The Atacama Cosmology Telescope: Summary of DR4 and DR5 Data Products and Data Access

While together the individual map splits span a large sky fraction, they do so in small patches and with the noise characteristics of individual seasons and detector arrays. To complement these smaller, noisier maps, DR4 includes full ACT-observed-sky co-added maps in the 98 and 150 GHz frequency channels, as described in N20. One of these maps is shown in the top panel of Figure 2. These maps combine ACT data from s08–s16 with data from Planck, preserving ACT's high resolution and sensitivity to small scales while adding Planck's sensitivity to large angular scales. The procedure results in individual temperature and polarization maps covering ∼18,000 deg² (${f}_{\mathrm{sky}}\sim 0.44)$ at a resolution of 05 × 05. Since these maps are deeper, and because quoted sky area is a function of noise level, these co-added maps cover marginally more area than the maps in Section 3.1. The full co-added depth is ≤20 $\mu {{\rm{K}}}_{\mathrm{CMB}}$' over ∼2600 deg² (see Figure 14 of N20). See Section 3.8 for the corresponding improvements in map-depth when s17–s18 data from the AdvACT survey are included in DR5.

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DR4 includes co-added maps with and without point sources, as ACT-only and ACT+Planck, and in the 98 and 150 GHz channels. In addition to the maps themselves, DR4 includes associated inverse-variance maps, which can be used to characterize the noise in the maps.

The co-added maps are not recommended for precision cosmology as they lack map splits needed to generate noise simulations or run null tests; the DR4 frequency maps in Section 3.1 are more appropriate. Section 3.8 describes applications that are well suited for the co-added maps.

DR4 includes component-separated maps of the CMB+kSZ blackbody component, and the thermal Sunyaev–Zel'dovich Compton-y parameter, presented in Madhavacheril et al. (2020a). These maps combine multifrequency data from ACT and the Planck satellite to construct arcminute resolution, component-separated maps that cover a wide area (∼2100 deg²). The CMB+kSZ and Compton y-maps are provided for the BN and D56 regions shown in Figure 1. We also show one of these component-separated maps in Figure 2.

These maps are constructed from an internal linear combination of the ACT maps at 98 and 150 GHz and the Planck maps at 30, 44, 70, 100, 143, 217, 353, and 545 GHz. The algorithm (see, e.g., Remazeilles et al. 2011) uses the frequency dependence of a signal of interest to create a map that preserves that specific signal while minimizing the overall variance. This minimization is done in the 2D Fourier domain to adapt to the noise properties of a ground-based experiment like ACT. Maps that explicitly null foreground contamination from specific components with assumed frequency dependence are also provided; in particular (a) Compton-y maps that null the contribution of a dust/cosmic infrared background–like spectral energy distribution (useful for checks of systematic contamination in cross correlations) and (b) CMB+kSZ maps with thermal Sunyaev–Zel'dovich (tSZ) deprojected for use in lensing estimators, among others. See Madhavacheril et al. (2020a) for more discussion of these maps, the procedure used to generate them, and the relevant caveats.

The DR4 s14–s15 data were also used to construct gravitational lensing maps, as described in Darwish et al. (2020). The maps are available for the D56 and BN regions (see Figure 1), in versions with and without Planck data. One of the lensing maps is shown in Figure 2. The lensing maps are produced by first co-adding the maps at 98 and 150 GHz and over two seasons (s14–s15) to produce input maps for the lensing estimator. The maps are then convolved to a common beam, inpainted around bright sources in order to account for foreground biases, and cleaned to reduce the effect of ground contamination. These maps are then passed through the lensing reconstruction pipeline, which uses a minimum variance quadratic estimator. The end result of this process is a set of maps that covers ∼2100 deg² on the sky and is signal dominated on large scales. They also overlap with a number of optical surveys, which enables them to be used for cross correlations with BOSS CMASS (Reid et al. 2016) galaxies (for example, see Darwish et al. 2020). DR4 also includes lensing maps with the tSZ signal removed, following the procedure outlined in Darwish et al. (2020), building on the method from Madhavacheril & Hill (2018), which has a minimal effect on the lensing signal-to-noise ratio.

This notebook gives an introduction to the two data releases, including an explanation of the CAR map format used in DR4 and DR5. It is important to understand how this format differs from HEALPix when using these maps. While the notebooks do not need to be completed in order, we encourage users to read through this first one in order to get a sense of the scope and use of the notebooks.

