HURÉ, J.-M.; HERSANT, F.

doi:10.1051/0004-6361/201015854

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

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

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Astronomy and Astrophysics - A&A. 2011, vol. 531, p. A36

EDP Sciences

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The one-dimensional, ordinary differential equation (ODE) by Huré & Hersant (2007) that satisfies the midplane gravitational potential of truncated, flat power-law disks is extended to the whole physical space. It is shown that thickness effects (i.e. non-flatness) can be easily accounted for by implementing an appropriate "softening length" $\lambda$. The solution of this "softened ODE" has the following properties: i) it is regular at the edges (finite radial accelerations), ii) it possesses the correct long-range properties, iii) it matches the Newtonian potential of a geometrically thin disk very well, and iv) it tends continuously to the flat disk solution in the limit $\lambda \rightarrow 0$. As illustrated by many examples, the ODE, subject to exact Dirichlet conditions, can be solved numerically with efficiency for any given colatitude at second-order from center to infinity using radial mapping. This approach is therefore particularly well-suited to generating grids of gravitational forces in order to study particles moving under the field of a gravitating disk as found in various contexts (active nuclei, stellar systems, young stellar objects). Extension to non-power-law surface density profiles is straightforward through superposition. Grids can be produced upon request.< Réduire

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Astrophysics

Instrumentation and Methods for Astrophysics

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The Newtonian potential of thin disks

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