- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Eccentric motion of spinning compact binaries

Manuel Tessmer*

Gerhard Schäfer†

  • Institut für Angewandte Physik, Friedrich–Schiller Universität, Albert-Einstein-Straße 15, 07745 Jena, Germany, European Union

  • Theoretisch–Physikalisches Institut, Friedrich–Schiller–Universität, Max–Wien–Platz 1, 07743 Jena, Germany, European Union

  • *M.Tessmer@uni-jena.de
  • †Gerhard.Schaefer@uni-jena.de
PDF

Phys. Rev. D 89, 104055 – Published 27 May, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.104055

Abstract

The equations of motion for spinning compact binaries on eccentric orbits are treated perturbatively in powers of a fractional mass-difference ordering parameter. The solution is valid through first order in the mass-difference parameter. A canonical point transformation removes the leading-order terms of the spin-orbit Hamiltonian which induce a wiggling precession of the orbital angular momentum around the conserved total angular momentum, a precession which disappears in the case of equal masses or one single spin. Action-angle variables are applied that make a canonical perturbation theory easily treatable.

View figure in article

Article Text

References (53)

  1. P. C. Peters and J. Mathews, Phys. Rev. 131, 435 (1963).
  2. P. C. Peters, Phys. Rev. 136, B1224 (1964).
  3. A. Gopakumar and B. R. Iyer, Phys. Rev. D 56, 7708 (1997).
  4. K. G. Arun, L. Blanchet, B. R. Iyer, and M. S. S. Qusailah, Phys. Rev. D 77, 064035 (2008).
  5. K. G. Arun, L. Blanchet, B. R. Iyer, and M. S. S. Qusailah, Phys. Rev. D 77, 064034 (2008).
  6. K. G. Arun, L. Blanchet, B. R. Iyer, and S. Sinha, Phys. Rev. D 80, 124018 (2009).
  7. H. P. Pfeiffer, Classical Quantum Gravity 29, 124004 (2012).
  8. R. M. O’Leary, B. Kocsis, and A. Loeb, Mon. Not. R. Astron. Soc. 395, 2127 (2009).
  9. N. Yunes, K. G. Arun, E. Berti, and C. M. Will, Phys. Rev. D 80, 084001 (2009).
  10. R. Gold and B. Brügmann, Phys. Rev. D 88, 064051 (2013).
  11. D. A. Brown and P. J. Zimmerman, Phys. Rev. D 81, 024007 (2010).
  12. A. B. Nielsen, Classical Quantum Gravity 30, 075023 (2013).
  13. T. Damour, P. Jaranowski, and G. Schäfer, Phys. Rev. D 89, 064058 (2014).
  14. T. Damour, P. Jaranowski, and G. Schäfer, Phys. Lett. B 513, 147 (2001).
  15. T. Damour, P. Jaranowski, and G. Schäfer, Phys. Rev. D 77, 064032 (2008).
  16. T. Damour, P. Jaranowski, and G. Schäfer, Phys. Rev. D 78, 024009 (2008).
  17. J. Hartung and J. Steinhoff, Ann. Phys. (Berlin) 523, 783 (2011).
  18. J. Hartung and J. Steinhoff, Phys. Rev. D 83, 044008 (2011).
  19. M. Tessmer, J. Steinhoff, and G. Schäfer, Phys. Rev. D 87, 064035 (2013).
  20. Z. Keresztes, B. Mikóczi, and L. Á. Gergely, Phys. Rev. D 72, 104022 (2005).
  21. J. Majár and M. Vasúth, Phys. Rev. D 77, 104005 (2008).
  22. L. Blanchet, A. Buonanno, and G. Faye, Phys. Rev. D 84, 064041 (2011).
  23. T. A. Apostolatos, Phys. Rev. D 52, 605 (1995).
  24. L. Blanchet, A. Buonanno, and G. Faye, Phys. Rev. D 74, 104034 (2006).
  25. L. Blanchet, A. Buonanno, and G. Faye, Phys. Rev. D 75, 049903(E) (2007).
  26. L. Blanchet, A. Buonanno, and G. Faye, Phys. Rev. D 81, 089901(E) (2010).
  27. G. Faye, L. Blanchet, and A. Buonanno, Phys. Rev. D 74, 104033 (2006).
  28. K. G. Arun, A. Buonanno, G. Faye, and E. Ochsner, Phys. Rev. D 79, 104023 (2009).
  29. C. Königsdörffer and A. Gopakumar, Phys. Rev. D 71, 024039 (2005).
  30. M. Tessmer, J. Hartung, and G. Schäfer, Classical Quantum Gravity 27, 165005 (2010).
  31. M. Tessmer, J. Hartung, and G. Schäfer, Classical Quantum Gravity 30, 015007 (2013).
  32. M. Tessmer, Phys. Rev. D 80, 124034 (2009).
  33. T. Damour and G. Schäfer, Gen. Relativ. Gravit. 17, 879 (1985).
  34. G. Schäfer, Ann. Phys. (N.Y.) 161, 81 (1985).
  35. A. Sommerfeld, Atombau und Spektrallinien, Vol. 1 (Friedr. Vieweg & Sohn, Braunschweig, 1951), 7th ed.
  36. M. E. Alexander, Mon. Not. R. Astron. Soc. 227, 843 (1987).
  37. J. P. Vinti, Orbital and Celestial Mechanics, Progress in Astronautics and Aeronautics. Vol. 177 (American Institute of Aeronautics and Astronautics, Reston, VA, 1998).
  38. S. Hergt, A. Shah, and G. Schäfer, Phys. Rev. Lett. 111, 021101 (2013).
  39. E. Mai, M. Schneider, and C. Cui, Zur Entwicklung von Bahntheorien: Methodik und Anwendung. Deutsche Geodätische Kommission, Reihe A: Theoretische Geodäsie, Heft Nr. 122 (Verlag der Bayerischen Akademie der Wissenschaften, München, Germany, 2008).
  40. A. Gupta and A. Gopakumar, arXiv:1308.1315v1.
  41. P. Gurfil, A. Elipe, W. Tangren, and M. Efroimsky, Reg. Chaotic Dyn. 12, 389 (2007).
  42. J. R. Cary and R. G. Littlejohn, Ann. Phys. (N.Y.) 151, 1 (1983).
  43. P. Colwell, Solving Kepler’s Equation over Three Centuries (Willman-Bell, Inc., Richmond, VA, 1993).
  44. R.-M. Memmesheimer, A. Gopakumar, and G. Schäfer, Phys. Rev. D 70, 104011 (2004).
  45. H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, MA, 1981), 2nd ed.
  46. T. Damour and G. Schäfer, Nuovo Cimento Soc. Ital. Fis. 101B, 127 (1988).
  47. C. Howison and K. R. Meyer, Notes on Delaunay and Poincare Elements; https://math.uc.edu/ meyer/delaunay.pdf.
  48. M. Tessmer and G. Schäfer, Phys. Rev. D 82, 124064 (2010).
  49. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University Press, Cambridge, 1980), 2nd ed.
  50. M. Tessmer and G. Schäfer, Ann. Phys. (Berlin) 523, 813 (2011).
  51. C. E. Wayne, An Introduction to KAM Theory; http://math.bu.edu/people/cew/preprints/introkam.pdf
  52. V. I. Arnold, Mathematical Methods of Classical Mechanics, Vol. 1 (Springer-Verlag, New York, 1974), 2nd ed., p. 408.
  53. N. Wex, Classical Quantum Gravity 12, 983 (1995).

Outline

Information

Phys. Rev. D 89, 104055– Published 27 May, 2014
  • Received 28 November 2013

© 2014 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation