Slim Disk Research Articles

FORMATION OF OVERHEATED REGIONS AND TRUNCATED DISKS AROUND BLACK HOLES: THREE-DIMENSIONAL GENERAL RELATIVISTIC RADIATION-MAGNETOHYDRODYNAMICS SIMULATIONS

ABSTRACT Using three-dimensional general relativistic radiation-magnetohydrodynamics simulations of accretion flows around stellar mass black holes, we report that the relatively cold disk ( ) is truncated near the black hole. Hot and less dense regions, of which the gas temperature is and more than 10 times higher than the radiation temperature (overheated regions), appear within the truncation radius. The overheated regions also appear above as well as below the disk, sandwiching the cold disk, leading to the effective Compton upscattering. The truncation radius is for , where are the gravitational radius, mass accretion rate, Eddington luminosity, and light speed, respectively. Our results are consistent with observations of a very high state, whereby the truncated disk is thought to be embedded in the hot rarefied regions. The truncation radius shifts inward to with increasing mass accretion rate , which is very close to an innermost stable circular orbit. This model corresponds to the slim disk state observed in ultraluminous X-ray sources. Although the overheated regions shrink if the Compton cooling effectively reduces the gas temperature, the sandwich structure does not disappear at the range of . Our simulations also reveal that the gas temperature in the overheated regions depends on black hole spin, which would be due to efficient energy transport from black hole to disks through the Poynting flux, resulting in gas heating.

Critical luminosity of Super-Dddington accretion disks

Slim disk is a kind of optically thick, advection dominated accretion flow, in which the disk height can be comparable with the disk radius. The Slim disk has been widely used to explain the observation phenomena of various Super Eddington accretion disks. Outflows are always present in the numerical simulations of Super Eddington accretion disks, which implies that only a small fraction of gas in the disk is finally swallowed by the black hole. In the study of the Slim disk, we adopt an explicit vertical gravitational force in the thermal equilibrium solutions. The results of our calculation show that there is a maximum for the gravitational force of a black hole in the vertical direction of the accretion disk, and there exists a maximally possible accretion rate for each radius in the outer region of the slim disk. The existence of a maximally possible accretion rate in the case of Super-Eddington accretion implies that only the inner region of these flows can possibly take the form of Slim disk, and strong outflows from the outer region are required to reduce the accretion rate in order for Slim disks to be realized. This result is in agreement with the numerical simulation result. Finally, we fit the curve of the disk luminosity L disk/ L Edd with the dimensionless accretion rate m ˙ , and derive an analytic relation between the total luminosity and the mass accretion rate.

THE X-RAY PROPERTIES OF MILLION SOLAR MASS BLACK HOLES

ABSTRACT We present new Chandra X-ray observations of seven low-mass black holes ( ) accreting at low-bolometric Eddington ratios between . We compare the X-ray properties of these seven low-mass active galactic nuclei (AGNs) to a total of 73 other low-mass AGNs in the literature with published Chandra observations (with Eddington ratios extending from ). We do not find any statistical differences between the low and high Eddington ratio low-mass AGNs in the distributions of their X-ray to ultraviolet luminosity ratios ( ), or in their X-ray spectral shapes. Furthermore, the distribution of low- AGNs displays an X-ray weak tail that is also observed within high- objects. Our results indicate that between , there is no systematic change in the structure of the accretion flow for active galaxies hosting black holes. We examine the accuracy of current bolometric luminosity estimates for our low- objects with new Chandra observations, and it is plausible that their Eddington ratios could be underestimated by up to an order of magnitude. If so, then in analogy with weak emission line quasars, we suggest that accretion from a geometrically thick, radiatively inefficient “slim disk” could explain their diverse properties in . Alternatively, if current Eddington ratios are correct (or overestimated), then the X-ray weak tail would imply that there is diversity in disk/corona couplings among individual low-mass objects. Finally, we conclude by noting that the distribution for low-mass black holes may have favorable consequences for the epoch of cosmic reionization being driven by AGN.

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.

