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: 1203.2758, 1303.6564

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?

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

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

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

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

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

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

What has been learnt so far?

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)

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)

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)

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' = 2.078 ± 0.027 with an intrinsic scatter of 0.16 ± 0.02

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)

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)

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)

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)

The density profile of the Horseshoe Cosmology with Strong Lensing. 19 The density profile of the Horseshoe Dye+ 2010 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

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

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

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

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)

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)

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)

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)

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!

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

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

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

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

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

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

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

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

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

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

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

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?

Cosmology with Strong Lensing. 40

Cosmology with Strong Lensing. 41

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

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

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

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

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

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

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

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?

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

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

Cosmology with Strong Lensing. 52

... 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

Cosmology with Strong Lensing. 54

Cosmology with Strong Lensing. 55

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.

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.

Cosmology with Strong Lensing. 58

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

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

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