ComPACT: combined Atacama Cosmology Telescope + Planck galaxy cluster catalogue

ABSTRACT

Galaxy clusters are the most massive gravitationally bound systems consisting of dark matter, hot baryonic gas, and stars. They play an important role in observational cosmology and galaxy evolution studies. We develop a deep learning model for segmentation of Sunyaev–Zeldovich (SZ) signal on Atacama Cosmology Telescope (ACT) + Planck intensity maps and construct a pipeline for microwave cluster detection in the ACT footprint. The proposed model allows us to identify previously unknown galaxy clusters, i.e. it is capable of detecting SZ sources below the detection threshold adopted in the published galaxy clusters catalogues [such as ACT DR5 and Planck Sunyaev–Zeldovich 2 (PSZ2)]. In this paper, we use the derived SZ signal map to considerably improve a cluster purity in the extended catalogue of Sunyaev–Zeldovich objects from Planck data (SZcat) in the ACT footprint. From SZcat, we create a new microwave galaxy cluster catalogue (ComPACT), which includes 2962 SZ objects with cluster purity conservatively estimated as ≳74–84 per cent. We categorize objects in the catalogue into three categories, based on their cluster reliability. Within the ComPACT catalogue, there are ≳977 new clusters with respect to the ACT DR5 and PSZ2 catalogues.

1 INTRODUCTION

Galaxy clusters are the most massive gravitationally bound systems in the Universe (see Allen, Evrard & Mantz 2011; Kravtsov & Borgani 2012, for reviews). These objects are located at the nodes of the cosmic web and serve as reliable tracers of the underlying dark matter distribution. The cluster mass function, which describes the number density of galaxy clusters as a function of their mass, and its evolution with redshift provide a critical test of structure formation models and allows to constrain cosmological parameters (e.g. Vikhlinin et al. 2009; Burenin & Vikhlinin 2012; Mantz et al. 2015; Pratt et al. 2019, among others).

Galaxy clusters are composed of dark matter, which makes up around 85 per cent of their total mass, the intracluster medium (ICM; ∼12 per cent of the total mass), which is an ionized hot gas, and stars (∼3 per cent). Consequently, they can be detected at several wavelength bands. In the optical range, galaxy clusters represent a concentration of elliptical galaxies. Clusters are also bright in X-rays mainly due to thermal bremsstrahlung and line emission produced by the ionized ICM (Sarazin 1988). X-ray catalogues may provide a wealth of information about galaxy clusters, such as their temperature, luminosity, and gas mass, which are essential for understanding the formation and evolution of these structures. The same hot ICM (namely, the high-energy electrons) also interacts with low-energy cosmic microwave background (CMB) radiation through the inverse-Compton scattering creating a distortion in the blackbody spectrum [the thermal Sunyaev–Zeldovich (SZ) effect; Sunyaev & Zeldovich 1970, 1972]. The ICM boosts CMB photons to higher frequencies resulting in a characteristic increase/decrease in the CMB intensity depending on the specific microwave frequency in which a galaxy cluster is being observed. Studying galaxy clusters in (sub)millimetre range via the SZ effect has several advantages over other wavelength ranges. First, the magnitude of the SZ effect does not depend on redshift, thus providing a powerful tool for detecting clusters at high redshifts. Second, the SZ signal is proportional to the integrated gas pressure along the line of sight through the cluster, which is directly linked to the total mass of a cluster. The relationship between the integrated Compton parameter Y_SZ (the total SZ flux) and a cluster mass M has already proved to be particularly tight (see Kravtsov, Vikhlinin & Nagai 2006; Planck Collaboration III 2013, among many others). Although, a scatter in the Y_SZ–mass relation is not negligible since clusters are not spherical, they have different accretion histories, a contribution of the non-thermal pressure support in cluster outskirts may be significant (e.g. Battaglia et al. 2012; Yu, Nelson & Nagai 2015; Green et al. 2020). Moreover, the presence of non-thermal pressure in the cluster introduces a bias in mass determination from the SZ (or X-ray) observations as masses are typically estimated under the assumption of the hydrostatic equilibrium between the gravitational potential and the observed thermal (not total) pressure (Nagai, Vikhlinin & Kravtsov 2007; Rasia et al. 2012; Battaglia et al. 2013; Biffi et al. 2016, among many others). The third advantage of studying clusters via the SZ effect is the ability to build a virtually mass-limited sample. SZ-selected clusters are shown to be less biased in favour of cool-core and/or relaxed systems compared with X-ray selected samples (e.g. Eckert, Molendi & Paltani 2011; Rossetti et al. 2016; Lovisari et al. 2017).

The number of SZ catalogues have been released in recent years including the Planck survey (Planck Collaboration XXI 2014b; Planck Collaboration XXXVI 2016a), the South Pole Telescope (SPT; Bleem et al. 2015), and the Atacama Cosmology Telescope (ACT; Hilton et al. 2021). With ongoing and upcoming CMB surveys, more than 10⁴ galaxy clusters are expected to be detected (Raghunathan et al. 2022). Together with reliable mass estimates,¹ such cluster samples may have a ground-breaking impact on our understanding of the structure growth in the Universe, the dark energy equation of state, and modified gravity theories (e.g. Burenin & Vikhlinin 2012; Burenin 2013, 2018; Bocquet et al. 2015; Mantz et al. 2015; Planck Collaboration XIII 2016b).

