The Atacama Cosmology Telescope: Map-Based Noise Simulations for DR6

TL;DR

This work develops and rigorously tests three Gaussian, map-based noise models for ACT DR6 (tiled, isotropic wavelet, and directional wavelet) to capture the intricate noise covariance structure induced by atmospheric fluctuations and ACT's scan strategy. By leveraging split-map differences and a small set of sky realizations, the authors produce realistic noise realizations via mnms and demonstrate that analytic covariances underpredict variance by up to ~20% in polarization, underscoring the necessity of detailed, non-white noise modeling. The models reproduce large-scale correlations, 2D noise anisotropy, and scale-dependent map depth, with the directional wavelet model offering the most comprehensive coverage of anisotropy while the wavelet model excels at scale-depth characterization. The public mnms code provides a practical tool for ACT DR6 and will inform noise modeling for future ground-based CMB experiments like the Simons Observatory and CMB-S4.

Abstract

The increasing statistical power of cosmic microwave background (CMB) datasets requires a commensurate effort in understanding their noise properties. The noise in maps from ground-based instruments is dominated by large-scale correlations, which poses a modeling challenge. This paper develops novel models of the complex noise covariance structure in the Atacama Cosmology Telescope Data Release 6 (ACT DR6) maps. We first enumerate the noise properties that arise from the combination of the atmosphere and the ACT scan strategy. We then prescribe a class of Gaussian, map-based noise models, including a new wavelet-based approach that uses directional wavelet kernels for modeling correlated instrumental noise. The models are empirical, whose only inputs are a small number of independent realizations of the same region of sky. We evaluate the performance of these models against the ACT DR6 data by drawing ensembles of noise realizations. Applying these simulations to the ACT DR6 power spectrum pipeline reveals a $\sim 20\%$ excess in the covariance matrix diagonal when compared to an analytic expression that assumes noise properties are uniquely described by their power spectrum. Along with our public code, $\mathtt{mnms}$, this work establishes a necessary element in the science pipelines of both ACT DR6 and future ground-based CMB experiments such as the Simons Observatory (SO).

Figures (23)

• Figure 1: Top: The inverse-variance map, $\mathbf h$, for PA5 f090, first split. Larger values correspond to deeper regions of the map. The ACT scanning strategy is also discernible. Border ticks give the declination (Dec) and right-ascension (R.A.) in degrees. Bottom: The cross-linking map, $1-\mathbf f_p$, for the PA5 f090 coadd (see Equation \ref{['eq: coadd_def']}). Values close to 0 indicate poor cross-linking, and vice versa for values close to 1, in arbitrary units (henceforth, a.u.).
• Figure 2: Ratios of BB pseudospectra between the corrected difference maps, $\bm\nu_i$, and the individual split maps, $\mathbf m_i$, for each array and frequency channel in ACT DR6. All pseudospectra are measured within this paper's "pseudospectrum mask" described in §\ref{['sec: implementation_masks']}. The dashed black line is the nominal result (ratio of unity), the solid lines (shaded bands) are the means ($1\sigma$ range) over the eight splits of each dataset. To mitigate any expected BB signal, in addition to masking the Galaxy, all maps are point-source subtracted and filtered using the ACT DR4 ground pickup filter C20, where we remove Fourier modes with $|k_x|\leq 90$ and $|k_y|\leq 50$. Spectra are smoothed with a tophat kernel of size $\Delta\ell=250$ to better visualize their overall trend.
• Figure 3: Top, large-scale noise correlations: Noise power spectra by polarization autocorrelation (TT, EE, BB), for each detector array and frequency band. The power spectra are evaluated on the corrected difference maps (Equation \ref{['eq: diff_def_3']}), after applying the apodized pseudospectrum mask described in §\ref{['sec: implementation_masks']}. Shaded bands give the $1\sigma$ range over the eight split maps for each array/frequency. All spectra are smoothed with a tophat kernel of size $\Delta\ell=25$. Both the TT and polarization (EE, BB) spectra are normalized by the value of the TT spectrum at $\ell=10,800$ to suppress the effect of variable data volume between arrays. Polarization spectra plateau at a value of $\sim$2, owing to each polarized component receiving approximately half the TOD volume as intensity. Both the intensity and polarization spectra are steep and red at large scales. Bottom, correlated frequencies: Correlation spectra ($r_{\ell}$, Equation \ref{['eq: correlation_spectra']}) evaluated from the mean cross-power spectrum of the eight difference maps, for each detector array. The same mask is applied as in the top panel, and shaded regions again correspond to the $1\sigma$ range over the eight split maps. For legibility, we only plot the cross-spectra between different frequency bands --- all crosses are between the same polarization components (i.e., TT, EE, or BB). The colored series indicate cross-spectra between frequency bands on the same physical detector array, while the grey series indicate the cross-spectra between bands on different physical detector arrays. The only significant cross-spectra come from the same physical detector array.
• Figure 4: Spatially-varying noise anisotropy: TT power spectra in 2D Fourier space for PA5 f090, first split. The 2D spectra are normalized radially by average power in annuli of $\Delta k=50$ and smoothed by a uniform 2D tophat kernel of sidelength $\Delta k=100$. The left spectrum is measured in the region from $0^\circ$ to $15^\circ$ Dec and $-120^\circ$ to $-180^\circ$ R.A.. The right spectrum is measured in the region from $-45^\circ$ to $-30^\circ$ Dec and $45^\circ$ to $-15^\circ$ R.A.. The edge of both regions is apodized with a $2^\circ$-wide cosine taper before taking Fourier transforms. Coordinates at the image perimeter give the vertical and horizontal Fourier modes. Because the 2D spectra are normalized by their overall radial profile, the colorscale is unitless. As is explained in the text, the noise exhibits stripy patterns that align with the local scan strategy. In Fourier space, these patterns manifest as bars perpendicular to the local scan strategy. We outline the primary features from the scanning strategy in black. The left (right) panel outlined region contains an average power excess of 8% (25%). Secondary features --- such as detector-detector correlations on the top and bottom of the right panel --- are also visible. The regions of low noise power near the center result from the removal of the radial, or "isotropic," part of the power spectrum.
• Figure 5: Scale-dependent map depth: "Inverse-variance maps" as measured directly from the PA5 f090 difference maps. Top: After filtering $\bm\nu_i$ for small scales, $2000\leq\ell\leq5000$, and averaging over Stokes Q and U in only the first split. Bottom: After filtering $\bm\nu_i\sqrt{\mathbf h_i}$ for large scales, $200\leq\ell\leq500$, and averaging over Stokes Q and U in all eight splits. We square the filtered maps to assess local noise variance, smooth them for legibility (Gaussian $\mathrm{FWHM}=4\pi/5000\, \mathrm{rad}\approx0.14^o$ and $\mathrm{FWHM}=2\pi/500\, \mathrm{rad}\approx0.72^o$, respectively), and take their inverse. We also multiply by pixel area to account for declination-dependent loss of power from the filtering. Because we invert the variance, small values indicate larger noise power. As is explained in the text, the small-scale noise power is modulated by the mapmaker inverse-variance, and the large-scale noise power traces the mapmaker cross-linking.