MEASURING THE TIME DELAYS IN GRAVITATIONALLY LENSED QUASARS IN THE PRESENCE OF MICROLENSING
A method to measure the time delays in gravitationally lensed quasars is proposed, which provides a simple and transparent procedure to eliminate the effects of microlensing events. The procedure is based on fundamental properties of representation of quadratically integrable functions by their expa...
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Radio physics and radio astronomy |
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2017-06-26T15:24:41Z |
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time delays quasar microlensing light curves gravitational lensing ortogonal polynomial |
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time delays quasar microlensing light curves gravitational lensing ortogonal polynomial Tsvetkova, V. S. Shulga, V. M. Berdina, L. A. MEASURING THE TIME DELAYS IN GRAVITATIONALLY LENSED QUASARS IN THE PRESENCE OF MICROLENSING |
| topic_facet |
time delays quasar microlensing light curves gravitational lensing ortogonal polynomial временные запаздывания квазар микролинзирование кривые блеска гравитационное линзирование ортогональный полином часові запізнення квазар мікролінзування криві блиску гравітаційне лінзування ортогональний поліном |
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Article |
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Tsvetkova, V. S. Shulga, V. M. Berdina, L. A. |
| author_facet |
Tsvetkova, V. S. Shulga, V. M. Berdina, L. A. |
| author_sort |
Tsvetkova, V. S. |
| title |
MEASURING THE TIME DELAYS IN GRAVITATIONALLY LENSED QUASARS IN THE PRESENCE OF MICROLENSING |
| title_short |
MEASURING THE TIME DELAYS IN GRAVITATIONALLY LENSED QUASARS IN THE PRESENCE OF MICROLENSING |
| title_full |
MEASURING THE TIME DELAYS IN GRAVITATIONALLY LENSED QUASARS IN THE PRESENCE OF MICROLENSING |
| title_fullStr |
MEASURING THE TIME DELAYS IN GRAVITATIONALLY LENSED QUASARS IN THE PRESENCE OF MICROLENSING |
| title_full_unstemmed |
MEASURING THE TIME DELAYS IN GRAVITATIONALLY LENSED QUASARS IN THE PRESENCE OF MICROLENSING |
| title_sort |
measuring the time delays in gravitationally lensed quasars in the presence of microlensing |
| title_alt |
ИЗМЕРЕНИЕ ВРЕМЕННЫХ ЗАПАЗДЫВАНИЙ В ГРАВИТАЦИОННО ЛИНЗИРОВАННЫХ КВАЗАРАХ ПРИ НАЛИЧИИ МИКРОЛИНЗИРОВАНИЙ ВИМІРЮВАННЯ ЧАСОВИХ ЗАПІЗНЕНЬ У ГРАВТАЦІЙНО ЛІНЗОВАНИХ КВАЗАРАХ ЗА НАЯВНОСТІ МІКРОЛІНЗУВАННЯ |
| description |
A method to measure the time delays in gravitationally lensed quasars is proposed, which provides a simple and transparent procedure to eliminate the effects of microlensing events. The procedure is based on fundamental properties of representation of quadratically integrable functions by their expansion in orthogonal polynomials. The method is tested on the seven-year duration light curves of the gravitationally lensed quasar НЕ 0435-223. The corresponding photometry was downloaded from the Strasbourg Astronomical Data Center archive. The analysis of time delay estimates in the НЕ 0435-1223 system, as well as comparison with the results published by other authors, are presented.Key words: time delays, quasar, microlensing, light curves gravitational lensing, ortogonal polynomialManuscript submitted 26.08.2014Radio phys. radio astron. 2014, 19(4): 307-316 REFERENCES1. REFSDAL, S.,1964. On the possibility of determining Hubble's parameter and the masses of galaxies from the gravitational lens effect. Mon. Not. R. Astron. Soc,. vol. 128, no. 4, pp. 307–310. DOI: https://doi.org/10.1093/mnras/128.4.307 2. WALSH, D., CARSWELL, R. and WEYMANN, R., 1979. 