1. Cosmology with Strong Lensing.
Obstacles and Solutions
Thomas Collett
Based on work with Matt Auger, Vasily Belokurov, Phil Marshall, Alex Hall, Stefan Hilbert, Sherry Suyu, Zach Greene, Tommaso Treu, Chris Fassnacht, Léon Koopmans, Maruša Bradač and Roger Blandford. arXiv: ,

2. What can strong lensing teach us?
Cosmology with Strong Lensing. 2
What can strong lensing teach us?
Why does the arcs form where they do?

3. What can strong lensing teach us?
Cosmology with Strong Lensing. 3
What can strong lensing teach us?
Why does the arcs form where they do?
Because of the:
Lens mass
Source and lens distances
Unlensed source position

4. What can strong lensing teach us?
Cosmology with Strong Lensing. 4
What can strong lensing teach us?
Why does the arcs form where they do?
Because of the:
Lens mass
Source and lens distances
Unlensed source position

5. What can strong lensing teach us?
Cosmology with Strong Lensing. 5
What can strong lensing teach us?
Why does the arcs form where they do?
Because of the:
Lens mass
Source and lens distances
Unlensed source position

6. What do we measure? Einstein radius Easy, very Robust.
Cosmology with Strong Lensing. 6
What do we measure?
Einstein radius
Easy, very Robust.

7. What do we measure? Einstein radius Easy, very Robust.
Cosmology with Strong Lensing. 7
What do we measure?
Einstein radius
Easy, very Robust.
Lens Ellipticity

8. What do we measure? Einstein radius Easy, very Robust.
Cosmology with Strong Lensing. 8
What do we measure?
Einstein radius
Easy, very Robust.
Lens Ellipticity
Local Density Slope
Harder to measure

10. What has been
learnt so far?

11. The Ellipticity of Mass and Light
Cosmology with Strong Lensing. 11
The Ellipticity of Mass and Light
Mass and light are well aligned in SLACS
(Koopmans+ 2006)

12. The Ellipticity of Mass and Light
Cosmology with Strong Lensing. 12
The Ellipticity of Mass and Light
Mass and light are well aligned in SLACS
(Koopmans+ 2006)
Not as well aligned in SL2S
(Gavazzi+ 2012)

13. ρ=ρ0r-γ' Probing the mass profile of galaxies
Cosmology with Strong Lensing. 13
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)

14. ρ=ρ0r-γ' Probing the mass profile of galaxies
Cosmology with Strong Lensing. 14
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

15. Multiple Source Planes: Strong constraints on the mass profile
Cosmology with Strong Lensing. 15
Multiple Source Planes:
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)

16. Multiple Source Planes: Strong constraints on the mass profile
Cosmology with Strong Lensing. 16
Multiple Source Planes:
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)

17. Multiple Source Planes: Strong constraints on the mass profile
Cosmology with Strong Lensing. 17
Multiple Source Planes:
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)

18. Multiple Source Planes: Strong constraints on the mass profile
Cosmology with Strong Lensing. 18
Multiple Source Planes:
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
Vegetti+ 2010
γTOT = 2.2
(Sonnenfeld+ 2012)

19. The density profile of the Horseshoe
Cosmology with Strong Lensing. 19
The density profile of the Horseshoe
Dye found
γ = 1.96 ± 0.02
Spinello+ 2011
γ = 1.72 ± 0.06
Something (or somebody) is wrong
Lenses are not perfect power-laws
It's easy to introduce systematics by using an inflexible model

20. Problem: Power-laws aren't the perfect model
Cosmology with Strong Lensing. 20
Problem: Power-laws aren't the perfect model
Newman+ 2013

21. What about probing cosmological distances?
Cosmology with Strong Lensing. 21
What about probing cosmological distances?
Uncertainty in the mass model makes cosmography hard

22. What about probing cosmological distances?
Cosmology with Strong Lensing. 22
What about probing cosmological distances?
Uncertainty in the mass model makes cosmography hard
Hubble constant
+ can add a term for spatial curvature
Matter Density
Dark Energy
Equation of State

23. Different path lengths Different Shapiro delays
Cosmology with Strong Lensing. 23
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)

24. Different path lengths Different Shapiro delays
Cosmology with Strong Lensing. 24
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)

25. Multiple Source Planes: Ratio of Einstein Radii:
Cosmology with Strong Lensing. 25
Multiple Source Planes:
Ratio of Einstein Radii:
ηSIS=(Dls1 Ds2) / (Dls2Ds1)
(Sonnenfeld+ 2012)

26. Multiple Source Planes: Ratio of Einstein Radii:
Cosmology with Strong Lensing. 26
Multiple Source Planes:
Ratio of Einstein Radii:
ηSIS=(Dls1 Ds2) / (Dls2Ds1)
(Sonnenfeld+ 2012)

27. Weak lensing by matter along the line of sight
Cosmology with Strong Lensing. 27
Weak lensing by matter along the line of sight
Isn't as complicated as it looks!

