The Atacama Cosmology Telescope: DR6 Power Spectrum Foreground Model and Validation

TL;DR

The paper details a comprehensive, parametric foreground model for ACT DR6 multi-frequency power spectra and validates it with ACT, Planck, and SPT data, as well as with realistic non-Gaussian sky simulations. It shows that cosmological constraints under $\Lambda$CDM and $\Lambda$CDM+$N_{ m eff}$ are robust to a wide range of foreground-model extensions, with $\Delta \text{(parameters)} \lesssim 0.5\sigma$ in most cases. A non-detection of a significant kSZ signal yields conservative limits on reionization duration, $\Delta z_{\rm rei}$, while end-to-end simulations demonstrate unbiased recovery of the input cosmology. The work also emphasizes systematic uncertainties in foreground parameters, highlighting the interplay between SZ, CIB, and radio components. Collectively, the results validate the ACT DR6 foreground model and support the reliability of its cosmological inferences, while outlining avenues for increased complexity in future high-sensitivity surveys.

Abstract

We discuss the model of astrophysical emission at millimeter wavelengths used to characterize foregrounds in the multi-frequency power spectra of the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6), expanding on Louis et al. (2025). We detail several tests to validate the capability of the DR6 parametric foreground model to describe current observations and complex simulations, and show that cosmological parameter constraints are robust against model extensions and variations. We demonstrate consistency of the model with pre-DR6 ACT data and observations from Planck and the South Pole Telescope. We evaluate the implications of using different foreground templates and extending the model with new components and/or free parameters. In all scenarios, the DR6 $Λ$CDM and $Λ$CDM+$N_{\rm eff}$ cosmological parameters shift by less than $0.5σ$ relative to the baseline constraints. Some foreground parameters shift more; we estimate their systematic uncertainties associated with modeling choices. From our constraint on the kinematic Sunyaev-Zel'dovich power, we obtain a conservative limit on the duration of reionization of $Δz_{\rm rei} < 4.4$, assuming a reionization midpoint consistent with optical depth measurements and a minimal low-redshift contribution, with varying assumptions for this component leading to tighter limits. Finally, we analyze realistic non-Gaussian, correlated microwave sky simulations containing Galactic and extragalactic foreground fields, built independently of the DR6 parametric foreground model. Processing these simulations through the DR6 power spectrum and likelihood pipeline, we recover the input cosmological parameters of the underlying cosmic microwave background field, a new demonstration for small-scale CMB analysis. These tests validate the robustness of the ACT DR6 foreground model and cosmological parameter constraints.

Figures (22)

• Figure 1: Templates for the $\ell$-dependence of the thermal and kinetic SZ and clustered CIB components of the baseline foreground model, as described in L25. These templates are normalized to unity at $\ell_0 = 3000$ and at a reference frequency $\nu_0 = 150~{\rm GHz}$ (for the tSZ and CIB), which is shown here.
• Figure 2: Templates for $\ell$-dependence of the cross-correlation terms considered in this work. The templates are normalized to unity at $\ell = 3000$ and at the reference frequency $\nu_0 = 150~{\rm GHz}$, which is shown here. The AGORA tSZ--CIB correlation is negative for $\ell \gtrsim 6500$. As discussed in Omori:2022uox, the shape of this template depends on the redshift limit in the tSZ and CIB maps used to measure this correlation. The CIB--radio cross-power spectrum is predicted to increase even more steeply on small scales than the fiducial tSZ--CIB cross-power spectrum.
• Figure 3: Posterior distribution of the foreground parameters for the ACT DR6 baseline foreground model. The first two rows show the TT-related foreground parameters and last row reports the TE/EE foregrounds. Note that $\beta_s$ is assumed to be the same in temperature and polarization. The red dashed lines show the effect of neglecting beam chromaticity (the frequency dependence of the beams across the passbands). The green dotted lines show the priors imposed on the Galactic dust amplitudes.
• Figure 4: Constraints on the duration of reionization, obtained by interpretation of the $a_\mathrm{kSZ}$ posteriors for ACT DR6 and P-ACT DR6 using the B13 scaling, under various assumptions. The shaded regions represent the 95% exclusion limits. The baseline reionization kSZ treatment is shown in black, using ACT data with an assumed $z_\mathrm{mid} = 8$ and the most conservative treatment of the low-$z$ kSZ, in which all the signal is ascribed to the kSZ contribution from reionization. Left: Small variations to the inferred limit are apparent for the P-ACT data (red) and for the ACT data when assuming $z_\mathrm{mid} = 10$ rather than 8. Right: allowing for a non-zero low-$z$ kSZ signal with the given amount of feedback (parametrized by the AGN heating temperatures), as implemented in the AGORA model, yields tighter constraints on the reionization duration. Note that all models considered here are informative over the prior (dotted grey).
• Figure 5: Posterior distributions of the foreground parameters in the ACT DR6 baseline model, for various datasets. The top row shows the parameters used for a model common to ACT, SPT, and Planck. The black, red, and green boxes in the second and third rows represent respectively the ACT-, SPT-, and Planck-specific parameters. Note that the Planck tSZ and clustered CIB amplitudes are rescaled to $150\:{\rm GHz}$. The SPT clustered CIB is the sum of the $1$- and $2$-halo contributions introduced in R21. Going from the green to the dark blue case removes the small-scale information in Planck data and hence we find a broadening of the Planck-related point source parameters in the last row.