The future of strong gravitational lensing by galaxy clusters

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

Mass map resolution improves with density of multiple images Mass map resolution improves with density of multiple images

-Sean Carroll Bullet Cluster: Clowe06 COSMOS: Massey07 Jee07 Weak lensing analyses get press because they map out mass without assuming light traces it. Weak lensing analyses get press because they map out mass without assuming light traces it.

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

Hubble’s constant km/s/Mpc Cosmological Constraints from Gravitational Lens Time Delays Dan Coe with Leonidas Moustakas Caltech postdoc at JPL

Cosmological constraints from LSST time delays assuming a flat universe, constant w, and a Planck prior: h ≈ 0.7 ± (1%)  de ≈ 0.7 ± w ≈ -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: * III. Systematics b. Fisher Matrices: quick-start guide –arXiv: *

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 (w 0, w a ) [ w(z) = w 0 + (1-a) w a ] –Curvature (  k )

Time Delays as a measure of H 0 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 H 0 resulting from: –Variation in lens properties –Variation in lens models assumed Both of these issues are now being overcome

Haven’t we already measured H 0 ? H 0 = 72 ± 8 km/s/Mpc (HST Key Project, Freedman01) More precise H 0 helps us constrain w H 0 = 74.2 ± 3.6 km/s/Mpc (SH 0 ES, Riess09) SH 0 ES + WMAP5  w = ± 0.12

“PixeLens” models minimal assumptions analytic assuming isothermal lens Current time delay constraints on H 0 Oguri07 (16 lenses): H 0 = 68 ± 6 (stat.) ± 8 (syst.) km/s/Mpc Saha06 (10 lenses): H 0 = km/s/Mpc Coles08 (11 lenses): H 0 = km/s/Mpc

A bright future With 16 time delay lenses, we have already matched the HST Key Project’s precision on H 0 (~10%) which required 40 Cepheids Future surveys should yield thousands of time delay lenses

H 0 constrained to 9% from 16 time delay lenses (Oguri07) (Note the wide spread in h for individual lenses when all are assumed to be isothermal.)

We can now measure H 0 (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) :  ’ = ± 0.20 (scat.) (However, this offset from  ’ = 2 could bias H 0 low by 8.5% assuming an isothermal model.) We can now measure H 0 (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 H 0 ) cosmologylens + enviro TCTC TLTL  D LS DLDL DSDS

Time delays constrain T C, not just H 0. TCTC The current 8.6% uncertainty on H 0 is actually an 8.6% uncertainty on T C ! Here we plot  T C = 8.6% for z L, z S = 0.5, 2.0.

But so far you have all been correct in quoting uncertainties on H 0 Even marginalizing over 0 <   < 1 only raises the uncertainty on H 0 from 8.6% to 8.72% (a 1% increase). TCTC

In the future, we will need to consider the full cosmological dependencies If LSST can constrain T C to 0.7%, marginalizing over 0 <   < 1 would raise the uncertainty on H 0 from 0.7% to 2.5% (a 3.5x increase). In practice, a prior on   will mitigate this increase, but it will still be significant.

Degeneracies are broken significantly by redshift distributions LSST redshift distributions can be roughly approximated by Gaussians: z L = 0.5 ± 0.15 z S = 2.0 ± 0.75 (Dobke09) T C 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  T C from future experiments TCTC TLTL    T L  2 + [  z] 2 +   )  2 =   T C  2 lens modelredshiftstime delayscosmology 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.  z L = 0.04(1 + z L ) as in CFHTLS  z S = 0.10(1 + z S ) as roughly found for SDSS quasars

The Search for the “Golden Lens” For a golden lens, T L would be measured extremely well. Its owner would have the power to constrain T C extremely well.

A golden lens? B has been studied extensively (e.g., Koopmans03, Fassnacht06, Suyu09) Koopmans03 found H 0 = 75 ± 6 km/s/Mpc and claimed the systematic errors were <~5% Suyu09 find 6% uncertainty statistical + systematic

Quads have shorter time delays (from simulations performed 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  T C from future experiments

Quality vs. Quantity

OMEGA Mission Concept Moustakas 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  T C from future experiments

Cosmological constraints from LSST time delays assuming a flat universe, constant w, and a Planck prior: h ≈ 0.7 ± (1%)  de ≈ 0.7 ± w ≈ -1 ± 0.026

Comparison to other “Stage IV” experiments Expected constraints for future WL / SN / CL / BAO experiments provided by the Dark Energy Task Force encoded in Fisher matrices in their DETFast software There’s an app for that! Fisher matrix “Quick-start guide” and software arXiv: (online this morning!) also see DETFast, Fisher4Cast

Comparison to other “Stage IV” experiments Expected constraints for future WL / SN / CL / BAO experiments provided by the Dark Energy Task Force encoded in Fisher matrices in their DETFast software Again, assuming:Again, assuming: –Flat universe –Constant w (can be ≠ -1, but not time-varying) –Planck prior

Comparison to other methods Flat universe Constant w Planck Prior

Comparison to other methods Flat universe Constant w Planck Prior Flat universe Constant w Planck Prior

Comparison to other methods Flat universe Constant w Planck Prior

Now for a general cosmology Curvature allowed (  k ) Time-varying w allowed (w 0, w a ) 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 = 1.67 H FOM = 1.24 (relative to prior)

Dark Energy Task Force “Figure of Merit” (prior)

Pivot redhsift: where w(z) is constrained best HutererTurner0 1

Dark Energy Task Force “Figure of Merit” (prior)

Yes we can obtain cosmological constraints with gravitational lens time delays! LSST time delays from 4,000 lenses should constrain h ≈ 0.7 ± (1%)  de ≈ 0.7 ± w ≈ -1 ± assuming 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.