0957 + 561 A, B: twin quasistellar objects or gravitational lens? Nature, vol. 279, no. 5712. pp. 381–384. DOI: 0.1038/279381a0 3. PRESS, W., RYBICKI, G. and HEWITT, J., 1992.The time delay of gravitational lens 0957 + 561. I. Methodology and analysis of optical photometric data. Astrophys. J., vol. 385, pp. 404–415. DOI: https://doi.org/10.1086/170951 4. PRESS, W., RYBICKI, G. and HEWITT, J., 1992. The time delay of gravitational lens 0957 + 561. II. Analysis of radio data and combined optical-radio analysis. Astrophys. J., vol. 385,pp. 416–420. DOI:https://doi.org/10.1086/170952 5. PELT, J., KAYSER, R., REFSDAL, S. and SCHRAMM, T., 1996. The light curve and the time delay of QSO 0957 + 561. Astron. Astrophys., vol. 305, pp. 97–107. 6. HIRV, A., OLSPERT, N. and PELT, J., 2011. Towards the Automatic Estimation of Time Delays of Gravitational Lenses. Baltic Astronomy, vol. 20, pp. 125–144. 7. TEWES, M., COURBIN, F. and MEYLAN, G., 2013. COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses – XI. Techniques for time delay measurement in presence of microlensing. Astron. Astrophys., vol. 553, id. A120. DOI: https://doi.org/10.1051/0004-6361/201220123 8. EULAERS, E., TEWES, M., MAGAIN, P., COURBIN, F., ASFANDIYAROV, I., EHGAMBERDIEV, SH., RATHNA, KUMAR, S., STALIN, C. S., PRABHU, T. P., MEYLAN, G. and VAN WINCKEL, H. 2013., COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses – XII. Time delays of the doubly lensed quasars SDSS J1206+4332 and HS 2209+1914. Astron. Astrophys., vol. 553, id. A121. DOI: https://doi.org/10.1051/0004-6361/201321140 9. RATHNA KUMAR, S., TEWES, M., STALIN, C. S., COURBIN, F., ASFANDIYAROV, I., MEYLAN, G., EULAERS, E., PRABHU, T. P., MAGAIN, P., VAN WINCKEL, H. and EHGAMBERDIEV, SH., 2013. COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses – XIV. Time delay of the doubly lensed quasar SDSS J1001+5027. Astron. Astrophys., vol. 557, id. A44. DOI: https://doi.org/10.1051/0004-6361/201322116 10. KOCHANEK, C. and SCHECHTER, P., 2003. The Hubble Constant from Gravitational Lens Time Delays. In: Freedman W. L., editor. Carnegie Observatories Astrophysics Series, Vol. 2: Measuring and Modeling the Universe. – Cambridge: Cambridge University Press, pp. 117–137. 11. BARKANA, R., 1997. Analysis of time delays in the gravitational lens PG 1115+080. Astrophys. J., vol. 489, no. 1,pp. 21–28. 12. MINAKOV, A. A., VASYLYEV, S. A. and VAKULIK, V., G. 2001. Lightcurve spesial and temporal variations and gravitaitionally lensed sourse image. Radio Phys. Radio Astron., vol. 6, no. 2, pp. S43-S48. (in Russian). 13. COURBIN, F., CHANTRY, V., REVAZ, Y., SLUSE, D., FAURE, C., TEWES, M., EULAERS, E., KOLEVA, M., ASFANDIYAROV, I., DYE, S., MAGAIN, P., VAN WINCKEL, H., COLES, J., SAHA, P., IBRAHIMOV, M. and MEYLAN, G., 2011. COSMOGRAIL: the COSmological Monitoring of GRAvItational Lenses – IX. Time delays, lens dynamics and baryonic fraction in HE 0435-1223. Astron. Astrophys., vol. 536, id A53. DOI: 10.1051/0004-361/201015709 14. TEWES, M., COURBIN, F., MEYLAN, G., KOCHANEK, C. S., EULAERS, E.,CANTALE, N., MOSQUERA, A. M., ASFANDIYAROV, I., MAGAIN, P., VAN WINCKEL, H., SLUSE, D., KEERTHI, R. K. S., STALIN, C. S., PRABHU, T. P., SAHA, P. and DYE, S., 2012. COSMOGRAIL: Measuring Time Delays of Gravitationally Lensed Quasars to Constrain Cosmology. The Messenger, no. 150, pp. 49–52. 15. LEHAR, J., HEWITT, J., N., BURKE, B. F. and ROBERTS, D. H., 1992. The radio time delay in the double quasar 0957 + 561. Astrophys. J., vol. 384, pp. 453– 466. 16. KOCHANEK, C. S., MORGAN, N. D., FALCO, E. E., MCLEOD, B. A., WINN, J. N., DEMBICKY, J. and KETZEBACK, B., 2006. The Time Delays of Gravitational Lens HE 0435-1223: An Early-Type Galaxy with a Rising Rotation Curve. Astrophys. J., vol. 640, no. 1, pp. 47– 61. 