129 research outputs found
A Note on the Toda Criterion for Interacting Dipole-Quadrupole Vibrations
The Toda criterion of the Gaussian curvature is applied to calculate
analytically the transition energy from regular to chaotic motion in a
schematic model describing the interaction between collective dipole and
quadrupole modes in atomic nuclei.Comment: Latex, 9 pages, 2 figures (available upon request), to be published
in Modern Physics Letters
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
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
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
On Universal Halos and the Radial Orbit Instability
The radial orbit instability drives dark matter halos toward a universal
structure. This conclusion, first noted by Huss, Jain, and Steinmetz, is
explored in detail through a series of numerical experiments involving the
collapse of an isolated halo into the non-linear regime. The role played by the
radial orbit instability in generating the density profile, shape, and orbit
structure is carefully analyzed and, in all cases, the instability leads to
universality independent of initial conditions. New insights into the
underlying physics of the radial orbit instability are presented.Comment: 31 pages, 11 figures, submitted to the Astrophysical Journa
Classical Monopoles: Newton, NUT-space, gravomagnetic lensing and atomic spectra
Stimulated by a scholium in Newton's Principia we find some beautiful results
in classical mechanics which can be interpreted in terms of the orbits in the
field of a mass endowed with a gravomagnetic monopole. All the orbits lie on
cones! When the cones are slit open and flattened the orbits are exactly the
ellipses and hyperbolae that one would have obtained without the gravomagnetic
monopole.
The beauty and simplicity of these results has led us to explore the similar
problems in Atomic Physics when the nuclei have an added Dirac magnetic
monopole. These problems have been explored by others and we sketch the
derivations and give details of the predicted spectrum of monopolar hydrogen.
Finally we return to gravomagnetic monopoles in general relativity. We
explain why NUT space has a non-spherical metric although NUT space itself is
the spherical space-time of a mass with a gravomagnetic monopole. We
demonstrate that all geodesics in NUT space lie on cones and use this result to
study the gravitational lensing by bodies with gravomagnetic monopoles.
We remark that just as electromagnetism would have to be extended beyond
Maxwell's equations to allow for magnetic monopoles and their currents so
general relativity would have to be extended to allow torsion for general
distributions of gravomagnetic monopoles and their currents. Of course if
monopoles were never discovered then it would be a triumph for both Maxwellian
Electromagnetism and General Relativity as they stand!Comment: 39 pages, 9 figures and 2 tables available on request from the
author
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
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