with Time Delay

Phil Marshall

Kavli Institute for Particle Astrophysics and Cosmology, SLAC National Accelerator Laboratory

ASIAA/CCMS/IAMS/LeCosPA/NTU-Physics Joint Colloquium National Taiwan University, March 2014

Measuring Distances

with Time Delay

Gravitational Lenses

Time

The Initial Expansion was Fast

The Initial Expansion was Fast

BICEP2 Results

Monday March 17, 2014

The Initial Expansion was Fast

BICEP2 Results

Monday March 17, 2014

Chao-Lin

Kuo

Fainter

Riess et al, Perlmutter et al 1998

“D ist an ce Mo du lu s”

“Redshift”

The Universe is Still Expanding...

Hubble and others found that

distant galaxies all appear to be

receding from us, with recession

speed (“redshift”) proportional to

distance.

Fainter

Riess et al, Perlmutter et al 1998

“D ist an ce Mo du lu s”

“Redshift”

The Universe is Still Expanding...

Hubble and others found that distant galaxies all appear to be receding from us, with recession speed (“redshift”) proportional to distance.

Hubble’s Law is what you get in a

uniformly

expanding

Universe

... And at an Accelerating Rate

Type Ia Supernovae are

“standard candles” - their brightness tells you their distance, and they are very luminous

The most distant Type Ia Supernovae are fainter than we expected

Fainter

Riess et al, Perlmutter et al 1998

... And at an Accelerating Rate

Type Ia Supernovae are

“standard candles” - their brightness tells you their distance, and they are very luminous

The most distant Type Ia Supernovae are fainter than we expected

Fainter

Riess et al, Perlmutter et al 1998

... And at an Accelerating Rate

Type Ia Supernovae are

“standard candles” - their brightness tells you their distance, and they are very luminous

The most distant Type Ia Supernovae are fainter than we expected

Fainter

Riess et al, Perlmutter et al 1998

... And at an Accelerating Rate

Type Ia Supernovae are

“standard candles” - their brightness tells you their distance, and they are very luminous

The most distant Type Ia Supernovae are fainter than we expected

Fainter

Riess et al, Perlmutter et al 1998

... And at an Accelerating Rate

Type Ia Supernovae are

“standard candles” - their brightness tells you their distance, and they are very luminous

The most distant Type Ia Supernovae are fainter than we expected

Fainter

Riess et al, Perlmutter et al 1998

Why?

Albrecht et al 2006 Dark Energy Task Force report

Dark Energy

“Dark energy appears to be the dominant component of the physical Universe, yet there is no persuasive

theoretical explanation for its existence or magnitude.”

Albrecht et al 2006 Dark Energy Task Force report

Dark Energy

“Dark energy appears to be the dominant component of the physical Universe, yet there is no persuasive

theoretical explanation for its existence or magnitude.”

“The nature of dark energy ranks among the very most compelling of all outstanding problems in physical science.These circumstances demand an ambitious observational program to determine the dark energy properties as well as possible.”

Albrecht et al 2006 Dark Energy Task Force report

Dark Energy

Fainter

The Expansion of the Universe has been Accelerating

Measuring distance as a function of redshift quantifies this history

Fainter Hubble’s Law:

Measure distance D(r) and redshift z,

Then infer parameters H 0 , w(a), curvature etc .

The Expansion of the Universe has been Accelerating

Measuring distance as a function of redshift quantifies this history

• 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

• Clusters of galaxies - should contain the universal gas fraction wherever they are

Standard candles, rulers, buckets, 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

• 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

• Clusters of galaxies - should contain the universal gas fraction wherever they are

Standard candles, rulers, buckets, 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

• 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

• Clusters of galaxies - should contain the universal gas fraction wherever they are

Standard candles, rulers, buckets, 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

• 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

• Clusters of galaxies - should contain the universal gas fraction wherever they are

Standard candles, rulers, buckets, 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

• 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

• Clusters of galaxies - should contain the universal gas fraction wherever they are

Standard candles, rulers, buckets, 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

What is this?

Here’s 4% of it in detail

Here it is, slightly better measured

• 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

• Clusters of galaxies - should contain the universal gas fraction wherever they are

• Something else?

Standard candles, rulers, buckets, 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

Gravitational Lensing

Weak lensing

(small distortions, ubiquitous) Strong lensing

(multiple imaging, rare)

Strongly Lensed Galaxies

Strongly Lensed AGN

Point-like, variable sources

Time Delay Gravitational Lenses

Point-like, variable sources:

different path lengths,

different travel times

Signals from the AGN appear at different times -

this effect can be predicted with a model of the lens:

Time delay distances

Lens potential Image position Source

position

Signals from the AGN appear at different times -

this effect can be predicted with a model of the lens:

We can only measure time delays t: these can be predicted as t ^AB = D x (1/c A ’ - 1/c B ’)

Compare predicted and observed time delays with

likelihood function Pr(obs|pred) - multiply by terms for image positions, arc surface brightness etc, infer D(H 0 ,w)

Lens potential Image position Source

position

Time delay distances

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•Dark Energy from B1608 and RXJ1131

•Time delay lens cosmography with LSST

Outline

Two Accurate Time-Delay Distances from Strong Lensing:

Implications for Cosmology

Sherry Suyu (ASIAA)

Matt Auger (IoA), Stefan Hilbert (MPE),

Phil Marshall (KIPAC), Tommaso Treu (UCSB),

Malte Tewes, Frederic Courbin, Georges Meylan (EPFL), Chris Fassnacht (UC Davis), Roger Blandford (KIPAC),

