Distances in cosmology

Distances

I implemented a bunch of routines to calculate cosmological
distances. I was motivated to do this 1) because I wanted to
generate a volume limited set of random redshifts, so I needed
a formula for the volume element and 2) I wanted some routines
that worked for more general cosmologies; I only had flat universe
code. Still don't have evolving dark energy code, but I'll write
that when I need it.

So I started from the bottom up and wrote an integration routine
to calculate the comoving distance, then all the steps needed to get
to the angular diameter distance (see Hogg astro-ph/9905116, which
mostly comes from Peebles 1993 book).

One thing I noted about that paper: I believe there is no
need to go to equation 19, which is not general. Because
you can calculate Dc, the comoving distance, between two different
redshifts, call it Dc_12, then you can implement the difference of two
DM's (comoving transverse distance) simply by using the Dc_12 in
formula 16. This will also work in any curvature and so is
general. I tested that it works for the cases where equation 19 holds
(curvature >= 0).

Now that I have this stuff going I'm generating 48 sets of 500,000
randoms from z=0.04 to 0.35. I'll set them running through the lensing
code in the background. I don't need these at the
moment since the randoms I have cover the redshift range for maxBCG,
but it will be good to have them for the future.

Corrected Lensing Profiles

Yesterday I finished to code to match the histograms of redshift, so
today I was able to do the random point corrections to the maxBCG
lensing profiles. These look OK, but there are some worrying features
in the profiles. The features are similar to what I saw in the LRG profiles.
Tomorrow I will do the jackknifing so we can do some more meaningful
analysis. I will also do sub-sampling in the "paper" versions of the
catalog. These are the clusters which will be published in Ben's catalog
paper. Essentially it is an Ngals cut and a redshift cut.

Erin