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With: Matt Auger, Vasily Belokurov, Phil Marshall and others ArXiv: , ArXiv: and unpublished work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. 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?

3. 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.

4. 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

5. 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

6. 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

7. 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

8. Two important quantities:
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Two important quantities:
The Einstein Radius:
Angular diameter distances (flat universe, w constant):
Image configurations depend on the underlying cosmology.

9. 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.

10. 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.

11. 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.

12. 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!

13. 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

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

15. 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
Let's assume some redshifts, and a 1% uncertainty on η.

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

17. 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

18. 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

19. 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 the most massive galaxies

20. Constraints with 6 systems.
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Constraints with 6 systems.
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

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

22. Beyond wCDM Evolving models of dark energy:
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Beyond wCDM
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)

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

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

25. ~105 galaxy scale strong lenses (based on COSMOS )
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
~105 galaxy scale strong lenses (based on COSMOS )
1 in galaxy scale lenses will be doubles (Gavazzi+ 2008)
Expect at least hundreds! (maybe even thousands)

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

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

28. (Other cool science we can do with double source plane lenses)
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Systematics
(Other cool science we can do with double source plane lenses)

29. 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

30. 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

31. Systematics If ignored 1-10% systematic error, detectable effect
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Systematics
If ignored 1-10% systematic
error, detectable effect
→ Include in model.
Sonnenfeld+ 2012
Mass between the two rings
Mass of the
intermediate source
Mass along the line of sight

32. Systematics Fit more complicated mass models
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Systematics
Fit more complicated mass models
Suyu+2013, Sonnenfeld+ 2012
Mass between the two rings
Mass of the
intermediate source
Mass along the line of sight

33. 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
Undetectable in the lens model. Less important than for time-delays.
Have to infer mass along the line of sight by prescribing dark matter halos to galaxies.
Collett % precision on η achievable.
Talk to me if you're interested in individual objects at z>1

34. Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Summary
Double source plane lenses provide another way to probe dark energy.
A simple geometrical probe, with independent systematics and no h dependence
A handful of double source plane systems have the potential to provide 10 percent constraints on w
Hundreds of double source plane lenses will be discovered in the near future → FoM ~ 40+
We can control systematics with flexible models and precise reconstructions of the line of sight

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

36. Perturbations by the intermediate source
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Perturbations by the intermediate source
Infer the mass of high redshift galaxies
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)

37. Density profile of massive galaxies:
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Density profile of massive galaxies:
Probe of Baryonic feedback
This uncertainty dominates the statistical error.
Effect of deviations from power-law seem to be small
(Sonnenfeld+ 2012, Fixed cosmology, photometric zs2)

38. Perturbations by structures along the line of sight
Constraining Dark Energy with Double Source Plane Strong Lenses
Thomas Collett
Perturbations by structures along the line of sight
Part of the effect cancels; less significant than for time-delay cosmography
Infer mass along the line of sight: Collett+ 2013
Width of
ensemble P(κext)
1% precision

39. 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 39 39 39
What about the assumption of flatness?
Ωk ≠ 0
Ωk ≡ 0

40. 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

41. 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.

42. 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

43. Constraining Dark Energy with Double Source Plane Strong Lenses43 43 43
Planck+6