A new equation for the mid-plane potential of power law discs. II. Exact solutions and approximate formulae
hal.structure.identifier | Laboratoire d'astrodynamique, d'astrophysique et d'aéronomie de bordeaux [L3AB] | |
hal.structure.identifier | Observatoire aquitain des sciences de l'univers [OASU] | |
hal.structure.identifier | Université Sciences et Technologies - Bordeaux 1 [UB] | |
hal.structure.identifier | Laboratoire d'Astrophysique de Bordeaux [Pessac] [LAB] | |
dc.contributor.author | HURÉ, J.-M. | |
hal.structure.identifier | Laboratoire d'astrodynamique, d'astrophysique et d'aéronomie de bordeaux [L3AB] | |
hal.structure.identifier | Observatoire aquitain des sciences de l'univers [OASU] | |
hal.structure.identifier | Université Sciences et Technologies - Bordeaux 1 [UB] | |
hal.structure.identifier | Laboratoire d'Astrophysique de Bordeaux [Pessac] [LAB] | |
hal.structure.identifier | Laboratoire d'études spatiales et d'instrumentation en astrophysique [LESIA] | |
hal.structure.identifier | Département d'Astrophysique (ex SAP) [DAP] | |
dc.contributor.author | HERSANT, F. | |
hal.structure.identifier | Université Sciences et Technologies - Bordeaux 1 [UB] | |
dc.contributor.author | CARREAU, C. | |
hal.structure.identifier | Laboratoire d'astrodynamique, d'astrophysique et d'aéronomie de bordeaux [L3AB] | |
hal.structure.identifier | Observatoire aquitain des sciences de l'univers [OASU] | |
hal.structure.identifier | Université Sciences et Technologies - Bordeaux 1 [UB] | |
hal.structure.identifier | Laboratoire d'Astrophysique de Bordeaux [Pessac] [LAB] | |
dc.contributor.author | BUSSET, J. -P. | |
dc.date.created | 2008 | |
dc.date.issued | 2008 | |
dc.identifier.issn | 0004-6361 | |
dc.description.abstractEn | The first-order ordinary differential equation (ODE) that describes the mid-plane gravitational potential in flat finite size discs in which the surface density is a power-law function of the radius R with exponent s (Huré & Hersant 2007) is solved exactly in terms of infinite series. The formal solution of the ODE is derived and then converted into a series representation by expanding the elliptic integral of the first kind over its modulus before analytical integration. Inside the disc, the gravitational potential consists of three terms: a power law of radius R with index 1+s, and two infinite series of the variables R and 1/R. The convergence of the series can be accelerated, enabling the construction of reliable approximations. At the lowest-order, the potential inside large astrophysical discs (s ~ -1.5 +/- 1) is described by a very simple formula whose accuracy (a few percent typically) is easily increased by considering successive orders through a recurrence. A basic algorithm is given. Applications concern all theoretical models and numerical simulations where the influence of disc gravity must be checked and/or reliably taken into account. | |
dc.language.iso | en | |
dc.publisher | EDP Sciences | |
dc.subject.en | Gravitation — Methods : analytical — Accretion | |
dc.subject.en | accretion discs | |
dc.title.en | A new equation for the mid-plane potential of power law discs. II. Exact solutions and approximate formulae | |
dc.type | Article de revue | |
dc.identifier.doi | 10.1051/0004-6361:200809682 | |
dc.subject.hal | Physique [physics]/Astrophysique [astro-ph]/Cosmologie et astrophysique extra-galactique [astro-ph.CO] | |
dc.subject.hal | Planète et Univers [physics]/Astrophysique [astro-ph] | |
dc.identifier.arxiv | 0808.1634 | |
bordeaux.journal | Astronomy and Astrophysics - A&A | |
bordeaux.page | 477-486 | |
bordeaux.volume | 490 | |
bordeaux.issue | 2 | |
bordeaux.peerReviewed | oui | |
hal.identifier | hal-00319462 | |
hal.version | 1 | |
hal.popular | non | |
hal.audience | Internationale | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-00319462v1 | |
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