463 research outputs found
On the stability of circular orbits in galactic dynamics: Newtonian thin disks
The study of off-equatorial orbits in razor-thin disks is still in its
beginnings. Contrary to what was presented in the literature in recent
publications, the vertical stability criterion for equatorial circular orbits
cannot be based on the vertical epicyclic frequency, because of the
discontinuity in the gravitational field on the equatorial plane. We present a
rigorous criterion for the vertical stability of circular orbits in systems
composed by a razor-thin disk surrounded by a smooth axially symmetric
distribution of matter, the latter representing additional structures such as
thick disk, bulge and (dark matter) halo. This criterion is satisfied once the
mass surface density of the thin disk is positive. Qualitative and quantitative
analyses of nearly equatorial orbits are presented. In particular, the analysis
of nearly equatorial orbits allows us to construct an approximate analytical
third integral of motion in this region of phase-space, which describes the
shape of these orbits in the meridional plane.Comment: 3 pages, 1 figure. In Proceedings of the MG13 Meeting on General
Relativity, Stockholm University, Sweden, 1-7 July 2012. World Scientific,
Singapore. Based on arXiv:1206.6501. in The Thirteenth Marcel Grossmann
Meeting: On Recent Developments in Theoretical and Experimental General
Relativity, Astrophysics, and Relativistic Field Theories (In 3 Volumes),
chap. 438, pages 2346-2348 (2015
Axially Symmetric Post-Newtonian Stellar Systems
We introduce a method to obtain self-consistent, axially symmetric, thin
disklike stellar models in the first post-Newtonian (1PN) approximation. The
models obtained are fully analytical and corresponds to the post-Newtonian
generalizations of classical ones. By introducing in the field equations
provided by the 1PN approximation a known distribution function (DF)
corresponding to a Newtonian model, two fundamental equations determining the
1PN corrections are obtained, which are solved using the Hunter method. The
rotation curves of the 1PN-corrected models differs from the classical ones
and, for the generalized Kalnajs discs, the 1PN corrections are clearly
appreciable with values of the mass and radius of a typical galaxy. On the
other hand, the relativistic mass correction can be ignored for all models.Comment: 13 pages, 4 figures, to be published at Rev.Integr.Temas Ma
Distribution functions for a family of axially symmetric galaxy models
We present the derivation of distribution functions for the first four
members of a family of disks, previously obtained in (MNRAS, 371, 1873, 2006),
which represent a family of axially symmetric galaxy models with finite radius
and well behaved surface mass density. In order to do this we employ several
approaches that have been developed starting from the potential-density pair
and, essentially using the method introduced by Kalnajs (Ap. J., 205, 751,
1976) we obtain some distribution functions that depend on the Jacobi integral.
Now, as this method demands that the mass density can be properly expressed as
a function of the gravitational potential, we can do this only for the first
four discs of the family. We also find another kind of distribution functions
by starting with the even part of the previous distribution functions and using
the maximum entropy principle in order to find the odd part and so a new
distribution function, as it was pointed out by Dejonghe (Phys. Rep., 133, 217,
1986). The result is a wide variety of equilibrium states corresponding to
several self-consistent finite flat galaxy models.Comment: 12 pages, 7 figures, updated version, accepted for publication in
Rev. Acad. Colomb. Cienc. Ex. Fis. Na
Motion around a Monopole + Ring system: I. Stability of Equatorial Circular Orbits vs Regularity of Three-dimensional Motion
We study the motion of test particles around a center of attraction
represented by a monopole (with and without spheroidal deformation) surrounded
by a ring, given as a superposition of Morgan & Morgan discs. We deal with two
kinds of bounded orbits: (i) Equatorial circular orbits and (ii) general
three-dimensional orbits. The first case provides a method to perform a linear
stability analysis of these structures by studying the behavior of vertical and
epicyclic frequencies as functions of the mass ratio, the size of the ring
and/or the quadrupolar deformation. In the second case, we study the influence
of these parameters in the regularity or chaoticity of motion. We find that
there is a close connection between linear stability (or unstability) of
equatorial circular orbits and regularity (or chaoticity) of the
three-dimensional motion.Comment: 13 pages, 17 figures, to appear in MNRA
Vertical stability of circular orbits in relativistic razor-thin disks
During the last few decades, there has been a growing interest in exact
solutions of Einstein equations describing razor-thin disks. Despite the
progress in the area, the analytical study of geodesic motion crossing the disk
plane in these systems is not yet so developed. In the present work, we propose
a definite vertical stability criterion for circular equatorial timelike
geodesics in static, axially symmetric thin disks, possibly surrounded by other
structures preserving axial symmetry. It turns out that the strong energy
condition for the disk stress-energy content is sufficient for vertical
stability of these orbits. Moreover, adiabatic invariance of the vertical
action variable gives us an approximate third integral of motion for oblique
orbits which deviate slightly from the equatorial plane. Such new approximate
third integral certainly points to a better understanding of the analytical
properties of these orbits. The results presented here, derived for static
spacetimes, may be a starting point to study the motion around rotating,
stationary razor-thin disks. Our results also allow us to conjecture that the
strong energy condition should be sufficient to assure transversal stability of
periodic orbits for any singular timelike hypersurface, provided it is
invariant under the geodesic flow.Comment: 13 pages, 4 figures; Accepted for publication in Physical Review
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