Euclid preparation: The flat-sky approximation for the clustering of Euclid's photometric galaxies

TL;DR

This paper evaluates the flat-sky and Limber approximations for Euclid's photometric galaxy clustering, finding the flat-sky approach more accurate for detailed data analysis in the final data release.

Contribution

It demonstrates that the flat-sky approximation provides a more precise modeling of galaxy clustering than the Limber approximation for Euclid's DR3 data.

Findings

Limber approximation is accurate for DR1 wide bins.

Flat-sky approximation is accurate within 5% for DR3 bins.

Flat-sky simplifies power spectrum computation for Euclid analysis.

Abstract

We compare the performance of the flat-sky approximation and Limber approximation for the clustering analysis of the photometric galaxy catalogue of Euclid. We study a 6 bin configuration representing the first data release (DR1) and a 13 bin configuration representative of the third and final data release (DR3). We find that the Limber approximation is sufficiently accurate for the analysis of the wide bins of DR1. Contrarily, the 13 bins of DR3 cannot be modelled accurately with the Limber approximation. Instead, the flat-sky approximation is accurate to below $5\%$ in recovering the angular power spectra of galaxy number counts in both cases and can be used to simplify the computation of the full power spectrum in harmonic space for the data analysis of DR3.