17. CUEVAS-TELLO, J., TINO, P. and RAYCHAUDHURY, S., 2006. How accurateare the time delay estimates in gravitational lensing? Astron. Astrophys., vol. 454, no. 3, pp. 695–706. DOI: https://doi.org/10.1051/0004-6361:20054652 18. VAKULIK, V. G., SHULGA, V. M., SCHILD, R. E., TSVETKOVA, V. S., DUDINOV, V. N., MINAKOV, A. A., NURITDINOV, S. N., ARTAMONOV, B. P., KOCHETOV, A. YE, SMIRNOV,G. V., SERGEYEV, A. A., KONICHEK, V. V., SINELNIKOV, I. YE, BRUEVICH, V. V., AKHUNOV, T. and BURKHONOV, O., 2009. Time delays in PG 1115+080: new estimates. Mon. Not. R. Astron. Soc., vol. 400, no.1,pp. L90–L93. DOI: https://doi.org/10.1111/j.1745-3933.2009.00770.x 19. VANDEN BERK, D. E., WILHITE, B. C., KRON, R. G., ANDERSON, S. F.,BRUNNER, R. J., HALL, P. B., IVEZIĆ, Ž., RICHARDS, G. T., SCHNEIDER, D. P., YORK, D. G., BRINKMANN, J. V., LAMB, D. Q., NICHOL, R. C. and SCHLEGEL, D. J., 2004. The Ensemble Photometric Variability of ~25,000 Quasars in the Sloan Digital Sky Survey. Astrophys. J., vol. 601, no. 2, pp. 692–714. DOI:https://doi.org/10.1086/380563 20. KORN, G. and KORN, T., 1973. Mathematical Handbook for Scientists and Engineers. Moscow: Nauka Publ. (in Russian). 21. Centre de Données astronomiques de Strasbourg [Electronic resource]: R-band light curves of HE 0435-1223 [online] Available from: http://cdsarc.u-strasbg.fr/ 22. Wisotzki, L., Schechter, P. L., Bradt, H. V., Heinmüller, J. and Reimers, D. , 2002. HE 0435-1223: A wide separation quadruple QSO and gravitational lens. Astron. Astrophys., vol. 395, no. 1, pp. 17–23. DOI: https://doi.org/10.1051/0004-6361:20021213 23. MORGAN, N., KOCHANEK, V., PEVUNOVA, O. and SCHECHTER, P. L., 2005. The lens redshift and galaxy environment for HE0435-1223. Astron. J., vol. 129, no. 6, pp. 2531–2541. DOI: https://doi.org/10.1086/430145 |
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Видавничий дім «Академперіодика» |
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2015 |
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http://rpra-journal.org.ua/index.php/ra/article/view/1189 |
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rpra-journalorgua-article-11892017-06-26T15:24:41Z MEASURING THE TIME DELAYS IN GRAVITATIONALLY LENSED QUASARS IN THE PRESENCE OF MICROLENSING ИЗМЕРЕНИЕ ВРЕМЕННЫХ ЗАПАЗДЫВАНИЙ В ГРАВИТАЦИОННО ЛИНЗИРОВАННЫХ КВАЗАРАХ ПРИ НАЛИЧИИ МИКРОЛИНЗИРОВАНИЙ ВИМІРЮВАННЯ ЧАСОВИХ ЗАПІЗНЕНЬ У ГРАВТАЦІЙНО ЛІНЗОВАНИХ КВАЗАРАХ ЗА НАЯВНОСТІ МІКРОЛІНЗУВАННЯ Tsvetkova, V. S. Shulga, V. M. Berdina, L. A. time delays; quasar; microlensing; light curves gravitational lensing; ortogonal polynomial временные запаздывания; квазар; микролинзирование; кривые блеска; гравитационное линзирование; ортогональный полином часові запізнення; квазар; мікролінзування; криві блиску; гравітаційне лінзування; ортогональний поліном A method to measure the time delays in gravitationally lensed quasars is proposed, which provides a simple and transparent procedure to eliminate the effects of microlensing events. The procedure is based on fundamental properties of representation of quadratically integrable functions by their expansion in orthogonal polynomials. The method is tested on the seven-year duration light curves of the gravitationally lensed quasar НЕ 0435-223. The corresponding photometry was downloaded from the Strasbourg Astronomical Data Center archive. The analysis of time delay estimates in the НЕ 0435-1223 system, as well as comparison with the results published by other authors, are presented.Key words: time delays, quasar, microlensing, light curves gravitational lensing, ortogonal polynomialManuscript submitted 26.08.2014Radio phys. radio astron. 