The Impact of Nonlinear Structure Formation on the Power Spectrum of Transverse Momentum Fluctuations and the Kinetic Sunyaev-Zel'dovich Effect

TL;DR

This paper investigates how nonlinear structure formation affects the transverse momentum power spectrum and the kinetic Sunyaev-Zel'dovich effect, revealing that higher-order terms significantly influence small-scale anisotropies in the cosmic microwave background.

Contribution

The study derives the next-to-leading order expression for the transverse momentum power spectrum, including the connected term often neglected, and quantifies its impact on the kSZ effect.

Findings

Connected term contributes up to 10% at small scales for the kSZ power spectrum.

Both leading and next-to-leading order terms are necessary to reproduce the expected $k^2$ scaling.

The connected term reduces the reionization contribution estimate by about 20%.

Abstract

Cosmological transverse momentum fields, whose directions are perpendicular to Fourier wave vectors, induce temperature anisotropies in the cosmic microwave background via the kinetic Sunyaev-Zeldovich (kSZ) effect. The transverse momentum power spectrum contains the four-point function of density and velocity fields, $\langle\delta\delta v v\rangle$. In the post-reionization epoch, nonlinear effects dominate in the power spectrum. We use perturbation theory and cosmological $N$-body simulations to calculate this nonlinearity. We derive the next-to-leading order expression for the power spectrum with a particular emphasis on the connected term that has been ignored in the literature. While the contribution from the connected term on small scales ($k>0.1\,h\,\rm{Mpc}^{-1}$) is subdominant relative to the unconnected term, we find that its contribution to the kSZ power spectrum at $\ell = 3000$ at $z<6$ can be as large as ten percent of the unconnected term, which would reduce the allowed contribution from the reionization epoch ($z>6$) by twenty percent. The power spectrum of transverse momentum on large scales is expected to scale as $k^2$ as a consequence of momentum conservation. We show that both the leading and the next-to-leading order terms satisfy this scaling. In particular, we find that both of the unconnected and connected terms are necessary to reproduce $k^2$.