin disk, and a hot corona. Photon trapping in the slim disk triggered by the high initial Ṁ was characterized by a low radiation efficiency (3%), which later more than doubled (8%) after Ṁ dropped sufficiently low for the disk to transition to a geometrically thin state. The blackbody temperature profile T ∝ R −0.60 for the inner overheated zone matches the theoretical expectations of a slim disk, while the effective temperature profile of T ∝ R −0.69 for the outer zone is consistent with the predictions of a thin disk. Both profiles flatten toward the inner boundary of the disk as a result of Compton cooling in the corona. Our work presents compelling observational evidence for the existence of slim accretion disks and elucidates the key parameters governing their behavior, paving the way for further exploration in this area.

Sustained super-Eddington accretion around neutron stars & black holes

ABSTRACT Recently, it was shown that the formation of a photon-trapping surface might not be sufficient to ensure unimpeded super-Eddington (SE) accretion. In light of this finding, here we derive a condition such that sustained and unimpeded SE accretion could be achieved in optically thick slim accretion discs surrounding neutron stars (NSs) and black holes (BHs). For this, we calculate a semi-analytic approximation of the self-similar global radial velocity expression for an advection-dominated flow. Neglecting the influence of relativistic jets on the accretion flow, we find that for Eddington fraction $\dot{m} \gtrsim 1.5 (\epsilon /0.1)^{3/5}$ (ϵ being the accretion efficiency) sustained SE accretion might be possible in slim discs around BHs irrespective of their spin. The same condition holds for NSs when ϵ ≳ 0.03. The presence of a surface magnetic field might truncate the disc at the magnetosphere of the NS, resulting in lower efficiencies and consequently changing the condition to $\dot{m} \gt 0.013 \epsilon ^{-19/31}$. Our approach suggests that sustained SE accretion might almost always be possible around NSs and BHs hosting accretion discs.

Hard X-Ray Flares and Spectral Variability in NGC 4395 ULX1

We report the detection of flaring events in NGC 4395 ULX1, a nearby ultraluminous X-ray source (ULX), for the first time, using recent XMM-Newton observations. The flaring episodes are spectrally harder than the steady-emission intervals, resulting in higher fractional variability in the high-energy regime. A thin Keplerian and a slim accretion disk provide the best-fit continuum for XMM-Newton spectra. All observations show a broad hump-like feature around ∼0.9 keV, which can be associated with a collection of blended emission lines, and suggests the presence of a wind or outflow in this ULX through comparison with other ULXs that show a similar feature. The flaring spectra correspond to higher slim-disk temperatures due to a higher mass accretion rate under an advection-dominated accretion scenario. The luminosity–temperature (L-T) values in different flux states show a positive trend. When characterized with a power-law relation, the L-T profile is broadly consistent with both L ∝ T 2 and L ∝ T 4 relations for the analyzed data. The empirical predictions for a slim accretion disk in the case of super-Eddington accretion onto a stellar-mass compact object is L ∝ T 2, which is a possible scenario in ULX1. The origin of the flaring events is understood as an intrinsic change in accretion rate or presence of variable clumpy wind in the inner region of the accretion disk.

XMM-Newton spectrum of the radio-loud quasar 3C 215: Slim accretion disk or SMBH binary