Leon Koopmans (Kapteyn), Dominique Sluse (AIFA)

RXJ1131 & B1608 cosmography: Suyu et al (2013), astro-ph/1208.6010 RXJ1131 time delays: Tewes et al (2013), astro-ph/1208.6009

B1608 modeling: Suyu et al (2010), astro-ph/0910.2773

Precision Time Delays

VLA monitoring campaign Relative time delays:

Δt _AB = 31.5 days Δt _CB = 36.0 ± 1.5 days Δt _DB = 77.0 days

(Fassnacht et al. 1999, 2002)

+2.0 –1.0

+2.0 –1.0

RXJ1131 is optically variable, monitored by the

COSMOGRAIL team. Long-term monitoring essential Tewes et al 2012, in prep

Precision Time Delays

Lens modeling

z _d = 0.63 [Myers et al. 1995]

z _s = 1.39 [Fassnacht et al. 1996]

Model the lens mass distribution, to predict the time delays and derive the distance.

Q: How do you model

a gravitational lens?

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

Lens modeling

Model surface brightness ()

Look up predicted surface brightness

(())

 =   (())





z _d z _s

log Pr(| ^obs ) ~  ² ( ^obs )/2 + S(,())

Q: How do you model

a gravitational lens?

B1608+656: lens model

2 elliptically-symmetric, power-law density profile (index γ), galaxies, plus pixelated linear corrections to lens potential; good fit ^to

HST/ACS imaging, after dust correction, and radio image positions

Source reconstruction on a

grid of pixels

B1608+656: lens model

Potential is smooth to 2%!

2 elliptically-symmetric, power-law density profile (index γ), galaxies, plus pixelated linear corrections to lens potential; good fit ^to

HST/ACS imaging, after dust correction, and radio image positions

RXJ1131-1231

Bright, quad-lensed quasar, observed with HST/ACS.

Modeled in the same way as B1608 Cosmological constraints from time-delay lenses 11

Fig. 4.— ACS image reconstruction of the most probable model with a source grid of 64×64 pixels. Top left: observed ACS F814W image. Top middle: predicted lensed image of the background AGN host galaxy. Top right: predicted light of the lensed AGNs and the lens galaxies. Bottom left: predicted image from all components, which is a sum of the top-middle and top-right panels. Bottom middle: image residual, normalized by the estimated 1σ uncertainty of each pixel. Bottom right: the reconstructed source. Our lens model reproduces the global features of the data.

as

ρ _G (r) = (κ _ext − 1)Σ ^crit θ _E ^γ

^!

⁻¹ D ^γ _d

^!

⁻¹ Γ( ^γ ₂

^!

) π ^1/2 Γ( ^γ

^!

₂ ⁻³ )

1 r ^γ

^!

.

(22) Note that the projected mass of the lens galaxy en- closed within θ _E is (1 − κ ^ext )M _E , while the projected mass associated with the external convergence is κ _ext M _E ; the sum of the two is the Einstein mass M _E that was given in Equation (13). We employ spherical Jean’s modeling to infer the line-of-sight velocity dispersion, σ ^P (π, γ ^" , θ _E , r _ani , κ _ext ), from ρ _G by assuming the Hern- quist profile (Hernquist 1990) for the stellar distribution (e.g., Binney & Tremaine 1987; Suyu et al. 2010). ¹⁴ An anisotropy radius of r _ani = 0 corresponds to pure radial stellar orbits, while r _ani → ∞ corresponds to isotropic orbits with equal radial and tangential velocity disper- sions. We note that σ ^P is independent of H ₀ , but is dependent on the other cosmological parameters (e.g.,w and Ω de ) through Σ crit and the physical scale radius of the stellar distribution.

The likelihood for the velocity dispersion is P (σ|π, γ ^" , θ _E , r _ani , κ _ext )

= 1

!2πσ ² _σ exp

"

− (σ − σ ^P (π, γ ^" , θ _E , r _ani , κ _ext )) ² 2σ ² _σ

# ,(23)

14

Suyu et al. (2010) found that Hernquist (1990) and Jaffe (1983) stellar distribution functions led to nearly identical cosmo- logical constraints.

where σ = 323 km s ⁻¹ and σ _σ = 20 km s ⁻¹ from Sec- tion 4.3. Recall that the priors on γ ^" and θ _E were assigned to be uniform in the lens modeling. We also impose a uniform prior on r _ani in the range of [0.5, 5]R _eff for the kinematics modeling, where the effective radius based on the two-component S´ersic profiles in Table 1 is 1. ^"" 85 from the photometry. ¹⁵ The uncertainty in R _eff has negligible impact on the predicted velocity dispersion. The prior PDF for π is discussed in Section 8.1, while the PDF for κ _ext is described in the next section.

7.2. Lens environment

We combine the relative galaxy counts from Sec- tion 4.4, the measured external shear in Section 6.4, and the Millennium Simulation (MS; Springel et al. 2005) to obtain an estimate of P (κ _ext |d ^env , γ _ext , MS). This builds on the approach presented in Suyu et al. (2010) that used only the relative galaxy counts.

Tracing rays through the Millennium Simulation (see Hilbert et al. 2009, for details of the method), we create 64 simulated survey fields, each of solid angle 4×4 deg ² . In each field we map the convergence and shear to the source redshift z _s , and catalog the galaxy content, which we derive from the galaxy model by Guo et al.

(2010). For each line of sight in each simulated field, we record the convergence, shear, and relative galaxy

15

Before unblinding, we used an effective radius of 3.

^!!

