A consistent, physical, and analytical model for CMB observables of reionisation I. Derivation, constraining power, and detectability of the auto-spectra

Abstract

The Epoch of Reionisation imprints its history and morphology on the Cosmic Microwave Background temperature and polarisation anisotropies through two effects: The kinetic Sunyaev Zel'dovich (kSZ) effect and Thomson scattering. To perform joint analyses of these observables and put tight constraints on the reionisation history and morphology, a common reionisation model is necessary. We present a quick, physically-accurate analytical approach to derive consistently the angular power spectra of the three main resulting imprints that are the spatial fluctuations of the Thomson optical depth, the patchy kSZ effect, and the scattering and screening B-modes. The approach differs from existing analytical models, as it is calibrated on high-resolution hydrodynamical simulations and depends on physical parameters of reionisation. Our predicted power spectra are consistent with the ones derived from cosmological simulations, whilst including more physical information -- such as the typical size of ionised bubbles and the duration of reionisation. We provide an updated detectability assessment and show that both $C_\ell^{\tau\tau}$ and $C_\ell^{BB}$ could be measured by experiments similar to CMB Stage 4 and CMB-HD, respectively. We show the complementarity of the three observables in constraining reionisation history and morphology, and illustrate the potential of their joint analysis to get a global picture of reionisation. This analytical model will be a powerful tool in the analysis of upcoming CMB data, either alone or in combination with independent datasets such as measurements of the high-redshift 21cm signal. The code to derive these spectra is publicly available online as the preion Python package.