Combining Weak and Strong Gravitational Lensing

Transcription

1 Combining Weak and Strong Gravitational Lensing Julian Merten INAF - Osservatorio Astronomico di Bologna Institut fu r Theoretische Astrophysik Zentrum fu r Astronomie Universita t Heidelberg October 27th, 2009 with: Massimo Meneghetti (OA Bologna) Matthias Bartelmann (ITA Heidelberg) Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27th, / 13

2 Gravitational Lensing Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27 th, / 13

3 Gravitational Lensing Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27 th, / 13

4 Combining Weak and Strong Lensing (JM et al. 2009) The lensing potential α 1 = ψ,1 α 2 = ψ,2 γ 1 = 1 2 (ψ,11 ψ,22 ) γ 2 = ψ,12 κ = 1 2 (ψ,11 + ψ,22 ) Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27 th, / 13

5 Combining Weak and Strong Lensing (JM et al. 2009) The lensing potential α 1 = ψ,1 α 2 = ψ,2 γ 1 = 1 2 (ψ,11 ψ,22 ) γ 2 = ψ,12 κ = 1 2 (ψ,11 + ψ,22 ) Maximum-likelihood approach χ 2 (ψ) = χ 2 w(ψ) + χ 2 s(ψ) χ 2 (ψ) ψ! = 0 Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27 th, / 13

6 Combining Weak and Strong Lensing (JM et al. 2009) The lensing potential α 1 = ψ,1 α 2 = ψ,2 γ 1 = 1 2 (ψ,11 ψ,22 ) γ 2 = ψ,12 κ = 1 2 (ψ,11 + ψ,22 ) Maximum-likelihood approach χ 2 (ψ) = χ 2 w(ψ) + χ 2 s(ψ) χ 2 (ψ) ψ! = 0 Non-parametric method χ 2 (ψ k ) ψ l! = 0 Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27 th, / 13

7 Combining Weak and Strong Lensing (JM et al. 2009) The lensing potential α 1 = ψ,1 α 2 = ψ,2 γ 1 = 1 2 (ψ,11 ψ,22 ) γ 2 = ψ,12 κ = 1 2 (ψ,11 + ψ,22 ) Maximum-likelihood approach χ 2 (ψ) = χ 2 w(ψ) + χ 2 s(ψ) χ 2 (ψ) ψ! = 0 Non-parametric method χ 2 (ψ k ) ψ l! = 0 Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27 th, / 13

8 Combining Weak and Strong Lensing (JM et al. 2009) The lensing potential α 1 = ψ,1 α 2 = ψ,2 γ 1 = 1 2 (ψ,11 ψ,22 ) γ 2 = ψ,12 κ = 1 2 (ψ,11 + ψ,22 ) Maximum-likelihood approach χ 2 (ψ) = χ 2 w(ψ) + χ 2 s(ψ) χ 2 (ψ) ψ! = 0 Non-parametric method χ 2 (ψ k )! = 0 ψ l ε = γ 1 κ Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27 th, / 13

9 Combining Weak and Strong Lensing (JM et al. 2009) The lensing potential α 1 = ψ,1 α 2 = ψ,2 γ 1 = 1 2 (ψ,11 ψ,22 ) γ 2 = ψ,12 κ = 1 2 (ψ,11 + ψ,22 ) Maximum-likelihood approach χ 2 (ψ) = χ 2 w(ψ) + χ 2 s(ψ) χ 2 (ψ) ψ! = 0 Non-parametric method χ 2 (ψ k )! = 0 ψ l ε = γ 1 κ (1 κ) 2 (γ) 2 crit = 0 Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27 th, / 13

10 A Matter of Scale: weak lensing χ2w (ψ) = X i,j Z (z)γ(ψ) ε 1 Z (z)κ(ψ) Julian Merten (ITA HD / OA BO) Cij 1 i Cluster Mass Reconstruction ε Z (z)γ(ψ) 1 Z (z)κ(ψ) j October 27th, / 13

11 A Matter of Scale: strong lensing ((1 Z(z)κ(ψ)) 2 (Z(z)γ(ψ)) 2) 2 χ 2 s (ψ) = i σ 2 i i Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27 th, / 13

