A Novel Bispectrum Estimator of the Kinematic Sunyaev-Zel'dovich Effect using Projected Fields

TL;DR

This paper introduces a novel full kSZ bispectrum estimator $\langle\Theta^{\mathrm{kSZ}}\times\Theta^{\mathrm{kSZ}}\times\delta_g\rangle$ that cross-correlates two CMB temperature maps with a LOS-projected LSS tracer, enabling extraction of the late-time kSZ signal without needing precise redshifts. By binning the bispectrum in harmonic space and accounting for CMB lensing and an analytical covariance, the authors forecast high cumulative SNRs ($\sim$100–200) for upcoming experiments (SO or CMB-S4) paired with WISE, with squeezed-triangle configurations driving the signal. They demonstrate that restricting $\delta_g$ to linear scales reduces dependence on nonlinear bias while preserving strong signal, and they quantify cosmological sensitivities, including notable constraints on the sum of neutrino masses when combined with external priors. The work highlights the projected-fields kSZ bispectrum as a robust, information-rich probe of baryon content and beyond-$\Lambda$CDM cosmology, offering complementary constraints to Planck and BAO measurements and broad applicability to diverse LSS tracers.

Abstract

With the advent of current and future high-resolution CMB experiments, the kinematic Sunyaev-Zel'dovich (kSZ) effect has become a unique observational probe of the distribution of baryons and velocities in the Universe. In this work, we propose a novel binned bispectrum of the form temperature-temperature-density to extract the late-time kSZ effect from cleaned CMB maps. Unlike 'kSZ tomography' methods, this estimator can use any tracer of the large-scale structure density field projected along the line-of-sight and does not require individual redshifts. With our method, we forecast signal-to-noise ratios (SNR) of $\sim$100-200 for the upcoming Simons Observatory (SO) and CMB-S4 correlated with a galaxy sample from WISE that is restricted to the linear regime. We also extend galaxy modes into the non-linear regime and explore this harmonic space to show that the SNR peaks for squeezed triangles that have a short (linear) density mode and long temperature modes in harmonic space. The existing kSZ$^{2}-$density projected-fields estimator compresses the rich information contained in this bispectrum across various scales and triangle shapes. Moreover, we find that the lensing correction to this estimator's signal is relatively small for high-SNR squeezed triangle configurations. We study the dependence of this kSZ signal on $Λ$CDM parameters for SO and CMB-S4 and forecast initial constraints on the sum of neutrino masses while restricting to the linear galaxy bias regime. Our work illustrates the potential of the projected-fields kSZ bispectrum as a novel probe of baryonic abundance and beyond-$Λ$CDM cosmology with upcoming precision measurements.

Figures (7)

• Figure 1: Schematic diagram of the type of squeezed triangles that are found to have a significant SNR with the projected-fields $B^{\mathrm{kSZ},\mathrm{kSZ},\delta_g}$ bispectrum (see Section \ref{['fore']}). This class of configurations is roughly defined here as consisting of two small-scale (large $\ell>2000$) kSZ modes and one large-scale (small $\ell\lesssim700$) $\delta_g$ mode in harmonic space.
• Figure 2: Examples of 2D slices in 3D harmonic space in the default scenario with a fixed $\ell_1$-bin of [3900,4000] and [4400,4500] for SO$\times$WISE (top-left) and CMB-S4$\times$WISE (bottom-left) respectively, showing the individual signal-to-noise-ratios (SNR) of $B^{\mathrm{kSZ},\mathrm{kSZ},\delta_g}$ within each 3D bin. The absolute value of the lensing contribution relative to the noise covariance in each bin $\left(|\Delta B^{\mathrm{kSZ},\mathrm{kSZ},\delta_g}|/\sqrt{V^{\mathrm{kSZ},\mathrm{kSZ},\delta_g}}\right)$ is displayed for SO$\times$WISE (top-right) and CMB-S4$\times$WISE (bottom-right) respectively using the same colorbars as their corresponding SNR plots. The grey bins do not contain any $\ell$-triplet satisfying the triangle inequality (i.e. no signal under isotropy).
• Figure 3: A 2D slice in 3D harmonic space in the extended scenario with a fixed $\ell_1$-bin of [3900,4000] showing the individual SNR ($= \left(B^{\mathrm{kSZ},\mathrm{kSZ},\delta_g}/\sqrt{V^{\mathrm{kSZ},\mathrm{kSZ},\delta_g}}\right)$ within each bin (left), and the absolute value of the lensing contribution relative to the noise covariance in each bin $\left(|\Delta B^{\mathrm{kSZ},\mathrm{kSZ},\delta_g}|/\sqrt{V^{\mathrm{kSZ},\mathrm{kSZ},\delta_g}}\right)$ (right) for SO$\times$WISE using the same colorbar. The SNR peaks for squeezed triangles (of the type in Fig. 1), with a maximum of $\sim4.5$ for a bin within the slice shown here, while the relative magnitude of the lensing correction peaks for different triangle shapes.
• Figure 4: Fisher forecasts for marginalized errors and degeneracies among $\Lambda$CDM parameters, $\Sigma m_{\nu}$ (in eV here), $A$, and $b_g$ using the projected-fields kSZ bispectrum alone, without assuming any external priors, and with realistic post-ILC noise for SO and CMB-S4. Contours show the 2D marginalized 68$\%$ (darker) and 95$\%$ confidence ellipses for SO$\times$WISE (green) and CMB-S4$\times$WISE (blue).
• Figure 5: A 2D slice in harmonic space in the extended scenario with a fixed $\ell_1$-bin of [3900,4000]. The absolute value of the lensing contribution in each bin, $|\Delta B^{\mathrm{kSZ},\mathrm{kSZ},\delta_g}|$, (in units of $\mu$K$^2$) is visualized here for SO$\times$WISE; it peaks for squeezed triangle configurations having both CMB modes $\lesssim 4500$.