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Gravitationally Lensed Quasars in SDSS: Statistical Properties and Implications

This study investigates the statistical properties of gravitationally lensed quasars in the Sloan Digital Sky Survey (SDSS). By analyzing cases of quasars lensed by galaxies and clusters, the research highlights well-defined lens systems, their image separations, and classification into reliable categories. The study reveals insights into the lensing probability, complicating factors, and detectors for quasar candidates, all of which contribute to our understanding of cosmology and the evolution of massive galaxies. The results emphasize the need for careful statistical analysis in drawing models of cosmic structures.

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Gravitationally Lensed Quasars in SDSS: Statistical Properties and Implications

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

  2. 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”

  3. 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.)

  4. 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

  5. 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

  6. 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

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

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

  9. 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

  10. 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

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

  12. SDSS image

  13. Follow-up imaging

  14. Spectroscopic confirmation

  15. 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

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

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

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

  19. numbers of lensed quasars • likelihood

  20. image separation distribution

  21. flat universe

  22. without galaxy evolution

  23. with galaxy evolution

  24. redshift evolution of velocity function

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

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

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

  28. JVAS vs SQLS

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

  30. Spearman rank correlation test for • 76 lensed QSOs

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

  32. differential probability

  33. concordance model • expected vs observed

  34. Likelihood

  35. z > 2.2 sample

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

  37. With galaxy evolution

  38. constraints on galaxy evolution

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

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