This notebook introduces both the tools we use to analyze our maps as well the co-added maps presented in N20 and discussed in Sections 3.2.1 and 3.8. Currently, the majority of public CMB data are presented as HEALPix maps, which differ from the format of the ACT maps. Due to this difference, we walk through the basics of how to interact with maps in the CAR format. We use the Python library pixell, ⁶⁰ which is designed for use with CAR maps, and we demonstrate how to load and examine the co-added map.

The co-added maps are reasonably large data files (∼5 Gbyte), and so, while we encourage users to use the full maps if their laptops permit, we also offer a low memory option. This option involves reading in a low-resolution version of the full co-added map as well as a map of a smaller patch of the sky at full resolution. The low-resolution version is created by taking the intensity map from the full co-added map, down-sampling pixels by a factor of four, and then saving the output. The smaller area map was created with the same input map, but instead of down-sampling, we cut out the D56 region using the D56 footprint included in the DR4 release and then save that as our output. These two maps combined represent ∼150 Mbyte of data, compared to the ∼5 Gbyte full-resolution data, and so are easier to handle, while still allowing users to appreciate the significant depth and resolution of the ACT co-added maps (see Figure 3).

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In many instances, it is necessary to convert maps between the CAR and HEALPix format; pixell provides functions that do just that. We give an example of how pixell can be used to convert a Planck map to the same CAR format used for the ACT maps. Similarly, we offer an example of converting the ACT data products to the HEALPix format if users wish to do so.

In order to convert between formats, we calculate the spherical harmonics of the given map and then inverse-transform—or "re-project"—those ${a}_{{\ell }m}{\rm{s}}$ onto the new geometry. For that reason, the re-projections are bandwidth limited by the initial harmonic transform. The re-projection functions can also be used to rotate between different coordinate frames such as from Planck's Galactic frame to ACT's equatorial one.

While these conversions are possible, there are certain benefits to using the pixell framework for the ACT maps. In particular, HEALPix maps do not support analysis using Fourier methods ⁶¹ and instead must be analyzed using spherical harmonics. Furthermore, pixell simplifies working with smaller and/or arbitrary patches from the full footprint maps.

One of the advantages of using pixell is that it makes it easier to examine small patches of a map. In this notebook, we show how to use the DR5 cluster catalog (Hilton et al. 2021), together with our maps, to manipulate compact sources and their surrounding regions. We first examine the cluster catalog and plot the distribution of the objects in 3D space. We then turn to the maps and extract small patches of the sky around compact sources. We then re-project those cutouts to a plane that is tangential to the sky and centered on the compact source. Switching to this tangential plane, as opposed to the CAR projection used for the full maps, recenters the coordinates such that flat-sky distortions for each cutout are radially symmetric. This is especially helpful for sources at high decl. whose cutouts would otherwise be particularly distorted in the CAR projection. As shown in Figure 4, we extend this analysis by demonstrating how to make stacks of clusters from the re-projected cutouts for use in a variety of analyses.

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In order to demonstrate the utility of these cutouts, we show users how to calculate the radially binned profile of the stacked clusters. Users can then fit profiles to the clusters and use these to study a variety of astronomical objects in our maps. We also give an example of how users could apply an aperture photometry filter, such as the one shown in Figure 5, to the stack in order to study the brightness and extent of the clusters that we see. We do this by taking the average of a disk centered on a compact source of radius r and subtracting off the mean of a surrounding annulus of radius $\sqrt{2}r$. We repeat this for a range of radii and then plot the result against the radius of the inner circle.

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We read in a single lensing map (Darwish et al. 2020) and give an example of how to cross correlate the lensing-κ signal with a galaxy density map. This example uses CMASS galaxies ⁶⁴ from the SDSS data release 12 (Reid et al. 2016). To create a galaxy density map, $g(\hat{n})$, from this catalog we use

$$\begin{eqnarray}&&g(\hat{n})=\displaystyle \frac{n(\hat{n})-\tilde{n}}{\tilde{n}},\end{eqnarray} \tag{ 1 }$$

where $n(\hat{n})$ represents the number of galaxies in a specific pixel, and $\tilde{n}$ gives the average number of galaxies per pixel.

