CHAOTIC ZONES AROUND GRAVITATING BINARIES
Abstract
The extent of the continuous zone of chaotic orbits of a smallmass tertiary around a system of two gravitationally bound primaries of comparable masses (a binary star, a binary black hole, a binary asteroid, etc.) is estimated analytically, as a function of the tertiary's orbital eccentricity. The separatrix map theory is used to demonstrate that the central continuous chaos zone emerges (above a threshold in the primaries' mass ratio) due to overlapping of the orbital resonances corresponding to the integer ratios p:1 between the tertiary and the central binary periods. In this zone, the unlimited chaotic orbital diffusion of the tertiary takes place, up to its ejection from the system. The primaries' mass ratio, above which such a chaotic zone is universally present at all initial eccentricities of the tertiary, is estimated. The diversity of the observed orbital configurations of biplanetary and circumbinary exosystems is shown to be in accord with the existence of the primaries' mass parameter threshold.
 Authors:
 Pulkovo Observatory of the Russian Academy of Sciences, Pulkovskoje ave. 65, St. Petersburg 196140 (Russian Federation)
 Publication Date:
 OSTI Identifier:
 22364582
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Astrophysical Journal; Journal Volume: 799; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ASTEROIDS; BINARY STARS; BLACK HOLES; CHAOS THEORY; COMPARATIVE EVALUATIONS; DIFFUSION; MASS; ORBITS; PLANETS; SATELLITES; STABILITY; ZONES
Citation Formats
Shevchenko, Ivan I., Email: iis@gao.spb.ru. CHAOTIC ZONES AROUND GRAVITATING BINARIES. United States: N. p., 2015.
Web. doi:10.1088/0004637X/799/1/8.
Shevchenko, Ivan I., Email: iis@gao.spb.ru. CHAOTIC ZONES AROUND GRAVITATING BINARIES. United States. doi:10.1088/0004637X/799/1/8.
Shevchenko, Ivan I., Email: iis@gao.spb.ru. 2015.
"CHAOTIC ZONES AROUND GRAVITATING BINARIES". United States.
doi:10.1088/0004637X/799/1/8.
@article{osti_22364582,
title = {CHAOTIC ZONES AROUND GRAVITATING BINARIES},
author = {Shevchenko, Ivan I., Email: iis@gao.spb.ru},
abstractNote = {The extent of the continuous zone of chaotic orbits of a smallmass tertiary around a system of two gravitationally bound primaries of comparable masses (a binary star, a binary black hole, a binary asteroid, etc.) is estimated analytically, as a function of the tertiary's orbital eccentricity. The separatrix map theory is used to demonstrate that the central continuous chaos zone emerges (above a threshold in the primaries' mass ratio) due to overlapping of the orbital resonances corresponding to the integer ratios p:1 between the tertiary and the central binary periods. In this zone, the unlimited chaotic orbital diffusion of the tertiary takes place, up to its ejection from the system. The primaries' mass ratio, above which such a chaotic zone is universally present at all initial eccentricities of the tertiary, is estimated. The diversity of the observed orbital configurations of biplanetary and circumbinary exosystems is shown to be in accord with the existence of the primaries' mass parameter threshold.},
doi = {10.1088/0004637X/799/1/8},
journal = {Astrophysical Journal},
number = 1,
volume = 799,
place = {United States},
year = 2015,
month = 1
}

Small bodies of the solar system, like asteroids, transNeptunian objects, cometary nuclei, and planetary satellites, with diameters smaller than 1000 km usually have irregular shapes, often resembling dumbbells or contact binaries. The spinning of such a gravitating dumbbell creates around it a zone of chaotic orbits. We determine its extent analytically and numerically. We find that the chaotic zone swells significantly if the rotation rate is decreased; in particular, the zone swells more than twice if the rotation rate is decreased 10 times with respect to the “centrifugal breakup” threshold. We illustrate the properties of the chaotic orbital zones in examples ofmore »

Computer modeling of the evolution of plane rings of gravitating particles moving around the sun
The evolution of plane rings of gravitating particles (bodies or material points) moving around the sun is investigated by computer modeling. The algorithm used is investigated. The parameters of the rings of gravitating bodies, which combine during any collisions, correspond to the supply zones of the real planets. The densities of the bodies are close to the present densities of the planets. An analysis of the results obtained shows that the number of planets formed in the supply zone of planets of the terrestrial group would be larger than the actual number of planets if one assumes that all themore » 
Magnetohydrostatic atmosphere around a gravitating body
The axisymmetric magnetic structure around the gravitating body is considered. Using the similarity assumption, the author reduced the problem from a nonlinear elliptic partial differential equation to an ordinary nonlinear differential equation. The particular solution with a topology including a nondipole field structure is discussed. Gas pressure, density, and temperature, corresponing to this magnetic atmosphere, are obtained. 
Nada: A new code for studying selfgravitating tori around black holes
We present a new twodimensional numerical code called Nada designed to solve the full Einstein equations coupled to the general relativistic hydrodynamics equations. The code is mainly intended for studies of selfgravitating accretion disks (or tori) around black holes, although it is also suitable for regular spacetimes. Concerning technical aspects the Einstein equations are formulated and solved in the code using a formulation of the standard 3+1 ArnowittDeserMisner canonical formalism system, the socalled BaumgarteShapiro ShibataNakamura approach. A key feature of the code is that derivative terms in the spacetime evolution equations are computed using a fourthorder centered finite difference approximationmore » 
Chaotic dynamics around astrophysical objects with nonisotropic stresses
The existence of chaotic behavior for the geodesics of the test particles orbiting compact objects is a subject of much current research. Some years ago, Gueron and Letelier [Phys. Rev. E 66, 046611 (2002)] reported the existence of chaotic behavior for the geodesics of the test particles orbiting compact objects like black holes induced by specific values of the quadrupolar deformation of the source using as models the ErezRosen solution and the Kerr black hole deformed by an internal multipole term. In this work, we are interested in the study of the dynamic behavior of geodesics around astrophysical objects withmore »