Rapid modelling of the redshift-space power spectrum multipoles for a masked density field

TL;DR

This paper introduces a fast and efficient method for modeling the redshift-space power spectrum multipoles in galaxy surveys with masked density fields, significantly improving computational speed and spectral resolution.

Contribution

It provides a novel reformulation of the forward modeling process that accounts for masking effects, enabling rapid likelihood analyses across multiple models.

Findings

Achieves 10^3-10^4 times faster computations

Demonstrates applicability to complex survey geometries

Enhances spectral resolution in power spectrum analysis

Abstract

In this work we reformulate the forward modelling of the redshift-space power spectrum multipole moments for a masked density field, as encountered in galaxy redshift surveys. Exploiting the symmetries of the redshift-space correlation function, we provide a masked-field generalisation of the Hankel transform relation between the multipole moments in real and Fourier space. Using this result, we detail how a likelihood analysis requiring computation for a broad range of desired $P(k)$ models may be executed $10^3-10^4$ times faster than with other common approaches, together with significant gains in spectral resolution. We present a concrete application to the complex angular geometry of the VIPERS PDR-1 release and discuss the validity of this technique for finite-angle surveys.