The notebook also explains how to account for masking effects when using the lensing maps. In order to create the lensing maps, a mask, known as the CMB window (W_c ), was first applied to the input CMB maps before they were passed into the lensing reconstruction pipeline (Darwish et al. 2020). The released DR4 lensing maps are divided by a factor of W_c ², to correct for the loss of power resulting from the original masking. But since we are introducing a new mask applied to the galaxy map (in addition to the original lensing mask), we need to adjust this factor. This means that we must first remove the $1/{W}_{c}^{2}$ factor in the released map by multiplying by $\langle {W}_{c}^{2}\rangle$. From there we correct for any additional masking that is applied to the maps during the cross correlation as follows. Option 1: If the user is only applying a window to the galaxy map, as is done in this notebook, they would use

$$\begin{eqnarray}&&{C}_{L}\to \displaystyle \frac{1}{\langle {W}_{c}^{2}{W}_{L}\rangle }{C}_{L}.\end{eqnarray} \tag{ 2 }$$

Option 2: If the user would like to apply a mask to both maps, they would instead use

$$\begin{eqnarray}&&{C}_{L}\to \displaystyle \frac{1}{\langle {W}_{c}^{2}{W}_{L}^{2}\rangle }{C}_{L}.\end{eqnarray} \tag{ 3 }$$

The resulting cross-spectrum is shown in Figure 6 where we compare it to the full cross-spectrum from Darwish et al. (2020). The notebook's quick approach differs from the full result, in part, because we do not apply any cuts to the galaxy catalog nor do we apply any weights to individual galaxies when building the galaxy density map. In addition, we use a much smaller map area than that used in Darwish et al. (2020). Despite those limitations, the results follow a similar overall form and agree in their orders of magnitude.

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This notebook demonstrates how to examine the Compton-y and CMB+kSZ maps included with the component-separated maps (Madhavacheril et al. 2020a). We also show that it is possible to see galaxy clusters in the Compton-y map by eye and demonstrate how to stack on the locations of these clusters. This stacking is done using the code we first introduced in notebook 4, and the Deep 56 galaxy cluster catalog from ACT DR3 (Hilton et al. 2018). The same method can be applied to the DR5 catalog.

Notebook 7 focuses on how to perform fast harmonic analyses using the CAR maps, walking through both Fourier transforms and spherical harmonic transforms using pixell.

In order to generate a simple Fourier-based power spectrum, we make use of the Planck map, projected to the CAR format from notebook 3, and an ACT map from notebook 2. We apodize the maps to prevent ringing that would occur during the Fourier analysis of the maps due to sharp edges. This process involves smoothly tapering the edges of the maps such that the borders go to zero (an example of an apodized ACT map is shown in Figure 7). Once this apodization has been applied, we can Fourier transform the ACT and Planck maps, and then cross correlate them. Finally, we compare that cross correlation to the ACT auto-spectrum. This approach is fast and makes it easy to swap in other maps for users who are interested in analyzing their own data products.

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While the Fourier transform approach works well with smaller maps (where a flat-sky approximation is appropriate), we also provide an example using spherical harmonics. This approach uses pixell functions to generate ${a}_{{\ell }m}{\rm{s}}$ and healpy functions to produce a power spectrum.

Both of these approaches are reasonably straightforward to implement and also run quickly on the average laptop. However, they have a few drawbacks, most noticeably that we fail to properly handle mode-coupling effects from the map mask, as is required for cosmological analyses (Hivon et al. 2002). This method is also improved upon in the following notebook.

In this notebook, we continue our study of power spectra, but we pivot to using both the individual ACT map splits from A20 and Section 3.1, as well as the NaWrapper ⁶⁶ code base. This approach offers a few major improvements and much more closely resembles the power spectra analysis that is performed in C20. However, the improvements also make this notebook one of the most computationally intensive. Ordinarily, we would rarely use code like this in a notebook on a laptop; instead we would submit scripts to a computing cluster to make the process significantly more tractable.

With that in mind, the code still offers useful insight into the power spectrum analysis process. We begin by generating the correct mask for the region we are considering, in this case the D56 patch. The total mask consists of an apodized footprint combined with the point-source mask. The inverse-variance map is then used to correctly weight the pixels. This mask mixes harmonic modes in the naive power spectrum of the map relative to the true power spectrum of the unmasked full sky. This effect is fully captured in a mode-coupling matrix, which links the modes of the naive power spectrum to the true power spectrum (Hivon et al. 2002). NaWrapper, using the NaMaster code from Alonso et al. (2019), is designed to efficiently account for this mode-coupling matrix and recover an estimate for the true power spectrum of an unmasked map. Since this step can be relatively time consuming, we provide the matrix on disk so that users can avoid having to run the computation. Using NaWrapper allows us to improve our estimate of the cosmological power spectrum relative to the previous notebooks (which used healpy and pixell), which were unable to properly decouple mixed harmonic modes induced by the mask. Note that we utilize a slightly different code in the C20 pipeline, but the two codes have been shown to produce the same results (see C20).