Super- and sub-Eddington accreting massive black holes: a comparison of slim and thin accretion discs through study of the spectral energy distribution

We employ optical and UV observations to present SEDs for two reverberation-mapped samples of super-Eddington and sub-Eddington AGN with similar luminosity distributions. The samples are fitted with accretion disc models in order to look for SED differences that depend on the Eddington ratio. The fitting takes into account measured BH mass and accretion rates, BH spin and intrinsic reddening of the sources. All objects in both groups can be fitted by thin AD models over the range 0.2-1$\,\mu$m with reddening as a free parameter. The intrinsic reddening required to fit the data are relatively small, $E(B-V)\leq0.2$~mag, except for one source. Super-Eddington AGN seem to require more reddening. The distribution of $E(B-V)$ is similar to what is observed in larger AGN samples. The best fit disc models recover very well the BH mass and accretion for the two groups. However, the SEDs are very different, with super-Eddington sources requiring much more luminous far-UV continuum. The exact amount depends on the possible saturation of the UV radiation in slim discs. In particular, we derive for the super-Eddington sources a typical bolometric correction at 5100\AA{} of 60-150 compared with a median of $\sim$20 for the sub-Eddington AGN. The measured torus luminosity relative to $\lambda L_{\lambda}(5100\AA{}$) are similar in both groups. The $\alpha_{OX}$ distribution is similar too. However, we find extremely small torus covering factors for super-Eddington sources, an order of magnitude smaller than those of sub-Eddington AGN. The small differences between the groups regarding the spectral range 0.2-22$\,\mu$m, and the significant differences related to the part of the SED that we cannot observed may be consistent with some slim disc models. An alternative explanation is that present day slim-disc models over-estimate the far UV luminosity of such objects by a large amount.

The slimming effect of advection on black-hole accretion flows

At super-Eddington rates accretion flows onto black holes have been described as slim (aspect ratio $H/R \lesssim 1$) or thick (H/R >1) discs, also known as tori or (Polish) doughnuts. The relation between the two descriptions has never been established, but it was commonly believed that at sufficiently high accretion rates slim discs inflate, becoming thick. We wish to establish under what conditions slim accretion flows become thick. We use analytical equations, numerical 1+1 schemes, and numerical radiative MHD codes to describe and compare various accretion flow models at very high accretion rates.We find that the dominant effect of advection at high accretion rates precludes slim discs becoming thick. At super-Eddington rates accretion flows around black holes can always be considered slim rather than thick.

Growing massive black holes through supercritical accretion of stellar-mass seeds

The rapid assembly of the massive black holes that power the luminous quasars observed at $z \sim 6-7$ remains a puzzle. Various direct collapse models have been proposed to head-start black hole growth from initial seeds with masses $\sim 10^5\,\rm M_\odot$, which can then reach a billion solar mass while accreting at the Eddington limit. Here we propose an alternative scenario based on radiatively inefficient super-critical accretion of stellar-mass holes embedded in the gaseous circum-nuclear discs (CNDs) expected to exist in the cores of high redshift galaxies. Our sub-pc resolution hydrodynamical simulations show that stellar-mass holes orbiting within the central 100 pc of the CND bind to very high density gas clumps that arise from the fragmentation of the surrounding gas. Owing to the large reservoir of dense cold gas available, a stellar-mass black hole allowed to grow at super-Eddington rates according to the "slim disc" solution can increase its mass by 3 orders of magnitudes within a few million years. These findings are supported by simulations run with two different hydro codes, RAMSES based on the Adaptive Mesh Refinement technique and GIZMO based on a new Lagrangian Godunov-type method, and with similar, but not identical, sub-grid recipes for star formation, supernova feedback, black hole accretion and feedback. The low radiative efficiency of super-critical accretion flows are instrumental to the rapid mass growth of our black holes, as they imply modest radiative heating of the surrounding nuclear environment.