28. The Mass Sheet Degeneracy
Cosmology with Strong Lensing. 28
The Mass Sheet Degeneracy
Overdense dark matter halos cause convergence of rays

29. The Mass Sheet Degeneracy
Cosmology with Strong Lensing. 29
The Mass Sheet Degeneracy
Overdense dark matter halos cause convergence of rays
Underdense voids cause divergence of rays

30. κ = (4πGDlsDl/c2Ds) Σ The Mass Sheet Degeneracy Wrong lens mass
Cosmology with Strong Lensing. 30
The Mass Sheet Degeneracy
Wrong lens mass
Wrong lens slope
Wrong time delay distance
Convergence proportional to surface mass density
κ = (4πGDlsDl/c2Ds) Σ

31. Magnification-Absolute magnitude degeneracy
Cosmology with Strong Lensing. 31
The Mass Sheet Degeneracy
Magnification-Absolute magnitude degeneracy
Directly relevant to
High-z SNe
GRBs
High redshift galaxies

32. Ray tracing through simulations
Cosmology with Strong Lensing. 32
Ray tracing through simulations

33. Estimating the Global P(κext)
Cosmology with Strong Lensing. 33
Estimating the Global P(κext)
Hilbert+ 2010

34. Estimating individual P(κext) Estimating individual P(κext)
Cosmology with Strong Lensing. 34
Estimating individual P(κext)
Estimating individual P(κext)
(Suyu+ 2010)

35. Estimating individual P(κext) Estimating individual P(κext)
(Suyu+ 2010)

36. Estimating individual P(κext)
Cosmology with Strong Lensing. 36
Estimating individual P(κext)
(Suyu+ 2010)

37. Estimating individual P(κext)
Cosmology with Strong Lensing. 37
Estimating individual P(κext)
(Suyu+ 2010, Greene+ 2013)

38. Estimating individual P(κext)
Cosmology with Strong Lensing. 38
Estimating individual P(κext)
(Greene+ 2013)

39. Why not try to reconstruct the light cone?
Cosmology with Strong Lensing. 39
Why not try to reconstruct the light cone?
Can a simple halo prescription capture the convergence?

40. Cosmology with Strong Lensing.40

41. Cosmology with Strong Lensing.41

42. How well does the simple model do?
Cosmology with Strong Lensing. 42
How well does the simple model do?

43. Where is the convergence coming from?
Cosmology with Strong Lensing. 43
Where is the convergence coming from?
zs =1.4

44. Inferring dark mass from visible mass
Cosmology with Strong Lensing. 44
Inferring dark mass from visible mass

45. Width of the individual P(κext)
Cosmology with Strong Lensing. 45
Width of the individual P(κext)
Width of ensemble P(κext)

46. Width of the individual P(κext)
Cosmology with Strong Lensing. 46
Width of the individual P(κext)
High kappa lines of sight
are harder to reconstruct

47. What if we choose a subset of sightlines?
Cosmology with Strong Lensing. 47
What if we choose a subset of sightlines?

48. What if we choose a subset of sightlines?
Cosmology with Strong Lensing. 48
What if we choose a subset of sightlines?

49. What if the M*-Mh relation in the calibration set is wrong?
Cosmology with Strong Lensing. 49
What if the M*-Mh relation in the calibration set is wrong?

50. Constraining the Mass sheet degeneracy
Cosmology with Strong Lensing. 50
Constraining the Mass sheet degeneracy
We can estimate the convergence along any line of sight
Can use the Millennium Simulation as a calibration
Need to be very careful that the simulation is like the real universe
Choosing a subset of lines of sight can induce biases

51. Constraining the slope of the lens density profile
Cosmology with Strong Lensing. 51
Constraining the slope of the lens density profile
Matt has created some mock lenses using a realistic lens model.
I'm analysing them blindly, using a power-law lens model

52. Cosmology with Strong Lensing.52

53. ... giving a broken lens model
Cosmology with Strong Lensing. 53
If the source model is too limited, the lens model adjusts to try and compensate...
... giving a broken lens model

54. Cosmology with Strong Lensing.54

55. Cosmology with Strong Lensing.55

56. Cosmology with Strong Lensing.56
Preliminary Results
Mock ground imaging
Sum of 2,3,4,5 Sersic
Components for source
The recovered lens parameters depends on the allowed source complexity
The statistical errors don't seen to represent the real uncertainties.

57. Cosmology with Strong Lensing.57
Preliminary Results
Mock ground imaging
Sum of 2,3,4,5 Sersic
Components for source
The recovered lens parameters depends on the allowed source complexity
The statistical errors don't seen to represent the real uncertainties.

58. Cosmology with Strong Lensing.58

59. Cosmology with Strong Lensing.59
Pixelated Sources
(Suyu+ 2013)

60. Constraining the lens slope
Cosmology with Strong Lensing. 60
Constraining the lens slope
Need to be careful with choice of source model
If the source model is too simple lens science will be biased
If the lens model is too simple source science will be biased
Work in progress

61. Summary Strong Lensing is a powerful cosmological probe
Cosmology with Strong Lensing. 61
Summary
Strong Lensing is a powerful cosmological probe
High precision measurements mean we now have to worry about systematics that were unimportant previously
Constraining the mass sheet degeneracy is possible, but needs careful use of simulations
Constraining the lens density slope requires carefully chosen source models