452 research outputs found
Photon Bubbles and the Vertical Structure of Accretion Disks
We consider the effects of "photon bubble" shock trains on the vertical
structure of radiation pressure-dominated accretion disks. These density
inhomogeneities are expected to develop spontaneously in radiation-dominated
accretion disks where magnetic pressure exceeds gas pressure, even in the
presence of magnetorotational instability. They increase the rate at which
radiation escapes from the disk, and may allow disks to exceed the Eddington
limit by a substantial factor. We first generalize the theory of photon bubbles
to include the effects of finite optical depths and radiation damping.
Modifications to the diffusion law at low optical depth tend to fill in the
low-density regions of photon bubbles, while radiation damping inhibits the
formation of photon bubbles at large radii, small accretion rates, and small
heights above the equatorial plane. Accretion disks dominated by photon bubble
transport may reach luminosities of 10 to >100 times the Eddington limit (L_E),
depending on the mass of the central object, while remaining geometrically
thin. However, photon bubble-dominated disks with alpha-viscosity are subject
to the same thermal and viscous instabilities that plague standard radiation
pressure-dominated disks, suggesting that they may be intrinsically unsteady.
Photon bubbles can lead to a "core-halo" vertical disk structure. In
super-Eddington disks the halo forms the base of a wind, which carries away
substantial energy and mass, but not enough to prevent the luminosity from
exceeding L_E. Photon bubble-dominated disks may have smaller color corrections
than standard accretion disks of the same luminosity. They remain viable
contenders for some ultraluminous X-ray sources and may play a role in the
rapid growth of supermassive black holes at high redshift.Comment: 38 pages, 2 figures, accepted for publication in The Astrophysical
Journa
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, , to the viscous
heating rate, , i.e., , 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,
approaches , which corresponds to the advection-dominated
limit (), whereas outside the trapping radius, the radial dependence
of changes to , which corresponds to the
radiative-cooling-dominated limit. The analytical formula for 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
Geometrical Effect of Supercritical Accretion Flows: Observational Implications of Galactic Black-Hole Candidates and Ultraluminous X-ray Sources
We investigate 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. When the mass accretion rate
exceeds the critical rate, then the shape of the disk is geometrically thick
due to the enhanced radiation pressure. The model spectra of supercritical
accretion flows strongly depend on the inclination angle. Because the outer
disk blocks the emission from the disk inner region for high inclination angle.
We also find that the spectral properties of low-inclination angle and low
accretion-rate disks are very similar to those of high-inclination and high
accretion rate disks. That is, if an object has a high inclination and high
accretion rate, such a system suffers from self-occultation and the spectrum
will be extremely soft. Therefore, we cannot discriminate these differences
from spectrum shapes only. 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 near
face-on geometry, i < 40, and Galactic black hole candidate, XTE J1550-564,
possesses relatively high-inclination angles, i > 60.Comment: 13 pages, 6 figures, accepted for publication in PAS
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 ,
with being the height integrated pressure, and being the
parameter, and and being the total pressure and gas pressure
on the equatorial plane, respectively. Model with can produce the
overall time changes of \Tin and \Rin, but cannot give an excellent fit to
the observed amplitudes. Model with , 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
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., constant, where is the sound speed, is the Keplerian
angular velocity, and 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
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
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
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