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A new equation for the mid-plane potential of power law discs. II. Exact solutions and approximate formulae

hal.structure.identifierLaboratoire d'astrodynamique, d'astrophysique et d'aéronomie de bordeaux [L3AB]
hal.structure.identifierObservatoire aquitain des sciences de l'univers [OASU]
hal.structure.identifierUniversité Sciences et Technologies - Bordeaux 1 [UB]
hal.structure.identifierLaboratoire d'Astrophysique de Bordeaux [Pessac] [LAB]
dc.contributor.authorHURÉ, J.-M.
hal.structure.identifierLaboratoire d'astrodynamique, d'astrophysique et d'aéronomie de bordeaux [L3AB]
hal.structure.identifierObservatoire aquitain des sciences de l'univers [OASU]
hal.structure.identifierUniversité Sciences et Technologies - Bordeaux 1 [UB]
hal.structure.identifierLaboratoire d'Astrophysique de Bordeaux [Pessac] [LAB]
hal.structure.identifierLaboratoire d'études spatiales et d'instrumentation en astrophysique [LESIA]
hal.structure.identifierDépartement d'Astrophysique (ex SAP) [DAP]
dc.contributor.authorHERSANT, F.
hal.structure.identifierUniversité Sciences et Technologies - Bordeaux 1 [UB]
dc.contributor.authorCARREAU, C.
hal.structure.identifierLaboratoire d'astrodynamique, d'astrophysique et d'aéronomie de bordeaux [L3AB]
hal.structure.identifierObservatoire aquitain des sciences de l'univers [OASU]
hal.structure.identifierUniversité Sciences et Technologies - Bordeaux 1 [UB]
hal.structure.identifierLaboratoire d'Astrophysique de Bordeaux [Pessac] [LAB]
dc.contributor.authorBUSSET, J. -P.
dc.date.created2008
dc.date.issued2008
dc.identifier.issn0004-6361
dc.description.abstractEnThe 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.isoen
dc.publisherEDP Sciences
dc.subject.enGravitation — Methods : analytical — Accretion
dc.subject.enaccretion discs
dc.title.enA new equation for the mid-plane potential of power law discs. II. Exact solutions and approximate formulae
dc.typeArticle de revue
dc.identifier.doi10.1051/0004-6361:200809682
dc.subject.halPhysique [physics]/Astrophysique [astro-ph]/Cosmologie et astrophysique extra-galactique [astro-ph.CO]
dc.subject.halPlanète et Univers [physics]/Astrophysique [astro-ph]
dc.identifier.arxiv0808.1634
bordeaux.journalAstronomy and Astrophysics - A&A
bordeaux.page477-486
bordeaux.volume490
bordeaux.issue2
bordeaux.peerReviewedoui
hal.identifierhal-00319462
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00319462v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Astronomy%20and%20Astrophysics%20-%20A&A&rft.date=2008&rft.volume=490&rft.issue=2&rft.spage=477-486&rft.epage=477-486&rft.eissn=0004-6361&rft.issn=0004-6361&rft.au=HUR%C3%89,%20J.-M.&HERSANT,%20F.&CARREAU,%20C.&BUSSET,%20J.%20-P.&rft.genre=article


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