Squared-field cross-correlation between kinetic Sunyaev-Zel'dovich effect and 21-cm intensity mapping

TL;DR

This paper derives an analytic framework for the cross-correlation between the squared kSZ field and the projection of the squared HI 21-cm intensity mapping field, using a 2D flat-sky projection and linear perturbation theory. The cross-spectrum C_ℓ^{kSZ^2×HI^2} is obtained by convolving projections, applying Limber integration, and incorporating beam and RSD corrections, with the four-point (triple) spectrum evaluated via Wick’s theorem. The nonzero signal arises from terms that couple HI density, velocity, and electron density in three-point configurations, and the total spectrum is C_ℓ = 2 C_ℓ^{(6)} + 2 C_ℓ^{(7)} + 4 C_ℓ^{(8)}. Forecasts for SKA-MID HI surveys cross-correlated with ACT/SO kSZ maps predict maximal cumulative SNRs of about 1.92 (ACT) and 3.99 (SO), suggesting near-edge detections at low redshift and providing a validation path for Epoch of Reionization studies.

Abstract

Neutral hydrogen (HI) 21-cm intensity mapping is an effective method to track the distribution of baryonic matter, and extract astrophysical and cosmological information. The 21-cm intensity field has a nonvanishing cross-correlation with the kinetic Sunyaev-Zel'dovich (kSZ) effect that traces the velocity and density perturbations of free electrons. By using the linear perturbation theory, in this paper we calculate analytically, for the first time, the cross-correlation between the squared kSZ field and the projection of the squared HI intensity mapping field with the flat-sky approximation. This statistic remains nonvanishing even after the long-wavelength line-of-sight modes ($k_{\parallel}$) are removed due to foreground contamination. We further forecast for the prospects of detection with the SKA-MID 21-cm intensity mapping experiments (redshifts in range of $0.3 < z < 1$), and the kSZ maps measured by the Atacama Cosmology Telescope (ACT) and Simons Observatory (SO). The predicted cumulative signal-to-noise ratio is $1.92$ for SKA-ACT and $3.99$ for SKA-SO. These results show a possible on-the-edge detection on the cross-correlation signal at low redshifts, which in turn could serve as a validation step toward using it for the Epoch of Reionization studies.

Figures (7)

• Figure 1: An intuitive picture and notation explanation for the flat-sky approximation, with $\chi$ as the comoving distance and $\hat{n}_0$ as the line-of-sight. A harmonic decomposition under the flat-sky limit can be approximated to be a 2D Fourier transform over $\vec{\theta}$.
• Figure 2: The cross-correlation angular power spectrum with each individual term's contribution Eq. \ref{['eq:terms6-7-8']}, where the biases $b_\mathrm{e}$ and $b_\mathrm{HI}$ are set to be unity.
• Figure 3: Left: The angular power spectrum for primary (lensed) CMB (blue solid line), kSZ effect (orange solid line) and the (deconvolved) noise for the ACT telescope (dashed line) and Simons Observatory (SO; dot-dashed line). Right: The normalized filter for ACT (blue solid line) and SO (orange solid line) respectively.
• Figure 4: Power spectrum of the squared fields, in which the biases $b_\mathrm{e}$ and $b_\mathrm{HI}$ are set to be unity. Left: Power spectrum of the squared filtered kSZ field (Eq. (\ref{['eq:Cell_kSZ2']})) in which both ACT (blue solid line) and SO (orange solid line) are shown. Right: Power spectrum of the squared HI IM field with (orange dashed line) and without (blue solid line) thermal noise from instruments (Eq. (\ref{['eq: Cl HI PS field']})).
• Figure 5: Signal-to-noise ratio per-$\ell$ mode ($\mathrm{SNR}_\ell$, left) and cumulative SNR (SNR$_\mathrm{c}$, right) as functions of $\ell_{\mathrm{max}}$ for different CMB observations cross-correlating with SKA-MID, where in the right panel the horizontal dashed gray line denotes the benchmark ${\rm SNR}_{\rm c}=3$.