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General Relativity and Gravitation

, Volume 40, Issue 5, pp 1013–1027 | Cite as

Constraining the parameters of binary systems through time-dependent light deflection

  • Edmund Schluessel
Research Article

Abstract

A theory is derived relating the configuration of the cores of active galaxies, specifically candidates for presumed super-massive black hole binaries (SMBHBs), to time-dependent changes in images of those galaxies. Three deflection quantities, resulting from the monopole term, mass quadrupole term, and spin dipole term of the core, are examined. The resulting observational technique is applied to the galaxy 3C66B. This technique is found to under idealized circumstances surpass the technique proposed by Jenet et al. in accuracy for constraining the mass of SMBHB candidates, but is exceeded in accuracy and precision by Jenet’s technique under currently understood likely conditions. The technique can also under favorable circumstances produce results measurable by currently available astronomical interferometry such as very-long-baseline interferometry (VLBI).

Keywords

Light deflection SMBHB 3C66B VLBI 

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References

  1. 1.
    Dyson, F.W., Eddington, A.S., Davidson, C.: A Determination of the Deflection of Light by the Sun’s Gravitational Field, from Observations Made at the Total Eclipse of May 29, 1919. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, vol. 220, pp. 291–333 (1920)Google Scholar
  2. 2.
    Jenet, F.A., Lommen, A., Larson, S.L., Wen, L.: Constraining the properties of supermassive black hole systems using pulsar timing: application to 3C 66B. Astrophys. J. 606, 799–803 (2004)CrossRefADSGoogle Scholar
  3. 3.
    Landau, L.D., Lifshitz, E.M.: The Classical Theory of Fields. Fourth Revised English Edition. Pergamon Press, Oxford (1975)Google Scholar
  4. 4.
    Birkhoff, G.D., Langer, R.: Relativity and Modern Physics. Harvard University Press, Cambridge (1927)Google Scholar
  5. 5.
    Kopeikin, S.M., Schäfer, G., Gwinn, C.R., Eubanks, M.T.: Astrometric and timing effects of gravitational waves from localized sources. Phys. Rev. D. 59, 084023 (1999). Also available as Arxiv preprint gr-qc/9811003 (1998)Google Scholar
  6. 6.
    Damour, T., Esposito-Farese, G.: Light deflection by gravitational waves from localized sources. Phys. Rev. D 58, 044003 (1998)CrossRefADSGoogle Scholar
  7. 7.
    Adler, R., Bazin, M., Schiffer, M.: Introduction to General Relativity, 2nd edn. McGraw-Hill Inc, New York (1975)Google Scholar
  8. 8.
    Schwarzschild, K.: Uber das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie. Sitzungsberichte der Koniglichen Preussischen Akademie der Wissenschaften zu Berlin, Klasse fur Mathematik, Physik, und Technik, pp. 189–196 (1916)Google Scholar
  9. 9.
    Northover, K.J.E.: The radio galaxy 3C 66. Mon. Not. Roy. Astron. Soc. 165, 369–379 (1973)ADSGoogle Scholar
  10. 10.
    Matthews , T.A., Morgan, W.W., Schmidt, M.: Astrophys. J. 140, 35 (1964), quoted in Sudou et al.Google Scholar
  11. 11.
    Spergel, D.N. et al.: First-year Wilkinson microwave anisotropy probe (WMAP) observations: determination of cosmological parameters. Astrophys. J. Suppl. Ser. 148, 175–194 (2003)CrossRefADSGoogle Scholar
  12. 12.
    Ekejiuba, I.E., Okeke, P.N., Okoye, S.E.: Origin of the central radio gaps in extragalactic radio sources. Astrophys. Space. Sci. 187, 209–214 (1992)CrossRefADSGoogle Scholar
  13. 13.