2014, 19(4): 307-316 REFERENCES1. REFSDAL, S.,1964. On the possibility of determining Hubble's parameter and the masses of galaxies from the gravitational lens effect. Mon. Not. R. Astron. Soc,. vol. 128, no. 4, pp. 307–310. DOI: https://doi.org/10.1093/mnras/128.4.307 2. WALSH, D., CARSWELL, R. and WEYMANN, R., 1979. 0957 + 561 A, B: twin quasistellar objects or gravitational lens? Nature, vol. 279, no. 5712. pp. 381–384. DOI: 0.1038/279381a0 3. PRESS, W., RYBICKI, G. and HEWITT, J., 1992.The time delay of gravitational lens 0957 + 561. I. Methodology and analysis of optical photometric data. Astrophys. J., vol. 385, pp. 404–415. DOI: https://doi.org/10.1086/170951 4. PRESS, W., RYBICKI, G. and HEWITT, J., 1992. The time delay of gravitational lens 0957 + 561. II. Analysis of radio data and combined optical-radio analysis. Astrophys. J., vol. 385,pp. 416–420. DOI:https://doi.org/10.1086/170952 5. PELT, J., KAYSER, R., REFSDAL, S. and SCHRAMM, T., 1996. The light curve and the time delay of QSO 0957 + 561. Astron. Astrophys., vol. 305, pp. 97–107. 6. HIRV, A., OLSPERT, N. and PELT, J., 2011. Towards the Automatic Estimation of Time Delays of Gravitational Lenses. Baltic Astronomy, vol. 20, pp. 125–144. 7. TEWES, M., COURBIN, F. and MEYLAN, G., 2013. COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses – XI. Techniques for time delay measurement in presence of microlensing. Astron. Astrophys., vol. 553, id. A120. DOI: https://doi.org/10.1051/0004-6361/201220123 8. EULAERS, E., TEWES, M., MAGAIN, P., COURBIN, F., ASFANDIYAROV, I., EHGAMBERDIEV, SH., RATHNA, KUMAR, S., STALIN, C. S., PRABHU, T. P., MEYLAN, G. and VAN WINCKEL, H. 2013., COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses – XII. Time delays of the doubly lensed quasars SDSS J1206+4332 and HS 2209+1914. Astron. Astrophys., vol. 553, id. A121. DOI: https://doi.org/10.1051/0004-6361/201321140 9. RATHNA KUMAR, S., TEWES, M., STALIN, C. S., COURBIN, F., ASFANDIYAROV, I., MEYLAN, G., EULAERS, E., PRABHU, T. P., MAGAIN, P., VAN WINCKEL, H. and EHGAMBERDIEV, SH., 2013. COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses – XIV. Time delay of the doubly lensed quasar SDSS J1001+5027. Astron. Astrophys., vol. 557, id. A44. DOI: https://doi.org/10.1051/0004-6361/201322116 10. KOCHANEK, C. and SCHECHTER, P., 2003. The Hubble Constant from Gravitational Lens Time Delays. In: Freedman W. L., editor. Carnegie Observatories Astrophysics Series, Vol. 2: Measuring and Modeling the Universe. – Cambridge: Cambridge University Press, pp. 117–137. 11. BARKANA, R., 1997. Analysis of time delays in the gravitational lens PG 1115+080. Astrophys. J., vol. 489, no. 1,pp. 21–28. 12. MINAKOV, A. A., VASYLYEV, S. A. and VAKULIK, V., G. 2001. Lightcurve spesial and temporal variations and gravitaitionally lensed sourse image. Radio Phys. Radio Astron., vol. 6, no. 2, pp. S43-S48. (in Russian). 13. COURBIN, F., CHANTRY, V., REVAZ, Y., SLUSE, D., FAURE, C., TEWES, M., EULAERS, E., KOLEVA, M., ASFANDIYAROV, I., DYE, S., MAGAIN, P., VAN WINCKEL, H., COLES, J., SAHA, P., IBRAHIMOV, M. and MEYLAN, G., 2011. COSMOGRAIL: the COSmological Monitoring of GRAvItational Lenses – IX. Time delays, lens dynamics and baryonic fraction in HE 0435-1223. Astron. Astrophys., vol. 536, id A53. DOI: 10.1051/0004-361/201015709 14. TEWES, M., COURBIN, F., MEYLAN, G., KOCHANEK, C. S., EULAERS, E.,CANTALE, N., MOSQUERA, A. M., ASFANDIYAROV, I., MAGAIN, P., VAN WINCKEL, H., SLUSE, D., KEERTHI, R. K. S., STALIN, C. S., PRABHU, T. P., SAHA, P. and DYE, S., 2012. COSMOGRAIL: Measuring Time Delays of Gravitationally Lensed Quasars to Constrain Cosmology. The Messenger, no. 150, pp. 49–52. 15. LEHAR, J., HEWITT, J., N., BURKE, B. F. and ROBERTS, D. H., 1992. The radio time delay in the double quasar 0957 + 561. Astrophys. J., vol. 384, pp. 453– 466. 