Recently, Meshcheryakov et al. (2022) presented extended catalogue of Sunyaev–Zeldovich objects from Planck data (SZcat) – a catalogue of Planck-extended SZ sources with a low level of significance (so that nearly all possible Planck cluster candidates are there along with a large number of spurious detections). Here, we aim to develop a method for an automated cluster detection on publicly available combined ACT and Planck maps (Naess et al. 2020) and to apply it to the fields of SZcat sources. As a result, we obtain a new catalogue of galaxy clusters – ComPACT.

The paper is organized as follows. In the next section, we review deep learning (DL) models for SZ clusters detection proposed in literature. Section 2 describes data used in this work. In Section 3, we describe a DL model for cluster segmentation and a procedure for an object detection. Then, in Section 4, the ComPACT catalogue is described. In Section 5, our conclusions are presented.

1.1 DL models for SZ clusters detection

In the last few years, DL approaches based mostly on convolution neural network (CNN) architectures were successfully applied to various object detection and segmentation problems in observational astronomy in different spectral domains, e.g. to imaging data in radio (Hartley et al. 2023), microwave (Bonjean 2020; Lin et al. 2021; Meshcheryakov et al. 2022), and optical (Burke et al. 2019) spectral ranges. The key advantages of DL models over classical astronomical object detection methods [such as SExtractor (Bertin & Arnouts 1996) in the optical or matched multifilter approach (MMF, Melin, Bartlett & Delabrouille 2006; Williamson et al. 2011) in the microwave] are: (i) unification of an object detection model architecture over many spectral domains, and (ii) the amazing ability of a DL method to improve itself with the increase of size of available training sample. As it was shown in SKA Science Data Challenge 2 (Hartley et al. 2023), DL models trained on a large and representative enough knowledge base outperform classical approaches in the astronomical object detection tasks.

As mentioned previously, DL approaches were successfully applied to microwave imaging data. Bonjean (2020) proposed to use a DL model with the encoder–decoder architecture to make a segmentation map of SZ signal from Planck High Frequency Instrument (HFI) imaging data and detected SZ sources on it. Verkhodanov et al. (2021) trained a CNN classification model to recognize SZ sources in Planck intensity maps. Lin et al. (2021) proposed a hybrid model DeepSZ, based on a combination of CNN and a classical MMF approach and demonstrated its power in detecting SZ sources using the simulated CMB maps (with characteristics similar to SPT-3G survey).

In all aforementioned papers no catalogue of SZ sources was published. Recently, Meshcheryakov et al. (2022) trained a U-Net model on Planck HFI data and presented SZcat – a full catalogue of cluster candidates. SZcat is a large combined sample of galaxy cluster candidates (up to a low confidence threshold) selected by two methods: (i) using the DL model (described in Meshcheryakov et al. 2022) and applying it to Planck HFI intensity maps; and by (ii) using a classical detection approach (Burenin 2017) and applying it to Compton parameter maps published in Planck 2015 data release (Planck Collaboration XXIV 2016c). By its construction, SZcat is characterized by high completeness and low cluster purity of approximately 22 per cent. We use the SZcat catalogue further in our work.

Another approach to detect new objects is to combine data from different telescopes. It makes possible to lower the threshold for cluster detection and discover previously undetected galaxy clusters. For example, Melin et al. (2021) combined Planck and SPT microwave data; Tarrío, Melin & Arnaud (2019) combined Planck data with ROSAT X-ray catalogue. In both cases of Planck-SPT and Planck-ROSAT data combination, new cluster catalogues were published (with higher completeness/purity than cluster catalogues obtained from Planck/SPT/ROSAT data individually).

2 DATA

We use publicly available composite ACT + Planck intensity maps² from Naess et al. (2020) at 90, 150, and 220 GHz with 0.5 arcmin per pix resolution covering around 18 000 squared degrees of the sky area (which we call as the ACT footprint hereafter). To combine ACT and Planck data, Naess et al. (2020) used the HFI Planck maps at 100, 143, and 217 GHz, i.e. at frequencies close to the ACT ones. Authors split maps into tiles and model the tiles as noisy, transformed versions of a single underlying sky. They then used the overlap to seamlessly merge the tiles into a single map.

In order to train and test a SZ cluster segmentation model (see Section 3), we use the following catalogues of galaxy clusters and radio sources found in the ACT data:

• The ACT DR5 cluster catalogue (Hilton et al. 2021), which contains 4195 optically confirmed galaxy clusters. The sources were selected by using the MMF method for the ACT multifrequency data collected from 2008 to 2018. In Section 4.1, we illustrate the mass–redshift dependence for ACT clusters using the cluster masses from the M500cUncorr column (see table 1 in Hilton et al. 2021), which were obtained by assuming the universal pressure profile and the scaling relation between the integrated Compton parameter Y_SZ and M₅₀₀ (a halo mass contained within a radius inside of which the mean interior density is 500 times the critical density) from Arnaud et al. (2010);

• A catalogue of point sources [predominantly, active galactic nuclei (AGNs)] from Datta et al. (2019), which covers 680 squared degrees of the full ACT footprint; and

• The equatorial catalogue of extragalactic sources (Gralla et al. 2020), which contains 287 dusty star-forming galaxies (DSFGs) and 510 radio-loud AGNs.

