200 research outputs found
Three-Dimensional Simulations of Magnetized Thin Accretion Disks around Black Holes: Stress in the Plunging Region
We describe three-dimensional general relativistic magnetohydrodynamic
simulations of a geometrically thin accretion disk around a non-spinning black
hole. The disk has a thickness over the radial range
. In steady state, the specific angular momentum profile of the
inflowing magnetized gas deviates by less than 2% from that of the standard
thin disk model of
Novikov & Thorne (1973). Also, the magnetic torque at the radius of the
innermost stable circular orbit (ISCO) is only of the inward flux of
angular momentum at this radius. Both results indicate that magnetic coupling
across the ISCO is relatively unimportant for geometrically thin disks.Comment: 4 pages, 4 figures, ApJL accepte
Estimating the Spins of Stellar-Mass Black Holes by Fitting Their Continuum Spectra
We have used the Novikov-Thorne thin disk model to fit the continuum X-ray
spectra of three transient black hole X-ray binaries in the thermal state. From
the fits we estimate the dimensionless spin parameters of the black holes to
be: 4U 1543-47, a* = a/M = 0.7-0.85; GRO J1655-40, a* = 0.65-0.8; GRS 1915+105,
a* = 0.98-1. We plan to expand the sample of spin estimates to about a dozen
over the next several years. Some unresolved theoretical issues are briefly
discussed.Comment: 8 pages, 4 figures, 1 table; to appear in "Astrophysics of Compact
Objects" eds. Y. F. Yuan, X. D. Li, D. Lai, AI
The Case for Hypercritical Accretion in M33 X-7
The spin parameter of the black hole in M33 X-7 has recently been measured to
be a*=0.77+-0.05 (Liu et al. 2008). It has been proposed that the spin of the
15.65 M_sun black hole is natal. We show that this is not a viable evolutionary
path given the observed binary orbital period of 3.45 days since the explosion
that would produce a black hole with the cited spin parameter and orbital
period would disrupt the binary. Furthermore, we show that the system has to be
evolved through the hypercritical mass transfer of about 5 M_sun from the
secondary star to the black hole.Comment: 4 page
Precise Measurement of the Spin Parameter of the Stellar-Mass Black Hole M33 X-7
In prior work, {\it Chandra} and Gemini-North observations of the eclipsing
X-ray binary M33 X-7 have yielded measurements of the mass of its black hole
primary and the system's orbital inclination angle of unprecedented accuracy.
Likewise, the distance to the binary is known to a few percent. In an analysis
based on these precise results, fifteen {\it Chandra} and {\it XMM-Newton}
X-ray spectra, and our fully relativistic accretion disk model, we find that
the dimensionless spin parameter of the black hole primary is . The quoted 1- error includes all sources of observational
uncertainty. Four {\it Chandra} spectra of the highest quality, which were
obtained over a span of several years, all lead to the same estimate of spin to
within statistical errors (2%), and this estimate is confirmed by 11 spectra of
lower quality. There are two remaining uncertainties: (1) the validity of the
relativistic model used to analyze the observations, which is being addressed
in ongoing theoretical work; and (2) our assumption that the black hole spin is
approximately aligned with the angular momentum vector of the binary, which can
be addressed by a future X-ray polarimetry mission.Comment: 14 pages, 3 figures, 1 table, published in ApJ Letters; as explained
in the erratum at the end of the text, the spin parameter has been corrected
upward from a*=0.77 to a*=0.84. Apart from the addition of the erratum, the
paper is unchanged
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Viscous Torque and Dissipation in the Inner Regions of a Thin Accretion Disk: Implications for Measuring Black Hole Spin
We consider a simple Newtonian model of a steady accretion disk around a black hole. The model is based on height-integrated hydrodynamic equations, -viscosity, and a pseudo-Newtonian potential which results in an innermost stable circular orbit ( ISCO) that closely approximates the one predicted by general relativity. We find that, as the disk thickness H/R or the value of increases, the hydrodynamic model exhibits increasing deviations from the standard thin disk model of Shakura and Sunyaev. The latter is an analytical model in which the viscous torque is assumed to vanish at the ISCO. We consider the implications of the results for attempts to estimate black hole spin by using the standard disk model to fit continuum spectra of black hole accretion disks. We find that the error in the spin estimate is quite modest so long as H/R 0:1 and 0:2. At worst, the error in the estimated value of the spin parameter is 0.1 for a nonspinning black hole; the error is much less for a rapidly spinning hole. We also consider the density and disk thickness contrast between the gas in the disk and that inside the ISCO. The contrast needs to be large if black hole spin is to be successfully estimated by fitting the relativistically broadened X-ray line profile of fluorescent iron emission from reflection off an accretion disk. In our hydrodynamic models, the contrast in density and thickness is low when H/Rk0:1, suggesting that the iron line technique may be most reliable in extremely thin disks. We caution that these results have been obtained with a viscous hydrodynamic model. While our results are likely to be qualitatively correct, quantitative estimates of, e.g., the magnitude of the error in the spin estimate, need to be confirmed with MHD simulations of radiatively cooled thin disks.Astronom
Viscous Torque and Dissipation in the Inner Region of a Thin Accretion Disk: Implications for Measuring Black Hole Spin
We consider a simple Newtonian model of a steady accretion disk around a
black hole. The model is based on height-integrated hydrodynamic equations,
alpha-viscosity, and a pseudo-Newtonian potential that results in an innermost
stable circular orbit (ISCO) that closely approximates the one predicted by GR.
