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Measuring the Hubble Constant Using

Gravitational Lenses

Roger BlandfordKIPAC

Stanford

Sherry Suyu, Phil Marshall, Chris Fassnacht, Tommaso Treu, Leon Koopmans, Matt Auger, Stefan Hilbert, Tony Readhead, Steve Myers, Gabriela Surpi, Frederic Courbin, George Meylan…

http://www.slac.stanford.edu/~pjm/lensing/wineglasses22 ii 2011 STScI

22 ii 2011 STScI

Refraction of Light

Light travels faster in air

Light travels slower in glass

Wave crests

Light rays Light “travels slower” in glass

and is refracted

Lens

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Deflection of Light

Newton: Opticks, Query1: Do not bodies act upon Light at a distance, and by their action bend its rays; and is not this action (caeteris paribus) strongest at the least distance?

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Einstein’s General Theory of Relativity • 1915: Spacetime is curved

around a massive body. Light follows straight lines (geodesics) which appear to be curved. This doubles the effect.

• 1919: Eclipse measurements confirm that solar deflection is twice Newtonian expectation and makes Einstein a household name. Now measured to 1/1000.

• 1919: Eddington realizes that relativistic problem just like the Newtonian problem. Light travels slower in a gravitational field

Eddington

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Stars: ~ microarcsec

Galaxies: ~ arcsec

Clusters of galaxies: ~ 10 arcsec

Surface density ~ 1 g cm-2

Source

Lens

Observer

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Which way shall I go?

• Light makes the shortest (or the longest) journeys.

(Fermat)

Gravitational Lenses and the

Hubble Constant

S

DH0=V/d ~t -1 2

O

•Direct measurement•Insensitive to world model•Lens model dependence

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Q0957+561

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Walsh, Carswell & Weymann(1979)

John Bahcall (1934-2005)

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Moderated debate between Tammann and van den Bergin 1996

H0 features prominently in “Unsolved Problems”

• Type Ia supernovae: standard candles

• Fluctuations in the Cosmic Microwave Background radiation

• Baryon Acoustic Oscillations in the galaxy clustering power spectrum

• Periods of Cepheid variable stars in local galaxies

• Something else?

Standard candles, rulers, timers etc

(sound speed x age of universe) subtends ~1 degree

gas density fluctuations from CMB era are felt by dark matter - as traced by galaxies in the local(ish) universe

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The Measure of the Universe

• Historically, h= (H0/100 km s-1 Mpc-1) ~ 0.3-~5– 10 x Error!

• Recent determinations:– HST KP (Freedman et al)

• <h>=0.72+/-0.02+/-0.07

– Masers (Macri et al)• h=0.74+/-0.03+/-0.06

– WMAP (Komatsu et al)• h=0.71+/-0.025 (FCDM)

– BAO (Percival et al 2010)• h=0.70+/-0.015 (FCDM)

– Distance Ladder (Riess et al) • h=0.74+/-0.04

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B1608+656 (Myers, CLASS 1995)

STScI

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•Compact radio source (CLASS)

•VLBI Astrometry to 0.001”

•Relative magnifications

• A,C,D =2, 1, 0.35

•Time delays (Fassnacht)

•tA,C,D = 31.5, 36, 77 d (+/-1.5)

•Elliptical galaxy lenses (Fassnacht, Auger)

•G1: z=0.6304,=260(+/-15) km s-1; G2

•K+A galaxy source (Myers)

•z=1.394

•HST imaging

•V, I, H bands

Data

STScI

Modeling Gravitational Lenses• Surface brightness (flux per solid angle) changes along ray ~ a-3

– Unchanged by lens– Images of same region of source have same surface brightness

• Complications– Deconvolution (HST blurring)– Deredenning (dust)– Decontamination (source + lens)

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Image Source

Results

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Suyu et al (2010) H0=71+/-3 km s-1 Mpc-1H0=71+/-3 km s-1 Mpc-1

•Iterative modeling•Bayesian analysis •Potential residuals ~ 2%•Adopt fixed world model