Additionally, for training and testing our classification model (see Sections 3.1.2–3.1.3), we select a number of random fields which do not contain neither ACT DR5 clusters nor radio sources from Datta et al. (2019) and Gralla et al. (2020). Since the density of clusters on the sky is low (see our estimates in Section 3.1.3), these fields are expected to be free of galaxy clusters.

We construct a new catalogue of galaxy clusters on the basis of the extended Planck cluster candidates sample SZcat, which is expected to contain almost all microwave clusters seen in the Planck data. In the ACT footprint (which we consider here), the total number of SZcat sources is N_SZcat = 14 850.

To estimate the purity and completeness of cluster detections in a resulting catalogue (see Section 4), we have selected N_field = 14 850 random directions on the sky in the ACT footprint.

For test purposes, we cross-correlate a new catalogue with the following external X-ray and SZ cluster catalogues: MCXC, 4XMM DR12, SPT-SZ, ComPRASS, and PSZSPT (see Appendix  B).

3 METHOD

Fig. 1 illustrates the sequence of pipeline steps in constructing a catalogue of potential SZ sources. We convert the full ACT + Planck intensity map into a SZ signal segmentation map by using a DL classification model (see Section 3.1). Then, the detection procedure (described in Section 3.2) is applied to the SZ signal segmentation map, resulting in a catalogue of SZ sources candidates. Below, we describe the SZ signal segmentation and source detection procedures in detail.

3.1 DL SZ signal segmentation model

To recognize SZ signal on ACT + Planck intensity maps, one could follow the approach already presented in Bonjean (2020) and Meshcheryakov et al. (2022), i.e. to train a classical U-Net segmentation architecture on the microwave data. To do so, one needs to define a ground truth segmentation mask. For example, Bonjean (2020) and Meshcheryakov et al. (2022), for each source in the training sample of clusters, drew circles at the cluster positions with the average Planck point spread function (PSF) full width at half-maximum (FWHM) size. This approach implies that a galaxy cluster is approximated as a circle with the Planck PSF radius, thus some information about the real shape and size of galaxy clusters in the training set is lost.

In this work, we use a different approach to SZ signal DL segmentation. We train a DL classification model on snapshot images centred on ACT DR5 galaxy clusters (the positive class), snapshot images centred on radio sources (mainly, DSFGs and radio-loud AGNs), and snapshot images taken in random directions of the sky (the negative class). Then, we apply our classifier to each pixel of ACT + Planck intensity maps and thus obtain the SZ signal segmentation map in the ACT footprint. This approach has a potential benefit of retaining information about clusters shapes in the DL model.

Below we explain a construction of SZ signal classification model.

3.1.1 Classification model architecture

We aim to construct a classification algorithm that analyses a segment of a microwave ACT + Planck map and yields a probability of detecting a cluster at a centre of a segment. To do so, we use a convenient CNN + multilayer perceptron (MLP) architecture, the adopted version of Visual Geometry Group (VGG; Simonyan & Zisserman 2015).

Table 1 summarizes the architecture of the artificial neural network model. The CNN part contains four identical blocks. Each convolutional block (except for the first one, in which the first convolution has a kernel of size 5) has two convolution kernels of 3 × 3 pixels size (padding = 1, stride = 1), the rectified linear unit activation function [ReLU(x) = max (0, x); Maas et al. 2013] and the MaxPooling subsampling unit. The second part contains an MLP with three linear layers, each with a ReLU activation function. We use the batch normalization (Ioffe & Szegedy 2015) in CNN and MLP layers and DropOut with p = 0.5 (Hinton et al. 2012) in each MLP layer for the network regularization. We use the linear layer with the standard Logistic Sigmoid function (see e.g. Dubey, Singh & Chaudhuri 2022) to obtain a probability of SZ signal as the network output. Total number of trained parameters equals to 462 865.

3.1.2 Model training and validation

To create the model input, the ACT + Planck map is divided into two distinct regions: training and test sets. The training set is used to learn the optimal model parameters, while the test set is needed to evaluate a final model. We also include in the knowledge base (train and test samples) fields in random directions on the sky, which do not overlap neither with clusters from ACT DR5 nor with radio sources (within a 10-min radius).

For the training set, we select the western region of the sky in equatorial coordinates (α > 180°). This region encompasses a total of 2449 galaxy clusters from ACT DR5 (≃35.5 per cent of the train data set) and 1226 non-cluster radio sources (≃17.8 per cent). Random fields comprise approximately 46.7 per cent of the train sample.

To prepare our data set, we cut the ACT + Planck maps into 16 arcmin × 16 arcmin squares (32 × 32 pixels). To improve the model accuracy and to avoid overfitting, we apply image preprocessing and augmentation techniques to our input images. In particular, we normalize all the images in the following way:

where ||x||₂ is the Euclidean norm over rows. Further image transformations include standard augmentation techniques such as flipping and random perspective.

