Survey Science Group Workshop

1. 2013-02-15 Gravitationally Lensed Quasars in SDSS: Statistical Properties 박명구, 한두환 (경북대) Survey Science Group Workshop

3. Quasar gravitational lens • Quasar lensing • quasars lensed by galaxies/clusters/dark objects • images: 2 to 4 • separation • 0.34” ~ 15.9” • mostly in 0.5” ~ 4”

4. CASTLES • CfA-Arizona Space Telescope LEnsSurvey • lensed quasars (as of 2013/02) • Class A: 82 cases (I’d bet my life.) • Class B: 10 cases (I’d bet your life.) • Class C: 8 cases (I’d bet your life and you should worry.)

6. Quasar Lensing & SDSS • Quasar lensing • multiple image quasars lensed by galaxy/cluster • SDSS quasar sample • lensing probability: ~10-3 • 100 lens systems expected from spectroscopic sample of 105 SDSS quasars • 1000 lens systems plausible from 106 quasars expected in 104 deg2 • well-defined sample?? • Well-defined selection function needed for statistical analysis

7. Statistics of lensing • Tests • probability of lensing (number of lensed quasars) • configuration of lensing • image number, separation, geometry • brightness ratio • Depends on • cosmology • lenses • mass distribution • spatial distribution • evolution in z • sources • evolution in z

8. Probability Test • Fukugita et al. (1992) • Hewitt-Burbidge catalogue • expected number • : 3 • : 5 • : 18 • : 46 • observed number • 4 out of Hewitt-Burbidge catalogue • large rejected • Kochanek (1996) • likelihood test for probability and separation • at 95% CL

9. Lee & Park (1994, 1998) • Im et al. (1997) • Chiba & Yoshii (1997, 1999)

10. Chae et al. (2003) • radio selected sample

11. Complications in lensing statistics • mass model of individual galaxy • sample construction • selection effects of surveys • magnification bias • faint sources get brightened and detected • source distribution in luminosity and z needed

12. Sloan digital sky survey Quasar Lens Search (SQLS) • Algorithm to find lens candidates from quasars • typical FWHM for SDSS imaging data ≈ 1.”4 • small separation () system • blended • morphological selection • large separation () system • deblended • color selection • brightness ratio

13. Follow-up confirmation • spectroscopic observation • photometric observation

14. SDSS image

15. Follow-up imaging

17. Spectroscopic confirmation

18. Constraints on Dark Energy and Evolution of Massive Galaxies • Oguri et al. (2012) • SDSS DR7 quasar catalog: 105,783 QSOs • Selection function • 26 strongly lensed quasars

19. Theoretical model • singular isothermal ellipsoid • velocity function • redshift evolution

20. quasar luminosity function • lensing cross section over lensing area • lensing probability

21. quasars should be brighter than lens • completeness function • probability distribution

22. numbers of lensed quasars • likelihood

23. image separation distribution

24. flat universe

25. without galaxy evolution

26. with galaxy evolution

27. redshift evolution of velocity function

28. Worries • quasar luminosity function and its evolution • galaxy velocity function and its evolution • galaxy number evolution and its evolution

29. Image Separation Statistics • 한두환 • advantages & disadvantages • less sensitive to dark energy • magnitude bias not required • source information not needed

30. Sample • 17 SQLS quasars of with source and lens redshifts • 76 SQLS quasars with source redshifts

31. JVAS vs SQLS

32. Curvature test • mean image separation • magnitude selection: lens should be bright enough

33. Spearman rank correlation test for • 76 lensed QSOs

34. Image Separation Test • Theoretical model • singular isothermal sphere • velocity function • lensing probability

35. differential probability

36. concordance model • expected vs observed

37. Likelihood

38. z > 2.2 sample

39. MC check • generate mock sample from theoretical probability distribution: 100, 1000 • apply the same test

40. With galaxy evolution

41. constraints on galaxy evolution

42. Summary • Lensing statistics • contains information on cosmology and galaxies • need to be careful • the more, the better: eBOSS, BigBOSS …