346 research outputs found
Variation of the Dependence of the Transient Process Duration on the Initial Conditions in Systems with Discrete Time
Dependence of the transient process duration on the initial conditions is
considered in one- and two-dimensional systems with discrete time, representing
a logistic map and the Eno map, respectively.Comment: 4 pages, 2 figure
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
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
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
Dynamical stability analysis of the HD202206 system and constraints to the planetary orbits
Long-term precise Doppler measurements with the CORALIE spectrograph revealed
the presence of two massive companions to the solar-type star HD202206.
Although the three-body fit of the system is unstable, it was shown that a 5:1
mean motion resonance exists close to the best fit, where the system is stable.
We present here an extensive dynamical study of the HD202206 system aiming at
constraining the inclinations of the two known companions, from which we derive
possible ranges of value for the companion masses.
We study the long term stability of the system in a small neighborhood of the
best fit using Laskar's frequency map analysis. We also introduce a numerical
method based on frequency analysis to determine the center of libration mode
inside a mean motion resonance.
We find that acceptable coplanar configurations are limited to inclinations
to the line of sight between 30 and 90 degrees. This limits the masses of both
companions to roughly twice the minimum. Non coplanar configurations are
possible for a wide range of mutual inclinations from 0 to 90 degrees, although
configurations seem to be favored. We also confirm the
5:1 mean motion resonance to be most likely. In the coplanar edge-on case, we
provide a very good stable solution in the resonance, whose does not
differ significantly from the best fit. Using our method to determine the
center of libration, we further refine this solution to obtain an orbit with a
very low amplitude of libration, as we expect dissipative effects to have
dampened the libration.Comment: 14 pages, 18 figure
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
On the Origin of Cusps in Stellar Systems
An origin is sought for the ubiquity of cusps, both in computer simulations
of halo formation in hierarchical clustering cosmogonies and in observations of
galactic nuclei by the Hubble Space Telescope (HST). The encounters of merging
clumps that built the galaxies can be described by the collisional Boltzmann
equation. Using insights gained by studying the simpler Fokker-Planck equation,
we show that there is a steady-state, self-consistent, cusped solution of the
collisional Boltzmann equation corresponding to . This
equilibrium is both stable and an attractor. It is the natural end-point of the
diffusive encounters of an ensemble of equal mass clumps. The introduction of a
mass spectrum weakens the mass density cusp. The spike in the luminosity
density can be accentuated or softened, depending on the form of the
mass-luminosity relation. Possible applications to the cusped nuclei of
early-type galaxies are discussed.Comment: Latex, 14 pages, Needs aasms4.sty. The Astrophysical Journal
(Letters), in pres
A Two-Temperature Model of the Intracluster Medium
We investigate evolution of the intracluster medium (ICM), considering the
relaxation process between the ions and electrons. According to the standard
scenario of structure formation, ICM is heated by the shock in the accretion
flow to the gravitational potential well of the dark halo. The shock primarily
heats the ions because the kinetic energy of an ion entering the shock is
larger than that of an electron by the ratio of masses. Then the electrons and
ions exchange the energy through coulomb collisions and reach the equilibrium.
From simple order estimation we find that the region where the electron
temperature is considerably lower than the ion temperature spreads out on a Mpc
scale. We then calculate the ion and electron temperature profiles by combining
the adiabatic model of two-temperature plasma by Fox & Loeb (1997) with
spherically symmetric N-body and hydrodynamic simulations based on three
different cosmological models. It is found that the electron temperature is
about a half of the mean temperature at radii 1 Mpc. This could lead to
an about 50 % underestimation in the total mass contained within 1 Mpc
when the electron temperature profiles are used. The polytropic indices of the
electron temperature profiles are whereas those of mean
temperature for Mpc. This result is consistent both
with the X-ray observations on electron temperature profiles and with some
theoretical and numerical predictions about mean temperature profiles.Comment: 20 pages with 6 figures. Accepted for publication in Ap
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
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