Ken-ya Watarai

Slim-Disk Model for Ultraluminous X-Ray Sources

The ultraluminous X-ray sources (ULXs) are unique in exhibiting moderately bright X-ray luminosities, LX ~ 1038-1040 ergs s-1, and relatively high blackbody temperatures, Tin ~ 1.0-2.0 keV. From the constraint that LX cannot exceed the Eddington luminosity LE, we require relatively high black hole masses, M ~ 10-100 M☉; however, for such large masses the standard disk theory predicts lower blackbody temperatures, Tin < 1.0 keV. To understand a cause of this puzzling fact, we carefully calculate the accretion flow structure shining at ~LE, 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 ( 30LE/c2) an apparently compact region with a size of Rin (1-3)rg (with rg being the Schwarzschild radius) is shining with a blackbody temperature of Tin 1.8(M/10 M☉)-1/4 keV even for the case of a nonrotating black hole. Furthermore, Rin decreases as increases, 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 LX and Tin both on the logarithmic scales) are not straight but bent toward 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 ~ 10-30 M☉, and high accretion rates, 10LE/c2. Interestingly, IC 342 source 1, in particular, was observed to move along the constant M line (not constant Rin line) in our simulations. This provides firm evidence that at least some ULXs are shining at LE and contain black holes with M 10-100 M☉.

The Hot Disk Corona and Magnetic Turbulence in Radio-quiet Active Galactic Nuclei: Observational Constraints

We compile a sample consisting of 56 radio-quiet active galactic nuclei so as to investigate the statistical properties of the hot corona in accretion disks from ASCA observations. The black hole masses in the sample are estimated via several popular methods, and the bolometric luminosities from the multiwavelength 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 use the least- squares method of multivariate regression and find a strong correlation between F-X = L2-10 keV/L-bol and E as F-X proportional to E-064. 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 (Gamma) and E depends critically on the types of objects: Gamma is nearly constant (Gamma proportional to E-0) in broad- line Seyfert 1 galaxies, whereas Gamma proportional to log E-0.18 in narrow- line Seyfert 1 galaxies, although this is not very significant. We can set constraints on the forms of the 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 the magnetic energy density in the disk. We find that the shear stress tensor is favored by the correlation in the present sample, t. P where P-gas is the gas pressure.

Spectral Energy Distribution in Supercritical Disk Accretion Flows through Photon-trapping Effects

We investigate the spectral energy distribution (SED) of the supercritical disk accretion flows around black holes by solving the multifrequency zeroth-moment equation of the radiation transfer equation under the flux-limited diffusion approximation as well as the energy equation of gas. Special attention is paid to the photon-trapping effects, the effects that photons are trapped within accretion flow and are swallowed by a black hole, with little being radiated away. It is found that when flow luminosity is below about twice the Eddington luminosity (L 2LE), photon trapping is ineffective and the SED shifts to the higher energy side as L increases. The peak frequency at which the SED reaches its peak becomes at maximum 3 times higher than that given by the standard-disk model, which might resolve the too hot accretion disk problem. When L 2LE, in contrast, the peak frequency of the SED tends to decrease with increase of mass accretion rate. This is due to enhanced photon trapping. Since high-energy photons are generated near the equatorial plane, they can be more effectively trapped in flow than low-energy ones, and hence the high-energy part of radiation is suppressed. Finally, the observed time variation of IC 342 S1, which is an ultraluminous X-ray source, in the X-ray H-R diagram, can be explained by the modulation of the mass accretion rate. In comparison with the observational data, we estimate that the mass of black hole in IC 342 S1 is ~ 100 M☉.

Geometrical Effect of Supercritical Accretion Flows: Observational Implications of Galactic Black-Hole Candidates and Ultraluminous X-Ray Sources

We consider the dependence of the viewing angle in supercritical accretion flows and discuss the observational implications of galactic black-hole candidates and ultraluminous X-ray sources. Model spectra of supercritical accretion flows strongly depend on the inclination angle. For example, the maximum temperature of the supercritical disk (the accretion rate and the black-hole mass are M=1000LE/C 2 and M =IOM 8 , respectively) is kIin rv 2.0keV for a low-inclination angle, i ;S 40°, while kIin rv 0.6keV for a high-inclination angle, i 2: 60°. This spectral softening originates from self-occultation of the disk, i.e., the outer disk blocks emission from the disk inner region, even if we take into account the effect of general relativity (light bending, Doppler boosting). This is because, when the mass accretion rate exceeds the critical rate, then the shape of the disk is geometrically thick due to enhanced radiation pressure. We also find that the spectral properties of low-i and low accretion-rate disks are very similar to those of high-i and high accretion-rate disks. That is, if an object has a high i and a high accretion rate, such a system suffers from self-occultation and the spectrum will be extremely soft. Therefore, we cannot distinguish these disks by only the difference in their spectrum shapes. Conversely, if we use the self-occultation properties, we could constrain the inclination angle of the system. We suggest that some observed high-temperature ultraluminous X-ray sources have low-inclination angles, i.e., near face-on geometry, i ;S 40°, and the Galactic black-hole candidate XTE 11550-564 possesses relatively high-inclination angles, i 2: 60°.

Observational Appearance of Relativistic, Spherically Symmetric Massive Winds

The photon mean free path in a relativistically moving medium becomes long in the down-stream direction while short in the up-stream direction. As a result, the observed optical depth

On Black Hole Mass Estimation from X-Ray Spectra of Ultraluminous X-Ray Sources

\tau

Where is a Marginally Stable Last Circular Orbit in Super-Critical Accretion Flow?

becomes small in the downstream direction while large in the upstream direction. Hence, if a relativistic spherical wind blows off, the optical depth depends strongly on its speed and the angle between the velocity and the line-of-sight. Abramowicz et al. (1991) examined such a relativistic wind, and found that the shape of the photosphere at

Slim Disk: Viscosity Prescriptions and Observational Implications

\tau=1

Peculiar characteristics of the hyper-luminous X-ray source M82 X-1

appears convex in the non-relativistic case, but concave for relativistic velocities. We further calculated the temperature distribution and luminosity of the photosphere both in the comoving and inertial frames. We found that the limb-darkening effect would strongly modified in the relativistic regime. We also found that luminosities of the photosphere becomes large as the wind speed increases due to the relativistic effects. In addition, the luminosity in the inertial frame is higher than that in the comoving frame. These results suggest that the observed temperature and brightness in luminous objects may be overestimated when there are strong relativistic winds.

Accretion Disk Spectra of the Ultra-luminous X-ray Sources in Nearby Spiral Galaxies and Galactic Superluminal Jet Sources

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 relationTeff /rp ,w ithr being the disk radius andp being treated as a fitting parameter. We first numerically calcu- late the theoretical flow structure and its spectra for a given black-hole mass, M ,a nd accretion rate, P M.T hr ough fitting to the theoretical spectra by the extended DBB model, we can estimate the black-hole mass, Mx ,a ssuming that the innermost disk radius isrin =3rg./Mx/ ,w hererg is the Schwarzschild radius. We find, however, that the estimated mass deviates from that adopted in the spectral calculations,M ,e ven for low-P 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=Mx ,i n the super-critical regimes for some sets ofM and P M ,fi nding that am ass correction factor ranges between M=Mx � 1.2-1.6. The higher is P M ,t he largerdoes 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<100Mˇ.