The future of strong gravitational lensing by galaxy clusters

(An actual image would have cluster galaxies “in the way”)

Mass map resolution improves withdensity of multiple images

-Sean Carroll

Bullet Cluster: Clowe06

COSMOS: Massey07

Jee07

Weak lensing analyses get press because theymap out mass without assuming light traces it.

We will no longer need to assume light traces massonce hundreds of multiple images are detected.

70 60 50 40 30 20 10 0Hubble’sconstant km/s/Mpc

Cosmological Constraintsfrom Gravitational Lens Time Delays

Dan Coe with Leonidas Moustakas

Caltech postdoc at JPL

Cosmological constraints from LSST time delays assuming aflat universe, constant w, and a Planck prior:

h ≈ 0.7 ± 0.007 (1%)Wde ≈ 0.7 ± 0.005w ≈ -1 ± 0.026

Hot off the press!(papers online this morning*)

• I. Simulations– a la Chuck, Glenn, & Rachel M. ‘08 w/ Oguri07-like analysis

• II. Cosmological Constraints – arXiv:0906.4108*

• III. Systematics• b. Fisher Matrices: quick-start guide

– arXiv:0906.4123*

What else do you want to know?

• How I derived those constraints• How they compare to other methods (WL

/ SN / BAO / CL)• Constraints for a general cosmology,

allowing for curvature and time-varying w– Dark Energy (w0, wa) [ w(z) = w0 + (1-a) wa ]

– Curvature (Wk)

Time Delays as a measure of H0

• First proposed by Refsdal (1964)• Reliable time delays have now been

measured for ~16 gravitational lenses• Individual analyses historically yielded

a wide range of values for H0

resulting from:– Variation in lens properties– Variation in lens models assumed

• Both of these issues are now being overcome

Haven’t we already measured H0?

• H0 = 72 ± 8 km/s/Mpc (HST Key Project, Freedman01)

More precise H0 helps us constrain w

• H0 = 74.2 ± 3.6 km/s/Mpc

(SH0ES, Riess09)SH0ES + WMAP5 w = -1.12 ± 0.12

“PixeLens” modelsminimal assumptions

analytic assumingisothermal lens

Current time delay constraints on H0

• Oguri07 (16 lenses):H0 = 68 ± 6 (stat.) ± 8 (syst.) km/s/Mpc

• Saha06 (10 lenses):H0 = 72+8

-11 km/s/Mpc

• Coles08 (11 lenses):H0 = 71+6

-8 km/s/Mpc

A bright future

• With 16 time delay lenses, we have already matched the HST Key Project’sprecision on H0 (~10%)which required 40 Cepheids

• Future surveys should yieldthousands of time delay lenses

H0 constrained to 9%from 16 time delay lenses (Oguri07)

(Note the wide spreadin h for individual lenseswhen all are assumed to be isothermal.)

We can now measure H0 (and more) with time delays because:

Two main obstacles are being overcome

1. Insufficient statistics (Lenses have intrinsic scatter in slope, etc.)

a. HST Key Project required 40 Cepheids (Freedman01)

b. Detections of accelerating expansion required 50 & 60 supernovae (Riess98, Perlmutter99)

c. We have currently only measured reliable time delays for ~16 lenses. Future surveys may yield thousands.

2. We now believe the average lens is roughly isothermal(e.g., Koopmans09):

’g = 2.085 ± 0.20 (scat.)

(However, this offset from ’g = 2could bias H0 low by 8.5%assuming an isothermal model.)

We can now measure H0 (and more) with time delays because:

Two main obstacles are being overcome

Let us assume all systematics can be well controlled

• In this ideal case, how well can we constrain cosmology?

• All methods (WL / SN / BAO / CL) have sizeable systematics which are being aggressively addressed

• Main time delay systematics are lens slope and group mass sheet

Time delays actually constrain a ratio of angular diameter distances that depend on cosmology (not just H0)

cosmology lens + enviro

TC TL

DLS DL

DS

Time delays constrain TC, not just H0.

T C

The current 8.6% uncertainty on H0 is actually an 8.6% uncertainty on TC !

Here we plot dTC = 8.6% for zL, zS = 0.5, 2.0.

But so far you have all been correct in quoting uncertainties on H0

Even marginalizing over 0 < WL < 1 only raises the uncertainty on H0 from 8.6% to 8.72% (a 1% increase).

T C

In the future, we will need to considerthe full cosmological dependencies

If LSST can constrain TC to 0.7%,marginalizing over 0 < WL < 1 would raise the uncertainty on H0 from 0.7% to 2.5% (a 3.5x increase).In practice, a prior on WL will mitigate this increase, but it will still be significant.

