Astrophysics and Space Science

, Volume 315, Issue 1–4, pp 335–340 | Cite as

On the orbital and physical parameters of the HDE 226868/Cygnus X-1 binary system

  • Lorenzo Iorio
Original Article


In this paper we explore the consequences of the recent determination of the mass m=(8.7±0.8)M of Cygnus X-1, obtained from the Quasi-Periodic Oscillation (QPO)-photon index correlation scaling, on the orbital and physical properties of the binary system HDE 226868/Cygnus X-1. By using such a result and the latest spectroscopic optical data of the HDE 226868 supergiant star we get M=(24±5)M for its mass. It turns out that deviations from the third Kepler law significant at more than 1-sigma level would occur if the inclination i of the system’s orbital plane to the plane of the sky falls outside the range ≈41–56 deg: such deviations cannot be due to the first post-Newtonian (1PN) correction to the orbital period because of its smallness; interpreted in the framework of the Newtonian theory of gravitation as due to the stellar quadrupole mass moment Q, they are unphysical because Q would take unreasonably large values. By conservatively assuming that the third Kepler law is an adequate model for the orbital period we obtain i=(48±7) deg which yields for the relative semimajor axis a=(42±9)R (≈0.2 AU).


Black holes: individual (Cyg X-1) Stars: individual (HDE 226868) X-rays: binaries X-rays: individual (Cyg X-1) 


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  1. Bolton, C.T.: Nature 235, 271 (1972) CrossRefADSGoogle Scholar
  2. Brocksopp, C., Tarasov, A.E., Lyuty, V.M., Roche, P.: Astron. Astrophys. 343, 861 (1999) ADSGoogle Scholar
  3. Capderou, M.: Satellites Orbits and Missions. Springer, Berlin (2005) Google Scholar
  4. Castro-Tirado, A.J., Brandt, S., Lund, S.: IAU Circ. 5590 (1992) Google Scholar
  5. Damour, T., Deruelle, N.: Ann. Inst. H. Poincaré 44, 263 (1986) zbMATHMathSciNetGoogle Scholar
  6. Daniel, J.-Y.: Astron. Astrophys. 94, 121 (1981) ADSGoogle Scholar
  7. Dolan, J.F., Tapia, S.: Astrophys. J. 344, 830 (1989) CrossRefADSGoogle Scholar
  8. Friend, D.B., Castor, J.I.: Astrophys. J. 261, 293 (1982) CrossRefADSGoogle Scholar
  9. Giacconi, R., Gorenstein, P., Gursky, H., Waters, J.R.: Astrophys. J. 148, L119 (1967) CrossRefADSGoogle Scholar
  10. Gies, D.R., Bolton, C.T.: Astrophys. J. 260, 240 (1982) CrossRefADSGoogle Scholar
  11. Gies, D.R., Bolton, C.T.: Astrophys. J. 304, 371 (1986) CrossRefADSGoogle Scholar
  12. Gies, D.R., Bolton, C.T., Thomson, J.R., Huang, W., McSwain, M.V., Riddle, R.L., Wang, Z., Wiita, P.J., Wingert, D.W., Csák, B., Kiss, L.L.: Astrophys. J. 583, 424 (2003) CrossRefADSGoogle Scholar
  13. Greiner, J., Cuby, J.G., McCaughrean, M.G.: Nature 414, 522 (2001) CrossRefADSGoogle Scholar
  14. Herrero, A., Kudritzki, R.P., Gabler, R., Vilchez, J.M., Gabler, A.: Astron. Astrophys. 297, 556 (1995) ADSGoogle Scholar
  15. Iorio, L.: New Astron. 11, 490 (2006) CrossRefADSGoogle Scholar
  16. Laarakkers, W.G., Poisson, E.: Astropys. J. 512, 282 (1999) CrossRefADSGoogle Scholar
  17. Malysheva, L.K.: Astron. Lett. 23, 585 (1997) ADSGoogle Scholar
  18. Oda, M., Gorenstein, P., Gursky, H., Kellogg, E., Schreier, E., Tananbaum, H., Giacconi, R.: Astrophys. J. 166, L1 (1971) CrossRefADSGoogle Scholar
  19. Paczýnski, B.: Astron. Astrophys. 34, 161 (1974) ADSGoogle Scholar
  20. Petterson, J.A.: Astrophys. J. 224, 625 (1978) CrossRefADSGoogle Scholar
  21. Pollard, H.: Mathematical Introduction to Celestial Mechanics. Prentice-Hall, Englewood Cliffs (1966) zbMATHGoogle Scholar
  22. Roy, A.E.: Orbital Motion, 4th edn. Institute of Physics (2005) Google Scholar
  23. Shaposhnikov, N., Titarchuk, L.G.: Astrophys. J. 643, 1098 (2006) CrossRefADSGoogle Scholar
  24. Shaposhnikov, N., Titarchuk, L.G.: Astrophys. J. 663, 445 (2007) CrossRefADSGoogle Scholar
  25. Shrader, C., Titarchuk, L.G.: Astrophys. J. 598, 168 (2003) CrossRefADSGoogle Scholar
  26. Webster, B.L., Murdin, P.: Nature 235, 37 (1972) CrossRefADSGoogle Scholar
  27. Wen, L., Cui, W., Levine, A.M., Bradt, H.V.: Astrophys. J. 525, 968 (1999) CrossRefADSGoogle Scholar
  28. Ziółkowski, J.: Mon. Not. R. Astron. Soc. 358, 851 (2005) CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.INFN, Sezione di PisaPisaItaly

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