Measuring the Hubble Constant Using Gravitational Lenses

1. Measuring the Hubble Constant Using Gravitational Lenses Roger Blandford KIPAC 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… STScI

2. STScI http://www.slac.stanford.edu/~pjm/lensing/wineglasses

3. Refraction of Light Lens Light travels slower in glass Light travels faster in air Wave crests Light rays Light “travels slower” in glass and is refracted STScI

4. 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? STScI

5. 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 STScI Eddington

6.  Source Lens Observer Stars: a ~ microarcsec Galaxies: a ~ arcsec Clusters of galaxies: a ~ 10 arcsec Surface density ~ 1 g cm-2 STScI

7. Which way shall I go? • Light makes the shortest (or the longest) journeys. (Fermat) STScI

8.  S O D H0=V/d ~t -12 Gravitational Lenses and theHubble Constant • Direct measurement • Insensitive to world model • Lens model dependence STScI

9. Q0957+561 Walsh, Carswell & Weymann (1979) STScI

10. John Bahcall (1934-2005) Moderated debate between Tammann and van den Berg in 1996 H0 features prominently in “Unsolved Problems” STScI

11. Standard candles, rulers, timers etc • 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? (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 STScI

12. 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 (FCDM) • BAO (Percival et al 2010) • h=0.70+/-0.015 (FCDM) • Distance Ladder (Riess et al) • h=0.74+/-0.04 STScI

13. B1608+656 (Myers, CLASS 1995) STScI

14. Data • Compact radio source (CLASS) • VLBI Astrometry to 0.001” • Relative magnifications • mA,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, s=260(+/-15) km s-1; G2 • K+A galaxy source (Myers) • z=1.394 • HST imaging • V, I, H bands STScI

15. Modeling Gravitational Lenses Image Source • 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) STScI

16. Results • Iterative modeling • Bayesian analysis • Potential residuals ~ 2% • Adopt fixed world model • Major sensitivity is to zL • Assume lens model correct • Assume propagation model correct H0=71+/-3 km s-1 Mpc-1 Suyu et al (2010) • If relax world model, dh~0.05; • If combine with WMAP5 (+flatness), dw~0.2 STScI

17. 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 STScI

18. “Mass-sheet” model degeneracy κext [Courbin et. al. 2002] • To break this degeneracy, • we need more information about the mass distributions: • Stellar dynamics • Slope g from arc thickness • Structures along the LOS Lens mass, profile slope and line of sight mass distribution are all degenerate: STScI

19. Sachs Zel’dovich Feynman Refsdal Gunn Penrose\ Alcock Anderson Geodesic deviation equation O x Proper transverse Separation vector q Angle at observer G=c=H0=1 • Null geodesic congruence backward from observer • Convergence k and shear g • First focus, tangent to caustic, multiple imaging • Distance measure is affine parameter • dxa ~ ka dl where ka is a tangent vector along the geodesic • Choose where a =w0/w is the local scale factor • errors O(f) relative to homogeneous reference universe • For pure convergence, enthalpy density x=dq STScI angular diameter distance

20. Homogeneous Cosmology • For FLCDM universe w=rM • No contribution from L • Introduce h=x/a, comoving distance, radius dr=dl/a2 and RW line element to obtain Current separation For k=-1, h = qR0sinh (r/R0) STScI

21. Single deflector Time delays a Deviation relative to undeflected ray h Multi-sheet propagation STScI

22. r Inhomogeneous matter distribution Group Galaxy Void <r> rb Simple Model • Background density rb(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 x STScI

23. Multi-screen Propagation • Treat screens as “weak deflectors” • Potential: Y ~ L.x+x.Q.x/2+… ; deflections, linear • Distort appearance of source and lens • Many screens – multiply matrices • Model lens in lens plane not on sky STScI

24. B1608+656: Statistical approach Modeled external shear ~0.1; need k for H0 • B1608+656 has twice the average galaxy number density (Fassnacht et al. 2009) • Find κext along all LOS in MS that have 2x ‹ngal› • Ray-trace through Millennium S • Identify LOS where SL occurs • Find κext along LOS, excluding the SL plane (Hilbert et al. 2007) STScI

25. B1608+656-Particular Approach Groups (Fassnacht et al) • 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 STScI

26. Additional Lenses Courbin STScI

27. 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… STScI

28. 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 STScI

29. Thanks to: Sherry Suyu, Phil Marshall, Chris Fassnacht, Tommaso Treu, Leon Koopmans, Matt Auger, Stefan Hilbert, Tony Readhead, Steve Myers, Gabriela Surpi, Frederic Courbin, George Meylan… HST John Bahcall STScI