Astrophysics and Space Science

, Volume 12, Issue 1, pp 83–97 | Cite as

Rapidly rotating supermassive stars in the first post-Newtonian approximation to general relativity

  • G. G. Fahlman
  • S. P. S. Anand


The structure and stability of rapidly uniformly rotating supermassive stars is investigated using the full post-Newtonian equations of hydrodynamics. The standard model of a supermassive star, a polytrope of index three, is adopted. All rotation terms up to and including those of order Ω4, where Ω is the angular velocity, are retained. The effects of rotation and post-Newtonian gravitation on the classical configuration are explicitly evaluated and shown to be very small. The dynamical stability of the model is treated by using the binding energy approach. The most massive objects are found to be dynamically unstable when σ=1/c2.p c /ϱ c ≳ 2.2 × 10−3, wherep c andϱ c are the central pressure and density, respectively. Hence, the higher-order terms considered in this analysis do not appreciably alter the previously known stability limits.

The maximum mass that can be stabilized by uniform rotation in the hydrogen-burning phase is found to be 2.9×106M, whereM is the solar mass. The corresponding nuclear-generated luminosity of ∼6×1044 erg/sec−1 is too small for the model to be applicable to the quasi-stellar objects. The maximum kinetic energy of a uniformly rotating supermassive star is found to be 3×10−5Mc2, whereM is the mass of the star. Masses in excess of 1010M are required if an adequate store of kinetic energy is to be made available to a pulsar like QSO. However such large masses have rotation periods in excess of 100 yr and thus could not account for any short term periodic variability. It is concluded then that the uniformly rotating supermassive star does not provide a suitable base for a model of a QSO.


Dynamical Stability Stability Limit Rotation Period Central Pressure Maximum Mass 
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Copyright information

© D. Reidel Publishing Company 1971

Authors and Affiliations

  • G. G. Fahlman
    • 1
  • S. P. S. Anand
    • 1
  1. 1.David Dunlap ObservatoryUniversity of TorontoCanada

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