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Cosmological Parameters with Gravitational Lens systems from the SDSS Du-Hwan Han & Myeong-Gu Park Kyungpook National University Department of Astronomy.

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Presentation on theme: "Cosmological Parameters with Gravitational Lens systems from the SDSS Du-Hwan Han & Myeong-Gu Park Kyungpook National University Department of Astronomy."— Presentation transcript:

1 Cosmological Parameters with Gravitational Lens systems from the SDSS Du-Hwan Han & Myeong-Gu Park Kyungpook National University Department of Astronomy and Atmospheric Sciences 1

2 INTRODUCTION 2

3 Gravitational lens Deflection of light ray by gravitational fields of massive objects. 3

4 Gravitational lens Q0957+561 (SDSS J1001+5553) 1979 Walsh et al. Sloan Digital Sky Survey 4

5 Gravitational lens Geometry of gravitational lens 5

6 Statistical Analysis Turner, Ostriker, and Gott (1984) Mean image separation of lens systems have dependence on source redshift. Gott, Park, and Lee (1989) Calculation of the mean image separation for various cosmology. 6

7 MEAN IMAGE SEPARATION 7

8 Mean Image Separation Assumption : using lens model as Singular Isothermal Sphere & homogeneous & isotrophic universe described by Robertson-Walker Metric Comoving Distance Gott, Park, & Lee, 1989, ApJ, 338, 1 8

9 Mean Image Separation Flat Universe Open Universe Closed Universe Gott, Park, & Lee, 1989, ApJ, 338, 1 9

10 empty universe open universe flat universe closed universe Park & Cott, 1997 Park, 1998 Cosmological Models 10

11 LENS SYSTEMS FROM THE SDSS 11

12 Candidates for Lens systems from the SDSS 171 The SDSS is completed its 1 st of operation. ⇒ ~ 90,000 quasars Candidates selected by lens selection algorithm (Oguri et al.). ⇒ 171 candidates 12

13 Candidates for Lens systems from the SDSS 76 The SDSS is completed its 1 st of operation. ⇒ ~ 90,000 quasars Candidates selected by lens selection algorithm (Oguri, et. al.). ⇒ 171 candidates Select 76 candidates between 1” and 5” 13

14 Candidates for Lens systems from the SDSS The SDSS is completed its 1 st of operation. ⇒ ~ 90,000 quasars Candidates selected by lens selection algorithm (Oguri, et. al.). ⇒ 171 candidates Select 76 candidates between 1” and 5” Oguri, et. al., 2006, AJ, 132, 999 14

15 Candidates for Lens systems from the SDSS 76 candidates 15

16 CURVATURE TEST 16

17 Curvature Test Mean image separation Candidates for Lens systems 17

18 Spearman Rank Correlation Test Test of the strength of a correlation. Using the rank of two quantities. =+1 positive correlation correlation coefficient = 0 no correlation =-1 negative correlation ‘Normalized’ ⇒ Observed image separation divide by mean image separation of cosmological model. Null hypothesis there is no correlation between ‘normalized’ image separation versus source redshift. Curvature Test 18

19 Curvature Test Cosmological ModelsProbability K=-1 Empty universe 0.149 0.22 Open universe 0.100 0.38 K=0 Flat universe 0.044 0.70 K=+1 Closed universe -0.008 0.94 Closed universe -0.528 0.00 19

20 No Big Bang 0.01 0.05 0.32 K=0 0.70 Likelihood Map 0 ≤ Ω ≤ 3 0 ≤ Ω Λ ≤ 3 20 No Big Bang < 0.01 0.01 0.05 0.32 0.70 k=0 > 0.32

21 Ω m - Ω Λ TEST 21

22 Lensing Probability Probability distribution for image separation For elliptical (i=E) and lenticular (i=SO) galaxies, For spiral (i=S) galaxies, Where, Ai=0.12, 0.19, 0.69 for E,S0,S galaxy type and 22

23 Maximum Likelihood Method is a useful tool to set constraints on parameters of the statistical model with a given data set Likelihood function For the JVAS/CLASS sample For the SDSS sample Ω m - Ω Λ TEST 23

24 The JVAS/CLASS sample 24 Lensed QSOs from JVAS/CLASS Survey CasezLzL zszs Δθ obs (") B02180.9400.6800.33 B14223.6200.3391.30 MG04142.6300.4683.00 B10301.5350.5991.60 B16001.5890.4141.40 B07121.3390.4061.27 B16081.3900.6402.20 B20451.2800.8702.00 B11521.0190.4391.90 B21440.5880.3162.40 No Big Bang ▬ 99% CL ▬ 95% CL ▬ 68% CL

25 The SDSS sample 25 No Big Bang ▬ 99% CL ▬ 95% CL ▬ 68% CL Gravitational Lenses from the SDSS CasezLzL zszs Δθ obs (") SDSS J0145-09452.7320.4902.2 SDSS J0246-08251.6850.7241.0 SDSS J0746+44031.9980.3001.0 SDSS J0806+20061.5370.5701.4 SDSS J0903+50283.5840.3882.8 SDSS J0911+05502.7830.7703.2 SDSS J0913+52591.3770.8301.1 SDSS J0924+02191.5230.4001.3 SDSS J0951+26351.2460.2601.1 SDSS J1001+50271.8390.3002.9 SDSS J1004+41121.7400.6803.8 SDSS J1021+49131.7200.5001.0 SDSS J1118+07451.7360.3102.3 SDSS J1138+03142.4420.4451.1 SDSS J1155+63462.8880.1761.8 SDSS J1206+43321.7900.7483.0 SDSS J1226-00061.1250.5171.2 SDSS J1332+03471.4450.1911.0 SDSS J1335+01181.5710.5001.5 SDSS J1353+11381.6230.3001.3 SDSS J1406+61262.1340.2702.0 SDSS J1415+11292.5610.9001.7 SDSS J1650+42511.5410.5901.3

26 The SDSS sample 26 No Big Bang ▬ 99% CL ▬ 95% CL ▬ 68% CL Gravitational Lenses from the SDSS CasezLzL zszs Δθ obs (") SDSS J0145-09452.7320.4902.2 SDSS J0246-08251.6850.7241.0 SDSS J0746+44031.9980.3001.0 SDSS J0806+20061.5370.5701.4 SDSS J0903+50283.5840.3882.8 SDSS J0911+05502.7830.7703.2 SDSS J0913+52591.3770.8301.1 SDSS J0924+02191.5230.4001.3 SDSS J0951+26351.2460.2601.1 SDSS J1001+50271.8390.3002.9 SDSS J1004+41121.7400.6803.8 SDSS J1021+49131.7200.5001.0 SDSS J1118+07451.7360.3102.3 SDSS J1138+03142.4420.4451.1 SDSS J1155+63462.8880.1761.8 SDSS J1206+43321.7900.7483.0 SDSS J1226-00061.1250.5171.2 SDSS J1332+03471.4450.1911.0 SDSS J1335+01181.5710.5001.5 SDSS J1353+11381.6230.3001.3 SDSS J1406+61262.1340.2702.0 SDSS J1415+11292.5610.9001.7 SDSS J1650+42511.5410.5901.3

27 SUMMARY 27

28 Summary  Calculation of the mean image separation as a function of source redshift for various cosmological models  Distribution of Candidates for lens systems from the SDSS show slightly positive correlation or do not show any correlation.  Curvature Test Spearman test shows the curvature of the universe is ‘0’, ‘negative’ or ‘not-excessively’ positive.  Ω m -Ω Λ Test Calculated the probability distribution and maximum likelihood with the JVAS/CLASS sample and the SDSS sample. 28

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