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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. - PowerPoint PPT Presentation
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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.