Astrophysical Bulletin

, Volume 69, Issue 4, pp 461–471 | Cite as

An analytic algorithm to calculate the inclination, ascending node, and semimajor axis of spectroscopic binary orbits using a single speckle measurement and the parallax

  • J. A. Docobo
  • P. P. Campo
  • M. Andrade
  • E. P. Horch
Article

Abstract

It is well known that in spectroscopic binary orbits, the inclination, the ascending node, and the semimajor axis remain undetermined, therefore the principal objective of this research is to establish an analytic methodology for the calculation of these parameters for spectroscopic binaries, both single-lined (SB1) and double-lined (SB2). In other words, the goal is to determine their “three-dimensional” orbits using a single speckle measurement (ρ, θ, t) and the parallax (π). Moreover, estimates of the individual masses of each system can also be obtained. The proposed algorithm was successfully applied to SB1 systems: YSC 148 (HD 37393) and CHR 225 (HD 34318), and SB2 systems: LSC 1 Aa1,2 (HD 200077) and Mkt 11 Aa, Ab (HD 358). In this late case, previously determined spectroscopic and visual orbits have been used to compare and contrast the results obtained from them with our results. The methodology presented is especially interesting for those cases in which it is only possible to resolve the spectroscopic binary in the zones of maximum angular separation by optical means thereby making it impossible to avail of sufficient observations in order to calculate the visual orbit.

Keywords

techniques high angular resolution—techniques interferometric—binaries general 

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References

  1. 1.
    V. Straizys and G. Kuriliene, Astrophys. and Space Sci. 80, 353 (1981).ADSCrossRefGoogle Scholar
  2. 2.
    D. F. Gray, TheObservation and Analysis of Stellar Photospheres (Cambridge Univ. Press, 2005).Google Scholar
  3. 3.
    J. A. Docobo and M. Andrade, Astrophys. J. 652, 681 (2006).ADSCrossRefGoogle Scholar
  4. 4.
    J. W. Davidson, Jr., B. J. Baptista, E. P. Horch, et al., Astron. J. 138, 1354 (2009).ADSCrossRefGoogle Scholar
  5. 5.
    A. Labeyrie, Astron. and Astrophys. 6, 85 (1970).ADSGoogle Scholar
  6. 6.
    A. Labeyrie, D. Bonneau, R. V. Stachnik, and D. Y. Gezari, Astrophys. J. Lett. 194, L147 (1974).ADSCrossRefGoogle Scholar
  7. 7.
    K. T. Knox and B. J. Thompson, Astrophys. J. Lett. 182, L133 (1973).ADSCrossRefGoogle Scholar
  8. 8.
    H. A. McAlister, Publ. Astron. Soc. Pacific 88, 317 (1976).ADSCrossRefGoogle Scholar
  9. 9.
    H. A. McAlister, Publ. Astron. Soc. Pacific 88, 957 (1976).ADSCrossRefGoogle Scholar
  10. 10.
    Y. Y. Balega and N. A. Tikhonov, Sov. Astron. Lett. 3, 272 (1977).ADSGoogle Scholar
  11. 11.
    Y. Y. Balega and V. P. Ryadchenko, Sov. Astron. Lett. 10, 95 (1984).ADSGoogle Scholar
  12. 12.
    J. B. Breckinridge, H. A. McAlister, and W. G. Robinson, Appl. Opt. 18, 1034 (1979).ADSCrossRefGoogle Scholar
  13. 13.
    D. W. Latham, R. P. Stefaniz, G. Torres, et al., Astron. J. 124, 1144 (2002).ADSCrossRefGoogle Scholar
  14. 14.
    E. P. Horch, L. A. P. Bahi, J. R. Gaulin, et al., Astron. J. 143, 10 (2012).ADSCrossRefGoogle Scholar
  15. 15.
    J. M. Carquillat and J. L. Prieur, Astronomische Nachrichten 328, 527 (2007).ADSCrossRefGoogle Scholar
  16. 16.
    N. V. Kharchenko, Kinematika i FizikaNebesnykh Tel 17, 409 (2001).ADSGoogle Scholar
  17. 17.
    N. Ginestet and J. M. Carquillat, Astrophys. J. Suppl. 143, 513 (2002).ADSCrossRefGoogle Scholar
  18. 18.
    W. I. Hartkopf, B. D. Mason, H. A. McAlister, et al., Astron. J. 111, 936 (1996).ADSCrossRefGoogle Scholar
  19. 19.
    E. P. Horch, S. B. Howell, M. E. Everett, and D. R. Ciardi, Astron. J. 144, 165 (2012).ADSCrossRefGoogle Scholar
  20. 20.
    D. Goldberg, T. Mazeh, D. W. Latham, et al., Astron. J. 124, 1132 (2002).ADSCrossRefGoogle Scholar
  21. 21.
    M. Konacki, M. W. Muterspaugh, S. R. Kulkarni, and K. G. Hełminiak, Astrophys. J. 719, 1293 (2010).ADSCrossRefGoogle Scholar
  22. 22.
    D. Pourbaix, Astron. and Astrophys. Suppl. 145, 215 (2000).ADSCrossRefGoogle Scholar
  23. 23.
    X. Pan, M. Shao, M. M. Colavita, et al., Astrophys. J. 384, 624 (1992).ADSCrossRefGoogle Scholar
  24. 24.
    B. D. Mason, G. L. Wycoff, W. I. Hartkopf, et al., Astron. J. 122, 3466 (2001).ADSCrossRefGoogle Scholar
  25. 25.
    H. A. Abt, Astrophys. J. Suppl. 180, 117 (2009).ADSCrossRefGoogle Scholar
  26. 26.
    F. van Leeuwen, Astron. and Astrophys. 474, 653 (2007).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  • J. A. Docobo
    • 1
    • 2
  • P. P. Campo
    • 1
  • M. Andrade
    • 1
    • 3
  • E. P. Horch
    • 4
  1. 1.R. M. Aller Astronomical ObservatoryUniversity of Santiago de CompostelaSantiago de CompostelaSpain
  2. 2.Faculty of MathematicsUniversity of Santiago de CompostelaSantiago de CompostelaSpain
  3. 3.Higher Polytechnic SchoolUniversity of Santiago de CompostelaLugoSpain
  4. 4.Southern Connecticut State UniversityNew HavenUSA

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