16. KOCHANEK, C. S., MORGAN, N. D., FALCO, E. E., MCLEOD, B. A., WINN, J. N., DEMBICKY, J. and KETZEBACK, B., 2006. The Time Delays of Gravitational Lens HE 0435-1223: An Early-Type Galaxy with a Rising Rotation Curve. Astrophys. J., vol. 640, no. 1, pp. 47– 61. 17. CUEVAS-TELLO, J., TINO, P. and RAYCHAUDHURY, S., 2006. How accurateare the time delay estimates in gravitational lensing? Astron. Astrophys., vol. 454, no. 3, pp. 695–706. DOI: https://doi.org/10.1051/0004-6361:20054652 18. VAKULIK, V. G., SHULGA, V. M., SCHILD, R. E., TSVETKOVA, V. S., DUDINOV, V. N., MINAKOV, A. A., NURITDINOV, S. N., ARTAMONOV, B. P., KOCHETOV, A. YE, SMIRNOV,G. V., SERGEYEV, A. A., KONICHEK, V. V., SINELNIKOV, I. YE, BRUEVICH, V. V., AKHUNOV, T. and BURKHONOV, O., 2009. Time delays in PG 1115+080: new estimates. Mon. Not. R. Astron. Soc., vol. 400, no.1,pp. L90–L93. DOI: https://doi.org/10.1111/j.1745-3933.2009.00770.x 19. VANDEN BERK, D. E., WILHITE, B. C., KRON, R. G., ANDERSON, S. F.,BRUNNER, R. J., HALL, P. B., IVEZIĆ, Ž., RICHARDS, G. T., SCHNEIDER, D. P., YORK, D. G., BRINKMANN, J. V., LAMB, D. Q., NICHOL, R. C. and SCHLEGEL, D. J., 2004. The Ensemble Photometric Variability of ~25,000 Quasars in the Sloan Digital Sky Survey. Astrophys. J., vol. 601, no. 2, pp. 692–714. DOI:https://doi.org/10.1086/380563 20. KORN, G. and KORN, T., 1973. Mathematical Handbook for Scientists and Engineers. Moscow: Nauka Publ. (in Russian). 21. Centre de Données astronomiques de Strasbourg [Electronic resource]: R-band light curves of HE 0435-1223 [online] Available from: http://cdsarc.u-strasbg.fr/ 22. Wisotzki, L., Schechter, P. L., Bradt, H. V., Heinmüller, J. and Reimers, D. , 2002. HE 0435-1223: A wide separation quadruple QSO and gravitational lens. Astron. Astrophys., vol. 395, no. 1, pp. 17–23. DOI: https://doi.org/10.1051/0004-6361:20021213 23. MORGAN, N., KOCHANEK, V., PEVUNOVA, O. and SCHECHTER, P. L., 2005. The lens redshift and galaxy environment for HE0435-1223. Astron. J., vol. 129, no. 6, pp. 2531–2541. DOI: https://doi.org/10.1086/430145 УДК 523.163;524.316.7.082-82 Предложен метод определения временных запаздываний в гравитационно линзированных квазарах, который предоставляет простую и прозрачную процедуру устранения влияния событий микролинзирования, основанную на фундаментальных свойствах представления квадратично интегрируемых функций в виде разложения по ортогональным полиномам. Метод протестирован на семилетних кривых блеска гравитационно линзированного квазара НЕ 0435-1223, фотометрия для которого получена из архива CDS (Strasbourg astronomical Data Center). Приводится анализ полученных оценок временных запаздываний в системе НЕ 0435-1223 и их сравнение с результатами, опубликованными ранее в работах других авторов.Ключевые слова:временные запаздывания, квазар, микролинзирование, кривые блеска, гравитационное линзирование, ортогональный полиномСтатья посупила в редакцию 26.08.2014Radio phys. radio astron. 2014, 19(4): 307-316 СПИСОК ЛИТЕРАТУРЫ1. Refsdal S. On the possibility of determining Hubble’sparameter and the masses of galaxies from the gravitationallens effect // Mon. Not. R. Astron. Soc. – 1964. –Vol. 128, Is. 4. – P. 307–310.2. Walsh D., Carswell R., and Weymann R. 0957 + 561 A,B: twin quasistellar objects or gravitational lens? //Nature. – 1979. – Vol. 279, No. 5712. – P. 381–384.3. Press W., Rybicki G., and Hewitt J. The time delay ofgravitational lens 0957 + 561. I. Methodology and analysisof optical photometric data // Astrophys. J. – 1992. –Vol. 385. – P. 404–415.4. Press W., Rybicki G., and Hewitt J. The time delay of gravitationallens 0957 + 561. II. Analysis of radio data andcombined optical-radio analysis // Astrophys. J. – 1992. –Vol. 385. – P. 416–420.5. Pelt