To quantify the model performance, we use a binary cross-entropy loss function ℓ(y, f_θ):

where y is the actual class (y = 0 for non-clusters and y = 1 for clusters), and f_θ ∈ [0, 1] is the predicted label, which can be interpreted as the probability of detecting a cluster in a given field. The loss function compares predicted probabilities to the actual class output and calculates a penalty score based on the distance from the expected value. This loss function is a way to measure the accuracy of a DL algorithm in predicting expected outcomes and is useful in optimizing the model and increasing its accuracy.

For iterative updating the network parameters θ, we use the Adam optimization method (Kingma & Ba 2017) (with default parameters except weights_decay = 0.001). All hyperparameters, such as kernel size, padding, stride, etc., are selected manually by training different models to achieve the best performance.

3.1.3 Classification model test

The test data set includes 1745 galaxy clusters (≃30.7 per cent of the test data set), 519 point sources (≃9.1 per cent), and 3422 random fields (≃60.2 per cent) in the eastern part of the sky (α ≤ 180°).

To demonstrate the model behaviour, we show a distribution of predicted probabilities of detecting a cluster in a given patch of the sky for the test sample on Fig. 2 (we consider only the area with the galactic latitude |b| > 15° to avoid the Galactic plane). The test data set includes clusters, point sources, and random fields (see Section 3.1.2). From Fig. 2, we see that for most of the clusters (in grey) from the test data set, the model correctly assigns high probabilities (note that the vertical axis is shown in log-scale), while for most of the point sources (in red) and random fields (in blue) predicted probabilities are low. Approximately 0.06 per cent of point sources, the model misclassifies as galaxy clusters. The vertical line marks the probability threshold, which we further use to form a criterion for distinguishing cluster candidates from non-clusters. Most of the objects with probabilities <0.3 are non-clusters. Although, ∼2 per cent of genuine clusters are not recognized as clusters by our algorithm (i.e. the model predicts p < 0.3). There is a ∼3 per cent misclassification (p > 0.3) in random fields in test, i.e. some random fields are recognized as clusters.

In general, in data-driven DL-based modelling, data quality may affect classification performance (Sukhbaatar et al. 2014). Let us discuss possible sources of erroneous labels in the training data set and how such labels may impact the overall performance of our model. False labels in the ACT DR5 catalogue are not expected since all clusters there are optically confirmed. Erroneous labels in the negative class [which contain AGN, DSFG, and random (empty) fields] might be present, because some of the snapshots (more precisely, the central pixel of the snapshots) might contain a serendipitous cluster. We roughly estimate a probability of detecting a cluster in a given pixel by summing up the area³ occupied by clusters from ACT DR5 and dividing it by the total area covered by the catalogue (see Table 2). Then we multiply the resulting probability by the number of snapshots in the negative class of the train data set. So we conclude that ∼10 clusters might be present in the non-cluster class, or, in other words, there are ∼10 erroneous labels (less than 0.1 per cent) in our data set. Taking into account that the loss function is calculated by averaging values obtained in batches of size 64 objects, the influence of a few erroneous labels is not significant.

3.1.4 Segmentation map

We apply our classifier to each pixel of ACT + Planck intensity maps and obtain a segmentation map. Each pixel in the segmentation map denotes a probability of a presence of the SZ signal in the direction of pixel centre.

An example of a patch of the segmentation map containing a massive galaxy cluster is shown in Fig. 3. We choose the direction of SZ_G098.31-41.19 (marked as the red cross) from the SZcat catalogue. The top row and the bottom-left panel show three fragments of the ACT + Planck input maps at 98, 150, and 220 GHz. The probability map for this area is shown at the bottom-right panel. It contains only one connected group within a chosen window, and this group can be associated with the galaxy cluster PSZ2 G098.30−41.15 from the Planck Sunyaev–Zeldovich 2 (PSZ2) catalogue (marked with a magenta star) and ACT-CL J2334.3+1759 from ACT DR5 (its centre is shown with a brown circle). It is a massive cluster with M₅₀₀ ∼ (7–8)10¹⁴ M_⊙ (Hilton et al. 2021) located at z = 0.436.

3.2 Detection model

Since galaxy clusters are extended objects, in the segmentation map we look for connected groups of pixels with probabilities above a certain threshold. To do so, we use the scikit-image (van der Walt et al. 2014) library developed for scientific image analysis in Python. We analyse manually a sample of probability maps for known clusters (i.e. patches of the segmentation map which contain galaxy clusters) and random fields on the sky (with no clusters) and derived the optimal value of the threshold segmentation p_seg = 0.3 (see Fig. 2). For comparison, Bonjean (2020) used a threshold p_seg = 0.1 to select sources in the SZ signal segmentation map created from Planck HFI imaging data.

Additionally, we remove the complex Galactic plane from consideration and keep only objects with the galactic latitude |b| > 15°. The resulting catalogue contains more than 1 million potential SZ sources candidates with p > 0.3 in the ACT footprint.

