DETERMINING THE INTENSITY OF A POINT-LIKE SOURCE OBSERVED ON THE BACKGROUND OF AN EXTENDED SOURCE

DOI: https://doi.org/10.15407/rpra19.04.317

Y. V. Kornienko, S. I. Skuratovskiy

Abstract


The problem of determining the time dependence of intensity of a point-like source in case of atmospheric blur is formulated and solved by using the Bayesian statistical approach. A pointlike source is supposed to be observed on the background of an extended source with constant in time though unknown brightness. The equation system for optimal statistical estimation of the sequence of intensity values in observation moments is obtained. The problem is particularly relevant for studying gravitational mirages which appear while observing a quasar through the gravitational field of a far galaxy.

Key words: gravitational lensing, Bayesian statistical approach, optimum estimate

Manuscript submitted 21.07.2014

Radio phys. radio astron. 2014, 19(4): 317-323 

REFERENCES

1. BLIOKH, P.V. and MINAKOV, A. A., 1989. Gravitational lenses. Kyiv, Ukraine: Naukova dumka Publ. (in Russian).

2. WALSH, D., CARSWELL, R. F. and WEYMANN, R. J., 1979.0957+561 A, B: twin quasistellar objects or gravitational lens? Nature., vol. 279, no. 5712, pp. 381–384. DOI: https://doi.org/10.1038/279381a0

3. SCHNEIDER, P., EHLERS, J. and FALCO, E., 1992. Gravitational lenses. Berlin-Heidelberg-New York: Springer-Verlag, 345 p.

4. YEE, H. K. C., 1988. High-resolution imaging of the gravitational lens system candidate 2237+030. Astron. J., vol. 95, pp. 1331–1401. DOI: https://doi.org/10.1086/114729

5. VAKULIK, V. G., SCHILD, R. E., DUDINOV, V. N., MINAKOV, A. A., NURITDINOV, S. N., TSVETKOVA, V. S., ZHELEZNYAK, A. P., KONICHEK, V. V., SINELNIKOV, I. YE., BURKHONOV, O. A., ARTAMONOV, B. P. and BRUEVICH, V. V., 2004. Color effects associated with the 1999 microlensing brightness peaks in gravitationally lensed quasar Q2237+0305. Astron. Astrophys., vol. 420, no. 2, pp. 447–457. DOI: https://doi.org/10.1051/0004-6361:20034104

6. LAPLACE, P. S., 1891. Mémoire sur la probabilité des causes par lesévénements. Oeuvres Complètes. Paris: Gauthier-Villars, vol. 8, pp. 27–65.

7. GAUSS, C. F., 1878. Werke. Göttingen, vol. 8, pp. 116–147.

8. LEGENDRE, A. M., 1820. Nouvelles methodes pour la determination des orbites des cometes, Second supplement. Paris: De l'Imprimerie de Huzard-Courcier, pp. 79–80.

9. WALD, A.,1967. Statistical decision functions / Positional play. Moscow, USSR: Nauka Publ. (in Russian).

10. DE GROOT, M.,1974. Optimal statistical decisions. Moscow, USSR:Mir (in Russian).

11. TURCHIN, V. F., KOZLOV, V.P. and MALKEVICH, M. S., 1970. Using the methods of mathematical statistics for solving incorrect problems. Sov. Phys.Uspekhi, vol. 13 (6), no. 6, pp. 681–703. DOI: https://doi.org/10.1070/PU1971v013n06ABEH004273

12. KORNIENKO, YU. V., 2005. A statistical approach to filtering and the information content of the image. Radio Physics and Electronics: Sat. scientific. tr. - Kharkov Institute of Radio Physics and Electronics of NAS of Ukraine, vol. 10, Special Issue, pp. 652–676.

13. ALARD, C. and LUPTON, R. H., 1998. A method for optimal imagesubtraction.Astrophys. J., vol. 503, no. 1, pp. 325–331. DOI: https://doi.org/10.1086/305984

14. PAL, S. K. and KING, R. A., 1981. Image enhancement using smoothing with fuzzy sets. IEEE Trans. Syst. Man. Cyb., vol. 11, no. 7, pp. 494–501. DOI: https://doi.org/10.1109/TSMC.1981.4308726

15. TIKHONOV, A. N. and ARSENIN V. YA., 1974. Methods for solving incorrect problems. Moscow, USSR: Nauka Publ. (in Russian).

16. KOPTELOVA, E. A., SHIMANOVSKAYA, E. V., ARTAMONOV, B. P., BELOKUROV, V., SAZHIN, M. V. and YAGOLA, A. G., 2003. Reconstructing images of gravitational lenses with regularizing algorithms. In: Valls-Gabaud and Kneib J. P., editors. Gravitationallensing: a unique tool for cosmology. Proceedingsof the meeting, Jan 5-11, Aussois, France. – ASP Conference Series, vol. TBD, D.

17. KOPTELOVA, E. A., SHIMANOVSKAYA, E. V., ARTAMONOV, B. P., SAZHIN, M. V. and YAGOLA, A. G., 2004. Two-stage algorithm for reconstructing the images of the gravitational lens QSO 2237+0305. Astron. Rep., vol. 48, no. 10, pp. 826–833. DOI: https://doi.org/10.1134/1.1809395

18. KOPTELOVA, E. A., SHIMANOVSKAYA, E. V., ARTAMONOV, B. P., SAZHIN, M. V., YAGOLA, A. G., BRUEVICH, V. V. and BURKHONOV, O. M. 2005. Image reconstruction technique and optical monitoring of the QSO 2237+0305 from Maidanak Observatoryin 2002-2003. Mon. Not. R. Astron. Soc., vol. 356, no. 1, pp. 323–330. DOI: https://doi.org/10.1111/j.1365-2966.2004.08451.x

19. KOPTELOVA, E. A., ARTAMONOV, B. P., SHIMANOVSKAYA, E. V., BRUEVICH, V. V., GUSEV, A. S. and EZHOVA, O. V., 2007. The gravitationallens Q2237+0305: Reduction and analysis of the observational data. Astron. Rep., vol. 51, no. 10, pp. 797–807. DOI: https://doi.org/10.1134/S1063772907100034

20. KOCHANEK, C. S. 2004.Quantitative interpretation of quasar microlensinglight curves. Astrophys. J., vol. 605, no. 1, pp. 58–77. DOI: https://doi.org/10.1086/382180

21. KORNIENKO, V. 2011. Filtering images belonging to the finite-dimensional function space. Radio Physics and Electronics, vol. 2, no. 2, pp. 48–54 (in Russian).

22. KORN, G., KORN, T., 1973. Mathematical Handbook for Scientists and Engineers. Moscow: Nauka Publ. (in Russian).

23. GNEDENKO, B. V., 1988. The course of probability theory. Moscow, USSR: Nauka Publ (in Russian).

 


Keywords


gravitational lensing; Bayesian statistical approach; optimum estimate

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