An exact solution for arbitrarily rotating gaseous polytropes with index unity
Kong, Dali; Zhang, Keke; Schubert, Gerald
Date: 5 February 2015
Article
Journal
Monthly Notices of the Royal Astronomical Society
Publisher
Oxford University Press for Royal Astronomical Society
Publisher DOI
Abstract
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 ...
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.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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