HURÉ, J.-M.; PELAT, D.; PIERENS, A.

doi:10.1051/0004-6361:20066808

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

PELAT, D.
Departement d'Astrophysique Extragalactique et de Cosmologie [DAEC]

PIERENS, A.

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Astronomy and Astrophysics - A&A. 2007, vol. 475, n° 2, p. 401-407

EDP Sciences

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We report a simple method to generate potential/surface density pairs in flat axially symmetric finite size disks. Potential/surface density pairs consist of a ``homogeneous'' pair (a closed form expression) corresponding to a uniform disk, and a ``residual'' pair. This residual component is converted into an infinite series of integrals over the radial extent of the disk. For a certain class of surface density distributions (like power laws of the radius), this series is fully analytical. The extraction of the homogeneous pair is equivalent to a convergence acceleration technique, in a matematical sense. In the case of power law distributions, the convergence rate of the residual series is shown to be cubic inside the source. As a consequence, very accurate potential values are obtained by low order truncation of the series. At zero order, relative errors on potential values do not exceed a few percent typically, and scale with the order N of truncation as 1/N**3. This method is superior to the classical multipole expansion whose very slow convergence is often critical for most practical applications.< Leer menos

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Generation of potential/surface density pairs in flat disks Power law distributions

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