•Major sensitivity is to zL

•Assume lens model correct •Assume propagation model correct

•If relax world model, h~0.05; •If combine with WMAP5 (+flatness), w~0.2

Limits to the accuracy• Lens Model

– Mass sheet degeneracy• Velocity dispersion• Measuring width of ring

• Time delays– Not now limiting accuracy

• More monitoring

• Structure along line of sight– Distorts images of source and lens

• Current effort

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“Mass-sheet” model degeneracy

κext

To break this degeneracy,we need more information about the mass distributions:• Stellar dynamics• Slope from arc thickness• Structures along the LOS

[Courbin et. al. 2002]

Lens mass, profile slope andline of sight mass distributionare all degenerate:

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Geodesic deviation equation

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•Null geodesic congruence backward from observer•Convergence κ and shear

•First focus, tangent to caustic, multiple imaging•Distance measure is affine parameter

•dx ~ k dwhere k is a tangent vector along the geodesic•Choose where a =is the local scale factor

•errors O( relative to homogeneous reference universeFor pure convergence,

O Proper transverseSeparation vector

Angle at observer

da

G=c=H0=1G=c=H0=1

enthalpy density

=d =d angular diameter distance

SachsZel’dovichFeynmanRefsdalGunnPenrose\Alcock Anderson

Homogeneous Cosmology

• For FCDM universe w=M

– No contribution from

• Introduce a, comoving distance, radius dr=da2 and RW line element to obtain

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Current separation

For k= R0sinh (r/R0)

Time delays

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Multi-sheet propagation

t r r

2

2 dza

r 2

d

r dr

a

;

Single deflector

t [r n

r n2

n

ann

] n

1

an

n n

2 n

Deviation relative to undeflected ray

Inhomogeneous matter distribution

Simple Model– Background density b(a)

– halos modeled by spherical profiles centered on galaxy/group centers

• amplitude and size scaled to luminosity• incorporate bias?• NFW better than isothermal

– Use simulations, GGL to calibrate test convergence and estimate error

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x

GroupGalaxyVoid

b

Multi-screen Propagation

• Treat screens as “weak deflectors”• Potential: ~ L.+.Q./2+… ; deflections, linear

• Distort appearance of source and lens• Many screens – multiply matrices

• Model lens in lens plane not on sky

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t n

1

an

nn

2 n

0!!

B1608+656: Statistical approach

• Ray-trace through Millennium S• Identify LOS where SL occurs• Find κext along LOS, excluding the SL plane (Hilbert et al. 2007)

• B1608+656 has twice the average galaxy number density (Fassnacht et al. 2009)• Find κext along all LOS in MS that have 2x ‹ngal›22 ii 2011 STScI

Modeled external shear ~0.1; need κ for H0

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B1608+656-Particular Approach

• z=0.265– Off center =>

• z=0.63 (G1, G2) =150+/-60 km s-1

• z=0.426, 0.52– Centered lens => ~0

• Photometry– 1500 ACS galaxies over 10sm – 1700 P60 galaxies over 100 sm

• Redshifts– 100 zs

Experimenting with different prescriptions for assigning halos

Groups (Fassnacht et al)

Additional Lenses

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Courbin

Future lens cosmography (Marshall et al)

• 2010 - 2016: ~3000 new lensed quasars with PS1, DES, HSC • About 500 of these systems will be quads• A significant monitoring follow-up task!•A larger statistical sample of doubles would provided added value, once calibrated by the quads•The spectroscopic follow-up is not demanding given rewards• Intensive modeling approach seems unavoidable 100 lenses observed to B1608’s level of detail could yield Hubble’s constant to percent precision• LSST, WFIRST…

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Summary• Lens H0 is competitive

– ~4% with strong priors; ~7% after relaxing world model

• Promising results with B1608+656– h=0.71+/-0.03 with strong priors

• Limited by understanding of line of sight– External convergence and shear

• New formalism for multi-path propagation– Distortion not delay – matrix formalism

• Observations show overdense line of sight– Imaging and spectroscopy

• Other good candidates– Existing and future options

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Thanks to:

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Sherry Suyu, Phil Marshall, Chris Fassnacht, Tommaso Treu, Leon Koopmans, Matt Auger, Stefan Hilbert, Tony Readhead, Steve Myers, Gabriela Surpi, Frederic Courbin, George Meylan…

John Bahcall

HST