Geometric Biases in Power-Spectrum Measurements

TL;DR

This paper investigates geometric biases in power-spectrum measurements caused by varying line-of-sight directions in galaxy surveys, providing analytic and numerical correction formulas to improve accuracy of anisotropic clustering analysis.

Contribution

It derives simple analytic and numerical correction formulas for biases in higher-order Legendre moments of the power spectrum due to survey geometry and LOS variation.

Findings

Bias in quadrupole is less than 1% for k > 0.01h/Mpc at z > 0.32.

Bias in hexadecapole is below 5% for k > 0.05h/Mpc at z > 0.32.

Bias depends on observed area and scale, respectively.

Abstract

The observed distribution of galaxies has local transverse isotropy around the line-of- sight (LOS) with respect to the observer. The difference in the statistical clustering signal along and across the line-of-sight encodes important information about the ge- ometry of the Universe, its expansion rate and the rate of growth of structure within it. Because the LOS varies across a survey, the standard Fast Fourier Transform (FFT) based methods of measuring the Anisotropic Power-Spectrum (APS) cannot be used for surveys with wide observational footprint, other than to measure the monopole moment. We derive a simple analytic formula to quantify the bias for higher-order Legendre moments and we demonstrate that it is scale independent for a simple sur- vey model, and depends only on the observed area. We derive a similar numerical correction formula for recently proposed alternative estimators of the APS that are based on summing over galaxies rather than using an FFT, and can therefore in- corporate a varying LOS. We demonstrate that their bias depends on scale but not on the observed area. For a quadrupole the bias is always less than 1 per cent for k > 0.01h/Mpc at z > 0.32. For a hexadecapole the bias is below 5 per cent for k>0.05h/Mpc at z>0.32.