Journal Article

Finite element modelling of perturbed stellar systems

Mir Abbas Jalali

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 404, issue 3, pages 1519-1528
Published in print May 2010 | ISSN: 0035-8711
Published online May 2010 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2010.16365.x
Finite element modelling of perturbed stellar systems

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I formulate a general finite element method (FEM) for self-gravitating stellar systems. I split the configuration space to finite elements, and express the potential and density functions over each element in terms of their nodal values and suitable interpolating functions. General expressions are then introduced for the Hamiltonian and phase-space distribution functions of the stars that visit a given element. Using the weighted residual form of Poisson's equation, I derive the Galerkin projection of the perturbed collisionless Boltzmann equation, and assemble the global evolutionary equations of nodal distribution functions. The FEM is highly adaptable to all kinds of potential and density profiles, and it can deal with density clumps and initially non-axisymmetric systems. I use ring elements of non-uniform widths, choose linear and quadratic interpolation functions in the radial direction, and apply the FEM to the stability analysis of the cutout Mestel disc. I also integrate the forced evolutionary equations and investigate the disturbances of a stable stellar disc due to the gravitational field of a distant satellite galaxy. The performance of the FEM and its prospects are discussed.

Keywords: stellar dynamics; methods: analytical; methods: numerical; galaxies: interactions; galaxies: kinematics and dynamics; galaxies: spiral

Journal Article.  6090 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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