283 research outputs found
Self Similar Spherical Collapse Revisited: a Comparison between Gas and Dark Matter Dynamics
We reconsider the collapse of cosmic structures in an Einstein-de Sitter
Universe, using the self similar initial conditions of Fillmore & Goldreich
(1984). We first derive a new approximation to describe the dark matter
dynamics in spherical geometry, that we refer to the "fluid approach". This
method enables us to recover the self-similarity solutions of Fillmore &
Goldreich for dark matter. We derive also new self-similarity solutions for the
gas. We thus compare directly gas and dark matter dynamics, focusing on the
differences due to their different dimensionalities in velocity space. This
work may have interesting consequences for gas and dark matter distributions in
large galaxy clusters, allowing to explain why the total mass profile is always
steeper than the X-ray gas profile. We discuss also the shape of the dark
matter density profile found in N-body simulations in terms of a change of
dimensionality in the dark matter velocity space. The stable clustering
hypothesis has been finally considered in the light of this analytical
approach.Comment: 14 pages, 2 figures, 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
Exact Quantum Solutions of Extraordinary N-body Problems
The wave functions of Boson and Fermion gases are known even when the
particles have harmonic interactions. Here we generalise these results by
solving exactly the N-body Schrodinger equation for potentials V that can be
any function of the sum of the squares of the distances of the particles from
one another in 3 dimensions. For the harmonic case that function is linear in
r^2. Explicit N-body solutions are given when U(r) = -2M \hbar^{-2} V(r) =
\zeta r^{-1} - \zeta_2 r^{-2}. Here M is the sum of the masses and r^2 = 1/2
M^{-2} Sigma Sigma m_I m_J ({\bf x}_I - {\bf x}_J)^2. For general U(r) the
solution is given in terms of the one or two body problem with potential U(r)
in 3 dimensions. The degeneracies of the levels are derived for distinguishable
particles, for Bosons of spin zero and for spin 1/2 Fermions. The latter
involve significant combinatorial analysis which may have application to the
shell model of atomic nuclei. For large N the Fermionic ground state gives the
binding energy of a degenerate white dwarf star treated as a giant atom with an
N-body wave function. The N-body forces involved in these extraordinary N-body
problems are not the usual sums of two body interactions, but nor are forces
between quarks or molecules. Bose-Einstein condensation of particles in 3
dimensions interacting via these strange potentials can be treated by this
method.Comment: 24 pages, Latex. Accepted for publication in Proceedings of the Royal
Societ
The velocity and mass distribution of clusters of galaxies from the CNOC1 cluster redshift survey
In the context of the CNOC1 cluster survey, redshifts were obtained for
galaxies in 16 clusters. The resulting sample is ideally suited for an analysis
of the internal velocity and mass distribution of clusters. Previous analyses
of this dataset used the Jeans equation to model the projected velocity
dispersion profile. However, the results of such an analysis always yield a
strong degeneracy between the mass density profile and the velocity dispersion
anisotropy profile. Here we analyze the full (R,v) dataset of galaxy positions
and velocities in an attempt to break this degeneracy. We build an `ensemble
cluster' from the individual clusters under the assumption that they form a
homologous sequence. To interpret the data we study a one-parameter family of
spherical models with different constant velocity dispersion anisotropy. The
best-fit model is sought using a variety of statistics, including the overall
likelihood of the dataset. Although the results of our analysis depend slightly
on which statistic is used to judge the models, all statistics agree that the
best-fit model is close to isotropic. This result derives primarily from the
fact that the observed grand-total velocity histogram is close to Gaussian,
which is not expected to be the case for a strongly anisotropic model. The
best-fitting models have a mass-to-number-density ratio that is approximately
independent of radius over the range constrained by the data. They also have a
mass-density profile that is consistent with the dark matter halo profile
advocated by Navarro, Frenk & White, in terms of both the profile shape and the
characteristic scale length. This adds important new weight to the evidence
that clusters do indeed follow this proposed universal mass density profile.
[Abridged]Comment: 37 pages, LaTeX, with 11 PostScript figures. Accepted by the
Astronomical Journal, to appear in the May 2000 issue. This replacement
version contains an additional Appendix and one additional Figure with
respect to the version submitted to astro-ph originall
Partial suppression of the radial orbit instability in stellar systems
It is well known that the simple criterion proposed originally by Polyachenko
and Shukhman (1981) for the onset of the radial orbit instability, although
being generally a useful tool, faces significant exceptions both on the side of
mildly anisotropic systems (with some that can be proved to be unstable) and on
the side of strongly anisotropic models (with some that can be shown to be
stable). In this paper we address two issues: Are there processes of
collisionless collapse that can lead to equilibria of the exceptional type?
