Volume 531, July 2011
|Number of page(s)||8|
|Published online||07 June 2011|
The Newtonian potential of thin disks
Université de Bordeaux, OASU, 2 rue de l’Observatoire, BP 89, 33271 Floirac Cedex, France
2 CNRS, UMR 5804, LAB, 2 rue de l’Observatoire, BP 89, 33271 Floirac Cedex, France
Received: 1 October 2010
Accepted: 30 March 2011
The one-dimensional, ordinary differential equation (ODE) 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” λ. 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 λ → 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.
Key words: accretion, accretion disks / gravitation / methods: analytical / methods: numerical
© ESO, 2011
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.