NDLI: Orbital approach to studying the slow dynamics of stellar systems

Please wait, while we are loading the content...

Orbital approach to studying the slow dynamics of stellar systems

Content Provider	Springer Nature Link
Author	Polyachenko, V. L. Polyachenko, E. V. Shukhman, I. G.
Copyright Year	2008
Abstract	We develop new approaches to the numerical simulations of slowly evolving stellar systems with characteristic times of the order of the precession period for a typical orbit. This period is assumed to be long compared to the characteristic oscillation periods of individual stars in their orbits. For such processes, the standard numerical simulations using various N-body methods become inadequate, since the bulk of the computational time is spent on the repeated calculations of almost invariable orbits. We suggest a new N-orbit approach (called so by analogy and by contrast with N-body methods) that takes into account the specifics of the problems under consideration, in which whole orbits take the place of individual stars in N-body methods. Accordingly, the stellar system is represented by a set of N orbits the changes in the spatial orientation and shape of which lead to a slow evolution of the system. We derive the equations governing the nonlinear dynamics of orbits separately for 2D (disk) and 3D systems. These equations have the form of Hamiltonian equations for canonically conjugate pairs of variables. In the 2D case, one pair of such equations will suffice: for the angular momentum L and for the angle of direction to the apocenter Ψ. In the 3D case, there are two such pairs. The first pair of equations is for the modulus of the angular momentum L and the angle of direction to the apocenter in the orbital plane Ψ, while the second pair is for L $_{z}$ (the component of the angular momentum vector L along the z axis) and the orientation angle of the line of nodes W. Together with the energy E, which is an adiabatic invariant, these two (or four) parameters completely define the orbit (in the 2D and 3D cases, respectively). The evolution of the system is traced by solving these equations within the framework of the suggested N-orbit approach. We have in mind two versions of this approach. In the first version, a separate orbit corresponds to each star along which the mass of this star is “smeared.” In this version, the number of orbits N $_{orb}$ is equal to the total number of stars N in the system under consideration. This version is a complete analogue of the N-body approach, except that the motion of each star is averaged over the orbit and we consider not the behavior of the star but the behavior of its orbit. In the second version, all stars from one small cell in the phase space of orbit parameters correspond to the orbit. In fact, this version of the N-orbit approach represents the method of solving the collisionless Boltzmann kinetic equation for the distribution function of orbit parameters. The number of orbits N $_{orb}$ in this approach is equal to the chosen number of cells. There exist two types of objects to the description of which N-orbit methods can be applied. First, these include the central regions of galaxies containing no large point masses. The stars in these regions move in symmetric (about the center) elliptical orbits that slowly precess due to the small deviation of the self-consistent potential from an exactly quadratic form (when all orbits are closed, so that the precession velocity is exactly equal to zero). Second, these include the star clusters around massive black holes at the centers of these clusters. The orbit of a star revolving around a central mass is a closed Keplerian ellipse and, consequently, has no precession. Slow precession appears when the relatively weak (compared to the attraction of the massive black hole) self-consistent gravitational field produced by cluster stars is taken into account. In this paper, to be specific, we will mainly deal precisely with the latter, near-Keplerian systems.
Starting Page	163
Ending Page	178
Page Count	16
File Format	PDF
ISSN	10637737
Journal	Astronomy Letters
Volume Number	34
Issue Number	3
e-ISSN	15626873
Language	English
Publisher	SP MAIK Nauka/Interperiodica
Publisher Date	2011-03-11
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	stellar systems stars clusters and associations stellar dynamics simulations Astronomy, Observations and Techniques Astrophysics and Astroparticles
Content Type	Text
Resource Type	Article
Subject	Astronomy and Astrophysics Space and Planetary Science

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Slow modes in stellar systems with nearly harmonic potentials: II. Gravitational loss-cone instability

Slow modes in stellar systems with nearly harmonic potentials: I. Spoke approximation, radial orbit instability

On the instability of weakly radially anisotropic star clusters

Simulations of slow bars in anisotropic disk systems

Radially anisotropic models of collisionless spherical stellar systems without central singularity

Matrix methods of investigating the eigenmodes of stellar disks

Two scenarios of the radial orbit instability in spherically symmetric collisionless stellar systems

Gravitational loss-cone instability: Monotonic and nonmonotonic angular momentum distributions of stars

On one classical problem in the radial orbit instability theory

Orbital approach to studying the slow dynamics of stellar systems

Similar Documents

Slow modes in stellar systems with nearly harmonic potentials: II. Gravitational loss-cone instability

Slow modes in stellar systems with nearly harmonic potentials: I. Spoke approximation, radial orbit instability

On the instability of weakly radially anisotropic star clusters

Simulations of slow bars in anisotropic disk systems

Radially anisotropic models of collisionless spherical stellar systems without central singularity

Matrix methods of investigating the eigenmodes of stellar disks

Two scenarios of the radial orbit instability in spherically symmetric collisionless stellar systems

Gravitational loss-cone instability: Monotonic and nonmonotonic angular momentum distributions of stars

On one classical problem in the radial orbit instability theory

Orbital approach to studying the slow dynamics of stellar systems