Marek Biesiada

Department of Astrophysics and CosmologyInstitute of Physics, University of Silesia

Katowice, Poland

Strong Gravitational Lenses as

Standard Rulers in Cosmology

COSMO12 ConferenceBeijing

13 Sept. 2012

BASED ONresults obtained with: A.Piorkowska, B.MalecW.GodlowskiZ-H Zhu, S. Cao , Y. Pan B.N.U.new ideas: with R.Gavazzi I.A.P.

Ωb = 0.042

Ωm = 0.29 ± 0.04

BBN LSSCMBR

Gravitational LensingSNIa on high redshifts

Pilars of Modern Cosmology

2A revolution in cosmology – accelerating expansion of the Universe

How can we probe cosmic expansion history beyond local Universe ?

3 types of distances in cosmology:

•Comoving distance

•Luminosity distance

•Angular diameter distance

Standard candles – objects with known intrinsic luminosity L; what we measure is flux F, so we can assess luminosity distance:

L = 4πDL2 F

Standard rulers – objects of known size D; what we measure is angular diameterθ, so we can assess angular diameter distance:

D = DA θ

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Standard candles:

•Supernovae Ia Riess 1998, Perlmutter 1999, Wood-Vasey 2007, Kowalski 2008, Amanullah 2010

Gamma Ray Bursts (GRBs) Schaffer 1996 , Ghirlanda 2004, Amati 2006, Capozziello et al. 2011; Dainotti 2009

•NS-NS or BH-BH binaries observed in gravitational waves (standard sirens)

)

–> far future Schutz 1986, Finn 1993, Zhu 2001 , M.B. 2001, 2003,

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0 1 2 3 4 5 6 7

Redshift (z)

Dis

tan

ce M

od

ulu

s

What is the expansion

history for z>1.7?

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0 1 2 3 4 5 6 7

Redshift (z)

Dis

tan

ce M

odu

lus

(mag

)

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“Standardizable” Candles•Nearby supernovae used to study SNe light curve (z<0.1)

•Brightness not quite standard

•Intrinsically brighter SNe last longer

•Correction factor needed

Peak-magnitude dispersion

Branch 1990

Philips 1993

Riess, Press, Kirschner, 1996

3Ep - Ecorr

Ep - Eiso

Energy corrected for collimation GRB (Ecorr)

)

Amati relationGhirlanda relation

GRBs also have to be standardized

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Standard rulers:

Statistical standard rulers: *CMBR acoustic peaks Spergel et al. 2007, Komatsu et al. 2011,* BAO Eisenstein 2005

Individual standard rulers:* Ultracompact radio sources Kellermann 1993, Gurvitz 1994 * Fanaroff-Riley type IIb double-sided radio sources Daly 1994, Daly et al. 2002, 2007

* Clusters of galaxies: combined X-ray + SZ data

*Gravitational Lenses – a new class of standard(izable) rulers

Alcock-Paczyński testgives dA(z) H(z) if size is unknown

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Gravitational Lensing

Two lensing regimes:

Strong: •multiple images

•time delays between images – (a method to measure H0)

)

Weak: image distortionEinstein radius (determined by mass !) - defines characteristic angular scale

SL

LSE DD

DcGM

2

4=θ

Point lens 8

source

SIS lens model – the simplest realistic case

Einstein radius

1D velocity dispersion

Two images form on the opposite side of the lens

angle between directions to the lens and to the source

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Time delay between images in SIS lens

Stellar dynamics(spectroscopy)

(

Gravitational lensing

S

LSvE D

Dc

2

4

= σπθ

From angular separation of images

Velocity dispersion - spectroscopy

Ratio determined by cosmological model

Idea

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Quintessence

w < -0.67

Dynamical scalar fieldw(z) = w0 + w1 z

w0 > -0.1

w1 < -1.2

Chaplygin gas Models with A0 =1 preferred(equivalent to LCDM)

Brane world DGP

Lensing systemHST 14176+5226

zL=0.809

zs=3.4θE=1.”489

Lens modeled as SIE (singular isothermal ellipsoid)

M.B. 2006 Feasibility study

Just one lens … 11

BUT …

After L. Koopmans : www.angles.eu.org/meetings/mid_term/copenhagen_leon.pdf 12

After L. Koopmans : www.angles.eu.org/meetings/mid_term/copenhagen_leon.pdf 13

After L. Koopmans : www.angles.eu.org/meetings/mid_term/copenhagen_leon.pdf 14

After L. Koopmans : www.angles.eu.org/meetings/mid_term/copenhagen_leon.pdf 15

After Gavazzi R. : www2.iap.fr/pnc/PNC08-gavazzi.pdf16

After L. Koopmans : www.angles.eu.org/meetings/mid_term/copenhagen_leon.pdf 17

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The Method• mass density profile approximated by - SIS -Singular Isothermal Sphere model

S

• Einstein radius

• σSIS lens velocity dispersion is well approximated by σo - central stellar velocity dispersion (see eg. Grillo et al. 2008)

(

• observable: distance ratio

∫ ′′

+=

z

pzhzd

Hc

zpzD

00 );(11);(

),,( pzzD slth obsD

s

lsSISE D

Dc 2

2

4σπθ =

Els

s

cDD

θπ σ2

204 =

2

2 1 2

)(rG

r SIS

πσρ =

1919

SMC 201120

Cosmological models tested

• ΛCDM

• Quintessence

• Chevalier-Polarski-Linder

1 −=w

const.w =

zzwwzw a +

+=1

)( 0

( ) ΛΩ++Ω= 31)( zzh m

( ) )1(33 )1(1)( wQm zzzh ++Ω++Ω=

( )

