Abstract
The influence of the gravitational radiation damping on the evolution of the orbital elements of compact binary stars is examined by using the method of perturbation. The perturbation equations with the true anomaly as an independent variable are given. This effect results in both the secular and periodic variation of the semi-major axis, the eccentricity, the mean longitude at the epoch and the mean longitude. However, the longitude of periastron exhibits no secular variation, but only periodic variation. The effect of secular variation of the orbit would lead to collapse of the system of binary stars. The deduced formulae are applied to the calculation of secular variation of the orbital elements for three compact binary stars: PSR19 13 + 16, PSR J0737-3039 and M33X-7. The results obtained are discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Belczynski, K., Bulik, T., Kluzniak W. 2002, ApJ, 567, L63
Blanchet, L., Damour T., Iyer B. R., Will C. M. 1995, Phys. Rev. Lett., 24, 3515
Brouwer, D., Clemence G. M. 1961, Method of Celestial Mechanics. Academic Press, New York and London
Burgay, M. D. et al. 2003, Nature, 426, 531
Burgay, M. D. et al. 2005, in: Binary Radio Pulsar, ASP Conference series, 328, F. A Rasio and J. H. Stairs (eds), 53–58.
Damour, T., Gopakumar A., Iyer B. R. 2004, Gen. Relativ. Quantum Cosmol., 30, 1–49
Hulse, R. A., Taylor, J. H. 1975, ApJ, 195, L51.
Hulse, R. A., Taylor, J. H. 1993, http://nobelprize.org/nobel-prizes/physics/laureates/1993/press.html
Li L.-S. 2009, Il Nuovo Cimento, 124B(7), 709
Li L.-S. 2011, Astrophys. Space Sci., 334(N.1), 125
Lincoln, C. W., Will C. M. 1990, Phys. Rev., D42, 1123
Oroza, J. A., McClintock, J. E. et al. 2007, Nature, 449, 872
Peter, P. C. 1964, Phys. Rev., B136, 1224
Taylor, J. H. 1994, Rev. Mod. Phys., 66, 711
Taylor, J. H., Fowler L. A., McCulloch P. H. 1979, Nature, 277, 437
Van der Heuvel, E. P. J. 2003, Nature, 426, 504
Walker, M., Will C. M. 1979, Phys. Rev., D19, 2483
Weisberg, J. M., Taylor J. H. 2002, ApJ, 576, 942
Weisberg, J. M., Taylor, J. H. 2005, in: Binary radio pulsar, ASP conference series, 382, F. A. Rasio and J. H. Stairs (eds) 25–29.
Willems, B., Kalogera V., Henninger M. 2004, ApJ, 616, 414
Author information
Authors and Affiliations
Corresponding author
Appendix
Appendix
Rights and permissions
About this article
Cite this article
Li, LS. Gravitational Radiation Damping and Evolution of the Orbit of Compact Binary Stars (Solution by the Second Perturbation Method). J Astrophys Astron 35, 189–200 (2014). https://doi.org/10.1007/s12036-014-9275-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12036-014-9275-z