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)

THE 2013–2014 OUTBURST OF XTE J1908+094 OBSERVED WITHSWIFTANDNUSTAR: SPECTRAL EVOLUTION AND BLACK HOLE SPIN CONSTRAINT

We present a spectral study of the black hole candidate XTE J1908+094 during its 2013–2014 outburst. We analyzed 36 Swift/XRT observations together with a NuSTAR observation taken along this period. The outburst evolution is similar to what is previously observed in other black hole transients. The source transited from an initial low/hard state to a high/soft state and then went back to the low/hard state. The low/hard-state spectra are dominated by a hard component, while the high/soft-state spectra are dominated by a soft component. In the high/soft state, we find that the disk bolometric luminosity deviates weakly from the standard dependence, exhibiting a flatter dependence as The radial temperature profile is found to be flatter than that of the standard accretion disk. These results suggest an advection-dominated slim disk. During the NuSTAR observation, the source was in the high/soft state. A flare is seen in the NuSTAR light curves. During the flare, a spectral softening occurs with an increase in power-law flux. We suggest that the flare may be associated with the relativistic jets. A broad Fe Kα line and a disk reflection component are observed in the spectra, providing an opportunity to measure the black hole spin via the Fe-line method. We have fitted the NuSTAR spectra with different relativistically blurred disk reflection models. However, the data do not allow us to constrain the spin of the black hole.

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.

Efficiency of super-Eddington magnetically-arrested accretion

Abstract The radiative efficiency of super-Eddington accreting black holes (BHs) is explored for magnetically-arrested discs, where magnetic flux builds-up to saturation near the BH. Our three-dimensional general relativistic radiation magnetohydrodynamic (GRRMHD) simulation of a spinning BH (spin a/M = 0.8) accreting at ∼50 times Eddington shows a total efficiency ∼50 per cent when time-averaged and total efficiency ≳ 100 per cent in moments. Magnetic compression by the magnetic flux near the rotating BH leads to a thin disc, whose radiation escapes via advection by a magnetized wind and via transport through a low-density channel created by a Blandford–Znajek (BZ) jet. The BZ efficiency is sub-optimal due to inertial loading of field lines by optically thick radiation, leading to BZ efficiency ∼40 per cent on the horizon and BZ efficiency ∼5 per cent by r ∼ 400rg (gravitational radii) via absorption by the wind. Importantly, radiation escapes at r ∼ 400rg with efficiency η ≈ 15 per cent (luminosity L ∼ 50LEdd), similar to η ≈ 12 per cent for a Novikov–Thorne thin disc and beyond η ≲ 1 per cent seen in prior GRRMHD simulations or slim disc theory. Our simulations show how BH spin, magnetic field, and jet mass-loading affect these radiative and jet efficiencies.

Jet and disc luminosities in tidal disruption events

Tidal disruption events (TDE) in which a star is devoured by a massive black hole at a galac- tic center pose a challenge to our understanding of accretion processes. Within a month the accretion rate reaches super-Eddington levels. It then drops gradually over a time scale of a year to sub-Eddington regimes. The initially geometrically thick disk becomes a thin one and eventually an ADAF at very low accretion rates. As such, TDEs explore the whole range of accretion rates and configurations. A challenging question is what the corresponding light curves of these events are. We explore numerically the disk luminosity and the conditions within the inner region of the disk using a fully general relativistic slim disk model. Those conditions determine the magnitude of the magnetic field that engulfs the black hole and this, in turn, determines the Blandford-Znajek jet power. We estimate this power in two different ways and show that they are self-consistent. We find, as expected earlier from analytic argu- ments (Krolik & Piran 2012), that neither the disk luminosity nor the jet power follows the accretion rate throughout the disruption event. The disk luminosity varies only logarithmi- cally with the accretion rate at super-Eddington luminosities. The jet power follows initially the accretion rate but remains a constant after the transition from super- to sub- Eddington. At lower accretion rates at the end of the MAD phase the disk becomes thin and the jet may stop altogether. These new estimates of the jet power and disk luminosity that do not simply follow the mass fallback rate should be taken into account when searching for TDEs and analysing light curves of TDE candidates. Identification of some of the above mentioned transitions may enable us to estimate better TDE parameters.

