RADIO PHYSICS AND RADIO ASTRONOMY

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 polynomial

Manuscript submitted 26.08.2014

Radio phys. radio astron. 2014, 19(4): 307-316 

REFERENCES

1. 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