Dave Goldberg GLCW8 The Ohio State University June 2, 2007 Students: Sanghamitra Deb Vede Ramdass Where is the Information in Cluster Lenses?

There has been a great deal of discussion recently about how “Strong+Weak” nonparametric mass reconstructions can be performed on clusters. The “Bullet Cluster,” 1E , Bradac et al. (2006) astro-ph/

Current S+W techniques use two pieces of information: 1)The “Weak Part”    1 2 Convergence (magnification) Shear

2) The “strong part”:

Guess a potential field {   n-1) } on a coarse gridscale Compute {  (n-1) } Minimize   for: Typically, a weak prior is computed... Iteratively refine the grid scale

ACS Image of A1689 From Leonard et al ( astro-ph/ ) Here’s what the weak part looks like...

The weak is then generally used as a prior for the strong...  A B Lens (Just in case you forgot what a strong lens system looks like. Okay, so it’s a bit out of focus.) But the background source for both images is the same!

To get to the central question: Where is the information? As we can see, it’s on two different scales.

The weak noise is based on the intrinsic variance of source ellipticities: So to get S/N > 1, we’ll want 10’s of sources per gridcell. The weak and the strong operate on very different scales.

Q: How can we reconcile the different scales for strong and weak without introducing ad hoc regularization? A: Don’t use grids! How about Smoothed Particle Hydrodynamics (SPH)?

On the strong lensing side, we use: 0) Position Differences (2 constraints/pair) But we don’t use: 1)Flux ratios (1 constraint/pair) 2)Ellipticity Differences (2 constraints/pair) Why not? Naively, we might expect to increase our S/N by:

Magnification is a highly nonlinear function of the underlying fields:

We could construct a nearly linear flux estimator which doesn’t blow up:

We also want to estimate the ellipticity difference. In principle, since both images are lensed from the same source, the image should be less susceptible to the intrinsic ellipticity. However, we still have a parity problem.

If one image is weak and the other is strong (negative parity) then we need a relation along the lines of: with an error proportional to the square of the intrinsic ellipticity! But we still have a problem. We don’t know the parity in the first place.

We propose simulated annealing! Since the number of strong sources are relatively small, convergence should be very fast!

Conclusions & Summary Strong+Weak cluster reconstructions have produced some remarkable results, but... They currently do not account for widely differing scales of information They do not include flux ratios or ellipticity ratios They don’t explicitly explore into the strong regime This being a workshop, we figured some of you folks might have some thoughts about this approach.