Astronomy and Astrophysics – Astrophysics
Scientific paper
Jul 1971
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1971ap%26ss..12...58f&link_type=abstract
Astrophysics and Space Science, Volume 12, Issue 1, pp.58-82
Astronomy and Astrophysics
Astrophysics
5
Scientific paper
The study of uniformly polytropes with axial symmetry is extended to include all rotational terms of order Ω4, where Ω is the angular velocity, consistently within the first post-Newtonian approximation to general relativity. The equilibrium structure is determined by treating the effects of rotation and post-Newtonian gravitation as independent perturbations on the classical polytropic structure. The perturbation effects are characterized by a rotation parameter υ = Ω2/2πGϱ c and a relativity parameter, σ =p c /ϱ c C 2 , wherep c and ϱc are the central pressure and density respectively. The solution to the structural problem is obtained by following Chandrasekhar's series expansion technique and is complete to the post-Newtonian rotation terms of orderσυ 2. The critical rotation parameterv c , which characterizes the configuration with maximum uniform rotation, is accurately evaluated as a function of σ. Numerical values for all the structural parameters needed to determine the equilibrium configurations are presented for polytropes with indicesn=1, 1.5, 2, 2 5, 3, and 3.5.
Anand P. S. S.
Fahlmann G. G.
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