measuring the undetectable

Brewer, Foreman-Mackey, and I have been working hard on sampling all week, so we took a break today to discuss the astrophysics of the problem. We want to measure the number–flux relation (or luminosity function) of stars in a cluster, below where confusion becomes a problem for identifying or photometering stars. There is an old literature from radio astronomy in the sixties and seventies about inferring properties of faint, overlapping sources from looking at statistics of the resulting confusion noise. But nowadays with awesome probabilistic techniques like Brewer's, we might be able to directly generatively model the confused background, and thereby produce probabilistic information about the astrophysical systems that generate it. Could be huge, in these days of confused Herschel data, the PHAT data on M31, the Galactic Center, and so on.

One of the things we discussed is how to make the problem as challenging as possible. We don't want to do any cheating, where the brighter (resolved) stars are effectively giving us the information we seek about the fainter (unresolved) stars.