HURÉ, J.-M.; PIERENS, A.; HERSANT, F.

doi:10.1051/0004-6361/200911806

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HURÉ, J.-M.
Université Sciences et Technologies - Bordeaux 1 [UB]
Observatoire aquitain des sciences de l'univers [OASU]
Laboratoire d'Astrophysique de Bordeaux [Pessac] [LAB]
Laboratoire d'astrodynamique, d'astrophysique et d'aéronomie de bordeaux [L3AB]

PIERENS, A.

HERSANT, F.
Université Sciences et Technologies - Bordeaux 1 [UB]
Observatoire aquitain des sciences de l'univers [OASU]
Laboratoire d'Astrophysique de Bordeaux [Pessac] [LAB]
Laboratoire d'astrodynamique, d'astrophysique et d'aéronomie de bordeaux [L3AB]

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Astronomy and Astrophysics - A&A. 2009, vol. 500, n° 2, p. 617-620

EDP Sciences

Résumé en anglais

We present the exact calculus of the gravitational potential and acceleration along the symmetry axis of a plane, homogeneous, polar cell as a function of mean radius a, radial extension e, and opening angle f. Accurate approximations are derived in the limit of high numerical resolution at the geometrical mean of the inner and outer radii (a key-position in current FFT-based Poisson solvers). Our results are the full extension of the approximate formula given in the textbook of Binney & Tremaine to all resolutions. We also clarify definitely the question about the existence (or not) of self-forces in polar cells. We find that there is always a self-force at radius except if the shape factor a.f/e reaches ~ 3.531, asymptotically. Such cells are therefore well suited to build a polar mesh for high resolution simulations of self-gravitating media in two dimensions. A by-product of this study is a newly discovered indefinite integral involving complete elliptic integral of the first kind over modulus.< Réduire

Mots clés en anglais

accretion

accretion disks

gravitation

methods: analytical

methods: numerical

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Self-gravity at the scale of the polar cell

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