2 based on a single S´ ersic fit. The larger R

eff

changes the inference of D

∆t

at the < 0.5% level.

Inferring cosmological parameters

Let

(all model parameters)

(cosmological parameters)

We are after the posterior PD F for  given the data, marginalised over the nuisance parameters :

where

3-dataset likelihood

Prior

Method: importance sample from WMAP5 Pr() and

Pr(), using 3-dataset likelihood. What are  and Pr()?

“Mass-sheet” model degeneracy

κ _ext

To break this degeneracy,

we need more information about the mass distribution:

• Slope  from arc thickness

• Stellar dynamics

• Structures along the line of sight

[Courbin et. al. 2002]

Lens mass, profile slope and line of sight mass distribution are all degenerate

Lensing observables

do not change, but

The source gets strongly lensed by the lens galaxy - and weakly lensed by

everything else

The combined weak

lensing effect mimics a lens with a different density

profile - and makes the time

delays different

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!

“External Convergence”

The B1608+656 field has twice the average galaxy density

(Fassnacht et al. 2009)

Use this observation to

calibrate simulations of

mass along line of sight

to strong lenses, and

estimate convergence

The Millennium Simulation

Ray tracing to find lines of sight to strong lenses, including

stellar mass (Hilbert et al 2008)

Approximation: sum up

mass in planes to estimate

κ _ext and its PDF

External Convergence Pr(κ _ext )

• Only choosing fields with 2x over-dense in galaxy number counts (like B1608) gives a

broader, offset Pr(κ _ext )

RXJ1131-1231

Model requires external shear, consistent with nearby foreground cluster. Include shear in the ray tracing κ _ext analysis

12 Suyu et al.

Fig. 5.— 11.5^!×10.5^!R-band image obtained from stacking 60 hours of the best-quality images in the COSMOGRAIL monitoring. The lens system is marked by the box near the center. Galaxies (stars) in the field are indicated by solid (dashed) circles. The radius of the solid circle is proportional to the flux of the galaxy. X-ray map from Chartas et al. (2009) are overlaid on the image within the dashed box. The concentrations of mass structures to the east of the lens are consistent with the modeled external shear and convergence gradient directions.

counts in a 45

^!!

aperture having I-band magnitudes be- tween 18.5 and 24.5. These provide samples for the PDF P (κ

ext

, γ

ext

, d

^env

|MS). We assume that the constructed PDF is applicable to strong-lens lines of sight, following Suyu et al. (2010) who showed that the distribution of κ

ext

for strong lens lines of sight are very similar to that for all lines of sight.

Structures in front of the lens distort the time delays and the images of the lens/source, while structures be- hind the lens further affect the time delays and images of the source. However, to model simultaneously the mass distributions of the strong lens galaxies and all structures along the line of sight is well beyond the current state of the art. In practice, the modeling of the strong lens galaxies is performed separately from the description of line-of-sight structures, and we approximate the effects of the lines-of-sight structures into the single correction term κ

ext

, whose statistical properties we estimate from the Millennium Simulation.

By selecting the lines of sight in the Millennium Sim- ulation that match the properties of RXJ1131−1231, we can obtain P (d

^env

|κ

ext

, γ

ext

, MS) P (κ

ext

) and simultane- ously marginalize over γ

ext

in Equation (10). We as- sumed a uniform prior for γ

ext

in the lensing analysis, such that P (γ

ext

) is a constant. The lensing likelihood is the only other term that depends on γ

ext

, and from Sec- tion 6.4, the lensing likelihood provides a tight constraint on γ

ext

that is approximately Gaussian: 0.089 ± 0.006.

We can therefore simplify part of Equation (10) to

! dγ

ext

P (d

^ACS

, ∆t|D

∆t

, γ

^!

, θ

E

, γ

ext

, κ

ext

)

·P (d

^env

|κ

^ext

, γ

ext

, MS)

" P (d

^ACS

, ∆t|D

^∆t

, γ

^!

, θ

E

, κ

ext

)

·P (d

^env

|κ

ext

, γ

ext

= 0.089 ± 0.006, MS), (24) where the above approximation, i.e., neglecting the co- variance between γ

ext

and the other parameters in the lensing likelihood and then marginalizing γ

ext

separately,

Cosmological constraints from time-delay lenses 13

all

all, weigh ted 1.35 ! n _r " 1.45

1.35 ! n _r " 1.45, weigh ted

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0

5 10 15

Κ _ext pd f! Κ ex t "

Fig. 6.— The effective prior probability distribution for the ex- ternal convergence κ ext from combining ray tracing through the Millennium Simulation with the relative galaxy counts of 1.4 and the modeled external shear of 0.089 ± 0.006. Solid line: the con- vergence distribution for all lines of sight; Dotted line: the con- vergence distribution for lines of sight with relative galaxy count n r = 1.4 ± 0.05; Dashed line: the convergence distribution for all lines of sight weighted by the likelihood for γ ext from the lens model; Dot-dashed line: the γ ext -weighted convergence distribu- tion for lines of sight with n r = 1.4 ± 0.05. The effective prior for κ ext used in the final cosmological parameter inference is described by this, most informative, distribution.

is conservative since we would gain in precision by includ- ing the covariances with other parameters. Furthermore, by Bayes’ rule,

P (d ^env |κ ^ext , γ _ext = 0.089 ± 0.006, MS)P (κ ^ext )

∝ P (κ ^ext |d ^env , γ _ext = 0.089 ± 0.006, MS), (25) which is precisely the PDF of κ _ext by selecting the sam- ples in P (κ _ext , γ _ext , d ^env |MS) that satisfies d ^env with a relative galaxy count within 1.4 ± 0.05, and subsequently weighting these samples by the Gaussian likelihood for γ _ext . This effective prior PDF for κ _ext that is con- structed from the weighted samples, P (κ _ext |d ^env , γ _ext = 0.089 ± 0.006, MS), is shown by the dot-dashed line in Figure 6.

