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The Newtonian potential of thin disks

hal.structure.identifierObservatoire aquitain des sciences de l'univers [OASU]
hal.structure.identifierLaboratoire d'Astrophysique de Bordeaux [Pessac] [LAB]
hal.structure.identifierUniversité Sciences et Technologies - Bordeaux 1 [UB]
hal.structure.identifierLaboratoire d'astrodynamique, d'astrophysique et d'aéronomie de bordeaux [L3AB]
dc.contributor.authorHURÉ, J.-M.
hal.structure.identifierObservatoire aquitain des sciences de l'univers [OASU]
hal.structure.identifierLaboratoire d'Astrophysique de Bordeaux [Pessac] [LAB]
hal.structure.identifierUniversité Sciences et Technologies - Bordeaux 1 [UB]
hal.structure.identifierLaboratoire d'astrodynamique, d'astrophysique et d'aéronomie de bordeaux [L3AB]
dc.contributor.authorHERSANT, F.
dc.date.created2011-04-27
dc.date.issued2011
dc.identifier.issn0004-6361
dc.description.abstractEnThe 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.
dc.language.isoen
dc.publisherEDP Sciences
dc.subject.enAstrophysics
dc.subject.enInstrumentation and Methods for Astrophysics
dc.title.enThe Newtonian potential of thin disks
dc.typeArticle de revue
dc.identifier.doi10.1051/0004-6361/201015854
dc.subject.halPhysique [physics]/Astrophysique [astro-ph]/Instrumentation et méthodes pour l'astrophysique [astro-ph.IM]
dc.subject.halPlanète et Univers [physics]/Astrophysique [astro-ph]/Instrumentation et méthodes pour l'astrophysique [astro-ph.IM]
dc.identifier.arxiv1104.5079
bordeaux.journalAstronomy and Astrophysics - A&A
bordeaux.pageA36
bordeaux.volume531
bordeaux.peerReviewedoui
hal.identifierhal-00589211
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00589211v1
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