Context. Radio-loud active galactic nuclei (RL AGN) exhibit very powerful jet emission in the radio band, while the radio-quiet (RQ) AGN do not. This RL-RQ dichotomy would imply a sharp difference existing among these two classes, however, modern theoretical models and observations suggest a common nuclear environment that is possibly characterized by different working regimes. Aims. We explore the geometrical structure and mutual interactions of the innermost components of the broad line radio galaxy 3C 215, with a particular focus on the accretion and ejection mechanisms involving the central supermassive black hole (SMBH). We compare these observational features with those of the RQ Seyfert 1 galaxies. Investigating their differences is aimed at improving our understanding of the jet launching mechanisms and devising an explanation for why this phenomenon is efficient only in a small fraction of all the AGNs. Methods. Using high-quality data from a ∼60 ks observation with XMM-Newton, we carried out a detailed X-ray spectral analysis of 3C 215 in the broad energy range of 0.5−10 keV. We modeled the spectrum with an absorbed double power-law model for the primary continuum, reprocessed by reflection from ionized and cold neutral material and modified by relativistic blurring. We also compared our results with those of earlier multi-wavelength observations. Results. We obtained a primary continuum photon index from the corona, namely, Γ1 = 1.97 ± 0.06, along with evidence of a jet contribution, modeled as a power law with photon index of Γ2 ≃ 1.29. The reflector, which is possibly attributed to the accretion disk and portions of the broad-line region (BLR), is ionized (logξ = 2.31−0.27+0.37 erg s−1 cm) and relatively distant from the SMBH (Rin > 38 Rg), where Rg = GMBH/c2 is the gravitational radius. The obscuring torus seems patchy, dust-poor, and inefficient, while the jet emission shows a twisted and knotted geometry. We propose three scenarios to describe the following characteristics: 1. An ADAF state in the inner disk; 2. A slim accretion disk; and 3. A sub-pc SMBH binary system (SMBHB). Conclusions. While the first scenario is not in agreement with the SMBH accretion regime, the slim disk scenario is consistent with the observational features of this radio galaxy, showing that 3C 215 is similar to non-jetted AGNs, accreting at a high rate. Nonetheless, the first two scenarios are unable to account for the particular shape of 3C 215 jet emission. The SMBHB scenario seems to be in agreement with almost all 3C 215 observational features, but we are not able to unequivocally determine this source as a strong SMBHB candidate. A final determination will require further analysis.

A Global Solution to a Slim Accretion Disk with Radiation-driven Outflows

Abstract The thickness of a slim disk is determined by the balance between the radiation force and the vertical component of the gravity of the black hole (BH). Vertical gravity is found to increase with the disk height, and it will decrease with the disk height if the disk thickness is above a critical value, which implies that gas at the disk surface may be driven into outflows by radiation force when the disk thickness surpasses the critical value. In this work, we derive a global solution to a slim disk with radiation-driven outflows. We find that the outflows are driven from the disk surface if the mass accretion rate is m ˙ ≳ 1.78 − 1.91 ( m ˙ = M ˙ / M ˙ Edd and M ˙ Edd = L Edd / 0.1 c 2 ) depending on the BH mass, while the outflows are suppressed when the mass accretion rate is lower than this critical value. The mass accretion rate decreases with the decreasing radius in the disk with outflows, and the rate of the gas swallowed by the BH is always limited to m ˙ in ∼ 1.78 − 1.91 even if the mass accretion rate at the outer edge of the disk is very high. This may set constraints on the massive BH growth through accretion in the early universe. Due to the presence of outflows, there is an upper limit on the radiation flux of the disk, which leads to saturation of the continuum spectra of the disk with outflows at the high-energy band. This may be tested by the observations of quasars or/and BH X-ray binaries.

X-ray properties of reverberation-mapped AGNs with super-Eddington accreting massive black holes

AbstractActive Galactic Nuclei (AGN) exhibit multi-wavelength properties that are representative of the underlying physical processes taking place in the vicinity of the accreting supermassive black hole. The black hole mass and the accretion rate are fundamental for understanding the growth of black holes, their evolution, and the impact on the host galaxies. Recent results on reverberation-mapped AGNs show that the highest accretion rate objects have systematic shorter time-lags. These super-Eddington accreting massive black holes (SEAMBHs) show BLR size 3-8 times smaller than predicted by the Radius-Luminosity (R-L) relationship. Hence, the single-epoch virial black hole mass estimates of highly accreting AGNs have an overestimation of a factor of 3-8 times. SEAMBHs likely have a slim accretion disk rather than a thin disk that is diagnostic in X-ray. I will present the extreme X-ray properties of a sample of dozen of SEAMBHs. They indeed have a steep hard X-ray photon index, Γ, and demonstrate a steeper power-law slope, ασx.

