Covariance of cross-correlations: towards efficient measures for large-scale structure

Details Covariance of cross-correlations: towards efficient measures for large-scale structure Covariance of cross-correlations: towards efficient measures for large-scale structure

2008-10-13

arxiv.org/abs/0810.1960v2

Astronomy and Astrophysics

Astrophysics

Several significant improvements to the earlier version: for instance it is shown more clearly how shot noise corrections may

Scientific paper

We study the covariance of the cross-power spectrum of different tracers for the large-scale structure. We develop the counts-in-cells framework for the multi-tracer approach, and use this to derive expressions for the full non-Gaussian covariance matrix. We show, that for the usual auto-power statistic, besides the off-diagonal covariance generated through gravitational mode-coupling, the discreteness of the tracers and their associated sampling distribution can generate strong off-diagonal covariance, and that this becomes the dominant source of covariance as k>>k_f=2 pi/L. On comparison with the derived expressions for the cross-power covariance, we show that the off-diagonal terms can be suppressed, if one cross-correlates a high tracer-density sample with a low one. Taking the effective estimator efficiency to be proportional to the signal-to-noise ratio (SN), we show that, to probe clustering as a function of physical properties of the sample, i.e. cluster mass or galaxy luminosity, then the cross-power approach can out perform the auto-power one by factors of a few. We confront the theory with measurements of the mass-mass, halo-mass, and halo-halo power spectra from a large ensemble of N-body simulations. We show that there is a significant SN advantage to be gained from using the cross-power approach when studying the bias of rare haloes. The analysis is repeated in configuration space and again SN improvement is found. We estimate the covariance matrix for these samples, and find strong off-diagonal contributions. The covariance depends on halo mass, with higher mass samples having stronger covariance. In agreement with theory, we show that the covariance is suppressed for the cross-power. This work points the way towards improved estimators for clustering studies.

Affiliated with

Also associated with

No associations

Rating

Covariance of cross-correlations: towards efficient measures for large-scale structure does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Covariance of cross-correlations: towards efficient measures for large-scale structure, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Covariance of cross-correlations: towards efficient measures for large-scale structure will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-719824