Fourier analysis of multi-tracer cosmological surveys

TL;DR

This paper develops optimal quadratic estimators for Fourier analysis in multi-tracer cosmological surveys, enabling simultaneous measurement of power spectra, biases, and other effects, improving upon previous single-tracer methods.

Contribution

It introduces unbiased multi-tracer estimators that incorporate biases, RSDs, and NGs, extending existing single-tracer techniques and including the 1-halo term.

Findings

Estimators perform as expected on simulated data.

Multi-tracer estimators are unbiased and have covariance given by the inverse Fisher matrix.

Our method outperforms or matches the FKP approach in tests.

Abstract

We present optimal quadratic estimators for the Fourier analysis of cosmological surveys that detect several different types of tracers of large-scale structure. Our estimators can be used to simultaneously fit the matter power spectrum and the biases of the tracers - as well as redshift-space distortions (RSDs), non-Gaussianities (NGs), or any other effects that are manifested through differences between the clusterings of distinct species of tracers. Our estimators reduce to the one by Feldman, Kaiser & Peacock (ApJ 1994, FKP) in the case of a survey consisting of a single species of tracer. We show that the multi-tracer estimators are unbiased, and that their covariance is given by the inverse of the multi-tracer Fisher matrix (Abramo, MNRAS 2013; Abramo & Leonard, MNRAS 2013). When the biases, RSDs and NGs are fixed to their fiducial values, and one is only interested in measuring the underlying power spectrum, our estimators are projected into the estimator found by Percival, Verde & Peacock (MNRAS 2003). We have tested our estimators on simple (lognormal) simulated galaxy maps, and we show that it performs as expected, being either equivalent or superior to the FKP method in all cases we analyzed. Finally, we have shown how to extend the multi-tracer technique to include the 1-halo term of the power spectrum.