The Spectroscopic Signature of Variability in High-redshift Quasars

Abstract Using 16,421 spectra from a sample of 340 quasars (1.62 < z < 3.30) from the Sloan Digital Sky Survey (SDSS) Reverberation Mapping Project, we present an analysis of quasar spectral variability. We confirm the intrinsic Baldwin effect (BE) and brighter-means-bluer trends in which emission line strength and color are associated with changes in luminosity. We then create a composite differential spectrum that captures the wavelength dependence of quasar variability as a function of change in luminosity. When using a bandpass around 1740 Å to describe the luminosity, the differential spectrum follows a power law at longer wavelengths that breaks blueward of 1700 Å. However, the shape of the differential spectrum, the location of the power-law break, and the slope of the intrinsic BE all vary with the choice of bandpass used to define the change in quasar luminosity. We propose that the observed behavior can be explained by inhomogeneous accretion or slim accretion disk models where delays in the reprocessing of incident light on the accretion disk cause local deviations in temperature from the thin-disk model. Finally, we quantify the effects on cosmology studies that are due to the variations in the quasar spectrum in the Lyα forest wavelength range. Using the observed spectroscopic signatures to predict the quasar continuum over the interval 1040 < λ < 1200 Å, we find that the derived spectral templates can reduce the uncertainty of the Lyα forest continuum level in individual epochs from 17.2% to 7.7%, near the level where systematic errors in SDSS flux calibration are expected to dominate.

Slim Accretion Disks: Theory and Observational Consequences

The concept of slim accretion disks emerged over 30 years ago as an answer to several unsolved problems. Since that time there has been a tremendous increase in the amount of observational data where this model applies. However, many critical issues on the theoretical side remain unsolved, as they are inherently difficult. This is the issue of the disk stability under radiation pressure, the role of the magnetic field in the energy transfer inside the disk, the formation (or not) of a warm corona, and outflows. Thus the progress has to be done both through further developments of the model and through careful comparison with the observational data.

Supermassive Black Holes with High Accretion Rates in Active Galactic Nuclei. VIII. Structure of the Broad-line Region and Mass of the Central Black Hole in Mrk 142

Abstract This is the eighth in a series of papers reporting on a large reverberation mapping (RM) campaign to measure black hole (BH) mass in active galactic nuclei with high accretion rates. We employ the recently developed dynamical modeling approach for broad-line regions (BLRs) based on the method of Pancoast et al. to analyze the RM data set of Mrk 142 observed in the first monitoring season. In this approach, continuum variations are reconstructed using a damped random walk process, and BLR structure is delineated using a flexible disk-like geometry, in which BLR clouds move around the central BH with Keplerian orbits or inflow/outflow motion. The approach also includes the possibilities of anisotropic emission from BLR clouds, nonlinear response of the line emission to the continuum, and different long-term trends in the continuum and emission-line variations. We implement the approach in a Bayesian framework that is apt for parallel computation and use a Markov chain Monte Carlo technique to recover the parameters and uncertainties for the modeling, including the mass of the central BH. We apply three BLR models with different prescriptions of BLR cloud distributions and find that the best model for fitting the data of Mrk 142 is a two-zone BLR model, consistent with the theoretical BLR model surrounding slim accretion disks. The best model yields a BH mass of , resulting in a virial factor of for the full width at half maximum of the Hβ line measured from the mean spectrum. The virial factors for the other measures of the Hβ line width are also presented.

