We discuss distinctive features of luminous accretion disks shining at the Eddington luminosity in the context of galactic black-hole candidates (GBCs). We first note that the standard-disk picture is not applicable, although it is often postulated. Rather, the disk becomes advection-dominated while remaining optically thick (the so-called slim disk). The slim disk exhibits several noteworthy signatures: (1) The disk luminosity is insensitive to the mass-flow rates, Ṁ, and is always kept around the Eddington luminosity, LE, even if Ṁ greatly exceeds LE/c2. This reflects the fact that radiative cooling is no longer balanced by viscous heating and excess energy is carried by accreting matter to black holes. (2) The spectra of the slim disks are multi-color blackbody characterized by (i) a high maximum temperature, kTin ∼ a few keV, (ii) a small size of an emitting region, rin < 3 rg (with rg being Schwarzschild radius), due to substantial radiation coming out from inside 3 rg, and (iii) flatter spectra in the soft-X bands, vSv ∼ v0, because of a flatter effective temperature profile of the slim disk, Teff ∝ r−1/2 (in contrast with Teff ∝ r−3/4 in the standard disk). Thus, a small rin (≪ 3rg) does not necessarily mean the presence of a Kerr hole. Furthermore, (3) as Ṁ increases, Tin increases, while rin decreases as rin ∝ (Tin)−1 approximately. That is, the changes in rin derived from the fitting do not necessarily mean the changes in the physical boundary of the optically thick portions of the disk. Observational implications are discussed in relation to binary jet sources.

The Ultra Luminous X-ray Sources (ULXs) are unique in exhibiting moderately bright X-ray luminosities, L x ∼ 10 38−40 erg s −1 , and relatively high blackbody temperatures, T in ∼ 1.0 − 2.0keV. From the constraint that L x cannot exceed the Eddington luminosity, L E , we require relatively high black-hole masses, M ∼ 10 − 100M ⊙ , however, for such large masses the standard disk theory predicts lower blackbody temperatures, T in < 1.0 keV. To understand a cause of this puzzling fact, we carefully calculate the accretion flow structure shining at ∼ L E , fully taking into account the advective energy transport in the optically thick regime and the transonic nature of the flow. Our calculations show that at high accretion rate (Ṁ 30 L E /c 2 ) an apparently compact region with a size of R in ≃ (1 − 3)r g (with r g being Schwarzschild radius) is shining with a blackbody temperature of T in ≃ 1.8(M/10M ⊙ ) −1/4 keV even for the case of a non-rotating black hole. Further, R in decreases asṀ increases, on the contrary to the canonical belief that the inner edge of the disk is fixed at the radius of the marginally stable last circular orbit. Accordingly, the loci of a constant black-hole mass on the "H-R diagram" (representing the relation between L x and T in both on the logarithmic scales) are not straight but bent towards the lower M direction in the frame of the standard-disk relation.We also plot the ASCA data of some ULXs on the same H-R diagram, finding that they all fall on the regions with relatively high masses, M ∼ 10 − 30M ⊙ , and high accretion rates,Ṁ 10 L E /c 2 . Interestingly, IC342 source 1, in particular, was observed to move along the constant-M line (not constant R in line) in our simulations. This provides a firm evidence that at least some ULXs are shining at L E , and containing black holes with M ≃ 10 − 100M ⊙ .

We compile a sample consisting of 56 radio-quiet active galactic nuclei so as to investigate statistical properties of hot corona of accretion disks from ASCA observations. The black-hole masses in the sample are estimated via several popular methods and the bolometric luminosities from the multi-wavelength continuum. This allows us to estimate the Eddington ratio (E ≡ L Bol /L Edd ) so that the undergoing physical processes can be tested via hard X-ray data. We find a strong correlation between F X ≡ L 2−10keV /L Bol and E as F X ∝ E −0.64 with a multivariate regression. This indicates that the release of gravitational energy in the hot corona is controlled by the Eddington ratio. On the other hand, the correlation between the hard X-ray spectral index (Γ) and E depends critically on the types of objects: Γ is nearly constant (Γ ∝ E 0 ) in broad-line Seyfert 1's (BLS1s), whereas Γ ∝ log E 0.18 in narrow-line Seyfert 1's (NLS1s), although not very significant. We can set constraints on the forms of magnetic stress tensor on the condition that F X is proportional to the fraction f of gravitational energy dissipated in the hot corona and that f is proportional to magnetic energy density in the disk. We find that the shear stress tensor t rφ ∝ P gas is favored by the correlation in the present sample, where P gas is the gas pressure.

Ultra-luminous Compact X-ray Sources (ULXs) in nearby spiral galaxies and Galactic superluminal jet sources share the common spectral characteristic that they have unusually high disk temperatures which cannot be explained in the framework of the standard optically thick accretion disk in the Schwarzschild metric. On the other hand, the standard accretion disk around the Kerr black hole might explain the observed high disk temperature, as the inner radius of the Kerr disk gets smaller and the disk temperature can be consequently higher. However, we point out that the observable Kerr 1 Universities Space Research Association.-2 -disk spectra becomes significantly harder than Schwarzschild disk spectra only when the disk is highly inclined. This is because the emission from the innermost part of the accretion disk is Doppler-boosted for an edge-on Kerr disk, while hardly seen for a face-on disk. The Galactic superluminal jet sources are known to be highly inclined systems, thus their energy spectra may be explained with the standard Kerr disk with known black hole masses. For ULXs, on the other hand, the standard Kerr disk model seems implausible, since it is highly unlikely that their accretion disks are preferentially inclined, and, if edge-on Kerr disk model is applied, the black hole mass becomes unreasonably large ( 300M ⊙ ). Instead, the slim disk (advection dominated optically thick disk) model is likely to explain the observed super-Eddington luminosities, hard energy spectra, and spectral variations of ULXs. We suggest that ULXs are accreting black holes with a few tens of solar mass, which is not unexpected from the standard stellar evolution scenario, and that their X-ray emission is from the slim disk shining at super-Eddington luminosities.