4 THE COMPACT CATALOGUE

Here, we apply our method to the extended Planck cluster candidates sample SZcat (Meshcheryakov et al. 2022), having a low purity, in order to get a medium-sized cluster catalogue, ComPACT, dominated by SZ objects seen in Planck, and having a fairly high cluster purity. By its construction, our resulting catalogue does not contain any new detections relative to SZcat, but a certain fraction of clusters is barely distinguishable from the noise in the Planck maps but seen in the ACT data (see Appendix  D). That is why we consider ComPACT as a combined ACT + Planck cluster catalogue.

For each direction in the SZcat catalogue, we consider the nearest detected connected group of pixels in a window with R_match = 5 arcmin. For each object we calculate (i) the group area S (the total number of pixels in a given connected group), (ii) the maximum probability p_max in an object, and (iii) the distance R from the object centre (the pixel with p_max) to the input direction (see Appendix  C). Below we analyse different samples to form a criterion for distinguishing clusters from non-clusters among the connected groups (Figs 4 and C1 in Appendix  C).

Let us now illustrate how a distribution of objects looks like on the p_max–S plane for random directions⁴ on the sky (see the left panel of Fig. 4). Random fields are unlikely to contain galaxy clusters. We see that non-clusters tend to have low areas and lower values of p_max compared with clusters. In central panels of Fig. 4, we show distributions of clusters detected by our model along the input directions from the ACT DR5 test subsample (see Section 2) and from test PSZ2z (PSZ2z is the PSZ2 subsample of clusters with spectroscopic redshifts). All those objects are optically confirmed clusters. We see that real clusters tend to have large areas and large values of p_max. Right panel of Fig. 4 presents the p_max–S distribution of the nearest objects detected by our model in the 5-arcmin window along the SZcat directions. We detect a large number of sources with high area and high values of p_max, which are likely to be genuine clusters.

In order to select optimal thresholds to separate clusters from non-clusters, we analyse the behaviour of the following three characteristics whose dependence on the S–p_max threshold grid is shown in Fig. 5:

• Completeness (see equation D.1) on the left panel. We estimate completeness with respect to optically confirmed clusters from PSZ2z + ACT DR5 catalogues. We associate clusters from the PSZ2z + ACT sample in the test area with the nearest object from our full catalogue of SZ candidates (see Section 3.2);

• Purity with respect to Planck clusters (see equation D.4) on the central panel. This parameter is estimated from the number of random fields |$\hat{N}_{\rm field}$| in which our model detects a cluster (see Table 3 for typical |$\hat{N}_{\rm field}$| values for different area thresholds). We consider |$\hat{N}_{\rm field}$| as the number of false positive detections with respect to the Planck clusters; and

• The number of clusters N_ComPACT in a resulting catalogue on the right panel.

In Fig. 5, we show how the aforementioned metrics change with respect to different S and p_max thresholds. As the area S and p_max decrease, the number of objects in a catalogue and the catalogue completeness increase, but the percentage of Planck clusters, ‘recovered’ in the ACT data by our model, decreases. Therefore, it is important to choose thresholds that ensure high completeness and purity of the resulting catalogue. To strike a balance between the two, we choose the thresholds S = 20 and p_max = 0.8, which provide a compromise between the completeness and Purity_{cl, Planck}. The resulting sample of objects with S ≥ 20 and p_max ≥ 0.8 we call the ComPACT catalogue, and consider as one of the main deliveries of this work. Contours are plotted with C = 0.86 (the dashed white line) and Purity_{cl, Planck} = 0.68 (the dotted black lines). Choosing a higher threshold for p_max results in a loss of purity, so we select thresholds where the white and black contours intersect. Additionally, we create a column ‘Priority’ which indicates the reliability of clusters:

• ‘Priority’ = 1 is given to cluster candidates with S ≥ 30 and p_max ≥ 0.8 (marked with the triangle in Fig. 5);

• ‘Priority’ = 2 is assigned to objects with S ≥ 25 and p_max ≥ 0.8 (the star in Fig. 5); and

• ‘Priority’ = 3 is for objects with S ≥ 20 and p_max ≥ 0.8 (the circle in Fig. 5).

By definition, ‘Priority’ = 1 subsample has the highest purity among subsamples with different priorities.

In Fig. 6, we show a distribution of ComPACT clusters on the sky (in galactic coordinates).

4.1 Cross-correlation of ComPACT with external cluster catalogues

We cross-correlate the derived ComPACT sample with the following X-ray and SZ external cluster catalogues: MCXC, ACT DR5, PSZ2, SPT-SZ, ComPRASS, and PSZSPT. The cross-match radius is set to 5 arcmin. This choice is motivated by the analysis of average number density radial profiles (for different cluster catalogues) in the neighbourhood of ComPACT objects (see Fig. B1). Table 2 gives the summary information about external cluster catalogues in comparison with ComPACT.

In Fig. 7 (left panel), we show numbers of ComPACT clusters associated with different external cluster catalogues. ComPACT contains 2962 cluster candidates (see Table 3 for numbers related to different ‘Priority’ subsamples). In total, 1220 ComPACT objects are associated with sources from external cluster catalogues, among which 1135 clusters are found in Planck and/or ACT cluster catalogues. From ACT DR5, we identify 1027 matches, cross-correlation with the PSZ2 catalogue gives 466 clusters.