TODO (SHS): Update with figure from Stefan.

8. TIME-DELAY DISTANCE OF RXJ1131−1231

We combine all the PDFs obtained in the previous sec- tions to infer the time-delay distance D _∆t .

8.1. Cosmological priors

As written above, we could infer the time delay dis- tance D _∆t directly, given a uniform prior. However, we are primarily interested in the cosmological information contained in such a distance measurement, so prefer to infer these directly. The posterior probability distribu- tion on D _∆t can then be obtained by first calculating the posterior PDF of the cosmological parameters π through the marginalizations in Equations (11) and (10), and then changing variables to D _∆t . Such transformations are of course straightforward when working with sam- pled PDFs.

In Table 2, we consider the following five cosmological world models, each with its own prior PDF P (π):

• UH ⁰ : Uniform prior PDF for H ₀ between 0 and 150 km s ⁻¹ Mpc ⁻¹ in a ΛCDM cosmology with Ω _Λ = 1 − Ω ^m = 0.73. This is similar to the typical

priors that were assumed in most of the early lens- ing studies, which sought to constrain H ₀ at fixed cosmology.

• UwCDM: Uniform priors on the parameters {H ⁰ , Ω _de , w} in a flat wCDM cosmology, where w is time-independent and Ω _m = 1 − Ω ^de .

• WMAP7wCDM: The prior PDF for the parameters {H ⁰ , Ω _de , w} is taken to be the posterior PDF from the WMAP 7-year data set (Komatsu et al. 2011), assuming a flat wCDM cosmology, where w is time- independent and Ω _m = 1 − Ω ^de .

• WMAP7oΛCDM: The prior PDF for the parame- ters {H ⁰ , Ω _Λ , Ω _k } is taken to be the posterior PDF from the WMAP 7-year data set, assuming an open (or rather, non-flat) cosmology, with dark energy described by Λ and Ω _k = 1 − Ω ^Λ − Ω ^m as the cur- vature parameter.

• WMAP7owCDM: The prior PDF for the parame- ters {H ⁰ , Ω _de , w, Ω _k } is taken to be the posterior PDF from the WMAP 7-year data set, assum- ing an open wCDM cosmology, where w is time- independent and Ω _k = 1−Ω ^de −Ω ^m is the curvature parameter.

8.2. Posterior sampling

We sample the posterior PDF by weighting samples drawn from the prior PDF with the joint likelihood func- tion evaluated at those points (Suyu et al. 2010). We generate samples of the cosmological parameters π from the priors listed in Table 2. We then join these to samples of κ _ext drawn from P (κ _ext ) from Section 7.2 and shown in Figure 6, and to uniformly distributed samples of γ ^"

within [−1.5, 2.5] and r ^ani within [−0.5, 5] R ^eff . Rather than generating samples of θ _E from the uniform prior, we obtain samples of θ _E directly from the Gaussian approx- imation to the lensing and time-delay likelihood since θ _E is quite independent of other model parameters (as shown in Figure 3). This boosts sampling efficiency, and the θ _E samples are only used to evaluate the kinematics likelihood.

For each sample of {π, κ ^ext , γ ^" , r _ani , θ _E }, we obtain the weight (or importance) as follows: (1) we determine D _∆t from π via Equation (2), (2) we calculate D ^model _∆t via Equation (7), (3) we evaluate P (d ^ACS , ∆t|D ^model ∆t , γ ^" ) based on the Gaussian approximation shown in Figure 3 for D ^model _∆t and γ ^" , (4) we compute P (σ|π, γ ^" , κ _ext , θ _E , r _ani ) via Equation (23), and (5) we weight the sam- ple by the product of P (d ^ACS , ∆t|D ∆t ^model , γ ^" ) and P (σ|π, γ ^" , κ _ext , θ _E , r _ani ) from the previous two steps.

The projection of these weighted samples onto π or D _∆t effectively marginalizes over the other parameters.

8.3. Blind analysis in action

As a brief illustration of our blind analysis approach,

we show in the left panel of Figure 7 the blinded plot of

the time-delay distance measurement. For all cosmolog-

ical parameters such as D _∆t , D _∆t ^model , H ₀ , w, Ω _m , etc.,

we always plotted their probability distribution with re-

spect to the median during the blind analysis. There-

fore, we could use the shape of the PDFs to check our

Let

(all model parameters)

(cosmological parameters)

We are after the posterior PD F for  given the data, marginalised over the nuisance parameters :

where

3-dataset likelihood

Prior

Method: importance sample from WMAP5 Pr() and Millenium Simulation Pr(κ _ext ), using 3-dataset likelihood

Inferring cosmological parameters

Dark Energy from B1608

assuming flatness (assuming flatness)

WMAP prior

B1608 likelihood

Joint posterior

Dark Energy from B1608

assuming flatness (assuming flatness)

Dark Energy from B1608

assuming flatness (assuming flatness)

This one lens was more informative than the HST key project, and

comparable to SDSS+2DF BAO

RXJ1131-1231 + B1608+656

Joint cosmological parameter analysis

OwCDM model: variable w and curvature

• Comparable precision between probes

• Curvature well-constrained

• Interesting tension between D A and D L ?