    Sudou, H., Iguchi, S., Murata, Y., Taniguchi, Y.: Orbital motion in 3C 66B: evidence for a supermassive black hole binary. Science 300, 1263–1265 (2003)CrossRefADSGoogle Scholar
  14. 14.
    De Paolis, F., Ingrosso, G., Nucita, A.A.: A super massive black hole binary in 3C66B: future observational perspectives. Astron. Astrophys. 426, 379–385 (2004)CrossRefADSGoogle Scholar
  15. 15.
    Croston, J.H., Hardcastle, M.J., Birkinshaw, M., Worrall, D.M.: XMM-Newton observations of the hot-gas atmospheres of 3C 66B and 3C 449. Mon. Not. Roy. Astron. Soc. 4, 1041–1054 (2003)CrossRefADSGoogle Scholar
  16. 16.
    Darwin, C.G.: The gravity field of a particle. Proc. Roy. Soc. Lond. Ser. A. Math. Phys. Sci. 249, 180–194 (1959)zbMATHADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    Giovannini, G., Cotton, W.D., Feretti, L., Lara, L., Venturi, T.: VLBI obervations of a complete sample of radio galaxies: 10 years later. Astrophys. J. 552, 508–526 (2001)CrossRefADSGoogle Scholar
  18. 18.
    Fraix-Burnet, D.: An optical counterjet in 3C66B?. Mon. Not. Roy. Astron. Soc. 226, 1–7 (1996)Google Scholar
  19. 19.
    New VLBA Site. National Radio Astronomy Observatory (2007) http://www.vlba.nrao.edu/
  20. 20.
    Ulvestad, J.: ANGULAR RESOLUTION. National Radio Astronomy Observatory (2006) http://www.vlba.nrao.edu/astro/obstatus/current/node30.html
  21. 21.
    Hirabayashi, H., et al.: On the Near-term Space VLBI Mission VSOP-2. Arxiv preprint astro-ph/0501020 (2005)Google Scholar
  22. 22.
    MSC—Space Interferometry Mission. Michelson Space Center, California Institute of Technology (2006) http://msc.caltech.edu/missions/SIMPQ/
  23. 23.
    Edberg, S.J., Shao, M., Beichman, C.A. (ed.): SIM PlanetQuest: A Mission for Astrophysics and Planet Finding. Jet Propulsion Laboratory, California Institute of Technology, Pasadena (2005)Google Scholar
  24. 24.
    Gendreau, K.C., et al.: The MAXIM X-ray interferometry mission concept study. In: Surdej, J., Swings, J.P., Caro, D., Detal, A., (eds.) From optical to millimetric interferometry: scientific and technological challenges. Proceedings of the 36th Liège International Astrophysics Colloquium, Liège, Belgium, July 2–5, 2001, pp. 11–16. Université de Liège, Institut d’Astrophysique et de Géophysique, Liège, Belgium (2001)Google Scholar
  25. 25.
    Kopeikin, S., Masshoon, B.: Gravitomagnetic effects in the propagation of electromagnetic waves in variable gravitational fields of arbitrary-moving and spinning bodies. Phys. Rev. D 65, 064025 (2002)CrossRefADSGoogle Scholar
  26. 26.
    Weinberg, S.: Gravitation and Cosmology. Wiley, USA (1972)Google Scholar
  27. 27.
    Einstein, A.: Uber den Einfluss der Schwerkraft auf die Ausbreitung des Lichtes. In: Annalen der Physik, 35 898 (1911). Translated in English in Lorentz, H.A., Einstein, A., Minkowski, H., Weyl, H., The Principle of Relativity. Dover, New York (1952)Google Scholar
  28. 28.
    Bozza, V., Scarpetta, G.: Strong deflection limit of black hole gravitational lensing with arbitrary source distances. Arxiv preprint gr-qc/0705.0246 (2007)Google Scholar
  29. 29.
    Kopeikin, S.M., Makarov, V.: Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers. Arxiv preprint astro-ph/0611358v2 (2006)Google Scholar
  30. 30.
    Abramowitz, M., Stegun, I.A. (ed.): Handbook of Mathematical Functions, ninth printing. National Bureau of Standards Press, Washington (1970)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.School of Physics and Astronomy, 5, The ParadeCardiff UniversityCardiffUK

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