J., Kayser R., Refsdal S., and Schramm T. The lightcurve and the time delay of QSO 0957 + 561 // Astron.Astrophys. – 1996. – Vol. 305. – P. 97–107.6. Hirv A., Olspert N., Pelt J. Towards the Automatic Estimationof Time Delays of Gravitational Lenses // BalticAstronomy. – 2011. – Vol. 20. – P. 125–144.7. Tewes M., Courbin F., and Meylan G. COSMOGRAIL: theCOSmological MOnitoring of GRAvItational Lenses – XI.Techniques for time delay measurement in presence of microlensing// Astron. Astrophys. – 2013. – Vol. 553. – id. A120.8. Eulaers E., Tewes M., Magain P., Courbin F., AsfandiyarovI., Ehgamberdiev Sh., Rathna Kumar S., StalinC. S., Prabhu T. P., Meylan G., and Van Winckel H.COSMOGRAIL: the COSmological MOnitoring of GRAvItationalLenses – XII. Time delays of the doubly lensedquasars SDSS J1206+4332 and HS 2209+1914 // Astron.Astrophys. – 2013. – Vol. 553. – id. A121.9. Rathna Kumar S., Tewes M., Stalin C. S., Courbin F.,Asfandiyarov I., Meylan G., Eulaers E., Prabhu T. P.,Magain P., Van Winckel H., and Ehgamberdiev Sh.COSMOGRAIL: the COSmological MOnitoring of GRAvItationalLenses – XIV. Time delay of the doubly lensedquasar SDSS J1001+5027 // Astron. Astrophys. – 2013. –Vol. 557. – id. A44.10. Kochanek C. and Schechter P. The Hubble Constant fromGravitational Lens Time Delays. In: Freedman W. L.,editor. Carnegie Observatories Astrophysics Series, Vol. 2:Measuring and Modeling the Universe. – Cambridge: CambridgeUniversity Press, 2003. – P. 117–137.11. Barkana R. Analysis of time delays in the gravitational lens PG 1115+080 // Astrophys. J. – 1997. – Vol. 489, No. 1. – P. 21–28.12. Минаков А. А., Васильев C. A., Вакулик В. Г. Пространственно-временные вариации кривой блеска источника при прохождении излучения через гравитационную линзу-галактику // Радиофизика и радиоастрономия. – 2001. – Т. 6, № 2. – C. S43–S48.13. Courbin F., Chantry V., Revaz Y., Sluse D., Faure C., Tewes M., Eulaers E., Koleva M., Asfandiyarov I., Dye S., Magain P., van Winckel H., Coles J., Saha P., Ibrahimov M., and Meylan G. COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses – IX. Time delays, lens dynamics and baryonic fraction in HE 0435-1223 // Astron. Astrophys. – 2011. – Vol. 536. – id A53.14. Tewes M., Courbin F., Meylan G., Kochanek C. S., Eulaers E., Cantale N., Mosquera A. M., Asfandiyarov I., Magain P., van Winckel H., Sluse D., Keerthi R. K. S., Stalin C. S., Prabhu T. P., Saha P., and Dye S. COSMOGRAIL: Measuring Time Delays of Gravitationally Lensed Quasars to Constrain Cosmology // The Messenger. – 2012. – No. 150. – P. 49–52.15. Lehar J., Hewitt J., N., Burke B. F., and Roberts D. H. The radio time delay in the double quasar 0957 + 561 // Astrophys. J. – 1992. – Vol. 384. – P. 453– 466.16. Kochanek C. S., Morgan N. D., Falco E. E., McLeod B. A., Winn J. N., Dembicky J., and Ketzeback B. The Time Delays of Gravitational Lens HE 0435-1223: An Early-Type Galaxy with a Rising Rotation Curve // Astrophys. J. – 2006. – Vol. 640, No.1. – P. 47– 61.17. Cuevas-Tello J., Tino P., and Raychaudhury S. How accurate are the time delay estimates in gravitational lensing? // Astron. Astrophys. – 2006. – Vol. 454, No. 3. – P. 695–706.18. Vakulik V. G., Shulga V. M., Schild R. E., Tsvetkova V. S., Dudinov V. N., Minakov A. A., Nuritdinov S. N., Artamonov B. P., Kochetov A. Ye, Smirnov G. V., Sergeyev A. A., Konichek V. V., Sinelnikov I. Ye, Bruevich V. V., Akhunov T., and Burkhonov O. Time delays in PG 1115+080: new estimates // Mon. Not. R. Astron. Soc. – 2009. – Vol. 400, Is.1. – P. L90–L93.19. Vanden Berk D. E., Wilhite B. C., Kron R. G., Anderson S. F., Brunner R. J., Hall P. B., Ivezić Ž., Richards G. T., Schneider D. P., York D. G., Brinkmann J. V., Lamb D. Q., Nichol