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,
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Transcript 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,
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…
22 ii 2011
STScI
22 ii 2011
STScI
http://www.slac.stanford.edu/~pjm/lensing/wineglasses
Refraction of Light
Lens
Light travels
slower in glass
Light travels
faster in air
Wave crests
Light rays
22 ii 2011
STScI
Light “travels slower”
in glass
and is refracted
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?
22 ii 2011
STScI
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
22 ii 2011
STScI
Eddington
a
Source
Lens
Observer
Stars: a ~ microarcsec
Galaxies: a ~ arcsec
Clusters of galaxies: a ~ 10 arcsec
Surface density ~ 1 g cm-2
22 ii 2011
STScI
Which way shall I go?
• Light makes the shortest
(or the longest) journeys.
(Fermat)
22 ii 2011
STScI
Gravitational Lenses
and the
Hubble Constant
S
O
D
H0=V/d ~t -1 2
•Direct measurement
•Insensitive to world model
•Lens model dependence
22 ii 2011
STScI
Q0957+561
Walsh,
Carswell
& Weymann
(1979)
22 ii 2011
STScI
John Bahcall (1934-2005)
Moderated debate between
Tammann and van den Berg
in 1996
H0 features prominently in
“Unsolved Problems”
22 ii 2011
STScI
Standard candles, rulers, timers etc
• Type Ia supernovae: standard candles
• Fluctuations in the Cosmic Microwave Background
radiation
(sound speed x
age of universe)
subtends ~1
degree
• Baryon Acoustic Oscillations in the galaxy clustering
power spectrum
gas density
fluctuations from
CMB era are felt
by dark matter as traced by
galaxies in the
local(ish) universe
• Periods of Cepheid
variable stars in local
galaxies
22 ii 2011
• Something else?
STScI
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
22 ii 2011
STScI
B1608+656 (Myers, CLASS 1995)
22 ii 2011
STScI
Data
•Compact radio source (CLASS)
•VLBI Astrometry to 0.001”
•Relative magnifications
• m 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, s=260(+/-15) km s-1; G2
•K+A galaxy source (Myers)
•z=1.394
•HST imaging
•V, I, H bands
22 ii 2011
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
Image
Source
• Complications
– Deconvolution (HST blurring)
– Deredenning (dust)
– Decontamination (source + lens)
22 ii 2011
STScI
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
Suyu et al (2010)
H0=71+/-3 km s-1 Mpc-1
•If relax world model, dh~0.05;
•If combine with WMAP5 (+flatness), dw~0.2
22 ii 2011
STScI
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
22 ii 2011
STScI
“Mass-sheet” model degeneracy
ext
[Courbin et. al. 2002]
Lens mass, profile slope and
line of sight mass distribution
are all degenerate:
22 ii 2011
STScI
To break this degeneracy,
we need more information
about the mass distributions:
• Stellar dynamics
• Slope g from arc
thickness
Sachs
Zel’dovich
Feynman
Refsdal
Gunn
Penrose\
Alcock
Anderson
Geodesic deviation equation
O
x
Proper transverse
Separation vector
Angle at observer
•Null geodesic congruence backward from observer
G=c=H0=1
•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 l d a where a =w0/w is the local scale factor
•errors O(f) relative to homogeneous reference universe
enthalpy density
For pure convergence,
22 ii 2011
x=d
STScI
angular diameter distance
Homogeneous Cosmology
• For FCDM universe w=rM
– No contribution from
• Introduce hx/a, comoving distance,
radius dr=dl/a2 and RW line element to
obtain
Current separation
For k-1, h = R0sinh (r/R0)
22 ii 2011
STScI
Time delays
Single deflector
a
h
Deviation relative to
undeflected ray
r r
r
r
h a 2 dzf h
dh
t
- ; a
2
a
2 dr a
Multi-sheet propagation
t [
n
22 ii 2011
r
r
hn a n
2
-
n
an
]
n
1 x n n
- n
an 2
STScI
Inhomogeneous matter distribution
r
Group
Void
<r>
Galaxy
rb
x
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
22 ii 2011
STScI
Multi-screen Propagation
•
•
Treat screens as “weak deflectors”
Potential: Y ~ L.x+x.Q.x/2+… ; deflections, linear
t
•
•
•
n
1
an
xn n
- n 0!!
2
Distort appearance of source and lens
Many screens – multiply matrices
Model lens in lens plane not on sky
22 ii 2011
STScI
B1608+656: Statistical approach
Modeled external shear ~0.1; need k for H0
• Ray-trace through Millennium S
• Identify LOS where SL occurs
• Find ext along LOS, excluding
the SL plane (Hilbert et al. 2007)
22 ii 2011
• B1608+656 has twice the
average galaxy number density
(Fassnacht et al. 2009)
• Find ext along all LOS in MS that
have 2x ‹ngal›
STScI
B1608+656-Particular Approach
Groups (Fassnacht et al)
• z=0.265
– Off center => g 01
• z=0.63 (G1, G2)
s =150+/-60 km s-1
• z=0.426, 0.52
– Centered lens => g ~0
• Photometry
– 1500 ACS galaxies over 10sm
– 1700 P60 galaxies over 100 sm
• Redshifts
– 100 zs
Experimenting with different prescriptions for assigning halos
22 ii 2011
STScI
Additional Lenses
Courbin
22 ii 2011
STScI
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…
22 ii 2011
STScI
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
22 ii 2011
STScI
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
22 ii 2011
STScI
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…
22 ii 2011
STScI
22 ii 2011
STScI
http://www.slac.stanford.edu/~pjm/lensing/wineglasses
Refraction of Light
Lens
Light travels
slower in glass
Light travels
faster in air
Wave crests
Light rays
22 ii 2011
STScI
Light “travels slower”
in glass
and is refracted
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?
