Journal Article

New biorthogonal potential–density basis functions

Alireza Rahmati and Mir Abbas Jalali

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 393, issue 4, pages 1459-1466
Published in print March 2009 | ISSN: 0035-8711
Published online February 2009 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2008.14226.x
New biorthogonal potential–density basis functions

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We use the weighted integral form of spherical Bessel functions and introduce a new analytical set of complete and biorthogonal potential–density basis functions. The potential and density functions of the new set have finite central values and they fall off, respectively, similar to r−(1+l) and r−(4+l) at large radii, where l is the latitudinal quantum number of spherical harmonics. The lowest order term associated with l= 0 is the perfect sphere of de Zeeuw. Our basis functions are intrinsically suitable for the modelling of three-dimensional, soft-centred stellar systems and they complement the basis sets of Clutton-Brock, Hernquist & Ostriker and Zhao. We test the performance of our functions by expanding the density and potential profiles of some spherical and oblate galaxy models.

Keywords: stellar dynamics; methods: analytical; methods: numerical; celestial mechanics; galaxies: kinematics and dynamics

Journal Article.  4156 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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