2,447 research outputs found
Dynamical Cusp Regeneration
After being destroyed by a binary supermassive black hole, a stellar density
cusp can regrow at the center of a galaxy via energy exchange between stars
moving in the gravitational field of the single, coalesced hole. We illustrate
this process via high-accuracy N-body simulations. Regeneration requires
roughly one relaxation time and the new cusp extends to a distance of roughly
one-fifth the black hole's influence radius, with density rho ~ r^{-7/4}; the
mass in the cusp is of order 10% the mass of the black hole. Growth of the cusp
is preceded by a stage in which the stellar velocity dispersion evolves toward
isotropy and away from the tangentially-anisotropic state induced by the
binary. We show that density profiles similar to those observed at the center
of the Milky Way and M32 can regenerate themselves in several Gyr following
infall of a second black hole; the presence of density cusps at the centers of
these galaxies can therefore not be used to infer that no merger has occurred.
We argue that Bahcall-Wolf cusps are ubiquitous in stellar spheroids fainter
than M_V ~ -18.5 that contain supermassive black holes, but the cusps have not
been detected outside of the Local Group since their angular sizes are less
than 0.1". We show that the presence of a cusp implies a lower limit of
\~10^{-4} per year on the rate of stellar tidal disruptions, and discuss the
consequences of the cusps for gravitational lensing and the distribution of
dark matter on sub-parsec scales.Comment: Accepted for publication in The Astrophysical Journa
Long-Term Evolution of Massive Black Hole Binaries. III. Binary Evolution in Collisional Nuclei
[Abridged] In galactic nuclei with sufficiently short relaxation times,
binary supermassive black holes can evolve beyond their stalling radii via
continued interaction with stars. We study this "collisional" evolutionary
regime using both fully self-consistent N-body integrations and approximate
Fokker-Planck models. The N-body integrations employ particle numbers up to
0.26M and a direct-summation potential solver; close interactions involving the
binary are treated using a new implementation of the Mikkola-Aarseth chain
regularization algorithm. Even at these large values of N, two-body scattering
occurs at high enough rates in the simulations that they can not be simply
scaled to the large-N regime of real galaxies. The Fokker-Planck model is used
to bridge this gap; it includes, for the first time, binary-induced changes in
the stellar density and potential. The Fokker-Planck model is shown to
accurately reproduce the results of the N-body integrations, and is then
extended to the much larger N regime of real galaxies. Analytic expressions are
derived that accurately reproduce the time dependence of the binary semi-major
axis as predicted by the Fokker-Planck model. Gravitational wave coalescence is
shown to occur in <10 Gyr in nuclei with velocity dispersions below about 80
km/s. Formation of a core results from a competition between ejection of stars
by the binary and re-supply of depleted orbits via two-body scattering. Mass
deficits as large as ~4 times the binary mass are produced before coalescence.
After the two black holes coalesce, a Bahcall-Wolf cusp appears around the
single hole in one relaxation time, resulting in a nuclear density profile
consisting of a flat core with an inner, compact cluster, similar to what is
observed at the centers of low-luminosity spheroids.Comment: 21 page
Triaxial Black-Hole Nuclei
We demonstrate that the nuclei of galaxies containing supermassive black
holes can be triaxial in shape. Schwarzschild's method was first used to
construct self-consistent orbital superpositions representing nuclei with axis
ratios of 1:0.79:0.5 and containing a central point mass representing a black
hole. Two different density laws were considered, with power-law slopes of -1
and -2. We constructed two solutions for each power law: one containing only
regular orbits and the other containing both regular and chaotic orbits.