What is the intrinsic structural property that is responsible for the sometimes
noted exceptional stability behavior? To clarify these issues, we have
performed a series of simulations of collisionless collapse that start from
homogeneous, highly symmetrized, cold initial conditions and, because of such
special conditions, are characterized by very little mixing. For these runs,
the end-states can be associated with large values of the global pressure
anisotropy parameter up to 2K_r/K_T \approx 2.75. The highly anisotropic
equilibrium states thus constructed show no significant traces of radial
anisotropy in their central region, with a very sharp transition to a radially
anisotropic envelope occurring well inside the half-mass radius (around 0.2
r_M). To check whether the existence of such almost perfectly isotropic
"nucleus" might be responsible for the apparent suppression of the radial orbit
instability, we could not resort to equilibrium models with the above
characteristics and with analytically available distribution function; instead,
we studied and confirmed the stability of configurations with those
characteristics by initializing N-body approximate equilibria (with given
density and pressure anisotropy profiles) with the help of the Jeans equations.Comment: 26 pages, 9 figures, accepted for publication in The Astrophysical
Journa
Infinite ergodic theory and Non-extensive entropies
We bring into account a series of result in the infinite ergodic theory that
we believe that they are relevant to the theory of non-extensive entropie
Two-dimensional maps at the edge of chaos: Numerical results for the Henon map
The mixing properties (or sensitivity to initial conditions) of
two-dimensional Henon map have been explored numerically at the edge of chaos.
Three independent methods, which have been developed and used so far for the
one-dimensional maps, have been used to accomplish this task. These methods are
(i)measure of the divergence of initially nearby orbits, (ii)analysis of the
multifractal spectrum and (iii)computation of nonextensive entropy increase
rates. The obtained results strongly agree with those of the one-dimensional
cases and constitute the first verification of this scenario in two-dimensional
maps. This obviously makes the idea of weak chaos even more robust.Comment: 4 pages, 3 figure
Chaos in the one-dimensional gravitational three-body problem
We have investigated the appearance of chaos in the 1-dimensional Newtonian
gravitational three-body system (three masses on a line with pairwise
potential). We have concentrated in particular on how the behavior changes when
the relative masses of the three bodies change (with negative total energy).
For two mass choices we have calculated 18000 full orbits (with initial states
on a lattice on the Poincar\'e section) and obtained dwell time
distributions. For 105 mass choices we have calculated Poincar\'e maps for
starting points. Our results show that the Poincar\'e section
(and hence the phase space) divides into three well defined regions with orbits
of different characteristics: 1) There is a region of fast scattering, with a
minimum of pairwise collisions and smooth dependence on initial values. 2) In
the chaotic scattering region the interaction times are longer, and both the
interaction time and the final state depend sensitively on the starting point
on the Poincar\'e section. For both 1) and 2) the initial and final states
consists of a binary + single particle. 3) The third region consists of
quasiperiodic orbits where the three masses are bound together forever. At the
center of the quasiperiodic region there is the periodic Schubart orbit, whose
stability turns out to correlate strongly with the global behavior.Comment: 24 pages of text (REVTEX 3.0) + 21 pages of figures. Figures are only
available in paper form, ask for a preprint from the author
Orbital Instabilities in a Triaxial Cusp Potential
This paper constructs an analytic form for a triaxial potential that
describes the dynamics of a wide variety of astrophysical systems, including
the inner portions of dark matter halos, the central regions of galactic
bulges, and young embedded star clusters. Specifically, this potential results
from a density profile of the form , where the radial
coordinate is generalized to triaxial form so that . Using the resulting analytic form of the potential, and the
corresponding force laws, we construct orbit solutions and show that a robust
orbit instability exists in these systems. For orbits initially confined to any
of the three principal planes, the motion in the perpendicular direction can be
unstable. We discuss the range of parameter space for which these orbits are
unstable, find the growth rates and saturation levels of the instability, and
develop a set of analytic model equations that elucidate the essential physics
of the instability mechanism. This orbit instability has a large number of
astrophysical implications and applications, including understanding the
formation of dark matter halos, the structure of galactic bulges, the survival
of tidal streams, and the early evolution of embedded star clusters.Comment: 50 pages, accepted for publication in Ap
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