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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
3
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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48
49
50
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?
39
40
41
42
43
44
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49
50
0 1 2 3 4 5 6 7
Redshift (z)
Dis
tan
ce M
odu
lus
(mag
)
5
“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
6
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
7
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
9
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
10
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
18
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
23
p= w ρ
w(z) = w0 + wa z /(1+z)
24
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
25
Chevalier-Polarski-Linder: best fits and confidence regions
68% confidence region
95% confidence region
26
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
27
SIS lens model
2 images
28
SIS lens model
2 images
29
SIS lens model
2 images
Subsample of 2 image systems
36 SLACS lensessee also S.Suyu arXiv:1202.0287
Account for SIS model uncetrainty
30
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
31
Full sample
2 image lenssample
32
Chevalier-Polarski-Linder: best fits and confidence regions
E.V. Linder, Phys. Rev. D 70, 043534 (2004)
33
34
Degeneracies between w0 and wa change with the lens redshift
zl
E.V. Linder, Phys. Rev. D 70, 043534 (2004)
35
SLACS
E.V. Linder, Phys. Rev. D 70, 043534 (2004)
36
SLACS
BELLSBronstein et al.,ApJ 744:41, 2012
37
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
38
After Gavazzi R. : www2.iap.fr/pnc/PNC08-gavazzi.pdf
SLACS starts discovering multiple source galaxy lenses
39
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
41
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
45