Dark Matter in Galaxies using Einstein Rings

Brendon J. BrewerSchool 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

Lensing Basics

Elliptical Lens Models

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

Five Parameters:

b, q, (xc, yc),

Can have external shear:

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!

Our Prior for the Source

Multiscale Monkey Prior

≈ John Skilling’s “Massive Inference” prior

Least Squares Source Reconstruction (Dye and Warren)

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)

Marginals for Lens Parameters given QSO data only

Extended images break the lens model degeneracies

Why?

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.