The 3D HST proposal talked a lot about environment dependence of galaxy properties, but nobody has done anything with it, nor seem they eager to do so. I have started to do a little bit of reading up on the practicalities. There is a whole bunch of papers recently that discuss and compare different environment definitions, e.g. Muldrew et al (2012) and Skibba et al (2012). It looks to me that the mark (by stellar mass, compactness, etc..) correlation function is the most sensible way to go, at least Skibba claims it to be so.
I am now combing the literature for comments (solutions) on two specific issues, relevant for 3D-HST:
-- field size (typically 5-ish MPC transverse)
-- grism redshift accuracy: 750 km/s for emission line galaxies, 1500 km/s for absorption line galaxies (m<23); this us squarely between the photo-z surveys and the spectroscopic surveys.
It seems that the PRIMUS folks, in a -- at first glance very nice paper Skibba et al (2014) -- have gone a long way of working out this regime. They have, however, far larger sample sizes and larger (angular) fields. I still haven't found an explicit treatment of field-edges; perhaps the randomization takes care of it.
Basic method of redshift distortions is worked out in Fisher et al (1994).
Also: I don't understand why still "estimators" are used for correlation functions, marked or not,
used. I would presume that any parameterized model for a correlation function (power-law with r0 and gamma) should make a prediction for p(r_p,
π ), which then brings you to likelihood approaches. Why is that not done?
Post discussion lessons:
-- perhaps the simplest and first thing to try is to ask, whether indeed -- at a given mass -- quiescent galaxies ase more clustered than SF ones. How to do this: look at the quiescence-marked correlation, using the unmarked correlation as the "random" (D. Wake's suggestion).
