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

TL;DR

This work provides a complete first-principles treatment of the angular cross-power spectrum between the kSZ signal and reconstructed galaxy momentum, deriving both transverse and longitudinal contributions $C_\ell^{\rm ge}$ and their 3D counterparts $P_\perp^{ab}(k)$ and $P_\parallel^{ab}(k)$. It incorporates higher-order statistics via a halo-model framework, including the cross-term $P_{\perp,2}$ and the connected non-Gaussian trispectrum, and assesses the impact of satellite galaxies and the two-halo term. Through implementation with the Core Cosmology Library and a fiducial LRG HOD plus HE-based electron profiles, the authors forecast the detectability of these terms for Simons Observatory and CMB-S4, finding that the cross-term and trispectrum are observable at roughly $4$–$6\sigma$, while longitudinal contributions remain negligible. The results emphasize that accurate modeling of velocity–density correlations and baryonic feedback is essential for unbiased cosmological and astrophysical inferences from upcoming kSZ stacking analyses.

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 $\sim 4-6 σ$. 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.

Figures (7)

• Figure 1: The contributions to the 3D power spectrum (left) and angular power spectrum (right) for the perpendicular component of the momentum field. The individual contributions from $\rm \langle ge \rangle \langle mm \rangle$ (dark blue), $\rm \langle gm \rangle \langle em \rangle$ (light blue), and the connected non-Gaussian term (purple) are shown, with their total displayed in red. The dashed and dotted lines denote the $\rm \langle ge \rangle \langle mm \rangle$ term for the one-halo and two-halo contributions, respectively, in the electron-galaxy cross-correlation.
• Figure 2: The contributions to the 3D power spectrum (left) and angular power spectrum (right) for the parallel component of the momentum field. The contributions from the $\rm \langle ge \rangle \langle mm \rangle$ and $\rm \langle gm \rangle \langle em \rangle$ terms are shown in dark blue and light blue, respectively, with their total shown in red. The dashed and dotted lines denote the $\rm \langle ge \rangle \langle mm \rangle$ term for the one-halo and two-halo contributions, respectively, in the electron-galaxy cross-correlation.
• Figure 3: The contributions to the 3D power spectrum (left) and angular power spectrum (right) for the parallel component of the momentum field, including the bispectrum and trispectrum contributions from Equations \ref{['eq:P_par_amm']} and \ref{['eq:P_par_c']}, respectively. The contributions from $\rm \langle ge \rangle \langle mm \rangle - \rm \langle gm \rangle \langle em \rangle$ (dark blue), one-halo bispectrum (orange), three-halo bispectrum (yellow), one-halo trispectrum (pink), and four-halo trispectrum (purple) are shown, with their total displayed in red. The contribution from the purely linear term in Equation \ref{['eq:P_mm']}, $P_{\rm vv}$, is shown in grey. We include the total power of the transverse mode in dotted red. Negative contributions are shown as dashed lines. Note that the region below $k \lesssim 0.01 \, \rm Mpc^{-1}$ for the $T_{\rm 4h}$ contribution to $P_{q_\parallel}^{\rm ge}(k)$ has been masked due to numerical precision issues.
• Figure 4: The signal-to-noise ratio, $S/N$, as a function of the angular multipole cut-off, $\ell_{\rm max}$. Here, we fix the baryonic parameters to the fiducial values and we assume the baseline noise level of the Simons Observatory. We also show the $S/N$ of the relevant terms, as listed in Table \ref{['tab:S/N']}. Specifically, the $\rm \langle gm \rangle \langle em \rangle$ cross-term is shown in light blue, the connected trispectrum term in purple, the two-halo contribution to the $\rm \langle ge \rangle \langle mm \rangle$ term in dotted dark blue, and the $\rm \langle ge \rangle \langle mm \rangle$ term including satellites in the HOD model in dashed dark blue. Here, we compare the satellites case with $f_{\rm sat} = 1.0$ to the fiducial case where $f_{\rm sat} = 0.14$.
• Figure 5: Left: The ratio of the angular power spectrum of the perpendicular component between models that include satellite galaxies and the fiducial $(f_{\rm sat} = 0.14)$ case. The different lines correspond to HOD models with varying satellite fractions, as quoted in the legend. The large-scale galaxy bias is held fixed across all models to isolate the impact of satellites. The $\ell$-axis is restricted to small angular scales, where the satellite contribution becomes significant. Right: The signal-to-noise ratio, $S/N$, as a function of the fraction of satellites, $f_{\rm sat}$, in the HOD model relative to the fiducial case. We consider three different noise levels: the Simons Observatory (red), CMB-S4 (dark blue), and the cosmic variance limit (light blue).