18 Suyu et al.

! de

0.5 0.6 0.7 0.8 0.9

H ₀ [km s ⁻¹ Mpc ⁻¹ ]

40 50 60 70 80 90 100

WMAP7 + BAO WMAP7 + SN WMAP7 + RXJ1131 + B1608

! _k

−0.08

−0.06

−0.04

−0.02 0.00 0.02 0.04

w

−2.5 −2.0 −1.5 −1.0 −0.5 WMAP7 + BAO

WMAP7 + SN

WMAP7 + RXJ1131 + B1608

Fig. 11.— Posterior PDF of H

0

, Ω

_de

, w and Ω

_k

for BAO (blue dot-dashed; Percival et al. (2010)), SN (red dashed; Hicken et al. (2009)), time-delay lenses (black solid; this work) when each is combined with WMAP7 in an owCDM cosmology. Contours mark the 68%, and 95% credible regions. Time-delay lenses are highly complementary to other probes, particularly CMB and SN.

0 10 20 30 40 50 60

SDSS BAO Lenses _SN Cepheids Rec. BAO

Percent Precision

" _!

k (x10)

0 10 20 30 40 50 60

SDSS BAO Lenses _SN Cepheids Rec. BAO

Percent Precision

" _w

Fig. 12.— Precision of cosmological constraints on Ω

k

and w for five probes each in combination with WMAP7 in an owCDM cosmology: SDSS BAO (Percival et al. 2010), the two time-delay lenses RXJ1131−1231 and B1608+656 (this work), SN (Suzuki et al. 2012), Cepheids (Riess et al. 2011), and reconstructed BAO (Mehta et al. 2012). Precision for Ω

_k

and w is defined as half the 68% CI as a percentage of 1.

large parameter space. Nonetheless, the histogram plot shows that time-delay lenses are a valuable probe, espe- cially in constraining the spatial curvature of the Uni- verse.

10. _SUMMARY

We have performed a blind analysis of the time-delay lens RXJ1131−1231, modeling its high precision time de- lays from the COSMOGRAIL collaboration, deep HST imaging, newly measured lens velocity dispersion, and mass contribution from line-of-sight structures. The data sets were combined probabilistically in a joint analysis, via a comprehensive model of the lens system consisting of the light of the source AGN and its host galaxy, the light and mass of the lens galaxies, and structures along the line of sight characterized by external convergence and shear parameters. The resulting time-delay distance measurement for the lens allows us to infer cosmologi- cal constraints. From this study, we draw the following conclusions:

1. Our comprehensive lens model reproduces the global features of the HST image and the time delays. We quantify the uncertainty due to the deflector gravitational potential on the time-delay distance to be at the 4.6% level.

2. Based on the external shear strength from the lens model and the overdensity of galaxy count around the lens, we obtained a PDF for the external con- vergence by ray tracing through the Millennium Simulation. This κ ext PDF contributes to the un- certainty on D ∆t also at the 4.6% level.

3. Our robust time-delay distance measurement of 6%

takes into account all sources of known statistical and systematic uncertainty. We provide a fitting formula to describe the PDF of the time-delay dis- tance that can be used to combine with any other independent cosmological probe.

4. The time-delay distance of RXJ1131−1231 is mostly sensitive to H 0 , especially given the low red- shift of the lens.

5. Assuming a flat ΛCDM with fixed Ω Λ = 0.73 and uniform prior on H 0 , our unblinded H 0 measurement from RXJ1131−1231 is 78.7 ^+4.3 _−4.5 km s ⁻¹ Mpc ⁻¹ .

6. The constraint on H ₀ helps break parameter degeneracies in the CMB data. In combina- tion with WMAP7 in wCDM, we find H 0 = 80.0 ^+5.8 _−5.7 km s ⁻¹ Mpc ⁻¹ , Ω de = 0.79 ± 0.03, and w = −1.25 ^+0.17 _−0.21 . These are statistically consis- tent with the results from the gravitational lens B1608+656. There are no significant residual sys- tematics detected in our method based on this com- bined analysis of the two systems.

7. By combining RXJ1131−1231, B1608+656 and WMAP7, we derive the following constraints:

H ₀ = 75.2 ^+4.4 _−4.2 km s ⁻¹ Mpc ⁻¹ , Ω _de = 0.76 ^+0.02 _−0.03 and w = −1.14 ^+0.17 _−0.20 in flat wCDM, and H 0 =

18 Suyu et al.

!

de

0.5 0.6 0.7 0.8 0.9

H

₀

[km s

⁻¹

Mpc

⁻¹

]

40 50 60 70 80 90 100

WMAP7 + BAO WMAP7 + SN WMAP7 + RXJ1131 + B1608

!

k

−0.08

−0.06

−0.04

−0.02 0.00 0.02 0.04

w

−2.5 −2.0 −1.5 −1.0 −0.5

WMAP7 + BAO WMAP7 + SN

WMAP7 + RXJ1131 + B1608

Fig. 11.— Posterior PDF of H0, Ωde, w and Ωkfor BAO (blue dot-dashed; Percival et al. (2010)), SN (red dashed; Hicken et al. (2009)), time-delay lenses (black solid; this work) when each is combined with WMAP7 in an owCDM cosmology. Contours mark the 68%, and 95% credible regions. Time-delay lenses are highly complementary to other probes, particularly CMB and SN.

