ED Sciences Physiques et de l'Ingénieur
Theory of equilibrium figures for fast rotators: from spheroids to three-dimensional bodies
by Clément STAELEN (Laboratoire d'Astrophysique de Bordeaux)
The defense will take place at 14h00 - Univers Allée Geoffroy Saint-Hilaire, Bât. B18N, CS 50023, 33615 Pessac
in front of the jury composed of
- Jean-Marc HURE - Professeur des universités - Université de Bordeaux - Directeur de these
- Nicolas RAMBAUX - Maître de conférences - Sorbonne Université - Rapporteur
- Paolo TANGA - Astronome - Observatoire de la Côte d'Azur - Rapporteur
- Frédéric CHAMBAT - Maître de conférences - ENS Lyon - Examinateur
- François LIGNIERES - Directeur de recherche - Université de Toulouse - Examinateur
- Séverine ROSAT - Directrice de recherche - Université de Strasbourg - Examinateur
- Pascal BORDE - Professeur des universités - Université de Bordeaux - Examinateur
Self-gravitating rotating systems, like planets and stars, are everywhere in the Universe. Most information at our disposal on these celestial bodies are generally global properties or surface properties. If the interior of the Earth, the Moon, Mars and the Sun are well constrained thanks to seismology and helioseismology, the other objects of the Solar System cannot be studied with such observational techniques. However, knowing the internal structure give insights on the formation and the evolution of these bodies and their environment. This PhD thesis is interested in developing analytical and numerical tools to study the interior of a rotating self-gravitating fluid mass. The main difficulty of such a study is the computation of the gravitational potential produced by the mass itself. Indeed, this potential is the key to determine the figure of equilibrium; unfortunately, it is known analytically for a few objects only and the numerical computation is complex. In a first part, we look for analytical and semi-analytical approximations for axisymmetric and heterogeneous objects. We will rely on the theory of Nested Spheroidal Figures of Equilibrium, which assumes that the mass is composed of a several homogeneous spheroids, whose gravitational potential is known analytically. This theory is exact only in specific and unrealistic cases, but it is actually a good approximation for most cases. Foremost, we show that prolate cores can exist without the addition of magnetic field or meridional circulation: the core must be surrounded by faster rotation medium. To confirm these solutions, we will derive the Virial equations for nested spheroids. Then we study the continuous limit, that is to say we will consider an infinite number of spheroids. We will see that the general problem is approached by an integrodifferential equation linking the flattening profile and density. Using an iterative algorithm, we will solve this equation in the case of polytropic fluids. Fast rotators are well reproduced, except for configurations close to critical rotations. This approach then goes beyond the slow rotation limit that is commonly used. We will see that the integrodifferential equation is coherent with Clairaut's equation in this limit. In a second part, we go beyond the axial symmetry hypothesis to consider triaxial objects. As in the previous section, we will study a heterogeneous mass composed of several homogeneous layers. We first construct a numerical code which solves the hydrostatic equilibrium. The code takes full advantage of the piecewise homogeneous hypothesis by calculating the potential with a sum of surface integrals, whose integrand is finite. This allows a direct and fast computation. This code will then be used to explore the parameter space of the two-layer case and study the impact of heterogeneity on the possible shapes. We will show that the bifurcation between axially symmetric and triaxial sequences is shifted towards slower rotations in the case of a small core and towards faster rotations in the case of a large core. This shift is however too small for the recent models of transneptunian object Quaoar to be compatible with a mass at hydrostatic equilibrium. Finally, we will apply this method to dwarf planet Haumea, whose triaxial shape has been observed by stellar occultation. We will show that two-layer models are not able to describe this shape, but are close enough to motivate a future study of three-layer models.