12 Making it all work: Numerics α, γ, κ, F and G can be expressed by derivatives of ψ via finite differences. A specific finite difference can be written as a matrix multiplication κ i = K ij ψ j. The minimisation of the χ 2 -function can be translated into a linear system of equations. Furthermore the code uses a 2-level iteration scheme. Runtime: 2 mins - 6 hrs. Implementation Parallel C++ code medium sized lines Uses GSL, LAPACK, ATLAS, MPI Possibly, GPU implementation. More on that soon. Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27 th, / 13

13 The Reconstruction Method In our reconstruction method we try to combine the advantages of both lensing regimes into a joint method: Fully non-parametric, adaptive grid method (no initial model necessary). Reconstruction quantity is the lensing potential ψ. Maximum-likelihood method. We are searching for that lensing potential which is most likely to have caused the observations: Input data are: χ 2 (ψ) = χ 2 w (ψ) + χ 2 s (ψ) 1 Ellipticity catalogue 2 Arc positions 3 Flexion catalogue (come tomorrow if you are interested in that) 4 Multiple image positions (Bradač et al ) Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27 th, / 13

14 The Reconstruction Method In our reconstruction method we try to combine the advantages of both lensing regimes into a joint method: Fully non-parametric, adaptive grid method (no initial model necessary). Reconstruction quantity is the lensing potential ψ. Maximum-likelihood method. We are searching for that lensing potential which is most likely to have caused the observations: Input data are: χ 2 (ψ) = χ 2 w (ψ) + χ 2 s (ψ) 1 Ellipticity catalogue 2 Arc positions 3 Flexion catalogue (come tomorrow if you are interested in that) 4 Multiple image positions (Bradač et al ) Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27 th, / 13

15 The Reconstruction Method In our reconstruction method we try to combine the advantages of both lensing regimes into a joint method: Fully non-parametric, adaptive grid method (no initial model necessary). Reconstruction quantity is the lensing potential ψ. Maximum-likelihood method. We are searching for that lensing potential which is most likely to have caused the observations: Input data are: χ 2 (ψ) = χ 2 w (ψ) + χ 2 s (ψ) 1 Ellipticity catalogue 2 Arc positions 3 Flexion catalogue (come tomorrow if you are interested in that) 4 Multiple image positions (Bradač et al ) Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27 th, / 13

16 The Reconstruction Method In our reconstruction method we try to combine the advantages of both lensing regimes into a joint method: Fully non-parametric, adaptive grid method (no initial model necessary). Reconstruction quantity is the lensing potential ψ. Maximum-likelihood method. We are searching for that lensing potential which is most likely to have caused the observations: Input data are: χ 2 (ψ) = χ 2 w (ψ) + χ 2 s (ψ) 1 Ellipticity catalogue 2 Arc positions 3 Flexion catalogue (come tomorrow if you are interested in that) 4 Multiple image positions (Bradač et al ) Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27 th, / 13

17 The Reconstruction Method In our reconstruction method we try to combine the advantages of both lensing regimes into a joint method: Fully non-parametric, adaptive grid method (no initial model necessary). Reconstruction quantity is the lensing potential ψ. Maximum-likelihood method. We are searching for that lensing potential which is most likely to have caused the observations: Input data are: χ 2 (ψ) = χ 2 w (ψ) + χ 2 s (ψ) 1 Ellipticity catalogue 2 Arc positions 3 Flexion catalogue (come tomorrow if you are interested in that) 4 Multiple image positions (Bradač et al ) Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27 th, / 13

18 Results: Simulations (Meneghetti, Rasia, JM et al. 2009) Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27 th, / 13

19 Results: Simulations (Meneghetti, Rasia, JM et al. 2009) Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27 th, / 13

20 Results: MS2137 (JM et al. 2009) Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27 th, / 13

21 Results: COSMOS Julian Merten (ITA HD / OA BO) (preliminary, with Matteo Maturi) Cluster Mass Reconstruction October 27th, / 13

22 Results: SUBARU Cluster sample (JM et al. in prep.) with Masamune Oguri, Keiichi Umetsu and Tom Broadhurst Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27 th, / 13

23 Results: SUBARU Cluster sample (JM et al. in prep.) with Masamune Oguri, Keiichi Umetsu and Tom Broadhurst Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27 th, / 13

24 Results: SUBARU Cluster sample (JM et al. in prep.) with Masamune Oguri, Keiichi Umetsu and Tom Broadhurst Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27th, / 13

25 Thank You Julian Merten (ITA HD / OA BO) Cluster Mass Reconstruction October 27 th, / 13