We investigated the radiation fields of a self-similar slim disk and the behavior of wind particles, which are driven by the radiation pressure of a self-similar slim disk. When the accretion rate is of the order of a critical rate, the accretion disk must puff up in the vertical direction to form a so-called slim disk. In contrast to a standard alpha disk, this slim disk has two major features: i) the disk is geometrically (mildly) thick, and ii) the radial motion is comparable to the rotational motion (advection). These effects make the opening angle of the disk less than 180°, and the disk radiation fields are expected to enhance towards the center. However, we found that trajectories of wind particles are accelerated along the disk surface. This indicates that the shape of the disk strongly influence the motion of plasma particles. Furthermore, particles lose angular momentum by radiation drag, while gaining angular momentum from rotating radiation fields. Taking into consideration the Compton drag, the income and expenditure of angular momentum of wind particles is positive, and they tend to spread out in a radial direction.

To understand the bursting behavior of the microquasar GRS 1915+105, we calculate time evolution of a luminous, optically thick accretion disk around a stellar mass black hole undergoing limit-cycle oscillations between the high-and low-luminosity states. We, especially, carefully solve the behavior of the innermost part of the disk, since it produces significant number of photons during the burst, and fit the theoretical spectra with the multi-color disk model. The fitting parameters are T in (the maximum disk temperature) and R in (the innermost radius of the disk). We find an abrupt, transient increase in T in and a temporary decrease in R in during a burst, which are actually observed in GRS 1915+105. The precise behavior is subject to the viscosity prescription. We prescribe the radial-azimuthal component of viscosity stress tensor to be T rϕ = −αΠ(p gas /p) µ , with Π being the height integrated pressure, α and µ being the parameter, and p and p gas being the total pressure and gas pressure on the equatorial plane, respectively. Model with µ = 0.1 can produce the overall time changes of T in and R in , but cannot give an excellent fit to the observed amplitudes. Model with µ = 0.2, on the other hand, gives the right amplitudes, but the changes of T in and R in are smaller. Although precise matching is left as future work, we may conclude that the basic properties of the bursts of GRS 1915+105 can be explained by our "limit-cycle oscillation" model. It is then required that the spectral hardening factor at high luminosities should be about 3 at around the Eddington luminosity instead of less than 2 as is usually assumed.

We examine a new family of global analytic solutions for optically thick accretion disks, which includes the supercritical accretion regime. We found that the ratio of the advection cooling rate, Q adv , to the viscous heating rate, Q vis , i.e., f = Q adv /Q vis , can be represented by an analytical form dependent on the radius and the mass accretion rate. The new analytic solutions can be characterized by the photon-trapping radius, r trap , inside which the accretion time is less than the photon diffusion time in the vertical direction; the nature of the solutions changes significantly as this radius is crossed. Inside the trapping radius, f approaches f ∝ r 0 , which corresponds to the advection-dominated limit (f ∼ 1), whereas outside the trapping radius, the radial dependence of f changes to f ∝ r −2 , which corresponds to the radiative-cooling-dominated limit. The analytical formula for f derived here smoothly connects these two regimes. The set of new analytic solutions reproduces well the global disk structure obtained by numerical integration over a wide range of mass accretion rates, including the supercritical accretion regime. In particular, the effective temperature profiles for our new solutions are in good agreement with those obtained from numerical solutions. Therefore, the new solutions will provide a useful tool not only for evaluating the observational properties of accretion flows, but also for investigating the mass evolution of black holes in the presence of supercritical accretion flows.

We propose a methodology to derive a black-hole mass for super-critical accretion flow. Here, we use the extended disk blackbody (extended DBB) model, a fitting model in which the effective temperature profile obeys the relation $T_{\rm eff} \propto r^{-p}$, with $r$ being the disk radius and $p$ being treated as a fitting parameter. We first numerically calculate the theoretical flow structure and its spectra for a given black-hole mass, $M$, and accretion rate, $\dot{M}$. Through fitting to the theoretical spectra by the extended DBB model, we can estimate the black-hole mass, $M_{\rm x}$, assuming that the innermost disk radius is $r_{\rm in}=3r_{\rm g} (\propto M_{\rm x})$, where $r_{\rm g}$ is the Schwarzschild radius. We find, however, that the estimated mass deviates from that adopted in the spectral calculations, $M$, even for low-$\dot{M}$ cases. We also find that the deviations can be eliminated by introducing a new correction for the innermost radius. Using this correction, we calculate mass correction factors, $M/M_{\rm x}$, in the super-critical regimes for some sets of $M$ and $\dot M$, finding that a mass correction factor ranges between $M/M_{\rm x} \sim$1.2-1.6. The higher is $\dot{M}$, the larger does the mass correction factor tend to be. Since the correction is relatively small, we can safely conclude that the black holes in ULXs, which Vierdayanti et al. (2006, PASJ, 58, 915) analyzed, are stellar-mass black holes with the mass being $&lt;100M_{\odot}$.