In Fig. 7 (right panel), we show numbers of ComPACT clusters that are not found in PSZ2/ACT cluster catalogues (also see row N_new in Table 3) and are associated with objects from other cluster samples. 1827 ComPACT objects are new with respect to the existing ACT DR5 or PSZ2 cluster samples. One can see, that 85 objects are found in MCXC, SPT-SZ, ComPRASS, and PSZSPT catalogues. We identify three clusters in SPT-SZ, three clusters in PSZSPT, 13 in MCXC, and 71 in ComPRASS. All ComPACT objects identified as X-ray galaxy clusters with luminosity (in the energy band 0.5–2 keV) exceeding 7.5 · 10⁴⁴ erg s⁻¹ have p_max ∼ 1.

4.2 Catalogue metrics

The key characteristics of a cluster catalogue are its purity and completeness metrics. In Table 3, we show how the key characteristics of the catalogue change with the ‘Priority’ value: N_ComPACT – the number of objects in a catalogue, N_PSZ2 – the number of ComPACT clusters associated with PSZ2, and N_new – objects that are not found in ACT/PSZ2 samples. One can see that all these numbers decrease as the ‘Priority’ increases. In the catalogue with ‘Priority’ = 3 there are 2962 candidates, and the cleanest sample contains 1720 objects. In Table 3, we also provide |$\hat{N}_{\rm field}$| – the number of detections with chosen thresholds (p_max, S) in the random field directions. Then, we introduce the following estimates of purity:

• Purity_{cl, Planck} (see equation D.4) reflects the percentage of the Planck clusters found in the catalogue;

• Purity_cl, min (see equation D.6). The lower purity is estimated by using SZcat purity estimate of 21.7 per cent. We expect a higher purity, as we find more probable directions using our method; and

• Purity_cl, max (see equation D.8). In this evaluation, we used information about false detections that can be estimated by counting |$\hat{N}_{\rm field}$| and p_max, which is good corrected on the test sample.

In Table 3, we show the estimate of purity and N_new, cl – number of new clusters that are expected to be real with respect to ACT/PSZ2. |$\hat{N}_{\rm field}$| decreases from 946 to 337, so number of false detections decreases due to area threshold. We see that all purities increase from 74/94 per cent to 84/96 per cent as the threshold of S increases.

We estimate the ComPACT completeness with respect to PSZ2z (the subsample of PSZ2 objects with optical identification and cluster spectroscopic redshift measurements) and ACT DR5 cluster catalogues. We associate clusters from PSZ2z or ACT samples in the test area with the nearest object from our full catalogue of SZ candidates (see Section 3.2). All cluster associations are shown in the central panels of Figs C1 and 4. Then, we estimate the ComPACT catalogue completeness as in equation (D.1).

In Table 3, we show completeness for three ‘Priority’ tags for the ACT DR5 and PSZ2z cluster samples. For ACT DR5  + PSZ2z sample we get C ≈ 0.7–0.86, then for ACT DR5 separately C_ACT ≈ 0.71–0.88 and PSZ2z – C_PSZ2z ≈ 0.61–0.7. Some percentage of true clusters are not assigned to clusters by our (detection) model due to their low area, i.e. these objects have S < 20 (‘Priority’ = 3), S < 25 (‘Priority’ = 2), and S < 30 (‘Priority’ = 1). The decrease in the completeness of Planck cluster detection in ComPACT seems to be due to: (i) the way of combining ACT and Planck data in the joint intensity maps (Naess et al. 2020) and (ii) the wrong association between the connected group and SZcat for some ComPACT clusters.

Another variant of completeness loss is the appearance of AGN in the cluster centre. To check the influence we cross-correlate ACT DR5 test sample with a quasy stellar object (QSO) from SDSS DR17 in 1.4 arcmin (a diffraction-limited resolution of ACT in 150 GHz). We find 93 clusters with quasars in the centre. We then construct a cumulative function for the sample with and without QSOs, to which we apply the KS test. We check whether the samples belong to the same statistical population and obtain p-value = 7.6 · 10⁻⁶. This shows that the AGNs in the centre of the cluster do not affect the predictions of the model.

4.3 Mass–redshift

In Fig. 8, we illustrate the mass-redshift dependence for clusters in ACT DR5 and PSZ2z catalogues.⁵ The blue and orange contours represent the distributions of the full ACT DR5 and PSZ2z catalogues, respectively. For ACT DR5 cross-correlated with SZcat, we ‘recover’ 1027 clusters (shown as blue squares in the upper left panel), and 70 ACT clusters⁶ are missing in ComPACT (shown as green stars in the bottom-left panel). We miss low-mass cluster candidates at intermediate and high redshifts due to (i) detection limitations of the SZcat catalogue, and (ii) our area criterion (see the second panel of Fig. 4).

The mass–redshift distribution for PSZ2z matches (for candidates with measured masses and redshifts, 399 objects) in ComPACT is plotted as red squares in the upper right panel of Fig. 8. PSZ2z clusters that are not present in ComPACT are shown as purple stars (154 objects) in the bottom-right panel of Fig. 8.

