The Atacama Cosmology Telescope: Semi-Analytic Covariance Matrices for the DR6 CMB Power Spectra

TL;DR

The paper develops a semi-analytic covariance pipeline for ACT DR6 power spectra by extending the MASTER framework to accommodate inhomogeneous survey depth and atmosphere-driven noise. It combines an improved analytic covariance (via INKA and tailored Fourier-space filtering) with full-data Monte Carlo simulations and a novel simulation-based correction to achieve sub-percent agreement with MC covariances. The inhomogeneous approach reduces the required simulation corrections compared to a homogeneous model, enabling robust cosmological inference and offering a framework applicable to future high-resolution CMB experiments like the Simons Observatory. The work clarifies the sources of discrepancy with MC covariances and demonstrates a practical path toward accurate, scalable error modeling in complex CMB datasets.

Abstract

The Atacama Cosmology Telescope Data Release 6 (ACT DR6) power spectrum is expected to provide state-of-the-art cosmological constraints, with an associated need for precise error modeling. In this paper we design, and evaluate the performance of, an analytic covariance matrix prescription for the DR6 power spectrum that sufficiently accounts for the complicated ACT map properties. We use recent advances in the literature to handle sharp features in the signal and noise power spectra, and account for the effect of map-level anisotropies on the covariance matrix. In including inhomogeneous survey depth information, the resulting covariance matrix prescription is structurally similar to that used in the $\textit{Planck}$ Cosmic Microwave Background (CMB) analysis. We quantify the performance of our prescription using comparisons to Monte Carlo simulations, finding better than $3\%$ agreement. This represents an improvement from a simpler, pre-existing prescription, which differs from simulations by $\sim16\%$. We develop a new method to correct the analytic covariance matrix using simulations, after which both prescriptions achieve better than $1\%$ agreement. This correction method outperforms a commonly used alternative, where the analytic correlation matrix is assumed to be accurate when correcting the covariance. Beyond its use for ACT, this framework should be applicable for future high resolution CMB experiments including the Simons Observatory (SO).

Figures (15)

• Figure 1: Blue, Left: The power spectrum pipeline analysis mask for PA6 f150. Blue, Right: The same mask after including effective noise weights (arbitrarily normalized), described in §\ref{['sec: pipeline_analytic']}. The inset provides a zoomed-in view of the point-source holes. The outer mask borders (the point-source holes) have a $2^\circ$ ($0.3^\circ$) cosine apodization. Orange: The outline of the ACT survey footprint. Data within the orange outline, but not highlighted in blue, are excluded from the analysis.
• Figure 2: First and second rows: The noise in the first temperature split map for PA5 f090 measured in a $900$ deg$^2$ well-cross-linked region of the ACT scan strategy. The second row shows a region with less cross-linking where scans only move in the vertical (Dec.-only) direction. Third and fourth rows, left: 2D Fourier noise power spectra of the first temperature split map for PA5 f090. The average radial profiles of the power spectra have been divided-out to better highlight their anisotropic patterns. The third row is measured in the well-cross-linked region, where crossing scans induce the "x-like" bars in the power spectrum. The fourth row is measured in the poorly-cross-linked region, where the Dec.-aligned scans induce vertical noise stripes in the maps that appear as a horizontal bar in the power spectrum. Center and right: 2D power spectra from noise simulations following mnms (drawn from the tiled and directional wavelet models). The tiled model has a bandlimit of $\ell_{max}=10,800$; the wavelet model has $\ell_{\max}=5,400$, visible as a hard edge in 2D Fourier space.
• Figure 3: Signal and noise power spectra compared to the power spectra for their effective masks (for PA6 f150, first split). The difference between the signal and noise effective masks is shown in Figure \ref{['fig: data_masks']}: the effective mask for the noise includes the inhomogeneous survey depth and so has more structure than the signal mask, as reflected in its wider mask power spectrum. For both the signal and noise, the power spectrum of the mask does not appear to be significantly more compact, or steep, than the power spectrum of the field itself, calling the NKA into question for ACT. All power spectra are normalized at $\ell=2,000$.
• Figure 4: The "two-point" and "four-point" Fourier-space filter transfer functions have different shapes. Comparing our new method as part of the inhomogeneous matrix to the homogeneous matrix approach, the two methods agree on the two-point transfer functions to $<1\%$ but disagree on the four-point transfer functions on medium and large scales. The homogeneous matrix transfer function is determined by bin rather than by $\ell$. This figure shows the temperature case.
• Figure 5: Top: The main diagonal of the $\bm\Sigma_R$ matrix defined in Equation \ref{['eq: Sigma_R']}, for the PA5 f090 x PA5 f090 $EE$ block. If the analytic and Monte Carlo covariance matrices are sufficiently close, this is approximately the ratio of the eigenvalues of the two matrices. Bottom: The bin-wise diagonal of the covariance between the PA5 f090 x PA5 f090 $EE$ and PA5 f090 x PA5 f150 $EE$ blocks. In both cases, the $1\sigma$ scatter of the Monte Carlo estimates are shown, with a Gaussian process fit using data above the scale-cut, indicated by the grey region. The Gaussian processes do not account for correlations between bins.