0 10 20 30 40 50 60

SDSS BAO

Lenses

SN Cepheids Rec. BAO

Percent Precision

"

_!

k

(x10)

0 10 20 30 40 50 60

SDSS BAO

Lenses

SN Cepheids Rec. BAO

Percent Precision

"

_w

Fig. 12.— Precision of cosmological constraints on Ωk and w for five probes each in combination with WMAP7 in an owCDM cosmology: SDSS BAO (Percival et al. 2010), the two time-delay lenses RXJ1131−1231 and B1608+656 (this work), SN (Suzuki et al. 2012), Cepheids (Riess et al. 2011), and reconstructed BAO (Mehta et al. 2012). Precision for Ωkand w is defined as half the 68% CI as a percentage of 1.

large parameter space. Nonetheless, the histogram plot shows that time-delay lenses are a valuable probe, espe- cially in constraining the spatial curvature of the Uni- verse.

10. _SUMMARY

We have performed a blind analysis of the time-delay lens RXJ1131−1231, modeling its high precision time de- lays from the COSMOGRAIL collaboration, deep HST imaging, newly measured lens velocity dispersion, and mass contribution from line-of-sight structures. The data sets were combined probabilistically in a joint analysis, via a comprehensive model of the lens system consisting of the light of the source AGN and its host galaxy, the light and mass of the lens galaxies, and structures along the line of sight characterized by external convergence and shear parameters. The resulting time-delay distance measurement for the lens allows us to infer cosmologi- cal constraints. From this study, we draw the following conclusions:

1. Our comprehensive lens model reproduces the global features of the HST image and the time delays. We quantify the uncertainty due to the deflector gravitational potential on the time-delay distance to be at the 4.6% level.

2. Based on the external shear strength from the lens model and the overdensity of galaxy count around the lens, we obtained a PDF for the external con- vergence by ray tracing through the Millennium Simulation. This κ

ext

PDF contributes to the un- certainty on D

∆t

also at the 4.6% level.

3. Our robust time-delay distance measurement of 6%

takes into account all sources of known statistical and systematic uncertainty. We provide a fitting formula to describe the PDF of the time-delay dis- tance that can be used to combine with any other independent cosmological probe.

4. The time-delay distance of RXJ1131−1231 is mostly sensitive to H

0

, especially given the low red- shift of the lens.

5. Assuming a flat ΛCDM with fixed Ω

Λ

= 0.73 and uniform prior on H

0

, our unblinded H

0

measurement from RXJ1131−1231 is 78.7

^+4.3_−4.5

km s

⁻¹

Mpc

⁻¹

.

6. The constraint on H

0

helps break parameter degeneracies in the CMB data. In combina- tion with WMAP7 in wCDM, we find H

0

= 80.0

^+5.8_−5.7

km s

⁻¹

Mpc

⁻¹

, Ω

de

= 0.79 ± 0.03, and w = −1.25

^+0.17_−0.21

. These are statistically consis- tent with the results from the gravitational lens B1608+656. There are no significant residual sys- tematics detected in our method based on this com- bined analysis of the two systems.

7. By combining RXJ1131−1231, B1608+656 and WMAP7, we derive the following constraints:

H

0

= 75.2

^+4.4_−4.2

km s

⁻¹

Mpc

⁻¹

, Ω

de

= 0.76

^+0.02_−0.03

and w = −1.14

^+0.17_−0.20

in flat wCDM, and H

0

=

Next Steps

• To reach 10% precision on w, and to check for residual systematic errors, we need ~4 systems each as well-measured as B1608

• Time delays coming from COSMOGRAIL

project, HST data for modeling being analyzed

by Wong & Suyu at ASIAA

Conclusions, Outlook

 Time delay lenses are an interesting

independent cosmological probe, with very different systematics to BAO, SNe etc but providing comparable precision

• To reach sub-percent precision on H 0 (w), we

would need ~100-1000 time delay lens systems, each as well-measured as B1608

• Future samples of time-delay lenses could be a competitive cosmological probe -

but we are going to need to find a lot more,

and then measure them all...

•Dark Energy from B1608 and RXJ1131

•Time delay lens cosmography with LSST

Outline

High etendue survey telescope:

 5.7m effective aperture

 10 sq degree field

 24 mag in 30 seconds

 Visible sky mapped every few nights

 Cerro Pachon, Chile: 0.7” seeing Ten year movie of the

entire Southern sky

• 120 Petabytes of data (1Pb = every book ever published)

• All data to be made public: nightly transient alerts, yearly data releases starting 2021 (+2yrs, worldwide)

Overview

High etendue survey telescope:

 5.7m effective aperture

 10 sq degree field

 24 mag in 30 seconds

 Visible sky mapped every few nights

 Cerro Pachon, Chile: 0.7” seeing Ten year movie of the

entire Southern sky

• 120 Petabytes of data (1Pb = every book ever published)

• All data to be made public: nightly transient alerts, yearly data releases starting 2021 (+2yrs, worldwide)

Overview

• Now approved: federal

construction funding in the 2014 President’s budget

• Primary/Tertiary mirror was finished September 2013

• First light in 2019, 2 years commissioning, survey to start in 2021

Status

• Top-ranked ground-based project in the Astro 2010 Decadal Survey of US astronomy

• Joint NSF & DoE project (astronomers and HE physicists)

• Science collaborations, over 400 members. International

affiliates negotiating to join, & contribute to operating costs.

