Existence of slowly rotating bipolytropes with prolate cores

C. Staelen; J.-M. Huré; A. Meunier; P. Noé

doi:10.1051/0004-6361/202450619

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Volume 691 (November 2024)

A&A, 691 (2024) A276

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Issue		A&A Volume 691, November 2024


Article Number		A276
Number of page(s)		7
Section		Astrophysical processes
DOI		https://doi.org/10.1051/0004-6361/202450619
Published online		22 November 2024

A&A, 691, A276 (2024)

Existence of slowly rotating bipolytropes with prolate cores

C. Staelen¹^⋆, J.-M. Huré¹, A. Meunier² and P. Noé¹^,3

¹ Univ. Bordeaux, CNRS, LAB, UMR 5804, F-33600 Pessac, France
² Univ. Luxembourg, Department of Mathematics, L-4364 Esch-sur-Alzette, Luxembourg
³ Univ. Strasbourg, Télécom Physique Strasbourg, F-67400 Illkirch-Graffenstaden, France

^⋆ Corresponding author; clement.staelen@u-bordeaux.fr

Received: 6 May 2024
Accepted: 8 October 2024

Abstract

We report the existence of hydrostatic equilibrium states for a composite body made of two rigidly rotating, homogeneous layers bounded by spheroidal surfaces, where the core has a prolate shape. These new configurations require an oblate envelope that spins faster than the core. No solution with a prolate envelope is found. For some parameters, the prolate core can even be at rest. Numerical experiments based on the self-consistent field method support this result in the case of heterogeneous layers with polytropic equations of state. The possible cancellation of the first gravitational moment, J₂, is discussed.

Key words: gravitation / methods: analytical / planets and satellites: interiors / stars: interiors / stars: rotation

Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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