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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.

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Dark matter in galaxies using einstein rings

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
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
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
Pixellated Sources

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


Problems with least squares
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
Our Prior for the Source

Multiscale Monkey Prior

≈ John Skilling’s “Massive Inference” prior



Nonparametric source reconstruction summary
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



What constraints can we get from lensed qsos
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
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
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
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.