We find that the hydrodynamic models exhibit increasing deviations from the
standard disk model of Shakura & Sunyaev as disk thickness H/R or the value of
alpha increases. The latter is an analytical model in which the viscous torque
is assumed to vanish at the ISCO. We consider the implications of the results
for attempts to estimate black hole spin by using the standard disk model to
fit continuum spectra of black hole accretion disks. We find that the error in
the spin estimate is quite modest so long as H/R < 0.1 and alpha < 0.2. At
worst the error in the estimated value of the spin parameter is 0.1 for a
non-spinning black hole; the error is much less for a rapidly spinning hole. We
also consider the density and disk thickness contrast between the gas in the
disk and that inside the ISCO. The contrast needs to be large if black hole
spin is to be successfully estimated by fitting the relativistically-broadened
X-ray line profile of fluorescent iron emission from reflection off an
accretion disk. In our hydrodynamic models, the contrast in density and
thickness is low when H/R>0.1, sugesting that the iron line technique may be
most reliable in extemely thin disks. We caution that these results have been
obtained with a viscous hydrodynamic model and need to be confirmed with MHD
simulations of radiatively cooled thin disks.Comment: 32 pages, 10 figures; accepted by Ap
Inferring the Inclination of a Black Hole Accretion Disk from Observations of its Polarized Continuum Radiation
Spin parameters of stellar-mass black holes in X-ray binaries are currently
being estimated by fitting the X-ray continuum spectra of their accretion disk
emission. For this method, it is necessary to know the inclination of the
X-ray-producing inner region of the disk. Since the inner disk is expected to
be oriented perpendicular to the spin axis of the hole, the usual practice is
to assume that the black hole spin is aligned with the orbital angular momentum
vector of the binary, and to estimate the inclination of the latter from
ellipsoidal modulations in the light curve of the secondary star. We show that
the inclination of the disk can be inferred directly if we have both spectral
and polarization information on the disk radiation. The predicted degree of
polarization varies from 0% to 5% as the disk inclination changes from face-on
to edge-on. With current X-ray polarimetric techniques the polarization degree
of a typical bright X-ray binary could be measured to an accuracy of 0.1% by
observing the source for about 10 days. Such a measurement would constrain the
disk inclination to within a degree or two and would significantly improve the
reliability of black hole spin estimates. In addition, it would provide new
information on the tilt between the black hole spin axis and the orbital
rotation axis of the binary, which would constrain any velocity kicks
experienced by stellar-mass black holes during their formation.Comment: 46 pages, 8 figures, ApJ in pres
Measuring the Spin of GRS 1915+105 with Relativistic Disk Reflection
GRS 1915+105 harbors one of the most massive known stellar black holes in the
Galaxy. In May 2007, we observed GRS 1915+105 for 117 ksec in the low/hard
state using Suzaku. We collected and analyzed the data with the HXD/PIN and XIS
cameras spanning the energy range from 2.3-55 keV. Fits to the spectra with
simple models reveal strong disk reflection through an Fe K emission line and a
Compton back-scattering hump. We report constraints on the spin parameter of
the black hole in GRS 1915+105 using relativistic disk reflection models. The
model for the soft X-ray spectrum (i.e. < 10 keV) suggests a/M = 0.56(2) and
excludes zero spin at the 4 sigma level of confidence. The model for the full
broadband spectrum suggests that the spin may be higher, a/M = 0.98(1) (1 sigma
confidence), and again excludes zero spin at the 2 sigma level of confidence.
We discuss these results in the context of other spin constraints and inner
disk studies in GRS 1915+105.Comment: Accepted for publication in Ap
Area Invariance of Apparent Horizons under Arbitrary Boosts
It is a well known analytic result in general relativity that the
2-dimensional area of the apparent horizon of a black hole remains invariant
regardless of the motion of the observer, and in fact is independent of the slice, which can be quite arbitrary in general relativity.
Nonetheless the explicit computation of horizon area is often substantially
more difficult in some frames (complicated by the coordinate form of the
metric), than in other frames. Here we give an explicit demonstration for very
restricted metric forms of (Schwarzschild and Kerr) vacuum black holes. In the
Kerr-Schild coordinate expression for these spacetimes they have an explicit
Lorentz-invariant form. We consider {\it boosted} versions with the black hole
moving through the coordinate system. Since these are stationary black hole
spacetimes, the apparent horizons are two dimensional cross sections of their
event horizons, so we compute the areas of apparent horizons in the boosted
space with (boosted) , and obtain the same result as in the
unboosted case. Note that while the invariance of area is generic, we deal only
with black holes in the Kerr-Schild form, and consider only one particularly
simple change of slicing which amounts to a boost. Even with these restrictions
we find that the results illuminate the physics of the horizon as a null
surface and provide a useful pedagogical tool. As far as we can determine, this
is the first explicit calculation of this type demonstrating the area
invariance of horizons. Further, these calculations are directly relevant to
transformations that arise in computational representation of moving black
holes. We present an application of this result to initial data for boosted
black holes.Comment: 19 pages, 3 figures. Added a new section and 2 plots along with a
coautho
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