1. Thomas Collett Institute of Astronomy, Cambridge
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett Institute of Astronomy, Cambridge
With: Matt Auger, Vasily Belokurov, Phil Marshall and others ArXiv: , ArXiv: and unpublished work

2. Strong lensing is an optical bench
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Strong lensing is an optical bench

3. Strong lensing is an optical bench
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Strong lensing is an optical bench
Lens Source

4. Strong lensing is an optical bench
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Strong lensing is an optical bench
Lens Source

5. Strong lensing is an optical bench
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Strong lensing is an optical bench
Lens Source

6. Strong lensing is an optical bench
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Strong lensing is an optical bench
Lens Source

7. Strong lensing is an optical bench
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Strong lensing is an optical bench
Lens Source

8. Strong lensing is an optical bench
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Strong lensing is an optical bench
Lens Source
Image configurations depend on the distances

9. Strong lensing is an optical bench
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Strong lensing is an optical bench
Lens Source

10. Strong lensing is an optical bench
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Strong lensing is an optical bench
Lens Source

11. Strong lensing is an optical bench
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Strong lensing is an optical bench
Lens Source

12. Strong lensing is an optical bench
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Strong lensing is an optical bench
Lens Source

13. Strong lensing is an optical bench
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Strong lensing is an optical bench
Lens Source
Image configurations depend on the lensing mass.

14. Uncertainty in the mass model makes cosmography hard
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Uncertainty in the mass model makes cosmography hard
Hubble constant
+ can add a term for spatial curvature
Dark Energy
Equation of State
Matter Density

15. Different path lengths Different Shapiro delays
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Time Delays:
Different images:
Different path lengths
Different Shapiro delays
Δt ∝ DΔt = (1+ zl) (Dl Ds) / Dls
Need to get mass model right!
(Suyu, Collett+ 2013)

16. Different path lengths Different Shapiro delays
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Time Delays:
Different images:
Different path lengths
Different Shapiro delays
Δt ∝ DΔt = (1+ zl) (Dl Ds) / Dls
Need to get mass model right!
(Suyu+ 2013)
(Suyu+ 2013)

17. What is double source plane strong lensing?
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
What is double source plane strong lensing?

18. What is double source plane strong lensing?
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
What is double source plane strong lensing?
A gravitational lens system with two background sources, each at a different redshift.

19. What is double source plane strong lensing?
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
What is double source plane strong lensing?
A gravitational lens system with two background sources, each at a different redshift.
SLACS J

20. What is double source plane strong lensing?
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
What is double source plane strong lensing?
A gravitational lens system with two background sources, each at a different redshift.
Lens Galaxy
SLACS J

21. What is double source plane strong lensing?
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
What is double source plane strong lensing?
A gravitational lens system with two background sources, each at a different redshift.
Images of the intermediate source
SLACS J

22. What is double source plane strong lensing?
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
What is double source plane strong lensing?
A gravitational lens system with two background sources, each at a different redshift.
Images of the background source
SLACS J

23. The observable: The Ratio of Einstein Radii.
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
The observable:
The Ratio of Einstein Radii.

24. The observable: The Ratio of Einstein Radii.
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
The observable:
The Ratio of Einstein Radii.

25. The observable: The Ratio of Einstein Radii.
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
The observable:
The Ratio of Einstein Radii.

26. No dependence on the Hubble constant!
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
The observable:
The Ratio of Einstein Radii.
No dependence on the Hubble constant!

27. Jullo et al. (2010) Results: ΩM= 0.25 ± 0.05, wDE = −0.97 ± 0.07
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Jullo et al. (2010) Results:
ΩM= 0.25 ± 0.05, wDE = −0.97 ± 0.07
(Abel WMAP5 + X-ray cluster constraints)
The mass is very complicated
Hard to control systematics

28. BAD GOOD Jullo et al. (2010) Results:
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Jullo et al. (2010) Results:
BAD
GOOD

29. Constraining Cosmology.
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Constraining Cosmology.
Preliminary models of J0946 suggest statistical uncertainty of ~1% on the ratio of Einstein Radii.
Uncertainty is dominated by the lens' mass density slope

