The future of strong gravitational lensing by galaxy clusters

1. The future of strong gravitational lensing by galaxy clusters

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

3. Mass map resolution improves with density of multiple images

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

5. Wewill no longerneedtoassumelighttraces mass once hundredsofmultipleimages are detected.

6. Cosmological Constraints from Gravitational Lens Time Delays Dan Coe with Leonidas Moustakas Caltech postdoc at JPL Hubble’s constant 70 60 50 40 30 20 10 0 km/s/Mpc

7. 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

8. 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*

9. 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)

10. 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 yieldeda wide range of values for H0resulting from: • Variation in lens properties • Variation in lens models assumed • Both of these issues are now being overcome

11. 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

12. analytic assuming isothermal lens “PixeLens” models minimal assumptions 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

13. 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

14. H0 constrained to 9%from 16 time delay lenses (Oguri07) (Note the wide spreadin h for individual lenseswhen all are assumed to be isothermal.)

15. We can now measure H0 (and more) with time delays because: Two main obstacles are being overcome • Insufficient statistics (Lenses have intrinsic scatter in slope, etc.) • HST Key Project required 40 Cepheids(Freedman01) • Detections of accelerating expansion required 50 & 60 supernovae (Riess98, Perlmutter99) • We have currently only measured reliable time delays for ~16 lenses. Future surveys may yield thousands.

16. We can now measure H0 (and more) with time delays because: Two main obstacles are being overcome • We now believe the average lens is roughly isothermal(e.g., Koopmans09): g’ = 2.085 ± 0.20 (scat.) (However, this offset from g’ = 2 could bias H0 low by 8.5% assuming an isothermal model.)

17. 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

18. TC TL  cosmology lens + enviro DLS DL DS Time delays actually constrain a ratio of angular diameter distances that depend on cosmology (not just H0)

19. Time delays constrain TC, not just H0. The current 8.6% uncertainty on H0is actually an 8.6% uncertainty on TC ! Here we plot dTC= 8.6% for zL, zS = 0.5, 2.0. TC

20. 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). TC

21. 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.

22. Degeneracies are broken significantlyby redshift distributions TC to 0.7%?? LSST redshift distributions can be roughly approximated by Gaussians: zL = 0.5 ± 0.15 zS = 2.0 ± 0.75 (Dobke09)

23. 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)

24. Calculating expectations for dTCfrom future experiments 2. Assume systematics can be controlled well, and statistical uncertainties can be beat down as √N 1. Three main sources of uncertainty: lens models, redshifts, time delay measurements  TC TL lens model redshifts time delays cosmology TL2 + [z]2 + )2 = TC2

25. 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

26. The Search for the “Golden Lens” For a golden lens, TL would be measuredextremely well. Its owner would havethe power to constrainTC extremely well.

27. A golden lens? B1608+656 has been studied extensively (e.g., Koopmans03, Fassnacht06, Suyu09) Koopmans03 foundH0 = 75 ± 6 km/s/Mpc and claimed the systematic errors were <~5% Suyu09 find 6% uncertainty statistical + systematic

28. 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

29. So quads have higher fractional uncertainties

30. Expectations for dTCfrom future experiments

31. Quality vs. Quantity

32. OMEGA Mission ConceptMoustakaset 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

33. Expectations for dTCfrom future experiments

34. 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

35. 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

36. 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

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

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

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

40. Now for a general cosmology • Curvature allowed (Wk) • Time-varying wallowed (w0, wa) • Planck prior • Stage II (near-future) WL+SN+CL prior

41. Comparison to other methods Prior = Planck + Stage II (WL+SN+CL)

42. Comparison to other methods Prior = Planck + Stage II (WL+SN+CL)

43. Comparison to other methods Prior = Planck + Stage II (WL+SN+CL)

44. Comparison to other methods Prior = Planck + Stage II (WL+SN+CL)

45. Time delays are more than just a constraint on H TD FOM = 1.67 H FOM = 1.24 (relative to prior) Prior = Planck + Stage II (WL+SN+CL)

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

47. Pivot redhsift: where w(z) is constrained best HutererTurner01

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

49. 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.