Anisotropic effective redshift and evolving clustering amplitude

TL;DR

This paper examines how variations in effective redshift across galaxy pairs affect large-scale clustering measurements, revealing significant biases in anisotropic clustering signals if uncorrected.

Contribution

It introduces the concept of anisotropic effective redshift and demonstrates its impact on clustering measurements, especially for surveys with broad redshift ranges and evolving tracers.

Findings

Neglecting effective redshift variations causes a 4% tilt in the quadrupole.

Evolving clustering amplitude leads to a 40% bias in the hexadecapole.

Effective redshift effects are negligible for the monopole.

Abstract

A typical galaxy survey geometry results in galaxy pairs of different separation and angle to the line-of-sight having different distributions in redshift and consequently a different effective redshift. However, clustering measurements are analysed assuming that the clustering is representative of that at a single effective redshift. We investigate the impact of variations in the galaxy-pair effective redshift on the large-scale clustering measured in galaxy surveys. We find that galaxy surveys spanning a large redshift range have different effective redshifts as a function of both pair separation and angle. Furthermore, when considering tracers whose clustering amplitude evolves strongly with redshift, this combination can result in an additional scale-dependent clustering anisotropy. We demonstrate the size of this effect on the eBOSS DR16 Quasar sample and show that, while the impact on monopole is negligible, neglecting this effect can result in a large-scale tilt of $\sim 4\%$ and $\sim40\%$ in quadrupole and hexadecapole, respectively. We discuss strategies to mitigate this effect when making measurements.