velocity correlations

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Anze Slosar
Posts: 183
Joined: September 24 2004
Affiliation: Brookhaven National Laboratory
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velocity correlations

Post by Anze Slosar » January 26 2005

I found the following equation in the Peebles' book (part II, chap. 14):

[tex]
\langle v^2 \rangle = (Haf)^2 \int_0^\infty y {\rm d}y \xi(y)
[/tex]

This can be extended (by performing the right integral of 14.9) to correlations of neighbouring velocity fields as

[tex]
\langle v(\mathbf{x}) v(\mathbf{x+r}) \rangle = (Haf)^2 \left[ \int_0^r y^2r^{-1} {\rm d}y\xi(y) + \int_r^\infty y {\rm d}y \xi(y) \right)
[/tex]

and hence

[tex]
\langle v(\mathbf{x}) v(\mathbf{x+r}) \rangle = \langle v^2 \rangle \frac{ \int_0^r y^2r^{-1} {\rm d}y \xi(y) + \int_r^\infty y {\rm d}y \xi(y)}{\int_0^\infty y {\rm d}y \xi(y)}
[/tex]

I have two problems with this and would appreciate feedback:
  • I have never seen the equation above before and Peebles didn't put it in his book, although it is fairly obvious thing to do. Anybody has a ref, or is it wrong for some reason?
  • It doesn't work... On simulations it predicts correlations that are much stronger than observed (i tried comparing halo centers, whose correlation function DOES match the linear correlation functions and thus they should still be in linear mode). I think that this might be a selection function, simply due to the fact that by comparing velocity of halos you calculate the object weighted rather than volume weighted quantity.

Avery Meiksin
Posts: 1
Joined: February 24 2005
Affiliation: Institute for Astronomy, University of Edinburgh

velocity correlations

Post by Avery Meiksin » February 24 2005

See Gorski (1988) ApJ 332, L7, or Strauss & Willick (1995) Physics Reports 261, 271 (also
available at astro-ph/9502079), on how to do this.

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