Monday, March 21, 2011

Comparing Correlation Functions

I've been trying to figure out why my 2d Correlation Functions look weird. I've put out request to several Berkeley folks to compare my correlation function results on a data set with theirs, but while I wait for them to respond, I'm going to compare to some literature.

For the 2-d angular correlation function on SDSS LRG galaxies, I have the following plots from Connolly et al (2001):

And from Ross et al (2007):

I changed the angular bins of my correlation function to match these sets to try to form a comparison. Here is my 2D correlation function on BOSS data:

As you can see the slope of the function is much shallower for my correlation function, than it is the literature.

The 3D correlation functions are a better match:
From Ross et al (2007):

And here is mine:

At least the slopes seem to be comparable.

I am currently running the 3D correlation function on a larger los range to try to compare to Kazin et al. :

This will take a bit because I am correlating out to such large scales (180 Mpc/h).

Another thing I noticed that I wanted to talk to Alexia about is the actual computation of the correlation function in the code. Right now it is the following:

xi = (dd - dr - rd + rr)/rr


dd = # of data-data pairs in bin
dr = (# if data-random pairs in bin) / (Random Oversampling)
rd = (# if data-random pairs in bin) / (Random Oversampling)
rr = (# if random-random pairs in bin) / (Random Oversampling)

I am wondering if the rr should be divided by (random oversampling)^2 because there are that many more point in the RR set. I haven't changed this code from when I first got it from Alexia, so I assume it is correct. But I was looking the Landy, Szalay Paper and it seemed like they were using factors of n(n-1)/2 which is approximately n^2, and we are using factors of n.


3/21 5:15 Update: Here is my plot of the 3d Correlation function on the large los range, it looks very similar to the Kazin plot above, you can even see the BAO signal @ ~100 Mpc/h:

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