Simulating Partial Sky Cosmic Microwave Background Maps with 3D Fast Fourier Transforms

TL;DR

This paper introduces a 3D FFT-based method for simulating partial sky CMB maps, offering a more efficient alternative to traditional spherical harmonic approaches for intermediate sky coverage.

Contribution

The authors develop and demonstrate a novel 3D FFT-based simulation technique for partial sky CMB maps, improving efficiency over full-sky methods.

Findings

The method is more efficient than full-sky simulations for intermediate sky coverage.

It is applicable to scalar and potentially higher-spin CMB maps.

The approach bridges flat-sky and full-sky simulation regimes.

Abstract

Simulated maps of the microwave background (CMB) radiation are generally created using one of two methods: all-sky simulations use the spherical harmonic transform, while maps covering small areas approximate the sky as flat, allowing the use of fast Fourier transforms (FFTs). Current and near-future experiments, particularly ones like CMB S4, will cover areas too large for the flat-sky approximation but significantly less than the full sky. In this regime, it can be more efficient to simulate maps in a 3-D box using FFTs, and then sample onto the observed part of the celestial sphere. We present a method for performing such simulations and show that it can be more efficient than full-sky simulations. We develop the method for scalar maps, but we expect it to be applicable to higher-spin (e.g., polarization) simulations as well.