Realspace and redshift space correlation function questions

[1ytrewq]

why is the redshift space correlation function smaller than the realspace correlation function at small scales and the opposite on large scales?

 

[marcus]

could you give a link to some online source where the correlations are defined and this inequality is exhibited? that way everybody will know what you are talking about.

 

[1ytrewq]

well the 2-point correlation function $$\xi$$(r) is simply the Fourier transform of the power spectrum and in astronomy it is defined as the excess probability of finding a pair of galaxies at separation r.
the correlation function can be separated into a function of 2 variables by decomposing r as r= sigma + pi which represent perpendicular and parallel to the line of sight respectively.

this paper goes over it a bit: http://iopscience.iop.org/0004-637X/479/1/82/pdf/0004-637X_479_1_82.pdf

i made a plot of \xi(r) vs logr and \xi(sigma,pi) vs logr and found that for small scales, the correlation function in redshift space was smaller than the correlation function in real space and the opposite was true for large scales. I was wondering why this was the case?

 

[marcus]

Thanks,
for what it's worth here is my unauthoritative reaction (eventually someone else will reply, I expect).

I'd say, if I understand you, that this is the kind of thing that happens in all kinds of contexts whenever you have something like a density and you have two ways to plot it and a nonlinear map from one variable to the other.

Change of variable.