Let us now discuss cluster candidates that do not have any matches in ACT DR5 or PSZ2 catalogues. In Fig. 9, we plot matches (with available in the literature masses and redshifts) with SPT-SZ (red dots), ComPRASS (black stars), and MCXC (magenta crosses). Most of them lie at z < 0.8. Compared with the ACT DR5 catalogue, ComPACT is more complete at lower redshifts. We expect to find objects with low mass at low redshifts and clusters on the border of PSZ2z density distribution.

With regard to the mass–redshift dependence, it can be observed that a qualitative selection function is viewed in the identified clusters. Found objects do not descend at increasing redshift to small masses, which is related to the sensitivity of the SZcat catalogue, but at the same time we find low-mass clusters at small z. In order to recover selection function, it would be necessary to simulate clusters, which is beyond the scope of this paper but will be done in the future.

5 CONCLUSIONS

Galaxy clusters are the most massive gravitationally bound systems, consisting of dark matter, hot baryonic gas, and stars. They play an important role in observational cosmology and studies of galaxy evolution. We have developed a DL model for the segmentation of SZ signals on ACT + Planck intensity maps and constructed a pipeline for the detection of microwave clusters in the ACT footprint. The proposed model allows us to identify previously unknown galaxy clusters, i.e. it is capable of detecting SZ sources below the detection threshold adopted in the published galaxy cluster catalogues (such as ACT DR5 and PSZ2).

In this paper, we use the derived SZ signal map to considerably improve cluster purity in the SZcat in the ACT footprint. From SZcat, we create a new microwave galaxy cluster catalogue (ComPACT), which contains 2962 SZ-objects with cluster purity conservatively estimated as ≳74–84 per cent. We categorize objects in the catalogue into three categories according to their cluster reliability. The ComPACT catalogue includes more than 977 new clusters (with respect to ACT DR5 and PSZ2 catalogues).

In future work, we plan to identify these objects in optical and X-ray surveys and estimate their total masses and redshifts.

Acknowledgement

We acknowledge the publicly available software packages that were used throughout this work: NumPy (Oliphant 2006; van der Walt, Colbert & Varoquaux 2011; Harris et al. 2020), pandas (McKinney 2010; The Pandas Development Team 2023), Matplotlib (Hunter 2007), Astropy (The Astropy Collaboration et al. 2013, 2018, 2022), pixell,⁷ and pytorch (Paszke et al. 2019).

We also acknowledge the use of the Legacy Archive for Microwave Background Data Analysis (LAMBDA), part of the High Energy Astrophysics Science Archive Center (HEASARC). HEASARC/LAMBDA is a service of the Astrophysics Science Division at the NASA Goddard Space Flight Center.

DATA AVAILABILITY

The ComPACT cluster catalogue is publicly available: https://github.com/astromining/ComPACT.

Footnotes

References

APPENDIX A: DESCRIPTION OF THE COMPACT CATALOGUE

The ComPACT catalogue contains 2962 galaxy cluster candidates (Purity = 74–84 per cent). In Table A1 we show a sample of five rows from catalogue.

Below we describe columns of the catalogue.

• Name: ID of a ComPACT object;

• RA: Object right ascension (in degrees, J2000 epoch). Centre of object corresponds to pixel with highest SZ signal probability in the source area;

• DEC: Object declination (in degrees, J2000 epoch);

• S: Object area (pixels with p > 0.3) on the SZ signal segmentation map (in pixels);

• p_max: SZ signal probability (in the object centre);

• SZcat: SZcat object name;

• ACT: ACT DR5 cluster name;

• PSZ2: PSZ2 cluster name; and

• Priority: Reliability of objects:

  • 1 – the object has S > 30 and p_max = 0.8, Purity ∼ 0.84–0.95;

  • 2 – S > 25 and p_max = 0.8 and Purity ∼ 0.78–0.94; and

  • 3 – S > 20 and p_max = 0.8 and Purity ∼ 0.74–0.92.

APPENDIX B: DESCRIPTION OF EXTERNAL CLUSTER CATALOGUES

Below is a description of the catalogues used, which were not described in the main part of the article.

B1 PSZ2

The PSZ2 (Planck Collaboration XXVII 2016d) cluster catalogue contains clusters with a high level of significance (signal-to-noise ratio (S/N) > 4.5). The total number of objects is 1653. The PSZ2 catalogue includes galaxy clusters with redshifts up to z = 0.8. The multifrequency matched filter algorithm [MMF1 (Herranz et al. 2002) and MMF3 (Melin et al. 2006)] and PowellSnakes (Carvalho et al. 2012) were used to find SZ objects. In the ACT footprint, there are 782 clusters. Among those, 551 clusters have also measurements of spectroscopic redshifts. We call this subsample of the Planck catalogue as PSZ2z. Cluster masses in the PSZ2 catalogue were obtained from the scaling relation between the measured SZ flux, Y₅₀₀, and the total mass M₅₀₀ at a given redshift (for details, see Planck Collaboration XX 2014a).