Another difference between this notebook and notebook 7 is that we use four splits of the data (here D56). This allows us to generate six distinct cross spectra, which we average to estimate the power spectrum. We show two approaches that can be used to generate errors for the power spectra, again providing some of the data products on disk since the calculations can be difficult to run on the average laptop.

Simulations play a central role in understanding the ACT DR4 and DR5 products, from the power spectra to the component-separation pipeline. In particular, feeding large numbers of map-based simulations through those pipelines enables consistency and null tests to be run on spectra, the generation of bin–bin covariance matrices, and assessment of biases in the Compton y- and lensing reconstructions (C20; Madhavacheril et al. 2020a; Darwish et al. 2020). The DR4 release includes a suite of simulation products to complement the data, and in this notebook, we walk through an example of how to create simulations of the ACT noise in map-space.

The notebook follows Appendix B of C20 to recreate a "square-root covariance matrix," the on-disk product released for the DR4 noise simulations. As described in C20, the aim is to construct an unbiased noise model of the ACT DR4 maps on a per-season, patch, detector array, and frequency basis. Since, in general, the map-domain noise is anisotropic in a given patch (as set by the ACT scan strategy), the 2D Fourier-space power spectrum may contain azimuthally varying structure. Starting from the ACT maps, we follow C20 to make estimates of the 2D power spectra (including polarization auto- and cross spectra), which are assumed to capture all off-diagonal elements of the noise covariance matrix. In the notebook, we apply post-processing steps to remove bias from these estimates, and emerge with the square root of the noise covariance matrix. Therefore, when written to disk, the "square-root covariance matrix" enables users to draw fast Gaussian realizations of the underlying anisotropic noise power spectrum.

In Figure 8 we show the Stokes I-I 2D noise power spectrum for the D6 patch, observed by PA1 in s13, as an intermediate step in the C20 noise simulation prescription. The notebook shows corresponding cross spectra for each of the other polarization combinations. The full ACT map-based simulation pipeline, including signal simulations, is publicly available on GitHub. ⁶⁷

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In many cases the raw I, Q, and U maps provided on disk contain the information needed to perform a given analysis. For example, when studying point sources, Galactic dust, or doing component separation, users may require the Stokes Q and U maps instead of maps of E and B modes. However, many analyses require E and B modes as inputs instead. Because the E and B maps are not included in this release, we provide an example of how users can generate maps of the E and B modes from the Stokes components using pixell functions. The method used is straightforward, but as with many Fourier-space operations, decisions such as how users treat bright spots in the maps, or how one apodizes the boundary, can affect the final product.

The data release includes the likelihood of the CMB power spectrum measured by ACT from the individual DR4 patch maps discussed in A20 and Section 3.1. The pyactlike package used in this notebook is available on GitHub. ⁶⁸ The notebook demonstrates how to plot the best-fitting theoretical power spectra with the TT, TE, and EE data, compute the likelihood for a given cosmological model, and plot the residuals of the theoretical model compared to the data. We also show how to load one of the MCMC chains generated using the likelihood from A20, and use it to plot 1D and 2D parameter distributions. The chains allow us to visualize the joint distribution of different model parameters; in the notebook, we plot the distribution of H₀ and ${{\rm{\Omega }}}_{m}$. Another example of the notebook outputs can be found in the bottom row of Figure 2.

As discussed in Han et al. (2021) and Section 3.7, it is possible to use internally reconstructed lensing maps of the D56 region to undo the effect of CMB lensing in the 98 and 150 GHz ACT power spectra. This release includes the delensing likelihood for the D56 region, the best-fit parameters obtained from both lensed and delensed spectra, as well as a parameter-shift covariance matrix. The parameter-shift covariance matrix is used to quantify the shift in the best-fit parameters obtained from lensed and delensed spectra. The notebook demonstrates how to read in the various parameters and the covariance matrix, then uses these products to calculate the parameter-shift ${\chi }^{2}$ and probability-to-exceed values for the given set of lensed and delensed best-fit parameters.