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Solving the Darwin problem in the first post-Newtonian approximation of general relativity

Keisuke Taniguchi1 and Masaru Shibata2

  • 1Department of Physics, Kyoto University, Kyoto 606-01, Japan
  • 2Department of Earth and Space Science, Osaka University, Toyonaka 560, Japan

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Phys. Rev. D 56, 798 – Published 15 July, 1997

DOI: https://doi.org/10.1103/PhysRevD.56.798

Abstract

We analytically calculate the equilibrium sequence of the corotating binary stars of incompressible fluid in the first post-Newtonian (PN) approximation of general relativity. By calculating the total energy and total angular momentum of the system as a function of the orbital separation, we investigate the innermost stable circular orbit for a corotating binary (we call it ISCCO). It is found that by the first PN effect, the orbital separation of the binary at the ISCCO becomes small with increase of the compactness of each star, and as a result, the orbital angular velocity at the ISCCO increases. These behaviors agree with previous numerical works.

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Phys. Rev. D 56, 798– Published 15 July, 1997
  • Received 14 February 1997

© 1997 American Physical Society

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