Super-Eddington growth of the first black holes

The assembly of the first super massive black holes (SMBHs) at $z \gtrsim 6$ is still a subject of intense debate. If black holes (BHs) grow at their Eddington rate, they must start from $\gtrsim 10^4 \, M_\odot$ seeds formed by the direct collapse of gas. Here we explore the alternative scenario where $\sim 100 \, M_\odot$ BH remnants of the first stars grow at super-Eddington rate via radiatively inefficient slim accretion disks. We use an improved version of the cosmological, data-constrained semi-analytic model GAMETE/QSOdust, where we follow the evolution of nuclear BHs and gas cooling, disk and bulge formation of their host galaxies. Adopting SDSS J1148+5251 (J1148) at $z = 6.4$ as a prototype of luminous $z \gtrsim 6$ quasars, we find that $\sim$ 80% of its SMBH mass is grown by super-Eddington accretion, which can be sustained down to $z \sim 10$ in dense, gas-rich environments. The average BH mass at $z \sim 20$ is $M_{\rm BH} \gtrsim 10^4 \,M_\odot$, comparable to that of direct collapse BHs. At $z = 6.4$ the AGN-driven mass outflow rate is consistent with the observations and the BH-to-bulge mass ratio is compatible with the local scaling relation. However, the stellar mass in the central 2.5 kpc is closer to the value inferred from CO observations. Finally, $\sim 20 %$ of J1148 progenitors at $z=7.1$ have BH luminosities and masses comparable to ULAS J1120+0641, suggesting that this quasar may be one of the progenitors of J1148.

Emission of gravitational waves by precession of slim accretion disks dynamically driven by the Bardeen‐Petterson effect

AbstractThe electromagnetic radiation emitted from some astro‐physical objects such as active galactic nuclei (AGN), microquasars (M‐QSRs), and central engines of gamma‐ray burst (GRBs), seems to have a similar physical origin: a powerful jet of plasma ejected from a localized system, presumably composed of an accretion disk encircling a compact object. This radiation is generally beamed in the polar directions and in some cases, it appears to have a spiral‐like structure that could be explained if the central system itself precesses. In this work, we use the slim disk accretion model, presented by Popham et al. (1999), to studying the gravitational waves (GWs) emitted by the precession of the accretion disk around a solar‐mass Kerr black hole (KBH). For practical purposes, this model describes the central engine of a class of GRBs when some astro‐physical constrains are fulfilled. The induced precession considered here is driven by the Bardeen‐Petterson effect, which results from the combination of viscous effects in such disks and the relativistic frame‐dragging effect. We evaluate the feasibility of direct detection of the GWs computed for such a model and show that the precession of this kind of systems could be detected by gravitational wave observatories like DECIGO, ultimate‐DECIGO, and BBO, with higher probability if such a class of sources are placed at distances less than 1 Mpc. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Shining in the dark: the spectral evolution of the first black holes

Massive Black Hole (MBH) seeds at redshift $z \gtrsim 10$ are now thought to be key ingredients to explain the presence of the super-massive ($10^{9-10} \, \mathrm{M_{\odot}}$) black holes in place $ < 1 \, \mathrm{Gyr}$ after the Big Bang. Once formed, massive seeds grow and emit copious amounts of radiation by accreting the left-over halo gas; their spectrum can then provide crucial information on their evolution. By combining radiation-hydrodynamic and spectral synthesis codes, we simulate the time-evolving spectrum emerging from the host halo of a MBH seed with initial mass $10^5 \, \mathrm{M_{\odot}}$, assuming both standard Eddington-limited accretion, or slim accretion disks, appropriate for super-Eddington flows. The emission occurs predominantly in the observed infrared-submm ($1-1000 \, \mathrm{\mu m}$) and X-ray ($0.1 - 100 \, \mathrm{keV}$) bands. Such signal should be easily detectable by JWST around $\sim 1 \, \mathrm{\mu m}$ up to $z \sim 25$, and by ATHENA (between $0.1$ and $10 \, \mathrm{keV}$, up to $z \sim 15$). Ultra-deep X-ray surveys like the Chandra Deep Field South could have already detected these systems up to $z \sim 15$. Based on this, we provide an upper limit for the $z \gtrsim 6$ MBH mass density of $\rho_{\bullet} \lesssim 2.5 \times 10^{2} \, \mathrm{M_{\odot} \, Mpc^{-3}}$ assuming standard Eddington-limited accretion. If accretion occurs in the slim disk mode the limits are much weaker, $\rho_{\bullet} \lesssim 7.6 \times 10^{3} \, \mathrm{M_{\odot} \, Mpc^{-3}}$ in the most constraining case.

