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

A Note on the Slim Accretion Disk Model

We show that when the gravitational force is correctly calculated in dealing with the vertical hydrostatic equilibrium of black hole accretion disks, the relationship that is valid for geometrically thin disks, i.e., $c_s/\Omega_K H =$ constant, where $c_s$ is the sound speed, $\Omega_K$ is the Keplerian angular velocity, and $H$ is the half-thickness of the disk, does not hold for slim disks. More importantly, by adopting the correct vertical gravitational force in studies of thermal equilibrium solutions, we find that there exists a maximally possible accretion rate for each radius in the outer region of optically thick accretion flows, so that only the inner region of these flows can possibly take the form of slim disks, and strong outflows from the outer region are required to reduce the accretion rate in order for slim disks to be realized.Comment: 14 pages, 5 figures, accepted by 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

Why Is Supercritical Disk Accretion Feasible?

Although the occurrence of steady supercritical disk accretion onto a black hole has been speculated about since the 1970s, it has not been accurately verified so far. For the first time, we previously demonstrated it through two-dimensional, long-term radiation-hydrodynamic simulations. To clarify why this accretion is possible, we quantitatively investigate the dynamics of a simulated supercritical accretion flow with a mass accretion rate of ~10^2 L_E/c^2 (with L_E and c being, respectively, the Eddington luminosity and the speed of light). We confirm two important mechanisms underlying supercritical disk accretion flow, as previously claimed, one of which is the radiation anisotropy arising from the anisotropic density distribution of very optically thick material. We qualitatively show that despite a very large radiation energy density, E_0>10^2L_E/(4 pi r^2 c) (with r being the distance from the black hole), the radiative flux F_0 cE_0/tau could be small due to a large optical depth, typically tau 10^3, in the disk. Another mechanism is photon trapping, quantified by vE_0, where v is the flow velocity. With a large |v| and E_0, this term significantly reduces the radiative flux and even makes it negative (inward) at r<70r_S, where r_S is the Schwarzschild radius. Due to the combination of these effects, the radiative force in the direction along the disk plane is largely attenuated so that the gravitational force barely exceeds the sum of the radiative force and the centrifugal force. As a result, matter can slowly fall onto the central black hole mainly along the disk plane with velocity much less than the free-fall velocity, even though the disk luminosity exceeds the Eddington luminosity. Along the disk rotation axis, in contrast, the strong radiative force drives strong gas outflows.Comment: 8 pages, 7 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

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

Quantum Fluctuation-Induced Phase Transition in S=1/2 XY-like Heisenberg Antiferromagnets on the Triangular Lattice

The selection of the ground state among nearly degenerate states due to quantum fluctuations is studied for the S=1/2 XY-like Heisenberg antiferromagnets on the triangular lattice in the magnetic field applied along the hard axis, which was first pointed out by Nikuni and Shiba. We find that the selected ground state sensitively depends on the degree of the anisotropy and the magnitude of the magnetic field. This dependence is similar to that in the corresponding classical model at finite temperatures where various types of field induced phases appear due to the entropy effect. It is also found that the similarity of the selected states in the classical and quantum models are not the case in a two-leg ladder lattice, although the lattice consists of triangles locally and the ground state of this lattice in the classical case is the same as that of the triangular lattice.Comment: 15 pages, 35 figure

Photon Trapping Enables Super-Eddington Growth of Black-Hole Seeds in Galaxies at High Redshift

We identify a physical mechanism that would have resulted in rapid, obscured growth of seed super-massive black-holes in galaxies at z>6. Specifically, we find that the density at the centre of typical high redshift galaxies was at a level where the Bondi accretion rate implies a diffusion speed of photons that was slower than the gravitational infall velocity, resulting in photons being trapped within the accretion flow and advected into the black-hole. We show that there is a range of black-hole masses (M_bh ~ 10^3-10^5 solar masses) where the accretion flow traps radiation, corresponding to black-holes that were massive enough to generate a photon trapping accretion flow, but small enough that their Bondi radii did not exceed the isothermal scale height of self-gravitating gas. Under these conditions we find that the accretion reaches levels far in excess of the Eddington rate. A prediction of this scenario is that X-ray number counts of active galactic nuclei at z>6 would exhibit a cutoff at the low luminosities corresponding to black-hole masses below ~10^5 solar masses. At low redshifts we find photon trapping to be unimportant because it could only occur in rare low spin halos, and would require black-hole masses in excess of expectations from the observed black-hole - halo mass relation. The super-Eddington growth of ~10^5 solar mass seed black-holes at high redshift may have provided a natural acceleration towards the growth of super-massive black-holes at z~6-7, less than a billion years after the Big Bang.Comment: 10 pages, 4 figures. Submitted to MNRA

Vertically Self-Gravitating ADAFs in the Presence of Toroidal Magnetic Field

Force due to the self-gravity of the disc in the vertical direction is considered to study its possible effects on the structure of a magnetized advection-dominated accretion disc. We present steady-sate self similar solutions for the dynamical structure of such a type of the accretion flows. Our solutions imply reduced thickness of the disc because of the self-gravity. It also imply that the thickness of the disc will increase by adding the magnetic field strength.Comment: Accepted for publication in Astrophysics and Space Science

From Capillary Condensation to Interface Localization Transitions in Colloid Polymer Mixtures Confined in Thin Film Geometry

Monte Carlo simulations of the Asakura-Oosawa (AO) model for colloid-polymer mixtures confined between two parallel repulsive structureless walls are presented and analyzed in the light of current theories on capillary condensation and interface localization transitions. Choosing a polymer to colloid size ratio of q=0.8 and studying ultrathin films in the range of D=3 to D=10 colloid diameters thickness, grand canonical Monte Carlo methods are used; phase transitions are analyzed via finite size scaling, as in previous work on bulk systems and under confinement between identical types of walls. Unlike the latter work, inequivalent walls are used here: while the left wall has a hard-core repulsion for both polymers and colloids, at the right wall an additional square-well repulsion of variable strength acting only on the colloids is present. We study how the phase separation into colloid-rich and colloid-poor phases occurring already in the bulk is modified by such a confinement. When the asymmetry of the wall-colloid interaction increases, the character of the transition smoothly changes from capillary condensation-type to interface localization-type. The critical behavior of these transitions is discussed, as well as the colloid and polymer density profiles across the film in the various phases, and the correlation of interfacial fluctuations in the direction parallel to the confining walls. The experimental observability of these phenomena also is briefly discussed.Comment: 36 pages, 15 figure