Interior potential of a toroidal shell from pole values
| hal.structure.identifier | ECLIPSE 2019 | |
| dc.contributor.author | HURÉ, J.-M. | |
| dc.contributor.author | TROVA, A. | |
| hal.structure.identifier | Astronomical Institute of the Czech Academy of Sciences [ASU / CAS] | |
| dc.contributor.author | KARAS, V. | |
| hal.structure.identifier | Institut de pharmacologie et de biologie structurale [IPBS] | |
| dc.contributor.author | LESCA, C. | |
| dc.date.issued | 2019 | |
| dc.identifier.issn | 0035-8711 | |
| dc.description.abstractEn | We have investigated the toroidal analog of ellipsoidal shells of matter, which are of great significance in Astrophysics. The exact formula for the gravitational potential $\Psi(R,Z)$ of a shell with a circular section at the pole of toroidal coordinates is first established. It depends on the mass of the shell, its main radius and axis-ratio $e$ (i.e. core-to-main radius ratio), and involves the product of the complete elliptic integrals of the first and second kinds. Next, we show that successive partial derivatives $\partial^{n +m} \Psi/\partial_{R^n} \partial_{Z^m}$ are also accessible by analytical means at that singular point, thereby enabling the expansion of the interior potential as a bivariate series. Then, we have generated approximations at orders $0$, $1$, $2$ and $3$, corresponding to increasing accuracy. Numerical experiments confirm the great reliability of the approach, in particular for small-to-moderate axis ratios ($e^2 \lesssim 0.1$ typically). In contrast with the ellipsoidal case (Newton's theorem), the potential is not uniform inside the shell cavity as a consequence of the curvature. We explain how to construct the interior potential of toroidal shells with a thick edge (i.e. tubes), and how a core stratification can be accounted for. This is a new step towards the full description of the gravitating potential and forces of tori and rings. Applications also concern electrically-charged systems, and thus go beyond the context of gravitation. | |
| dc.language.iso | en | |
| dc.publisher | Oxford University Press (OUP): Policy P - Oxford Open Option A | |
| dc.subject.en | Astrophysics - Solar and Stellar Astrophysics | |
| dc.subject.en | Astrophysics - Instrumentation and Methods for Astrophysics | |
| dc.title.en | Interior potential of a toroidal shell from pole values | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1093/mnras/stz1226 | |
| dc.subject.hal | Planète et Univers [physics]/Astrophysique [astro-ph]/Planétologie et astrophysique de la terre [astro-ph.EP] | |
| dc.identifier.arxiv | 1905.01913 | |
| bordeaux.journal | Monthly Notices of the Royal Astronomical Society | |
| bordeaux.page | 5656-5669 | |
| bordeaux.volume | 486 | |
| bordeaux.issue | 4 | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02128517 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02128517v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Monthly%20Notices%20of%20the%20Royal%20Astronomical%20Society&rft.date=2019&rft.volume=486&rft.issue=4&rft.spage=5656-5669&rft.epage=5656-5669&rft.eissn=0035-8711&rft.issn=0035-8711&rft.au=HUR%C3%89,%20J.-M.&TROVA,%20A.&KARAS,%20V.&LESCA,%20C.&rft.genre=article |
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