An exact solution for arbitrarily rotating gaseous polytropes with index unity
Monthly Notices of the Royal Astronomical Society
Oxford University Press for Royal Astronomical Society
Many gaseous planets and stars are rapidly rotating and can be approximately described by a polytropic equation of state with index unity.We present the first exact analytic solution, under the assumption of the oblate spheroidal shape, for an arbitrarily rotating gaseous polytrope with index unity in hydrostatic equilibrium, giving rise to its internal structure and gravitational field. The new exact solution is derived by constructing the non-spherical Green’s function in terms of the oblate spheroidal wavefunction. We then apply the exact solution to a generic object whose parameter values are guided by the observations of the rapidly rotating star α Eridani with its eccentricity Eα = 0.7454, the most oblate star known. The internal structure and gravitational field of the object are computed from its assumed rotation rate and size. We also compare the exact solution to the three-dimensional numerical solution based on a finite-element method taking full account of rotation-induced shape change and find excellent agreement between the exact solution and the finite-element solution with about 0.001 per cent discrepancy.
Science & Technology Facilities Council (STFC)
National Science Foundation
This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society ©: 2015 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.
Vol. 448 (1), pp. 456 - 463