26 research outputs found
Secular Instabilities of Keplerian Stellar Discs
We present idealized models of a razor-thin, axisymmetric, Keplerian stellar
disc around a massive black hole, and study non-axisymmetric secular
instabilities in the absence of either counter-rotation or loss cones. These
discs are prograde mono-energetic waterbags, whose phase space distribution
functions are constant for orbits within a range of eccentricities (e) and zero
outside this range. The linear normal modes of waterbags are composed of
sinusoidal disturbances of the edges of distribution function in phase space.
Waterbags which include circular orbits (polarcaps) have one stable linear
normal mode for each azimuthal wavenumber m. The m = 1 mode always has positive
pattern speed and, for polarcaps consisting of orbits with e < 0.9428, only the
m = 1 mode has positive pattern speed. Waterbags excluding circular orbits
(bands) have two linear normal modes for each m, which can be stable or
unstable. We derive analytical expressions for the instability condition,
pattern speeds, growth rates and normal mode structure. Narrow bands are
unstable to modes with a wide range in m. Numerical simulations confirm linear
theory and follow the non-linear evolution of instabilities. Long-time
integration suggests that instabilities of different m grow, interact
non-linearly and relax collisionlessly to a coarse-grained equilibrium with a
wide range of eccentricities.Comment: Manuscript accepted for publication in MNRA
An order-disorder phase transition in black-hole star clusters
The centers of most galaxies contain massive black holes surrounded by dense
star clusters. The structure of these clusters determines the rate and
properties of observable transient events, such as flares from tidally
disrupted stars and gravitational-wave signals from stars spiraling into the
black hole. Most estimates of these rates enforce spherical symmetry on the
cluster. Here we show that, in the course of generic evolutionary processes, a
star cluster surrounding a black hole can undergo a robust phase transition
from a spherical thermal equilibrium to a lopsided equilibrium, in which most
stars are on high-eccentricity orbits with aligned orientations. The rate of
transient events is expected to be much higher in the ordered phase. Better
models of cluster formation and evolution are needed to determine whether
clusters should be found in the ordered or disordered phase.Comment: 5 pages, 2 figure
Caustics in Dark Matter Haloes
Caustics are formally singular structures, with infinite density, that form
in collisionless media. The non-negligible velocity dispersion of dark matter
particles renders their density finite. We evaluate the maximum density of the
caustics within the framework of secondary infall model of formation of dark
matter haloes. The result is then used to demonstrate that caustics can be
probed by properly stacking the weak-lensing signal of about 600 haloes. CFHTLS
accompanied by X-ray observations and the space-based experiments like SNAP or
DUNE can provide us with the required statistics and hence a way of
distinguishing between the viable dark matter particle candidates. The
extension of our results to more realistic models including the effects of
mergers of haloes is briefly outlined.Comment: Minor changes, two references added, 6 pages, 3 figures, to appear in
Proc. 21st IAP Colloquium "Mass Profiles and Shapes of Cosmological
Structures", Paris 4-9 July 2005, [EAS Publications Series, eds: G. Mamon, F.
Combes, C. Deffayet, B. Fort