225 research outputs found
Quantum to classical transition in a system with a mixed classical dynamics
We study how decoherence rules the quantum-classical transition of the Kicked
Harmonic Oscillator (KHO). When the amplitude of the kick is changed the system
presents a classical dynamics that range from regular to a strong chaotic
behavior. We show that for regular and mixed classical dynamics, and in the
presence of noise, the distance between the classical and the quantum phase
space distributions is proportional to a single parameter which relates the effective Planck constant
, the kick amplitude and the diffusion constant . This
is valid when , a case that is always attainable in the semiclassical
regime independently of the value of the strength of noise given by . Our
results extend a recent study performed in the chaotic regime.Comment: 10 pages, 7 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
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
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
New results on GP Com
We present high resolution optical and UV spectra of the 46 min orbital
period, helium binary, GP Com. Our data contains simultaneous photometric
correction which confirms the flaring behaviour observed in previous optical
and UV data. In this system all lines show a triple peaked structure where the
outer two peaks are associated with the accretion disc around the compact
object. The main aim of this paper is to constrain the origin of the central
peak, also called ``central spike''. We find that the central spike contributes
to the flare spectra indicating that its origin is probably the compact object.
We also detect that the central spike moves with orbital phase following an
S-wave pattern. The radial velocity semiamplitude of the S-wave is ~10 km/s
indicating that its origin is near the centre of mass of the system, which in
this case lies very close to the white dwarf. Our resolution is higher than
that of previous data which allows us to resolve structure in the central peak
of the line. The central spike in three of the HeI lines shows another peak
blueshifted with respect to the main peak. We propose that one of the peaks is
a neutral helium forbidden transition excited in a high electron density
region. This forbidden transition is associated with the permitted one (the
stronger peak in two of the lines). The presence of a high electron density
region again favours the white dwarf as their origin.Comment: 14 pages, 16 figures. Accepted for publication in A&
Mean Field Theory of Spherical Gravitating Systems
Important gaps remain in our understanding of the thermodynamics and
statistical physics of self-gravitating systems. Using mean field theory, here
we investigate the equilibrium properties of several spherically symmetric
model systems confined in a finite domain consisting of either point masses, or
rotating mass shells of different dimension. We establish a direct connection
between the spherically symmetric equilibrium states of a self-gravitating
point mass system and a shell model of dimension 3. We construct the
equilibrium density functions by maximizing the entropy subject to the usual
constraints of normalization and energy, but we also take into account the
constraint on the sum of the squares of the individual angular momenta, which
is also an integral of motion for these symmetric systems. Two new statistical
ensembles are introduced which incorporate the additional constraint. They are
used to investigate the possible occurrence of a phase transition as the
defining parameters for each ensemble are altered
Numerical stability of a family of Osipkov-Merrit models
We have investigated the stability of a set of non-rotating anisotropic
spherical models with a phase-space distribution function of the
Osipkov-Merritt type. The velocity distribution in these models is isotropic
near the center and becomes radially anisotropic at large radii. They are
special members of the family studied by Dehnen and Tremaine et al. where the
mass density has a power-law cusp at small radii and
decays as at large radii. The radial-orbit instability of
models with = 0, 1/2, 1, 3/2, and 2, was studied using an N-body code
written by one of us and based on the `self-consistent field' method developed
by Hernquist and Ostriker. These simulations have allowed us to delineate a
boundary in the -plane that separates the stable from the
unstable models. This boundary is given by , for
the ratio of the total radial to tangential kinetic energy. We also found that
the stability criterion , recently raised by Hjorth, gives lower
values compared with our numerical results.Comment: AASTEX, 22 pages, 11 figures, Figs. 5 available from author. Accepted
for publication in Astrophysical Journa
Reduction and Realization in Toda and Volterra
We construct a new symplectic, bi-hamiltonian realization of the KM-system by
reducing the corresponding one for the Toda lattice. The bi-hamiltonian pair is
constructed using a reduction theorem of Fernandes and Vanhaecke. In this paper
we also review the important work of Moser on the Toda and KM-systems.Comment: 17 page
Stellar remnants in galactic nuclei: mass segregation
The study of how stars distribute themselves around a massive black hole
(MBH) in the center of a galaxy is an important prerequisite for the
understanding of many galactic-center processes. These include the observed
overabundance of point X-ray sources at the Galactic center, the prediction of
rates and characteristics of tidal disruptions of extended stars by the MBH and
of inspirals of compact stars into the MBH, the latter being events of high
importance for the future space borne gravitational wave interferometer LISA.
In relatively small galactic nuclei, hosting MBHs with masses in the range
10^5-10^7 Msun, the single most important dynamical process is 2-body
relaxation. It induces the formation of a steep density cusp around the MBH and
strong mass segregation, as more massive stars lose energy to lighter ones and
drift to the central regions. Using a spherical stellar dynamical Monte-Carlo
code, we simulate the long-term relaxational evolution of galactic nucleus
models with a spectrum of stellar masses. Our focus is the concentration of
stellar black holes to the immediate vicinity of the MBH. We quantify this mass
segregation for a variety of galactic nucleus models and discuss its
astrophysical implications. Special attention is given to models developed to
match the conditions in the Milky Way nucleus; we examine the presence of
compact objects in connection to recent high-resolution X-ray observations.Comment: 28 pages, 24 figures, ApJ accepted. Small changes to follow referee's
suggestion
On stochastic sea of the standard map
Consider a generic one-parameter unfolding of a homoclinic tangency of an
area preserving surface diffeomorphism. We show that for many parameters
(residual subset in an open set approaching the critical value) the
corresponding diffeomorphism has a transitive invariant set of full
Hausdorff dimension. The set is a topological limit of hyperbolic sets
and is accumulated by elliptic islands.
As an application we prove that stochastic sea of the standard map has full
Hausdorff dimension for sufficiently large topologically generic parameters.Comment: 36 pages, 5 figure
- âŠ