Detailed theoretical modelling of the kinetic Sunyaev-Zel'dovich stacking power spectrum

Abstract: We examine, from first principles, the angular power spectrum between the kinematic Sunyaev-Zel'dovich effect (kSZ) and the reconstructed galaxy momentum - the basis of existing and future "kSZ stacking" analyses. We present a comprehensive evaluation of all terms contributing to this cross-correlation, including both the transverse and longitudinal modes of the density-weighted velocity field, as well as all irreducible correlators that contribute to the momentum power spectrum. This includes the dominant component, involving the convolution of the electron-galaxy and velocity-velocity power spectra, an additional disconnected cross-term, and a connected non-Gaussian trispectrum term. Using this framework, we examine the impact of other commonly neglected contributions, such as the two-halo component of the dominant term, and the impact of satellite galaxies. Finally, we assess the sensitivity of upcoming CMB experiments to these effects and determine that they will be sensitive to the cross-term, the connected non-Gaussian trispectrum term, the two-halo contribution and impact of satellite galaxies, at a significance level of $\sim 4-6 \sigma$. On the other hand, the contribution from longitudinal modes is negligible in all cases. These results identify the astrophysical observables that must be accurately modelled to obtain unbiased constraints on cosmology and astrophysics from near-future kSZ measurements.