One of the uncertainties in understanding the lensing results for the MaxBCG cluster sample is the center of mass. We know that some of the time our chosen center, the location of the brightest cluster galaxy, is not at the mass peak or the center of mass. On the other hand, the theoretical predictions for dark matter mass profiles are predicted around the mass peak.
We have put together two alternative centers, both based on finding a peak in smoothed density maps. One is in the number density and the other is in the luminosity weighted number density. It looks like we can flag bad centers when neither of these new centers agrees with the BCG location. Evidence comes from the X--ray concentration and also from lensing. I compared the mass profiles for "good" and "bad" centers at fixed cluster luminosity and found significant differences in the profiles. We still haven't figured out what is the best center, but we can now flag bad ones with some level of confidence.
The variance in the mass measurements we get from lensing are the convolution of many different sources of scatter. There is the scatter in mass at fixed richness, which is what we are interested in. But on top of this is the scatter from measurement noise sigma_err and the intrinsic variance among galaxy shapes for the background sources sigma_SN. These two sources of scatter are well known. But even on top of that is the variance from unknown sources of systematic error. We can guess at what these are, such as variance in the signal calibration as a function of observing conditions.
I looked at the inferred scatter sigma_tot^2 - sigma_err^2 - sigma_SN^2. I found that the residual scatter is much larger than the expected sigma_m^2 based on other measurements, such as X--ray properties and velocity measurements.
Next I want to figure out how to estimate other sources of variance. The goal is to design a measurement that does not also include the variance in mass of the lenses.