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### Dark Matter in Galaxies using Einstein Rings

Brendon J. Brewer

School of Physics, The University of Sydney

Supervisor: A/Prof Geraint F. Lewis

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

Elliptical Lens Models

- I use a pseudo-isothermal elliptical potential. Realistic enough for single galaxy lenses
- Five Parameters:

b, q, (xc, yc), q

- Can have external shear: g, qg

Pixellated Sources

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

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!

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

Can we infer the lens from from QSO images alone?

Claeskens et al, 2006

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)

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

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?

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.

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