Issue |
A&A
Volume 434, Number 1, April IV 2005
|
|
---|---|---|
Page(s) | 17 - 23 | |
Section | Astrophysical processes | |
DOI | https://doi.org/10.1051/0004-6361:20034196 | |
Published online | 01 April 2005 |
Solutions of the axi-symmetric Poisson equation from elliptic integrals
II. Semi-analytical approach
1
LUTh (CNRS UMR 8102), Observatoire de Paris-Meudon, Place Jules Janssen, 92195 Meudon Cedex, France e-mail: Arnaud.Pierens@obspm.fr
2
Université Paris 7 Denis Diderot, 2 place Jussieu, 75251 Paris Cedex 05, France e-mail: Jean-Marc.Hure@obspm.fr
Received:
14
August
2003
Accepted:
23
September
2004
In a series of two papers, we present numerical integral-based methods to compute accurately the self-gravitating field and potential induced by a tri-dimensional, axially symmetric fluid, with special regard for tori, discs and rings.
In this second article, we show that “point mass” singularities are integrable analytically for systems with aspect ratio . We derive second-order accurate, integral formulae for the field components and potential as well, assuming that the mass density locally expands following powers of the altitude (the parabolic case is treated in detail). These formulae are valid inside the entire system: from the equatorial plane to the surface, and especially at the inner and outer edges where they remain regular, in contrast to those derived in the classical bi-dimensional, “razor-thin” approach. Their relative precision ~
has been checked in many situations by comparison with highly accurate, numerical solutions of the Poisson equation obtained from splitting methods described in Paper I. Time inexpensive and reliable, they offer powerful means to investigate vertically stratified systems where self-gravity plays a role. Three formulae for “one zone” disc models are given.
Key words: gravitation / methods: numerical / methods: analytical
© ESO, 2005
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.