Astronomy Letters

, Volume 36, Issue 5, pp 329–337 | Cite as

Asymptotic formulas for the magnification of a gravitational lens system near a fold caustic

  • A. N. Alexandrov
  • V. I. Zhdanov
  • E. V. Fedorova
Article

Abstract

An approximate formula for the magnification of a point source near a fold caustic obtained in the first linear caustic approximation is widely used in the theory of gravitational lens systems. Here, this formula is refined to include the post-linear terms that have been found both for a point source and for an extended Gaussian source in the absence of continuous matter on the line of sight. The formulas are reduced to a form containing three additional parameters; the derivation of nontrivial corrections requires including the expansion terms in the lens equation up to the fourth order. The modified formula for an extended source is used to analyze strong microlensing events in the gravitational lens system Q2237+0305 (the Einstein Cross). For such an event on the light curve of image C (1999, OGLE data), the corrections found are statistically significant.

Key words

gravitational lenses microlensing Q2237+0305 Einstein Cross 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. Alcalde, E. Mediavilla, O. Moreau, et al., Astrophys. J. 572, 729 (2002).CrossRefADSGoogle Scholar
  2. 2.
    A. N. Alexandrov, V. I. Zhdanov, and E. V. Fedorova, Vestn. Kiev. un-ta, Astron. 39–40, 52 (2003) [in Ukrainian].Google Scholar
  3. 3.
    T. Anguita, R.W. Schmidt, E. L. Turner, et al., Astron. Astrophys. 480, 327 (2008).CrossRefADSGoogle Scholar
  4. 4.
    G. S. Bisnovatyi-Kogan and O. Yu. Tsupko, Astrophysics. 51, 99 (2008).CrossRefADSGoogle Scholar
  5. 5.
    P. V. Bliokh and A. A. Minakov, Gravitational Lenses (Naukova Dumka, Kiev, 1989) [in Russian].Google Scholar
  6. 6.
    M. B. Bogdanov and A. M. Cherepashchuk, Astron. Zh. 79, 693 (2002) [Astron. Rep. 46, 626 (2002)].Google Scholar
  7. 7.
    C. J. Fluke and R. L. Webster, Mon. Not. R. Astron. Soc. 302, 68 (1999).CrossRefADSGoogle Scholar
  8. 8.
    I. M. Gelfand and G. E. Shilov, Generalized Functions, 1: Properties and Operations (Moscow, GIFML, 1959; Academic, New York, 1968).Google Scholar
  9. 9.
    R. Gil-Merino, J. Gonzalez-Cadelo, L.J. Goicoechea, et al., Mon. Not. R. Astron. Soc. 371, 1478 (2006).CrossRefADSGoogle Scholar
  10. 10.
    L. J. Goicoechea, D. Alcalde, E. Mediavilla, et al., Astron. Astrophys. 397, 517 (2003).CrossRefADSGoogle Scholar
  11. 11.
    B. Grieger, R. Kayser, and S. Refsdal, Astron. Astrophys. 194, 54 (1988).ADSGoogle Scholar
  12. 12.
    J. Huchra, M. Gorenstein, S. Kent, et al., Astron. J. 90, 691 (1985).CrossRefADSGoogle Scholar
  13. 13.
    C. R. Keeton, B. S. Gaudi, and A.O. Petters, Astrophys. J. 635, 35 (2005).CrossRefADSGoogle Scholar
  14. 14.
    C. S. Kochanek, Astrophys. J. 605, 58 (2004).CrossRefADSGoogle Scholar
  15. 15.
    M. J. Mortonson, P. L. Schechter, and J. Wambsganss, Astrophys. J. 628, 594 (2005).CrossRefADSGoogle Scholar
  16. 16.
    D. Paraficz, J. Hjorth, I. Burud, et al., Astron. Astrophys. 455, L1 (2006).CrossRefADSGoogle Scholar
  17. 17.
    V. Perlick, Living Rev. Relativ. 7, 9 (2004), http://www.livingreviews.org/lrr-2004-9.ADSGoogle Scholar
  18. 18.
    P. Schneider and A. Weiss, Astron. Astrophys. 171, 49 (1987).ADSGoogle Scholar
  19. 19.
    P. Schneider, J. Ehlers, and E. E. Falko, Gravitational Lenses (Springer, New York, 1992).Google Scholar
  20. 20.
    V. N. Shalyapin, Pis’ma Astron. Zh. 27, 180 (2001) [Astron. Lett. 27, 150 (2001)].Google Scholar
  21. 21.
    V. N. Shalyapin, L. J. Goicoechea, D. Alcalde, et al., Astrophys. J. 579, 127 (2002).CrossRefADSGoogle Scholar
  22. 22.
    A. Udalski, M. K. Szymanski, M. Kubiak, et al., Acta Astron. 56, 293 (2006).ADSGoogle Scholar
  23. 23.
    V. G. Vakulik, R. E. Schild, G.V. Smirnov, et al., Mon. Not. R. Astron. Soc. 382, 819 (2007).CrossRefADSGoogle Scholar
  24. 24.
    J. Wambsganss, Living Rev. Relativ. 1, 12 (1998); http://www.livingreviews.org/lrr-1998-12.ADSGoogle Scholar
  25. 25.
    J. Wambsganss, in Gravitational Lensing: Strong, Weak & Micro, Ed. by G. Meylan, P. Jetzer, and P. North (Springer, Berlin, 2006), p. 457; arXiv:astro-ph/0604278.Google Scholar
  26. 26.
    P. Wozniak, C. Alard, A. Udalski, et al., Astrophys. J. 529, 88 (2000).CrossRefADSGoogle Scholar
  27. 27.
    J. S. Wyithe, R. L. Webster, and E. L. Turner, Mon. Not. R. Astron. Soc. 309, 261 (1999).CrossRefADSGoogle Scholar
  28. 28.
    J. S. Wyithe, R. L. Webster, E. L. Turner, and D. J. Mortlock, Mon. Not. R. Astron. Soc. 315, 62 (2000a).CrossRefADSGoogle Scholar
  29. 29.
    J. S. Wyithe, R. L. Webster, and E. L. Turner, Mon. Not. R. Astron. Soc. 318, 762 (2000b).CrossRefADSGoogle Scholar
  30. 30.
    A. Yonehara, Astron. J. 548, L127 (2001).ADSGoogle Scholar
  31. 31.
    A. F. Zakharov, Gravitation Lenses and Microlenses (Yanus-K, Moscow, 1997) [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • A. N. Alexandrov
    • 1
  • V. I. Zhdanov
    • 1
  • E. V. Fedorova
    • 1
  1. 1.Astronomical ObservatoryTaras Shevchenko Kiev National UniversityKievUkraine

Personalised recommendations