SUPERMASSIVE BLACK HOLES WITH HIGH ACCRETION RATES IN ACTIVE GALACTIC NUCLEI. IV. HβTIME LAGS AND IMPLICATIONS FOR SUPER-EDDINGTON ACCRETION

We have completed two years of photometric and spectroscopic monitoring of a large number of active galactic nuclei (AGNs) with very high accretion rates. In this paper, we report on the result of the second phase of the campaign, during 2013--2014, and the measurements of five new H$\beta$ time lags out of eight monitored AGNs. All five objects were identified as super-Eddington accreting massive black holes (SEAMBHs). The highest measured accretion rates for the objects in this campaign are $\dot{\mathscr{M}}\gtrsim 200$, where $\dot{\mathscr{M}}= \dot{M}_{\bullet}/L_{\rm Edd}c^{-2}$, $\dot{M}_{\bullet}$ is the mass accretion rates, $L_{\rm Edd}$ is the Eddington luminosity and $c$ is the speed of light. We find that the H$\beta$ time lags in SEAMBHs are significantly shorter than those measured in sub-Eddington AGNs, and the deviations increase with increasing accretion rates. Thus, the relationship between broad-line region size ($R_{_{\rm H\beta}}$) and optical luminosity at 5100\AA, $R_{_{\rm H\beta}}-L_{5100}$, requires accretion rate as an additional parameter. We propose that much of the effect may be due to the strong anisotropy of the emitted slim-disk radiation. Scaling $R_{_{\rm H\beta}}$ by the gravitational radius of the black hole, we define a new radius-mass parameter ($Y$) and show that it saturates at a critical accretion rate of $\dot{\mathscr{M}}_c=6\sim 30$, indicating a transition from thin to slim accretion disk and a saturated luminosity of the slim disks. The parameter $Y$ is a very useful probe for understanding the various types of accretion onto massive black holes. We briefly comment on implications to the general population of super-Eddington AGNs in the universe and applications to cosmology.

THE CASE FOR SUPERCRITICAL ACCRETION ONTO MASSIVE BLACK HOLES AT HIGH REDSHIFT

Short-lived intermittent phases of super-critical (super-Eddington) growth, coupled with star formation via positive feedback, may account for early growth of massive black holes (MBH) and coevolution with their host spheroids. We estimate the possible growth rates and duty cycles of these episodes, both assuming slim accretion disk solutions, and adopting the results of recent numerical simulations. The angular momentum of gas joining the accretion disk determines the length of the accretion episodes, and the final mass a MBH can reach. The latter can be related to the gas velocity dispersion, and in galaxies with low-angular momentum gas the MBH can get to a higher mass. When the host galaxy is able to sustain inflow rates at 1-100 msunyr, replenishing and circulation lead to a sequence of short (~1e4-1e7 years), heavily obscured accretion episodes that increase the growth rates, with respect to an Eddington-limited case, by several orders of magnitude. Our model predicts that the ratio of MBH accretion rate to star formation rate is 1e2 or higher, leading, at early epochs, to a ratio of MBH to stellar mass higher than the "canonical" value of ~1e-3, in agreement with current observations. Our model makes specific predictions that long-lived super-critical accretion occurs only in galaxies with copious low-angular momentum gas, and in this case the MBH is more massive at fixed velocity dispersion.