Degeneracies are broken significantlyby redshift distributions

LSST redshift distributions can be roughly approximatedby Gaussians:zL = 0.5 ± 0.15zS = 2.0 ± 0.75 (Dobke09)

TC to 0.7%??

How will cosmological constraints improve / vary with…

• Sample size• Redshift precision• Time delay precision• Quad-to-double ratio

– (4-image systems vs. 2-image systems)

Calculating expectations for dTC from future experiments

TC TL

TL2 + [z]2 + )2 = TC2 lens model redshifts time delays cosmology

1. Three main sources of uncertainty: lens models, redshifts, time delay measurements

2. Assume systematics can be controlled well,and statistical uncertainties can be beat down as √N

Lens model uncertainties currently dominate.Photometric redshift uncertainties

will be significant in the future.Time delay uncertainties are okay for now.

DzL = 0.04(1 + zL) as in CFHTLS DzS = 0.10(1 + zS) as roughly found for SDSS quasars

The Search for the “Golden Lens”

For a golden lens,TL would be measuredextremely well.

Its owner would havethe power to constrainTC extremely well.

A golden lens?B1608+656 has been studied extensively (e.g., Koopmans03, Fassnacht06, Suyu09)

Koopmans03 foundH0 = 75 ± 6 km/s/Mpcand claimed the systematic errors were <~5%

Suyu09 find 6% uncertaintystatistical + systematic

Quads have shorter time delays

(from simulationsperformed in Paper I, in prep.)

assume 2-day precision, anything less can’t be measured;lose ~30% of image pairs in quads

So quads have higher fractional uncertainties

Expectations for dTC from future experiments

Quality vs. Quantity

OMEGA Mission ConceptMoustakas et al.

(Bolton, Bullock, Cheng, Coe, Fassnacht, Keeton, Kochanek, Lawrence, Marshall, Metcalf, Natarajan, Peterson, Wambsganns)

• Dedicated space-based observatory monitoring ~100 time delay lenses

• ~1.5-m mirror, near-UV -- near-IR + spectra

• Precise measurements of fluxes, positions, and time delays

• Constraints on nature of dark matter particle from small-scale power cutoff

Expectations for dTC from future experiments

Cosmological constraints from LSST time delays assuming aflat universe, constant w, and a Planck prior:

h ≈ 0.7 ± 0.007 (1%)Wde ≈ 0.7 ± 0.005w ≈ -1 ± 0.026

Comparison to other “Stage IV” experiments

• Expected constraints for future WL / SN / CL / BAO experimentsprovided by the Dark Energy Task Forceencoded in Fisher matricesin their DETFast software

There’s an app for that!Fisher matrix “Quick-start guide” and software arXiv:0906.4123 (online this morning!)also see DETFast, Fisher4Cast

Comparison to other “Stage IV” experiments

• Expected constraints for future WL / SN / CL / BAO experimentsprovided by the Dark Energy Task Forceencoded in Fisher matricesin their DETFast software

• Again, assuming:– Flat universe– Constant w (can be ≠ -1, but not time-varying)

– Planck prior

Comparison to other methods

Flat universeConstant wPlanck Prior

Comparison to other methods

Flat universeConstant wPlanck Prior

Flat universeConstant wPlanck Prior

Comparison to other methods

Flat universeConstant wPlanck Prior

Now for a general cosmology

• Curvature allowed (Wk)

• Time-varying w allowed (w0, wa)

• Planck prior• Stage II (near-future) WL+SN+CL prior

Comparison to other methods

Prior = Planck + Stage II (WL+SN+CL)

Comparison to other methods

Prior = Planck + Stage II (WL+SN+CL)

Comparison to other methods

Prior = Planck + Stage II (WL+SN+CL)

Comparison to other methods

Prior = Planck + Stage II (WL+SN+CL)

Time delays are more than just a constraint on H

Prior = Planck + Stage II (WL+SN+CL)

TD FOM = 1.67H FOM = 1.24(relative to prior)

Dark Energy Task Force “Figure of Merit”

(prior)(prior)

Pivot redhsift: where w(z) is constrained best

HutererTurner01

Dark Energy Task Force “Figure of Merit”

(prior)(prior)

Yes we can obtain cosmological constraints with

gravitational lens time delays!

• LSST time delays from 4,000 lenses should constrainh ≈ 0.7 ± 0.007 (1%)Wde ≈ 0.7 ± 0.005w ≈ -1 ± 0.026assuming a flat universe, constant w, and Planck

• LSST and OMEGA (~4,000 vs. ~100 lenses)represent an even trade in “quality vs. quantity”. Combined constraints would be even tighter.

• Time delay uncertainties are good enough for now. Lens models and redshifts should be the focus.