Survey Science Group Workshop 박명구, 한두환 ( 경북대 )

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

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

Quasar Lensing & SDSS  Quasar lensing –multiple image quasars lensed by galaxy/cluster –SDSS quasar sample lensing probability: ~10 -3 lensing probability: ~ lens systems expected from spectroscopic sample of 10 5 SDSS quasars 100 lens systems expected from spectroscopic sample of 10 5 SDSS quasars 1000 lens systems plausible from 10 6 quasars expected in 10 4 deg lens systems plausible from 10 6 quasars expected in 10 4 deg 2 well-defined sample?? well-defined sample?? –Well-defined selection function needed for statistical analysis

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

Probability Test

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

 Chae et al. (2003) –radio selected sample

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

Sloan digital sky survey Quasar Lens Search (SQLS)

–Follow-up confirmation spectroscopic observation spectroscopic observation photometric observation photometric observation

–SDSS image

–Follow-up imaging

–Spectroscopic confirmation

Constraints on Dark Energy and Evolution of Massive Galaxies

 Theoretical model –singular isothermal ellipsoid –velocity function –redshift evolution

–quasar luminosity function –lensing cross section over lensing area –lensing probability

–quasars should be brighter than lens –completeness function –probability distribution

–numbers of lensed quasars –likelihood

 image separation distribution

 flat universe

 without galaxy evolution

 with galaxy evolution

 redshift evolution of velocity function

 Worries –quasar luminosity function and its evolution –galaxy velocity function and its evolution –galaxy number evolution and its evolution

Image Separation Statistics  한두환  advantages & disadvantages –less sensitive to dark energy –magnitude bias not required –source information not needed

 JVAS vs SQLS

Curvature test –mean image separation –magnitude selection: lens should be bright enough

Image Separation Test  Theoretical model –singular isothermal sphere –velocity function –lensing probability

–differential probability

–expected vs observed concordance model

 Likelihood

z > 2.2 sample

 MC check –generate mock sample from theoretical probability distribution: 100, 1000 –apply the same test

 With galaxy evolution

 constraints on galaxy evolution

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