Swift-XRT six-year monitoring of the ultraluminous X-ray source M33 X-8

The long term evolution of ULX with their spectral and luminosity variations in time give important clues on the nature of ULX and on the accretion process that powers them. We report here the results of a Swift-XRT 6-year monitoring campaign of the closest example of a persistent ULX, M33 X-8, that extends to 16 years the monitoring of this source in the soft X-rays. The luminosity of this source is a few 10^39 erg/s, marking the faint end of the ULX luminosity function. We analysed the set of 15 observations collected during the Swift monitoring. We searched for differences in the spectral parameters at different observing epochs, adopting several models commonly used to fit the X-ray spectra of ULX. The source exhibits flux variations of the order of 30%. No significant spectral variations are observed along the monitoring. The average 0.5-10 keV spectrum can be well described by a thermal model, either in the form of a slim disk, or as a combination of a Comptonized corona and a standard accretion disk.

The growth efficiency of high-redshift black holes

The observational evidence that Super-Massive Black Holes ($M_{\bullet} \sim 10^{9-10} \, \mathrm{M_{\odot}}$) are already in place less than $1 \, \mathrm{Gyr}$ after the Big Bang poses stringent time constraints on the growth efficiency of their seeds. Among proposed possibilities, the formation of massive ($\sim 10^{3-6} \, \mathrm{M_{\odot}}$) seeds and/or the occurrence of super-Eddington ($\dot{M}>\dot{M}_{Edd}$) accretion episodes may contribute to the solution of this problem. In this work we analytically and numerically investigate the accretion flow onto high-redshift ($z \sim 10$) black holes to understand the physical requirements favoring rapid and efficient growth. Our model identifies a "feeding-dominated" accretion regime and a "feedback-limited" one, the latter being characterized by intermittent (duty cycles ${\cal D} \lesssim 0.5$) and inefficient growth, with recurring outflow episodes. We find that low-mass seeds ($\lesssim 10^{3-4} \, \mathrm{M_{\odot}}$) evolve in the feedback-limited regime, while more massive seeds ($\gtrsim 10^{5-6} \, \mathrm{M_{\odot}}$) grow very rapidly as they are found in the feeding-dominated regime. In addition to the standard accretion model with a fixed matter-energy conversion factor ($\epsilon = 0.1$), we have also explored slim disk models, appropriate for super-Eddington accretion, where radiation is trapped in the disk and the radiative efficiency is reduced ($\epsilon \lesssim 0.04$), which may ensure a continuous growth with $\dot{M} \gg \dot{M}_{Edd}$ (up to $\sim 300\dot{M}_{Edd}$ in our simulations). Under these conditions, outflows play a negligible role and a black hole can accrete $80\%-100\%$ of the gas mass of the host halo ($\sim 10^7 \, \mathrm{M_{\odot}}$) in $\sim 10 \, \mathrm{Myr}$, while in feedback-limited systems we predict that black holes can accrete only up to $\sim 15\%$ of the available mass.

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.

X-RAY INSIGHTS INTO THE NATURE OF PHL 1811 ANALOGS AND WEAK EMISSION-LINE QUASARS: UNIFICATION WITH A GEOMETRICALLY THICK ACCRETION DISK?

We present an X-ray and multiwavelength study of 33 weak emission-line quasars (WLQs) and 18 quasars that are analogs of the extreme WLQ, PHL 1811, at z ~ 0.5-2.9. New Chandra 1.5-9.5 ks exploratory observations were obtained for 32 objects while the others have archival X-ray observations. Significant fractions of these luminous type 1 quasars are distinctly X-ray weak compared to typical quasars, including 16 (48%) of the WLQs and 17 (94%) of the PHL 1811 analogs with average X-ray weakness factors of 17 and 39, respectively. We measure a relatively hard ($\Gamma=1.16_{-0.32}^{+0.37}$) effective power-law photon index for a stack of the X-ray weak subsample, suggesting X-ray absorption, and spectral analysis of one PHL 1811 analog, J1521+5202, also indicates significant intrinsic X-ray absorption. We compare composite SDSS spectra for the X-ray weak and X-ray normal populations and find several optical-UV tracers of X-ray weakness; e.g., Fe II rest-frame equivalent width and relative color. We describe how orientation effects under our previously proposed "shielding-gas" scenario can likely unify the X-ray weak and X-ray normal populations. We suggest that the shielding gas may naturally be understood as a geometrically thick inner accretion disk that shields the broad line region from the ionizing continuum. If WLQs and PHL 1811 analogs have very high Eddington ratios, the inner disk could be significantly puffed up (e.g., a slim disk). Shielding of the broad emission-line region by a geometrically thick disk may have a significant role in setting the broad distributions of C IV rest-frame equivalent width and blueshift for quasars more generally.