R. C., and Schlegel D. J. The Ensemble Photometric Variability of ~25,000 Quasars in the Sloan Digital Sky Survey // Astrophys. J. – 2004. – Vol. 601, No. 2. – P. 692–714.20. Корн Г., Корн Т. Справочник по математике для научных работников и инженеров. – М.: Наука, 1973. – 832 с.21. Centre de Données astronomiques de Strasbourg [Электронный ресурс]: R-band light curves of HE 0435-1223 – Режим доступа: http://cdsarc.u-strasbg.fr/22. Wisotzki L., Schechter P., Bradt H., Heinmьller J., and Reimers D. HE 0435-1223: A wide separation quadruple QSO and gravitational lens // Astron. Astrophys. – 2002. – Vol. 395, No.1. – P. 17–23.23. Morgan N., Kochanek V., Pevunova O., and Schechter P. L.The lens redshift and galaxy environment for HE 0435-1223 // Astron. J. – 2005.– Vol. 129, Is. 6. – P. 2531–254 УДК 523.163;524.316.7.082-82 Запропоновано метод визначення часових запізнень у гравітаційно лінзованих квазарах, який надає просту і прозору процедуру усунення впливу подій мікролінзування, що грунтується на фундаментальних властивостях репрезентації квадратично інтегрованих функцій у вигляді розкладання за ортогональними поліномами. Метод протестовано на семирічних кривих блиску гравітаційно лінзованого квазара НЕ 0435-1223, фотометрію для котрого було отримано з архіву CDS (Strasburg Astronomical Data Center). Надається аналіз отриманих оцінок часових запізнень у системі НЕ 0435-1223 та їх порівняння з результатами, опублікованими раніше в роботах інших авторів. Ключові слова: часові запізнення, квазар, мікролінзування, криві блиску, гравітаційне лінзування, ортогональний поліномСтаття надійшла до редакції 26.08.2014Radio phys. radio astron. 2014, 19(4): 307-316 СПИСОК ЛІТЕРАТУРИ1. Refsdal S. On the possibility of determining Hubble’sparameter and the masses of galaxies from the gravitationallens effect // Mon. Not. R. Astron. Soc. – 1964. –Vol. 128, Is. 4. – P. 307–310.2. Walsh D., Carswell R., and Weymann R. 0957 + 561 A,B: twin quasistellar objects or gravitational lens? //Nature. – 1979. – Vol. 279, No. 5712. – P. 381–384.3. Press W., Rybicki G., and Hewitt J. The time delay ofgravitational lens 0957 + 561. I. Methodology and analysisof optical photometric data // Astrophys. J. – 1992. –Vol. 385. – P. 404–415.4. Press W., Rybicki G., and Hewitt J. The time delay of gravitationallens 0957 + 561. II. Analysis of radio data andcombined optical-radio analysis // Astrophys. J. – 1992. –Vol. 385. – P. 416–420.5. Pelt J., Kayser R., Refsdal S., and Schramm T. The lightcurve and the time delay of QSO 0957 + 561 // Astron.Astrophys. – 1996. – Vol. 305. – P. 97–107.6. Hirv A., Olspert N., Pelt J. Towards the Automatic Estimationof Time Delays of Gravitational Lenses // BalticAstronomy. – 2011. – Vol. 20. – P. 125–144.7. Tewes M., Courbin F., and Meylan G. COSMOGRAIL: theCOSmological MOnitoring of GRAvItational Lenses – XI.Techniques for time delay measurement in presence of microlensing// Astron. Astrophys. – 2013. – Vol. 553. – id. A120.8. Eulaers E., Tewes M., Magain P., Courbin F., AsfandiyarovI., Ehgamberdiev Sh., Rathna Kumar S., StalinC. S., Prabhu T. P., Meylan G., and Van Winckel H.COSMOGRAIL: the COSmological MOnitoring of GRAvItationalLenses – XII. Time delays of the doubly lensedquasars SDSS J1206+4332 and HS 2209+1914 // Astron.Astrophys. – 2013. – Vol. 553. – id. A121.9. Rathna Kumar S., Tewes M., Stalin C. S., Courbin F.,Asfandiyarov I., Meylan G., Eulaers E., Prabhu T. P.,Magain P., Van Winckel H., and Ehgamberdiev Sh.COSMOGRAIL: the COSmological MOnitoring of GRAvItationalLenses – XIV. Time delay of the doubly lensedquasar SDSS J1001+5027 // Astron. Astrophys. – 2013. –Vol. 557. – id. A44.10. Kochanek C. and Schechter P. The Hubble Constant fromGravitational Lens