2013-02-15
박명구, 한두환 (경북대)
Survey Science Group Workshop
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”
 CASTLES
– CfA-Arizona Space Telescope LEns Survey
– lensed quasars (as of 2013/02)
Class A:
 Class B:
 Class C:

82 cases
10 cases
8 cases
(I’d bet my life.)
(I’d bet your life.)
(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
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
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
Probability Test

Fukugita et al. (1992)
– Hewitt-Burbidge catalogue
– expected number




Ω𝑚
Ω𝑚
Ω𝑚
Ω𝑚
= 1, ΩΛ = 0: 3
= 0.1, ΩΛ = 0: 5
= 0.1, ΩΛ = 0.9: 18
= 0, ΩΛ = 1: 46
– observed number

4 out of Hewitt-Burbidge catalogue
– large Λ rejected

Kochanek (1996)
– likelihood test for probability and separation
– ΩΛ < 0.66 at 95% CL
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
 source distribution in luminosity and z needed

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 (Δ𝜃 < 2.5“) system

– blended
– morphological selection

large separation (Δ𝜃 > 2.5“) system
– deblended
– color selection

brightness ratio
– Follow-up confirmation
spectroscopic observation
 photometric observation

– SDSS image
– Follow-up imaging
– Spectroscopic confirmation
Constraints on Dark Energy and
Evolution of Massive Galaxies
Oguri et al. (2012)
 SDSS DR7 quasar catalog: 105,783 QSOs
 Selection function

–
–
–
–

0.6 < 𝑧 < 2.2
1" < Δ𝜃 < 20"
𝑖𝑃𝑆𝐹 < 19.1
Δ𝑚 < 1.5𝑚
26 strongly lensed quasars
 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
 Sample
– 17 SQLS quasars of Δ𝜃 < 2＂ with source
and lens redshifts
– 76 SQLS quasars with source redshifts
 JVAS
vs SQLS
Curvature test
– mean image separation
– magnitude selection: lens should be bright
enough
– Spearman rank correlation test
for
<Δ𝜃>𝑜𝑏𝑠
<Δ𝜃>𝑒𝑥𝑝
𝑧𝑠
– 76 lensed QSOs
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 …