30. Constraining Cosmology.
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Constraining Cosmology.
zl = 0.35
zs1 = 0.6
zs2 = 1.5
Collett+ 2012

31. Constraining Cosmology.
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Constraining Cosmology.
zl = 0.35
zs1 = 0.6
zs2 = 1.5
WMAP
Collett+ 2012

32. Constraining Cosmology.
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Constraining Cosmology.
zl = 0.35
zs1 = 0.6
zs2 = 1.5
WMAP
Combination
Collett+ 2012

33. Finding more systems Piggy-back on deep, large area surveys
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Finding more systems
Piggy-back on deep, large area surveys
Target known lenses
Target the most massive galaxies

34. Constraints with 6 systems.
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Constraints with 6 systems.
Collett+ 2012
Forecast the distribution of lens and source redshifts
WMAP+6 systems is ~2.5 times better than WMAP+1.
WMAP+
1 system wDE = −0.99 ± 0.27
6 systems wDE = −1.01 ± 0.11

35. Beyond wCDM Evolving models of dark energy:
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Beyond wCDM
Collett+ 2012
Evolving models of dark energy:
Olive: 6 double source plane lenses
Grey: Planck (Forecast, including polarization and weak lensing constraints)
Black: combination

36. Beyond wCDM Evolving models of dark energy:
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Beyond wCDM
Collett+ 2012
Evolving models of dark energy:
Olive: 6 double source plane lenses
Grey: Planck (Forecast, including polarization and weak lensing constraints)
Black: combination
FoM = 6.17π/A95 = 14.2
WMAP plus Union SNe → 15 (Mortonson+2010)

37. Euclid Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Euclid

38. Expect at least hundreds! (maybe even thousands) Euclid
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Euclid
Expect at least
hundreds!
(maybe even
thousands)
~105 galaxy scale strong lenses (based on COSMOS )
1 in galaxy scale lenses will be doubles (Gavazzi+ 2008)

39. Euclid Black: 6 lenses, Ωk = 0 FoM = 14.2 Red: 100 lenses, Ωk ≠ 0
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Euclid
Black: 6 lenses, Ωk = 0
FoM = 14.2
Red: 100 lenses, Ωk ≠ 0
FoM = 38
Collett+ in prep.

40. Systematics A.K.A. Learning cool stuff about mass in the universe
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Systematics
A.K.A. Learning cool stuff about mass in the universe

41. Systematics Mass between the two rings Mass of the intermediate source
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Systematics
Mass between the two rings
Mass of the
intermediate source
Mass along the line of sight

42. Perturbations by the intermediate source
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Perturbations by the intermediate source
If completely neglected:
LMC: ~1% systematic error on η
MW: ~10% systematic error on η
Effect is detectable: include in the lens model.
(Sonnenfeld+ 2012, Fixed cosmology, photometric zs2)

43. Strong constraints on the mass profile γTOT = 1.98 ± 0.02 ± 0.01 OR
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Profile of the Lens
Strong constraints on the mass profile
γTOT = 1.98 ± 0.02 ± 0.01 OR
γDM = 1.7 ± 0.2
Using dynamics and both Einstein radii
(Sonnenfeld+ 2012)

44. The Mass Sheet Degeneracy
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
The Mass Sheet Degeneracy
Overdense dark matter halos cause convergence of rays

45. The Mass Sheet Degeneracy
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
The Mass Sheet Degeneracy
Overdense dark matter halos cause convergence of rays
Underdense voids cause divergence of rays

46. κ = (4πGDlsDl/c2Ds) Σ The Mass Sheet Degeneracy
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
The Mass Sheet Degeneracy
Effect depends on the distance of the source – slightly perturbs the inferred cosmology
Convergence proportional to surface mass density
κ = (4πGDlsDl/c2Ds) Σ

47. EVERYTHING IS WEAKLY LENSED
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
The Mass Sheet Degeneracy
Magnification-Absolute magnitude degeneracy
Directly relevant to
High-z SNe
GRBs
High redshift luminosity functions
EVERYTHING IS WEAKLY LENSED

48. ? ? ? ? The Mass Sheet Degeneracy 0.01 change in κ approximately:
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
The Mass Sheet Degeneracy ? ? ? ?
0.01 change in κ approximately:
0.5% in ratio of Einstein radii, 1% in time-delay distance,
2% in magnification of an unlensed source