The LSST survey

• 20000 sq deg

• 6 filters, ugrizy

• 10 years planned, 800 visits per field

• 3 - 14 day cadence

• depth ~ 24 mag per visit,

~ 27 mag after 10 years

• resolution 0.4-1.0”

CFHTLS Deep

http://www.lsst.org

Strong Lenses with LSST: Simulated 10-year Movies of Multiply-Imaged Quasars

We use the LSST image simulator to generate realistic example datasets for a sample of strong galaxy-scale gravitational lenses expected to be measurable with the universal survey data. The 20 mock i-band images have sky brightness and atmospheric seeing drawn from plausible distributions for the Cerro Pachon site, and we use plausibly varying telescope optics and detector response to fully represent the expected image quality. Passing the simulated images through a standard astronomical object detection pipeline gives us our first view of what these rare and valuable objects will look like in the LSST database. We explore a very basic morphological selection algorithm, and find that even this achieves 50% completeness. The seeing and lens galaxy obscuration can reduce the survey yield by comparable amounts, highlighting the need for good object deblending.

Simulating the LSST Sky

We used the ImSim ray-tracing code to simulate reduced LSST 15-second exposures. The schematic diagram on the right shows the history of each photon, from

astronomical source to counts of electrons in pixels.

(See also the ImSim posters by S. Krughoff, S. Marshall, C. Chang and J. Pizagno)

Left: a single simulated, reduced 13.7x13.7 arcmin LSST chip i-band image, containing model stars, galaxies

and ~100 quad lenses. Artificially high density simulations like this provide an efficient way of

investigating the systematic errors involved in lens

detection and measurement. This mock observation is at median sky background with 0.4” atmospheric

seeing, and represents a typical “good” image.

J. Garrett Jernigan ¹ , P. J. Marshall ^2,6 , M. Oguri ³ , R. R. Gibson ⁴ , J. Pizagno ⁴ , A. Connolly ⁴ , J. R. Peterson ⁵ , Z. Ahmad ⁵ , J. Bankert ⁵ , D. Bard ⁶ , C. Chang ⁷ , E. Grace ⁵ , K. Gilmore ⁸ , M. Hannel ⁵ , L. Jones ⁴ , S. M. Kahn ⁸ , S. Krughoff ⁴ , S. Lorenz ⁵ , S. Marshall ⁸ , S. Nagarajan ⁵ , A. P. Rasmussen ⁸ , M. Shmakova ⁶ , N. Sylvestre ⁴ , N. Todd ⁵ , M. Young ⁵ , and the LSST Strong Lensing Science Collaboration

1 Space Sciences Laboratory, UC Berkeley, ² University of Oxford, UK, ³ NAOJ, Japan, ⁴ University of Washington, ⁵ Purdue University, ⁶ KIPAC/SLAC National Accelerator Laboratory, ⁷ Stanford University, ⁸ Stanford/SLAC National Accelerator Laboratory

Strong Gravitational Lenses with LSST

We expect to detect nearly ten thousand lensed quasars with LSST (Oguri & Marshall 2010). Focusing on the 4- image systems for their high scientific value, and

ensuring measurability at each observing epoch, we generated a sample of around 440 “quads” detected down to an i-band AB magnitude limit of 23.3 (right).

What will they look like in the LSST images?

Deblending, Detecting and Measuring

Above we show mock lenses with and without the lens galaxy subtracted: a perfect subtraction increases the number of morphologically-selectable quad lenses by more than a factor of two (right).

Varying sky brightness and seeing are illustrated in the 20- exposure movie clips below. The seeing ranges from

0.36” to 1.14” FWHM in this representative image subset, and it is this that drives the detection rate.

We used SExtractor to deblend the sources in each

exposure independently: color and variability selection, and then “MultiFitting,” should increase the lens yield.

ImSim

Cosmology OpSim

Reference image and catalog

Atmosphere

Detector Image

The number of detected quasar images is a rough indicator of quad identifiability. If we define 2 detected quasar images as the detection threshold for a lens candidate, we find that the completeness f n>2 (indicated by the plot symbol radius) increases by more than a factor of two when the lens galaxy is subtracted. Completeness is mostly sensitive to atmospheric seeing FWHM, decreasing by

a factor of 2-3 over the range 0.4” to 1.2”. LSST

single exposure

References: Oguri & Marshall, MNRAS, 405, 2579, (2010) Bertin & Arnouts, SExtractor (1996)

Model lens galaxies and sources are drawn from realistic distributions; image configurations for each system take magnification bias into account.

The LSST image archive will contain a lot of lenses

10 ^4-5 galaxy-scale lenses, 1000s of clusters...

CFHTLS images + Space Warps sims, SL2S lenses (More, Marshall et al)

How many lensed quasars?

(O gu ri & Ma rsh al l 2 01 0)

How many lensed quasars?

(O gu ri & Ma rsh al l 2 01 0)

• LSST should detect ~8000 lenses (1000 quads)

How many lensed quasars?

(O gu ri & Ma rsh al l 2 01 0)

• LSST should detect ~8000 lenses (1000 quads)

• HSC, DES, PS1: ~3000 lenses (400 quads);

How many lensed quasars?

•Until LSST, additional monitoring will be needed.

LSST itself should measure 3000 time delay lenses, including 400 quads

(O gu ri & Ma rsh al l 2 01 0)

• LSST should detect ~8000 lenses (1000 quads)

• HSC, DES, PS1: ~3000 lenses (400 quads);

Lens detection

Detect, Deblend, Cluster, Measure

Source, Object Tables

- - - - - - - - - - - -

Sim ula tio ns

• Catalog-based candidate detection. Needs: good

deblender , the right parameters (color, morphology,

variability) saved, rapidly executable DB queries.

Lens detection

Detect, Deblend, Cluster, Measure

Source, Object Tables

- - - - - - - - - - - -

Sim ula tio ns

• Catalog-based candidate detection. Needs: good deblender , the right parameters (color, morphology, variability) saved, rapidly executable DB queries.