Time Delays. In: Freedman W. L.,editor. Carnegie Observatories Astrophysics Series, Vol. 2:Measuring and Modeling the Universe. – Cambridge: CambridgeUniversity Press, 2003. – P. 117–137.11. Barkana R. Analysis of time delays in the gravitational lens PG 1115+080 // Astrophys. J. – 1997. – Vol. 489, No. 1. – P. 21–28.12. Минаков А. А., Васильев C. A., Вакулик В. Г. Пространственно-временные вариации кривой блеска источника при прохождении излучения через гравитационную линзу-галактику // Радиофизика и радиоастрономия. – 2001. – Т. 6, № 2. – C. S43–S48.13. Courbin F., Chantry V., Revaz Y., Sluse D., Faure C., Tewes M., Eulaers E., Koleva M., Asfandiyarov I., Dye S., Magain P., van Winckel H., Coles J., Saha P., Ibrahimov M., and Meylan G. COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses – IX. Time delays, lens dynamics and baryonic fraction in HE 0435-1223 // Astron. Astrophys. – 2011. – Vol. 536. – id A53.14. Tewes M., Courbin F., Meylan G., Kochanek C. S., Eulaers E., Cantale N., Mosquera A. M., Asfandiyarov I., Magain P., van Winckel H., Sluse D., Keerthi R. K. S., Stalin C. S., Prabhu T. P., Saha P., and Dye S. COSMOGRAIL: Measuring Time Delays of Gravitationally Lensed Quasars to Constrain Cosmology // The Messenger. – 2012. – No. 150. – P. 49–52.15. Lehar J., Hewitt J., N., Burke B. F., and Roberts D. H. The radio time delay in the double quasar 0957 + 561 // Astrophys. J. – 1992. – Vol. 384. – P. 453– 466.16. Kochanek C. S., Morgan N. D., Falco E. E., McLeod B. A., Winn J. N., Dembicky J., and Ketzeback B. The Time Delays of Gravitational Lens HE 0435-1223: An Early-Type Galaxy with a Rising Rotation Curve // Astrophys. J. – 2006. – Vol. 640, No.1. – P. 47– 61.17. Cuevas-Tello J., Tino P., and Raychaudhury S. How accurate are the time delay estimates in gravitational lensing? // Astron. Astrophys. – 2006. – Vol. 454, No. 3. – P. 695–706.18. Vakulik V. G., Shulga V. M., Schild R. E., Tsvetkova V. S., Dudinov V. N., Minakov A. A., Nuritdinov S. N., Artamonov B. P., Kochetov A. Ye, Smirnov G. V., Sergeyev A. A., Konichek V. V., Sinelnikov I. Ye, Bruevich V. V., Akhunov T., and Burkhonov O. Time delays in PG 1115+080: new estimates // Mon. Not. R. Astron. Soc. – 2009. – Vol. 400, Is.1. – P. L90–L93.19. Vanden Berk D. E., Wilhite B. C., Kron R. G., Anderson S. F., Brunner R. J., Hall P. B., Ivezić Ž., Richards G. T., Schneider D. P., York D. G., Brinkmann J. V., Lamb D. Q., Nichol R. C., and Schlegel D. J. The Ensemble Photometric Variability of ~25,000 Quasars in the Sloan Digital Sky Survey // Astrophys. J. – 2004. – Vol. 601, No. 2. – P. 692–714.20. Корн Г., Корн Т. Справочник по математике для научных работников и инженеров. – М.: Наука, 1973. – 832 с.21. Centre de Données astronomiques de Strasbourg [Электронный ресурс]: R-band light curves of HE 0435-1223 – Режим доступа: http://cdsarc.u-strasbg.fr/22. Wisotzki L., Schechter P., Bradt H., Heinmьller J., and Reimers D. HE 0435-1223: A wide separation quadruple QSO and gravitational lens // Astron. Astrophys. – 2002. – Vol. 395, No.1. – P. 17–23.23. Morgan N., Kochanek V., Pevunova O., and Schechter P. L.The lens redshift and galaxy environment for HE 0435-1223 // Astron. J. – 2005.– Vol. 129, Is. 6. – P. 2531–254 Видавничий дім «Академперіодика» 2015-01-13 Article Article application/pdf http://rpra-journal.org.ua/index.php/ra/article/view/1189 10.15407/rpra19.04.307 РАДИОФИЗИКА И РАДИОАСТРОНОМИЯ; Vol 19, No 4 (2014); 307 RADIO PHYSICS AND RADIO ASTRONOMY; Vol 19, No 4 (2014); 307 РАДІОФІЗИКА І РАДІОАСТРОНОМІЯ; Vol 19, No 4 (2014); 307 2415-7007 1027-9636 10.15407/rpra19.04 ru http://rpra-journal.org.ua/index.php/ra/article/view/1189/823 Copyright (c) 2014 RADIO PHYSICS AND RADIO ASTRONOMY |