New Analytical Formula for Supercritical Accretion Flows

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, $Q_{\rm adv}$, to the viscous heating rate, $Q_{\rm vis}$, i.e., $f=Q_{\rm adv}/Q_{\rm vis}$, 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, \rtrap, 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 $f \propto r^0$, which corresponds to the advection-dominated limit ($f \sim 1$), whereas outside the trapping radius, the radial dependence of $f$ changes to $f \propto r^{-2}$, 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.Comment: 14 pages, 7 figures, accepted for publication in the Astrophysical Journa

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

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 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 (> 300 M_solar). 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.Comment: ApJ, accepte

The X-ray Luminosity Function of "The Antennae" Galaxies (NGC4038/39) and the Nature of Ultra-Luminous X-ray Sources

We derive the X-ray luminosity function (XLF) of the X-ray source population detected in the Chandra observation of NGC4038/39 (the Antennae). We explicitly include photon counting and spectral parameter uncertainties in our calculations. The cumulative XLF is well represented by a flat power law ($\alpha=-0.47$), similar to those describing the XLFs of other star-forming systems (e.g. M82, the disk of M81), but different from those of early type galaxies. This result associates the X-ray source population in the Antennae with young High Mass X-ray Binaries. In comparison with less actively star-forming galaxies, the XLF of the Antennae has a highly significant excess of sources with luminosities above 10^{39} erg\s (Ultra Luminous Sources; ULXs). We discuss the nature of these sources, based on the XLF and on their general spectral properties, as well as their optical counterparts discussed in Paper III. We conclude that the majority of the ULXs cannot be intermediate mass black-holes (M > 10-1000 \msun) binaries, unless they are linked to the remnants of massive Population III stars (the Madau & Rees model). Instead, their spatial and multiwavelength properties can be well explained by beamed emission as a consequence of supercritical accretion. Binaries with a neutron star or moderate mass black-hole (up to 20\msun), and B2 to A type star companions would be consistent with our data. In the beaming scenario, the XLF should exibit caracteristic breaks that will be visible in future deeper observations of the Antennae.Comment: 15 pages, submitted to Ap

Model for Relaxation Oscillations of Luminous Accretion Disk in GRS1915+105: Variable Inner Edge

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 \Tin (the maximum disk temperature) and \Rin (the innermost radius of the disk). We find an abrupt, transient increase in \Tin and a temporary decrease in \Rin 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 $T_{r \phi}=-\alpha \Pi (p_{\rm gas}/p)^{\mu}$, with $\Pi$ being the height integrated pressure, $\alpha$ and $\mu$ being the parameter, and $p$ and $p_{\rm gas}$ being the total pressure and gas pressure on the equatorial plane, respectively. Model with $\mu=0.1$ can produce the overall time changes of \Tin and \Rin, but cannot give an excellent fit to the observed amplitudes. Model with $\mu=0.2$, on the other hand, gives the right amplitudes, but the changes of \Tin and \Rin 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.Comment: 11 pages, 5 figures, accepted for publication in Ap

Does the Slim-Disk Model Correctly Consider Photon-Trapping Effects?

We investigate the photon-trapping effects in the super-critical black hole accretion flows by solving radiation transfer as well as the energy equations of radiation and gas. It is found that the slim-disk model generally overestimates the luminosity of the disk at around the Eddington luminosity (L_E) and is not accurate in describing the effective temperature profile, since it neglects time delay between energy generation at deeper inside the disk and energy release at the surface. Especially, the photon-trapping effects are appreciable even below L ~ L_E, while they appear above ~ 3L_E according to the slim disk. Through the photon-trapping effects, the luminosity is reduced and the effective temperature profile becomes flatter than r^{-3/4} as in the standard disk. In the case that the viscous heating is effective only around the equatorial plane, the luminosity is kept around the Eddington luminosity even at very large mass accretion rate, Mdot>>L_E/c^2. The effective temperature profile is almost flat, and the maximum temperature decreases in accordance with rise in the mass accretion rate. Thus, the most luminous radius shifts to the outer region when Mdot/(L_E/c^2) >> 10^2. In the case that the energy is dissipated equally at any heights, the resultant luminosity is somewhat larger than in the former case, but the energy-conversion efficiency still decreases with increase of the mass accretion rate, as well. The most luminous radius stays around the inner edge of the disk in the latter case. Hence, the effective temperature profile is sensitive to the vertical distribution of energy production rates, so is the spectral shape. Future observations of high L/L_E objects will be able to test our model.Comment: 10 pages, 7 figures, accepted for publication in Ap

Dynamics of spin correlations in the spin-1/2 isotropic XY chain in a transverse field

Dynamic xx spin pair correlation functions for the isotropic spin-1/2 XY chain are calculated numerically for long open chains in the presence of a transverse magnetic field at finite temperature. As an application we discuss the temperature dependence of the spin-spin relaxation time in PrCl_3.Comment: 2 pages, latex, 2 figures, abstract of the paper presented at Ampere Summer School ``Applications of Magnetic Resonance in Novel Materials'' Nafplion, Greece, 3-9 September, 2000, partially published in J. Phys. A: Math. Gen. 33, 3063 (2000