The remarkable timing properties of a ‘hypersoft’ state in GRO J1655-40

We report the identification and study of an unusual soft state of the black hole low-mass X-ray binary GRO J1655-40, observed during its 2005 outburst by the Rossi X-ray Timing Explorer. Chandra X-ray grating observations have revealed a high mass-outflow accretion disc wind in this state, and we show that the broadband X-ray spectrum is remarkably similar to that observed in the so-called `hypersoft' state of the high mass X-ray binary Cyg X-3, which possesses a strong stellar wind from a Wolf-Rayet secondary. The power-spectral density (PSD) of GRO J1655-40 shows a bending power-law shape, similar to that of canonical soft states albeit with larger fractional rms. However, the characteristic bend-frequency of the PSD is strongly correlated with the X-ray flux, such that the bend-frequency increases by two decades for less than a factor 2 increase in flux. The strong evolution of PSD bend-frequency for very little change in flux or X-ray spectral shape seems to rule out the suppression of high-frequency variability by scattering in the wind as the origin of the PSD bend. Instead, we suggest that the PSD shape is intrinsic to the variability process and may be linked to the evolution of the scale-height in a slim disc. An alternative possibility is that variability is introduced by variable absorption and scattering in the wind. We further argue that the hypersoft state in GRO J1655-40 and Cyg X-3 is associated with accretion close to or above the Eddington limit.

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.

Limits on luminosity and mass accretion rate of a radiation-pressure-dominated accretion disc

There is a maximum for the gravity of a black hole in the vertical direction in the accretion disc. Outflows may probably be driven from the disc if the radiation flux of the disc is greater than a critical value corresponding to the maximal vertical gravity. We find that outflows are driven by the radiation force from the disc if the accretion rate is greater than the Eddington rate. The radiation of the disc is therefore limited by such outflows. The disc luminosity, L=L_Edd\propto ln mdot, at large-mdot cases. The Eddington ratio of the disc is ~3 for mdot~100, which is significantly lower than that of a conventional slim disc without outflows. This implies that the emission from some ultra-luminous X-ray sources with highly super Eddington luminosity should be Doppler beamed, or intermediate mass black holes are in these sources instead of stellar mass black holes. The spectra of the discs with outflows are saturated in the high frequency end provided mdot>2. We suggest that the saturated emission can be observed to estimate the masses of the black holes accreting at high rates, such as the narrow-line Seyfert galaxies, with the model calculations. The rate of the mass accreted by the black hole is always around the Eddington rate even if the mass accretion rate at the outer radius is very high, because most of the gas is removed into the outflows. This implies that the luminous quasars at high redshifts z>6 should have grown up through persistent accretion at a rate close to the Eddington rate.

The QPO states of 4U 1630−47

Among the transient black hole binary systems, 4U 1630-47 is one of the most active sources exhibiting outbursts every few hundred days, with every outburst lasting typically around hundred days. During the 2002-2004 outburst the appearance of quasi-periodic oscillations (QPOs) coincide with the onset of anomalous state. There are two distinct QPO states: namely the single QPO state with one QPO and the twin QPO state with two QPOs not related harmonically. The spectral features of this state are corroborated by a previous outburst in 1998. The evolution of the inner disc temperature and the inner disc radius suggest the possible onset of geometrically thicker, slim disc as a possible explanation of the energy spectral features. The other possibilities involving the Comptonizing cloud also exist that may explain the anomalous state. The two different QPO states exhibit different spectral features, and we provide a possible empirical physical scenario from the observation of the evolution of the spectral features.