1. Dark Matter in Galaxies using Einstein Rings Brendon J. Brewer School of Physics, The University of Sydney Supervisor: A/Prof Geraint F. Lewis

2. Gravitational Lens Inversion Use gravitational lens as a “natural telescope” and simultaneously measure total projected density profile ER 0047-2808 (source at redshift 3.6)J1131

3. Lensing Basics

4. Elliptical Lens Models I use a pseudo- isothermal elliptical potential. Realistic enough for single galaxy lenses Five Parameters: b, q, (x c, y c ),  Can have external shear:  

5. Pixellated Sources Note: A nonparametric model is one with a lot of parameters.

6. Problems with Least Squares Usually leads to negative pixels A non-unique solution is possible, especially if we try to use a lot of pixels Get spiky solutions due to PSF Constrained (nonnegative) least squares also has problems. Bayesian interpretation  it is a bad prior. The sky is dark!

7. Our Prior for the Source Multiscale Monkey Prior ≈ John Skilling’s “Massive Inference” prior

10. Least Squares Source Reconstruction (Dye and Warren)

11. Nonparametric Source Reconstruction Summary Achieved higher resolution This was only possible because the prior was actually chosen as a model of prior knowledge Also get tight constraints on lens parameters (no degeneracies) for the PIEP model

12. Can we infer the lens from from QSO images alone? Claeskens et al, 2006

13. What constraints can we get from lensed QSOs? Explore space of possible lens parameter values that lens the QSO images back to within ~1 milliarcsecond Take into account astrometric uncertainties Only weak information from flux ratios (microlensing, dust)

14. Marginals for Lens Parameters given QSO data only

15. Extended images break the lens model degeneracies

16. Why?

17. PixeLens, LensEnt, etc… Pixellated mass model allows more freedom Image positions provide linear constraints on mass pixels Very underdetermined linear system, solve by exploring space of possibilities May overestimate masses when we extend to uncertain astrometry

18. An Intermediate Way Build up mass models from sets of smooth basis functions. PIEPs, SPEMDs, NFWs, … Has been done by Phil Marshall for weak lensing Good but computationally challenging. The next step?

19. Trends in Observed Lenses Projected total mass profiles are almost all close to spherical (q of potential > 0.9) but rotated wrt light profile Total masses within an Einstein Ring are well constrained. Core not constrained without detection of faint central images Attempts to measure local properties such as inner slope have all used parametric models. This needs to change.