Shapes and Positions of Black Hole Shadows in Accretion Disks and Spin Parameters of Black Holes

Can we determine a spin parameter of a black hole by observation of a black hole shadow in an accretion disk? In order to answer this question, we make a qualitative analysis and a quantitative analysis of a shape and a position of a black hole shadow casted by a rotating black hole on an optically thick accretion disk and its dependence on an angular momentum of a black hole. We have found black hole shadows with a quite similar size and a shape for largely different black hole spin parameters and a same black hole mass. Thus, it is practically difficult to determine a spin parameter of a black hole from a size and a shape of a black hole shadow in an accretion disk. We newly introduce a bisector axis of a black hole shadow named a shadow axis. For a rotating black hole a shape and a position of a black hole shadow are not symmetric with respect to a rotation axis of a black hole shadow. So, in this case the minimum interval between a mass center of a black hole and a shadow axis is finite. An extent of this minimum interval is roughly proportional to a spin parameter of a black hole for a fixed inclination angle between a rotation axis of a black hole and a direction of an observer. In order to measure a spin parameter of a black hole, if a shadow axis is determined observationally, it is crucially important to determine a position of a mass center of a black hole in a region of a black hole shadow.Comment: 13 pages, 6 figures, accepted for publication in Ap

Super-critical Accretion Flows around Black Holes: Two-dimensional, Radiation-pressure-dominated Disks with Photon-trapping

The quasi-steady structure of super-critical accretion flows around a black hole is studied based on the two-dimensional radiation-hydrodynamical (2D-RHD) simulations. The super-critical flow is composed of two parts: the disk region and the outflow regions above and below the disk. Within the disk region the circular motion as well as the patchy density structure are observed, which is caused by Kelvin-Helmholtz instability and probably by convection. The mass-accretion rate decreases inward, roughly in proportion to the radius, and the remaining part of the disk material leaves the disk to form outflow because of strong radiation pressure force. We confirm that photon trapping plays an important role within the disk. Thus, matter can fall onto the black hole at a rate exceeding the Eddington rate. The emission is highly anisotropic and moderately collimated so that the apparent luminosity can exceed the Eddington luminosity by a factor of a few in the face-on view. The mass-accretion rate onto the black hole increases with increase of the absorption opacity (metalicity) of the accreting matter. This implies that the black hole tends to grow up faster in the metal rich regions as in starburst galaxies or star-forming regions.Comment: 16 pages, 12 figures, accepted for publication in ApJ (Volume 628, July 20, 2005 issue

Discovery of Spectral Transitions from Two Ultra-Luminous Compact X-Ray Sources in Ic342

Two {\it ASCA} observations were made of two ultra-luminous compact X-ray sources (ULXs), Source 1 and Source 2, in the spiral galaxy IC 342. In the 1993 observation, Source 2 showed a 0.5--10 keV luminosity of $6 \times 10^{39}$ ergs s$^{-1}$ (assuming a distance of 4.0 Mpc), and a hard power-law spectrum of photon index $\sim 1.4$. As already reported, Source 1 was $\sim 3$ times brighter on that occasion, and exhibited a soft spectrum represented by a multi-color disk model of inner-disk temperature $\sim 1.8$ keV. The second observation made in February 2000 revealed that Source 1 had made a transition into a hard spectral state, while Source 2 into a soft spectral state. The ULXs are therefore inferred to exhibit two distinct spectral states, and sometimes make transitions between them. These results significantly reinforce the scenario which describes ULXs as mass-accreting black holes.Comment: 11 pages, 3 figures; acceoted for ApJ

A Chandra X-ray Study of NGC 1068: II. The Luminous X-ray Source Population

We present an analysis of the compact X-ray source population in the Seyfert~2 galaxy NGC 1068, imaged with Chandra. We find a total of 84 compact sources, of which 66 are projected onto the galactic disk of NGC 1068. Spectra of the brightest sources have been modeled with both multi-color disk blackbody and power-law models. The power-law model provides the better description of the spectrum for most of these sources. Five sources have 0.4-8 keV intrinsic luminosities greater than 10^{39} erg/s, assuming that their emission is isotropic and that they are associated with NGC 1068. We refer to these sources as Intermediate Luminosity X-ray Objects (IXOs). If these five sources are X-ray binaries accreting with luminosities that are both sub-Eddington and isotropic, then the implied source masses are >7 solar masses, and so they are inferred to be black holes. The brightest source has a much harder spectrum (Gamma = 0.9\pm0.1) than that found in Galactic black hole candidates and other IXOs. It also shows large-amplitude variability on both short-term and long-term timescales. The ratio of the number of sources with luminosities greater than 2.1 x 10^{38} erg/s in the 0.4-8 keV band to the rate of massive star formation is the same, to within a factor of two, for NGC 1068, the Antennae, NGC 5194 (the main galaxy in M51), and the Circinus galaxy. This suggests that the rate of production of X-ray binaries per massive star is approximately the same for galaxies with currently active star formation, including ``starbursts''.Comment: 33 pages, 10 figures. To appear in The Astrophysical Journal, v591 n1, July 1, 2003 issu