49. ? ? ? ? The Mass Sheet Degeneracy 0.01 change in κ approximately:
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
The Mass Sheet Degeneracy ? ? ? ?
Hilbert+ 2010
0.01 change in κ approximately:
0.5% in ratio of Einstein radii, 1% in time-delay distance,
2% in magnification of an unlensed source

50. The Mass Sheet Degeneracy
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
The Mass Sheet Degeneracy
45 arcsec
0.01 change in κ approximately:
0.5% in ratio of Einstein radii, 1% in time-delay distance,
2% in magnification of an unlensed source

51. The Mass Sheet Degeneracy
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
The Mass Sheet Degeneracy
45 arcsec
Greene, Collett+ 2013
Greene, Collett+ 2013
0.01 change in κ approximately:
0.5% in ratio of Einstein radii, 1% in time-delay distance,
2% in magnification of an unlensed source

52. The Mass Sheet Degeneracy
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
The Mass Sheet Degeneracy
45 arcsec
Greene, Collett+ 2013
Greene, Collett+ 2013
0.01 change in κ approximately:
0.5% in ratio of Einstein radii, 1% in time-delay distance,
2% in magnification of an unlensed source

53. The Mass Sheet Degeneracy
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
The Mass Sheet Degeneracy
3 arcmin
0.01 change in κ approximately:
0.5% in ratio of Einstein radii, 1% in time-delay distance,
2% in magnification of an unlensed source

54. The Mass Sheet Degeneracy
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
The Mass Sheet Degeneracy
3 arcmin
0.01 change in κ approximately:
0.5% in ratio of Einstein radii, 1% in time-delay distance,
2% in magnification of an unlensed source

55. The Mass Sheet Degeneracy
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
The Mass Sheet Degeneracy
Collett+ 2013
0.01 precision on κ.
Unbiased*
Width of
ensemble P(κext)
3 arcmin
0.01 change in κ approximately:
0.5% in ratio of Einstein radii, 1% in time-delay distance,
2% in magnification of an unlensed source

56. I'm working hard to make sure the systematics are under control!
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Summary
Strong lensing provides powerful complementary constraints on cosmological parameters
I'm working hard to make sure the systematics are under control!

57. Thanks to for sponsoring my attendance
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Thanks to for sponsoring my attendance

58. Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Spare Slides

59. What about the assumption of flatness?
Constraining Dark Energy with Double Source Plane Strong Lenses
Constraining Dark Energy with Double Source Plane Strong Lenses
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Thomas Collett 59 59 59
What about the assumption of flatness?
Ωk ≠ 0
Ωk ≡ 0

60. What if we can't measure the ratio of Einstein radii to 1%?
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
What if we can't measure the ratio of Einstein radii to 1%?
1. Compound lensing – the intermediate source has mass
2. The lens is an astrophysical object – they aren't perfectly isothermal or perfectly spherical

61. Cosmology with a population of systems.
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Cosmology with a population of systems.
SLACS:
1.1mm, S > 1 mJy → ~1.5 double source plane systems (1.5 in 78)
1.1mm, S > 0.3 mJy → ~3 double source plane systems (3 in 78)
But can be more efficient if you focus only on the most massive lenses.

62. Constraints with 6 systems.
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Thomas Collett
Constraints with 6 systems.
Pick the set of systems that provided the median constraints on w.
WMAP+6 systems is ~2.5 times better than WMAP+1.
WMAP+
1 system wDE = −0.99 ± 0.27
6 systems wDE = −1.01 ± 0.11
WMAP+BAO+Time Delay+
6 systems wDE = −1.04 ± 0.09

63. Constraining Dark Energy with Double Source Plane Strong Lenses63 63 63
Planck+6

64. ρ=ρ0r-γ' Probing the mass profile of galaxies
Cosmology with Strong Lensing. 64
Probing the mass profile of galaxies
Combine Einstein Radius with stellar dynamics
Fit a power-law:
ρ=ρ0r-γ'
Lenses are approximately isothermal (γ'=2).
(Koopmans+ 2006)
(Auger+ 2010)
γ' = ± with an intrinsic scatter of 0.16 ± 0.02