SUPERMASSIVE BLACK HOLES WITH HIGH ACCRETION RATES IN ACTIVE GALACTIC NUCLEI. I. FIRST RESULTS FROM A NEW REVERBERATION MAPPING CAMPAIGN

We report first results from a large project to measure black hole (BH) mass in high accretion rate active galactic nuclei (AGNs). Such objects may be different from other AGNs in being powered by slim accretion disks and showing saturated accretion luminosities, but both are not yet fully understood. The results are part of a large reverberation mapping (RM) campaign using the 2.4-m Shangri-La telescope at the Yunnan Observatory in China. The goals are to investigate the gas distribution near the BH and the properties of the central accretion disks, to measure BH mass and Eddington ratios, and to test the feasibility of using such objects as a new type of cosmological candles. The paper presents results for three objects, Mrk 335, Mrk 142 and IRAS F12397+3333 with H$\beta$ time lags relative to the 5100\AA\ continuum of $10.6^{+1.7}_{-2.9}$, $6.4^{+0.8}_{-2.2}$ and $11.4^{+2.9}_{-1.9}$ days, respectively. The corresponding BH masses are $(8.3_{-3.2}^{+2.6})\times 10^6M_{\odot}$, $(3.4_{-1.2}^{+0.5})\times 10^6M_{\odot}$ and $(7.5_{-4.1}^{+4.3})\times 10^6M_{\odot}$, and the lower limits on the Eddington ratios 0.6, 2.3, and 4.6 for the minimal radiative efficiency of 0.038. Mrk 142 and IRAS F12397+333 (extinction corrected) clearly deviate from the currently known relation between H$\beta$ lag and continuum luminosity. The three Eddington ratios are beyond the values expected in thin accretion disks and two of them are the largest measured so far among objects with RM-based BH masses. We briefly discuss implications for slim disks, BH growth and cosmology.

Bolometric luminosity black hole growth time and slim accretion discs in active galactic nuclei

We investigate the accretion rate, bolometric luminosity, black hole (BH) growth time and BH spin in a large AGN sample under the assumption that all such objects are powered via thin or slim accretion discs (ADs). We use direct estimates of the mass accretion rate, Mdot, to show that many currently used values of Lbol and Ledd are either under estimated or over estimated because they are based on bolometric correction factors that are adjusted to the properties of moderately accreting active galactic nuclei (AGN) and do not take into account the correct combination of BH mass, spin and accretion rate. The consistent application of AD physics to our sample of Sloan Digital Sky Survey (SDSS) AGN leads to the following findings: 1. Even the most conservative assumption about the radiative efficiency of fast accreting BHs shows that many of these sources must contain slim ADs. We illustrate this by estimating the fraction of such objects at various redshifts. 2. Many previously estimated BH growth times are inconsistent with the AD theory. In particular, the growth times of the fastest accreting BHs were over estimated in the past by large factors with important consequences to AGN evolution. 3. Currently used bolometric correction factors for low accretion rate very massive SDSS BHs, are inconsistent with the AD theory. Applying the AD set of assumptions to such objects, combined with standard photoionization calculations of broad emission lines, leads to the conclusion that many such objects must contain fast spinning BHs.

Super-Eddington Accreting Massive Black Holes as Long-Lived Cosmological Standards

Super-Eddington accreting massive black holes (SEAMBHs) reach saturated luminosities above a certain accretion rate due to photon trapping and advection in slim accretion disks. We show that these SEAMBHs could provide a new tool for estimating cosmological distances if they are properly identified by hard x-ray observations, in particular by the slope of their 2-10 keV continuum. To verify this idea we obtained black hole mass estimates and x-ray data for a sample of 60 narrow line Seyfert 1 galaxies that we consider to be the most promising SEAMBH candidates. We demonstrate that the distances derived by the new method for the objects in the sample get closer to the standard luminosity distances as the hard x-ray continuum gets steeper. The results allow us to analyze the requirements for using the method in future samples of active black holes and to demonstrate that the expected uncertainty, given large enough samples, can make them into a useful, new cosmological ruler.