• Image-based candidate classification. Needs:

access to postage stamp images at data center in a

“Multi-Fit,” via level 3 API, reliable PSF models and

image registration. Joint w/ Euclid? Practise w/ HSC!

Lens detection

Detect, Deblend, Cluster, Measure

Source, Object Tables

- - - - - - - - - - - -

Sim ula tio ns

• Catalog-based candidate detection. Needs: good deblender , the right parameters (color, morphology, variability) saved, rapidly executable DB queries.

• Image-based candidate classification. Needs:

access to postage stamp images at data center in a

“Multi-Fit,” via level 3 API, reliable PSF models and image registration. Joint w/ Euclid? Practise w/ HSC!

• Candidate visualization for quality control. Needs:

optimally-viewable color images, potential for crowd-

sourcing

Lens measurement

• Time delay estimation. Needs:

good photocal, long seasons, regular sampling, optimal

lightcurve extraction, multi-filter AGN/SN+microlensing model.

Lens measurement

Time Delay Challenge

Time Delay Challenge

Goals:

Time Delay Challenge

Goals:

1. Assess performance of current time delay estimation

algorithms on LSST-like data

Time Delay Challenge

Goals:

1. Assess performance of current time delay estimation algorithms on LSST-like data

2. Assess impact of baseline LSST observing strategy on time

delay accuracy, and possibly recommend changes

Time Delay Challenge

Goals:

1. Assess performance of current time delay estimation algorithms on LSST-like data

2. Assess impact of baseline LSST observing strategy on time

delay accuracy, and possibly recommend changes

Time Delay Challenge

Goals:

1. Assess performance of current time delay estimation algorithms on LSST-like data

2. Assess impact of baseline LSST observing strategy on time delay accuracy, and possibly recommend changes

Plan:

Time Delay Challenge

Goals:

1. Assess performance of current time delay estimation algorithms on LSST-like data

2. Assess impact of baseline LSST observing strategy on time delay accuracy, and possibly recommend changes

Plan:

• “Evil Team” to generate large set of simulated lightcurves

spanning expectations for Stage II-IV

Time Delay Challenge

Goals:

1. Assess performance of current time delay estimation algorithms on LSST-like data

2. Assess impact of baseline LSST observing strategy on time delay accuracy, and possibly recommend changes

Plan:

• “Evil Team” to generate large set of simulated lightcurves spanning expectations for Stage II-IV

• Challenge community “Good Teams” to infer time delays

blindly, and submit results

Time Delay Challenge

Goals:

1. Assess performance of current time delay estimation algorithms on LSST-like data

2. Assess impact of baseline LSST observing strategy on time delay accuracy, and possibly recommend changes

Plan:

• “Evil Team” to generate large set of simulated lightcurves spanning expectations for Stage II-IV

• Challenge community “Good Teams” to infer time delays blindly, and submit results

• Publish paper on results together

Time Delay Challenge

Goals:

1. Assess performance of current time delay estimation algorithms on LSST-like data

2. Assess impact of baseline LSST observing strategy on time delay accuracy, and possibly recommend changes

Plan:

• “Evil Team” to generate large set of simulated lightcurves spanning expectations for Stage II-IV

• Challenge community “Good Teams” to infer time delays blindly, and submit results

• Publish paper on results together

Time Delay Challenge

Goals:

1. Assess performance of current time delay estimation algorithms on LSST-like data

2. Assess impact of baseline LSST observing strategy on time delay accuracy, and possibly recommend changes

Plan:

• “Evil Team” to generate large set of simulated lightcurves spanning expectations for Stage II-IV

• Challenge community “Good Teams” to infer time delays blindly, and submit results

• Publish paper on results together

Evil Team:

Time Delay Challenge

Goals:

1. Assess performance of current time delay estimation algorithms on LSST-like data

2. Assess impact of baseline LSST observing strategy on time delay accuracy, and possibly recommend changes

Plan:

• “Evil Team” to generate large set of simulated lightcurves spanning expectations for Stage II-IV

• Challenge community “Good Teams” to infer time delays blindly, and submit results

• Publish paper on results together Evil Team:

Kai Liao, Greg Dobler, Tommaso Treu (UCSB), Chris Fassnacht,

Nick Rumbaugh (UCDavis), Phil Marshall (SLAC)

Time Delay Challenge

Goals:

1. Assess performance of current time delay estimation algorithms on LSST-like data

2. Assess impact of baseline LSST observing strategy on time delay accuracy, and possibly recommend changes

Plan:

• “Evil Team” to generate large set of simulated lightcurves spanning expectations for Stage II-IV

• Challenge community “Good Teams” to infer time delays blindly, and submit results

• Publish paper on results together Evil Team:

Kai Liao, Greg Dobler, Tommaso Treu (UCSB), Chris Fassnacht,

Nick Rumbaugh (UCDavis), Phil Marshall (SLAC) Dead line: July 1 st, 20 14

LSST TDC: example lightcurves

Mock data

- without noise

- fully sampled

- no lensing

- microlensing

10 years, 3 day cadence 5 years, 3 days

TDC0: challenge qualifying

Metrics:

• Precision P

• ^{Accuracy A}

• ^{Fraction f}

• Goodness of fit TDC0 qualifying:

• ~50 datasets

• 7 teams, 27 entries

• 3 teams have beaten 15% P, A so far

• Goal: A=0.2%

● Shaded area = success

Liao (UCSB)

Lens measurement

• Time delay estimation. Needs:

good photocal, long seasons, regular sampling, optimal

lightcurve extraction, multi-filter AGN/SN+microlensing model.

Lens measurement