+−+Ω++Ω= ++

zzwzzzh aww

Qma

13exp)1(1)( )1(33 0

mΩ= p

w=p

aww , 0=p

Ωm fixed

Ωm fixed

Samples used

SLA

CS

LSD

15.058.0 ±=SLACSs

ls

DD

•full sample n=20•sub-sample n=7

•for comparison fit on Union08 sample –compilation of Kowalski et al. (2008)

(

n=307 SNIa21

43.073.0 ≤≥s

ls

s

ls

DDor

DD

Results; fits on the full sample n=20• Lens sample SLACS

+LSD(n=15+5)

)

prior on Ωm=0.27

• Union08

SNIa sample

(n=307)

)

prior on Ωm=0.27

Quintessence : whole 2σ CI from SNIa in agreement with 1σ CI from lenses

90.0,23.1 −− 74.0,22.1 −−22

Chevalier-Polarski-Linder: best fits and confidence regions

68% confidence region

95% confidence region

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p= w ρ

w(z) = w0 + wa z /(1+z)

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Results; fits on the restricted sample n=7

• on the restricted sample

(n=7)

)

prior on Ωm=0.27

•ΛCDM – agreement with SNIa fits

•Quintessence: 2σ interval for the Union08 falls into 2σ interval for lenses

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Chevalier-Polarski-Linder: best fits and confidence regions

68% confidence region

95% confidence region

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10 cluster lenses

+

70 galaxy lensesSLACS survey

New possibility – cluster + galaxy strong lenses

Hydrostatic equilibriumspherically symmetric beta- model

H. Yu and Z.-H. Zhu 2011 Res. Astron. Astrophys. 11, 776

Bolton A.S. et al. 2008 ApJ 682 : 964Newton E.R. et al. 2011 ApJ 734 : 104

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SIS lens model

2 images

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SIS lens model

2 images

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SIS lens model

2 images

Subsample of 2 image systems

36 SLACS lensessee also S.Suyu arXiv:1202.0287

Account for SIS model uncetrainty

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s

lsSISE D

Dc 2

2

4σπθ =

marginalize over fE

E.O. Ofek, et al. 2003 M.N.R.A.S. 343, 639

2 image lenssample

cluster + galaxy strong lenses

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Full sample

2 image lenssample

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Chevalier-Polarski-Linder: best fits and confidence regions

E.V. Linder, Phys. Rev. D 70, 043534 (2004)

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Degeneracies between w0 and wa change with the lens redshift

zl

E.V. Linder, Phys. Rev. D 70, 043534 (2004)

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SLACS

E.V. Linder, Phys. Rev. D 70, 043534 (2004)

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SLACS

BELLSBronstein et al.,ApJ 744:41, 2012

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New ideas for this method:

(in collaboration with Raphael Gavazzi - work in progress )

* Consider the evolution of mass density profile of lenses

* Assessment of line of sight contamination (secondary lensing)

A.Ruff , R.Gavazzi et al. 2010

Jullo E. et al. Science 329:924 (2010)

:

114 images from 34 background sources selected only 28

Observables

New possibilities – cluster strong lenses

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After Gavazzi R. : www2.iap.fr/pnc/PNC08-gavazzi.pdf

SLACS starts discovering multiple source galaxy lenses

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standard rulers

strong lenses (the same sample as before)

b

CMBR shift parameter R

BAO

standard candles - SN Ia Union2

Joint Likelihood

∑ −=i iD

thi

obsi DD

2,

22 )]([)(

σχ pp

∫Ω=lssz

m zhdzR

0 );()(

pp 2

22

019.0]71.1)([)( −= pp R

CMBχ

3/1235.0

0 );();35.0(35.0

35.0)(

Ω= ∫ pp

pzhdz

hA m

2

22

017.0]469.0)([)( −= pp A

BAOχ

∑=

=

−=

557

12

22 )];()([

)(N

i i

ith

iobs

SN

zzσ

µµχ

pp

Two more models tested (besides LCDM, Quintessence, CPL)

Q

Chaplygin Gas p = Ωm , A0 ,α

Braneworld scenario (DGP) p = Ωm 40

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Best fits and confidence regions

Chevalier-Polarski-Linder Quintessence

SMC 2011 42

Fits for:

•rulers;

•candles

•joint

20-22, January, Salerno, Italy SMC 201143

KdataAIC 2)|p(2 += χ

]21exp[)|p( idata ∆−∝L

minAICAICii −=∆AIC value for a single model is meaningless, instead the differences are used

Akaike weights –normalized relative likelihoods

Likelihood function

)ln(2))|p(ln(2 nKdataBIC +−= LBayesian Information Criterion (BIC)

number of parameters sample size

Akaike Information Criterion (AIC)

A

Which model is best supported by the data ?

Perspectives for strong lensing:

• use also time delays between images – will provide distances not just ratios !

* increasing number of strong lenses discovered bysearches such as CLASS , SLACS, SL2S, SQLS, HAGGLeS, AEGIS, COSMOS, CASSOWARY, BELLS

* new projects: Pan-STARRS1, LSST2, JDEM / IDECS3, SKA4 will yield an explosion in the number of strong lenses

•with very large catalogs of strong lenses – use photometryphoto-z + fundamental plane proxy for σ0 ? 44

Conclusions:

•strongly lensed systems with known central velocity dispersions are a new class of "standard rulers"(Einstein radius being standardized by stellar kinematics)

•their use entered the stage of providing first estimates on cosmological parameters

•they will certainly develop into a technique competitive with other methods

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