Suzaku Investigation into the Nature of the Nearest Ultraluminous X-Ray Source, M33 X-8

Abstract The X-ray spectrum of the nearest ultraluminous X-ray source, M 33 X-8, obtained by Suzaku during 2010 January 11–13, was closely analyzed in order to examine its nature. It is, by far, the only data with the highest signal statistic in the 0.4–10 keV range. Despite being able to reproduce the X-ray spectrum, Comptonization of the disk photons failed to give a physically meaningful solution. A modified version of the multi-color disk model, in which the dependence of the disk temperature on the radius is described as $ r^{-p}$ , with $ p$ being a free parameter, can also approximate the spectrum. From this model, the innermost disk temperature and bolometric luminosity were obtained as $ T_{\rm in}$$ =$ 2.00$ _{-0.05}^{+0.06}$ keV and $ L_{\rm disk}$$ =$ 1.36 $ \times$ 10$ ^{39}$ (cos $ i$ )$ ^{-1}$ erg s$ ^{-1}$ , respectively, where $ i$ is the disk inclination. A small temperature gradient of $ p$$ =$ 0.535$ _-0.005^{+0.004}$ , together with the high disk temperature, is regarded as signatures of the slim accretion disk model, suggesting that M 33 X-8 was accreting at a high mass-accretion rate. With a correction factor for the slim-disk taken into account, the innermost disk radius, $ R_{\rm in}$$ =$ 81.9$ _-6.5^{+5.9}$ (cos$ i$ )$ ^{-0.5}$ km, corresponds to a black-hole mass of $ M$$ \sim$ 10 $ M_{\odot}$ (cos $ i$ )$ ^{-0.5}$ . Accordingly, the bolometric disk luminosity is estimated to be about 80(cos $ i$ )$ ^{-0.5}$ % of the Eddington limit. A numerically calculated slim-disk spectrum was found to reach a similar result. Thus, the extremely super-Eddington luminosity is not required to explain the nature of M 33 X-8. This conclusion is utilized to argue for the existence of intermediate-mass black holes with $ M$$ \gtrsim$ 100$ M_{\odot}$ radiating at the sub/trans-Eddington luminosity, among ultraluminous X-ray sources with $ L_{\rm disk}$$ \gtrsim$ 10$ ^{40}$ erg s$ ^{-1}$ .

STUDIES OF THERMALLY UNSTABLE ACCRETION DISKS AROUND BLACK HOLES WITH ADAPTIVE PSEUDOSPECTRAL DOMAIN DECOMPOSITION METHOD. II. LIMIT-CYCLE BEHAVIOR IN ACCRETION DISKS AROUND KERR BLACK HOLES

For the first time ever, we derive equations governing the time-evolution of fully relativistic slim accretion disks in the Kerr metric, and numerically construct their detailed non-stationary models. We discuss applications of these general results to a possible limit-cycle behavior of thermally unstable disks. Our equations and numerical method are applicable in a wide class of possible viscosity prescriptions, but in this paper we use a diffusive form of the "standard alpha prescription" that assumes the viscous torque is proportional to the total pressure. In this particular case, we find that the parameters which dominate the limit-cycle properties are the mass-supply rate and the value of the alpha-viscosity parameter. Although the duration of the cycle (or the outburst) does not exhibit any clear dependence on the black hole spin, the maximal outburst luminosity (in the Eddington units) is positively correlated with the spin value. We suggest a simple method for a rough estimate of the black hole spin based on the maximal luminosity and the ratio of outburst to cycle durations. We also discuss a temperature-luminosity relation for the Kerr black hole accretion discs limit-cycle. Based on these results we discuss the limit-cycle behavior observed in microquasar GRS 1915+105. We also extend this study to several non-standard viscosity prescriptions, including a "delayed heating" prescription recently stimulated by the recent MHD simulations of accretion disks.