Monte-Carlo realizations of the models were then advanced in time using an
N-body code to verify their stability. All four models were found to retain
their triaxial shapes for many crossing times. The possibility that galactic
nuclei may be triaxial complicates the interpretation of stellar-kinematical
data from the centers of galaxies and may alter the inferred interaction rates
between stars and supermassive black holes.Comment: 4 pages, 4 postscript figures, uses emulateapj.st
Evolution of the Dark Matter Distribution at the Galactic Center
Annihilation radiation from neutralino dark matter at the Galactic center
(GC) would be greatly enhanced if the dark matter were strongly clustered
around the supermassive black hole (SBH). The existence of a dark-matter
"spike" is made plausible by the observed, steeply-rising stellar density near
the GC SBH. Here the time-dependent equations describing gravitational
interaction of the dark matter particles with the stars are solved. Scattering
of dark matter particles by stars would substantially lower the dark matter
density near the GC SBH over 10^10 yr, due both to kinetic heating, and to
capture of dark matter particles by the SBH. This result suggests that
enhancements in the dark matter density around a SBH would be modest whether or
not the host galaxy had experienced the scouring effects of a binary SBH.Comment: 5 pages, 3 figures. Submitted to Physical Review Letter
Instability of the Gravitational N-Body Problem in the Large-N Limit
We use a systolic N-body algorithm to evaluate the linear stability of the
gravitational N-body problem for N up to 1.3 x 10^5, two orders of magnitude
greater than in previous experiments. For the first time, a clear ~ln
N-dependence of the perturbation growth rate is seen. The e-folding time for N
= 10^5 is roughly 1/20 of a crossing time.Comment: Accepted for publication in The Astrophysical Journa
Spin Flips and Precession in Black-Hole-Binary Mergers
We use the `moving puncture' approach to perform fully non-linear evolutions
of spinning quasi-circular black-hole binaries with individual spins not
aligned with the orbital angular momentum. We evolve configurations with the
individual spins (parallel and equal in magnitude) pointing in the orbital
plane and 45-degrees above the orbital plane. We introduce a technique to
measure the spin direction and track the precession of the spin during the
merger, as well as measure the spin flip in the remnant horizon. The former
configuration completes 1.75 orbits before merging, with the spin precessing by
98-degrees and the final remnant horizon spin flipped by ~72-degrees with
respect to the component spins. The latter configuration completes 2.25 orbits,
with the spins precessing by 151-degrees and the final remnant horizon spin
flipped ~34-degrees with respect to the component spins. These simulations show
for the first time how the spins are reoriented during the final stage of
binary black hole mergers verifying the hypothesis of the spin-flip phenomenon.
We also compute the track of the holes before merger and observe a precession
of the orbital plane with frequency similar to the orbital frequency and
amplitude increasing with time.Comment: Revtex4, 17 figures, 14 pages. Accepted for publication in PR
Maximum gravitational recoil
Recent calculations of gravitational radiation recoil generated during
black-hole binary mergers have reopened the possibility that a merged binary
can be ejected even from the nucleus of a massive host galaxy. Here we report
the first systematic study of gravitational recoil of equal-mass binaries with
equal, but anti-aligned, spins parallel to the orbital plane. Such an
orientation of the spins is expected to maximize the recoil. We find that
recoil velocity (which is perpendicular to the orbital plane) varies
sinusoidally with the angle that the initial spin directions make with the
initial linear momenta of each hole and scales up to a maximum of ~4000 km/s
for maximally-rotating holes. Our results show that the amplitude of the recoil
velocity can depend sensitively on spin orientations of the black holes prior
to merger.Comment: 4 pages, 4 figs, revtex
Long Term Evolution of Massive Black Hole Binaries
The long-term evolution of massive black hole binaries at the centers of
galaxies is studied in a variety of physical regimes, with the aim of resolving
the ``final parsec problem,'' i.e., how black hole binaries manage to shrink to
separations at which emission of gravity waves becomes efficient. A binary
ejects stars by the gravitational slingshot and carves out a loss cone in the
host galaxy. Continued decay of the binary requires a refilling of the loss
cone. We show that the standard treatment of loss cone refilling, derived for
collisionally relaxed systems like globular clusters, can substantially
underestimate the refilling rates in galactic nuclei. We derive expressions for
non-equilibrium loss-cone dynamics and calculate time scales for the decay of
massive black hole binaries following galaxy mergers, obtaining significantly
higher decay rates than heretofore. Even in the absence of two-body relaxation,
decay of binaries can persist due to repeated ejection of stars returning to
the nucleus on eccentric orbits. We show that this recycling of stars leads to
a gradual, approximately logarithmic dependence of the binary binding energy on
time. We derive an expression for the loss cone refilling induced by the
Brownian motion of a black hole binary. We also show that numerical N-body
experiments are not well suited to probe these mechanisms over long times due
to spurious relaxation.Comment: Replaced to match the accepted version, ApJ, 596 (2003
Long-Term Evolution of Massive Black Hole Binaries. II. Binary Evolution in Low-Density Galaxies
We use direct-summation N-body integrations to follow the evolution of binary
black holes at the centers of galaxy models with large, constant-density cores.
Particle numbers as large as 400K are considered. The results are compared with
the predictions of loss-cone theory, under the assumption that the supply of
stars to the binary is limited by the rate at which they can be scattered into
the binary's influence sphere by gravitational encounters. The agreement
between theory and simulation is quite good; in particular, we are able to
quantitatively explain the observed dependence of binary hardening rate on N.
We do not verify the recent claim of Chatterjee, Hernquist & Loeb (2003) that
the hardening rate of the binary stabilizes when N exceeds a particular value,
or that Brownian wandering of the binary has a significant effect on its
evolution. When scaled to real galaxies, our results suggest that massive black
hole binaries in gas-poor nuclei would be unlikely to reach gravitational-wave
coalescence in a Hubble time.Comment: 13 pages, 8 figure
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