Improved constraints on reionisation from CMB observations: A parameterisation of the kSZ effect

We show that, in the context of patchy reionisation, an accurate description of the angular power spectrum of the kinetic Sunyaev-Zel'dovich (kSZ) effect is not possible with simple scaling relations between the amplitude of the spectrum and global parameters such as the reionisation midpoint and its duration. We introduce a new parameterisation of this spectrum, based on a novel description of the power spectrum of the free electrons density contrast Pee(k,z) in terms of reionisation global history and morphology. We directly relate features of the spectrum to the typical ionised bubble size at different stages in the process, and subsequently to the angular scale at which the patchy kSZ power spectrum reaches its maximum. We successfully calibrate our results on a custom set of advanced radiative hydrodynamical simulations and later find our parameterisation to be a valid description of a wide range of other simulations and therefore reionisation physics. In the end, and as long as the global reionisation history is known, two parameters are sufficient to derive the angular power spectrum. Because of their straightforward physical interpretation, related to the morphology of reionisation, these parameters will be constrained by future 21cm intensity mapping experiments. Conversely, a precise measurement of the patchy kSZ power spectrum will constrain these parameters, and consequently the physics of reionisation. This parameterisation is therefore found to be an innovative tool to extract information about reionisation from CMB data.