22 ii 2011
STScI
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
22 ii 2011
STScI
Eddington
a
Source
Lens
Observer
Stars: a ~ microarcsec
Galaxies: a ~ arcsec
Clusters of galaxies: a ~ 10 arcsec
Surface density ~ 1 g cm-2
22 ii 2011
STScI
Which way shall I go?
• Light makes the shortest
(or the longest) journeys.
(Fermat)
22 ii 2011
STScI
Gravitational Lenses
and the
Hubble Constant
S
O
D
H0=V/d ~t -1 2
•Direct measurement
•Insensitive to world model
•Lens model dependence
22 ii 2011
STScI
Q0957+561
Walsh,
Carswell
& Weymann
(1979)
22 ii 2011
STScI
John Bahcall (1934-2005)
Moderated debate between
Tammann and van den Berg
in 1996
H0 features prominently in
“Unsolved Problems”
22 ii 2011
STScI
Standard candles, rulers, timers etc
• Type Ia supernovae: standard candles
• Fluctuations in the Cosmic Microwave Background
radiation
(sound speed x
age of universe)
subtends ~1
degree
• Baryon Acoustic Oscillations in the galaxy clustering
power spectrum
gas density
fluctuations from
CMB era are felt
by dark matter as traced by
galaxies in the
local(ish) universe
• Periods of Cepheid
variable stars in local
galaxies
22 ii 2011
• Something else?
STScI
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
22 ii 2011
STScI
B1608+656 (Myers, CLASS 1995)
22 ii 2011
STScI
Data
•Compact radio source (CLASS)
•VLBI Astrometry to 0.001”
•Relative magnifications
• m 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, s=260(+/-15) km s-1; G2
•K+A galaxy source (Myers)
•z=1.394
•HST imaging
•V, I, H bands
22 ii 2011
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
Image
Source
• Complications
– Deconvolution (HST blurring)
– Deredenning (dust)
– Decontamination (source + lens)
22 ii 2011
STScI
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
Suyu et al (2010)
H0=71+/-3 km s-1 Mpc-1
•If relax world model, dh~0.05;
•If combine with WMAP5 (+flatness), dw~0.2
22 ii 2011
STScI
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
22 ii 2011
STScI
“Mass-sheet” model degeneracy
ext
[Courbin et. al. 2002]
Lens mass, profile slope and
line of sight mass distribution
are all degenerate:
22 ii 2011
STScI
To break this degeneracy,
we need more information
about the mass distributions:
• Stellar dynamics
• Slope g from arc
thickness
Sachs
Zel’dovich
Feynman
Refsdal
Gunn
Penrose\
Alcock
Anderson
Geodesic deviation equation
O
x
Proper transverse
Separation vector
Angle at observer
•Null geodesic congruence backward from observer
G=c=H0=1
•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 l d a where a =w0/w is the local scale factor
•errors O(f) relative to homogeneous reference universe
enthalpy density
For pure convergence,
22 ii 2011
x=d
STScI
angular diameter distance
Homogeneous Cosmology
• For FCDM universe w=rM
– No contribution from
• Introduce hx/a, comoving distance,
radius dr=dl/a2 and RW line element to
obtain
Current separation
For k-1, h = R0sinh (r/R0)
22 ii 2011
STScI
Time delays
Single deflector
a
h
Deviation relative to
undeflected ray
r r
r
r
h a 2 dzf h
dh
t
- ; a
2
a
2 dr a
Multi-sheet propagation
t [
n
22 ii 2011
r
r
hn a n
2
-
n
an
]
n
1 x n n
- n
an 2
STScI
Inhomogeneous matter distribution
r
Group
Void
<r>
Galaxy
rb
x
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
22 ii 2011
STScI
Multi-screen Propagation
•
•
Treat screens as “weak deflectors”
Potential: Y ~ L.x+x.Q.x/2+… ; deflections, linear
t
•
•
•
n
1
an
xn n
- n 0!!
2
Distort appearance of source and lens
Many screens – multiply matrices
Model lens in lens plane not on sky
22 ii 2011
STScI
B1608+656: Statistical approach
Modeled external shear ~0.1; need k for H0
• Ray-trace through Millennium S
• Identify LOS where SL occurs
• Find ext along LOS, excluding
the SL plane (Hilbert et al. 2007)
22 ii 2011
• B1608+656 has twice the
average galaxy number density
(Fassnacht et al. 2009)
• Find ext along all LOS in MS that
have 2x ‹ngal›
STScI
B1608+656-Particular Approach
Groups (Fassnacht et al)
• z=0.265
– Off center => g 01
• z=0.63 (G1, G2)
s =150+/-60 km s-1
• z=0.426, 0.52
– Centered lens => g ~0
• Photometry
– 1500 ACS galaxies over 10sm
– 1700 P60 galaxies over 100 sm
• Redshifts
– 100 zs
Experimenting with different prescriptions for assigning halos
22 ii 2011
STScI
Additional Lenses
Courbin
22 ii 2011
STScI
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…
22 ii 2011
STScI
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
22 ii 2011
STScI
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
22 ii 2011
STScI