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

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.