B2 SPT-SZ

The SPT observes the southern sky at 95, 150, and 220 GHz with an angular resolution of 1–1.6 min (Carlstrom et al. 2011). We use the SPT-SZ cluster catalogue⁸ (Bleem et al. 2015; Bocquet et al. 2019), which contains 677 SZ detections, among which 516 objects have been confirmed as clusters using optical and near-infrared observations. 597 SPT-SZ clusters lie in the ACT footprint. Mass estimates for the SPT-SZ clusters come from the weak-lensing calibrated scaling relations (Bocquet et al. 2019).

B3 PSZSPT

The PSZSPT (Melin et al. 2021) catalogue combines data from the Planck space telescope and the SPT ground-based telescope. The catalogue was obtained by using multifrequency matched filtering and contains 419 clusters (with S/N > 5), 373 of which lie in the ACT footprint.

B4 ComPRASS

Planck microwave data and ROSAT All-Sky Survey (Tarrío et al. 2019) X-ray data were combined to create the catalogue. The catalogue contains 2323 objects (including confirmed clusters and cluster candidates), with 1110 objects are in the ACT footprint.

B5 MCXC

The MCXC meta catalogue (Piffaretti et al. 2011) contains 1868 X-ray clusters detected in ROSAT and EXOSAT data (by various groups) with optical identifications. 867 X-ray clusters are in the ACT footprint.

APPENDIX C: DEPENDENCE BETWEEN R AND S

Let us now illustrate how a distribution of detected sources looks like on the R–S plane for random directions⁹ on the sky (see the left panel of Fig. C1). Random fields are unlikely to contain galaxy clusters.

We see that non-clusters tend to have low areas and are offset from the input direction. In central panels of Fig. C1 we show distributions of clusters detected by our model along the input directions from the ACT DR5 test subsample (see Section 2) and from PSZ2z (the PSZ2 subsample of clusters with spectroscopic redshifts). We see that real clusters tend to have large areas. For ACT DR5 sources, R is low (∼1 arcmin for majority of clusters) since ACT has a good spatial resolution. For PSZ2z, clusters are more widely distributed in the R–S plane because of poorer Planck resolution (compared with ACT). Right panel of Fig. C1 presents distributions of nearest connected groups of pixels detected by our model in the 5-arcmin window along the SZcat directions. We do not use R as a threshold because it varies from catalogue to catalogue FWHM.

APPENDIX D: CATALOGUE METRICS

The key characteristics of a cluster catalogue are purity and completeness metrics.

• Completeness, which we define as

  $$\begin{eqnarray} C=\cfrac{N_{\rm {cl,thresh}}}{N_{\rm cl}} ~, \end{eqnarray}$$

  (D.1)

  where N_{cl, thresh} is the total number of galaxy clusters with chosen threshold on p_max and S, N_cl is the total number of clusters in the considered catalogue.

• We define the purity of the ComPACT cluster catalogue as

  $$\begin{eqnarray} Purity=1-\cfrac{N_{\rm {F,ComPACT}}}{N_{\rm {ComPACT}}} ~, \end{eqnarray}$$

  (D.2)

  where N_F, ComPACT and N_ComPACT are the number of false detections and the total number of objects in the ComPACT catalogue, respectively. The total number of galaxy clusters in the ComPACT catalogue (N_{cl, ComPACT} = N_ComPACT − N_F, ComPACT) can be divided into three parts:

  • Planck clusters (N_cl, Planck). SZ objects seen in Planck data, which correspond to excess of objects in ComPACT catalogue with respect to random fields directions:

    $$\begin{eqnarray} N_{\rm {cl,Planck}} = N_{\rm {ComPACT}}-\hat{N}_{\rm field} ~, \end{eqnarray}$$

    (D.3)
    where |$\hat{N}_{\rm field}$| – the number of detections (p_max > 0.8, S > 20) in the random fields directions (N_field = N_SZcat, see Section 2). One can obtain the following estimate of ComPACT purity with respect to Planck clusters:

    $$\begin{eqnarray} Purity_{\rm {cl,Planck}} = 1-\cfrac{\hat{N}_{\rm field}}{N_{\rm {ComPACT}}} ~. \end{eqnarray}$$

    (D.4)
  • ACT clusters (N_{cl, ACT}). SZ objects, which are seen in ACT data only. The lower bound estimate of this number one can obtain as follows. According to Meshcheryakov et al. (2022), only 21.7 per cent SZcat objects are associated with eROSITa clusters (1-yr all-sky survey data) on the Eastern galactic hemisphere. Thus for non-Planck clusters we have

    $$\begin{eqnarray} Purity_{\rm ACT} \approx \cfrac{0.217\cdot {}N_{\rm SZcat}-N_{\rm PSZ2}}{N_{\rm SZcat}-N_{\rm PSZ2}}, \end{eqnarray}$$

    (D.5)
    where N_PSZ2 means number of objects in the ComPACT catalogue associated with PSZ2. ComPACT purity

    $$\begin{eqnarray} Purity_{\rm min} \approx \cfrac{N_{\rm {cl, Planck}} + Purity_{\rm ACT}\hat{N}_{\rm field}}{N_{\rm {ComPACT}}} ~. \end{eqnarray}$$

    (D.6)
  • The number of false detections can be estimated as

    $$\begin{eqnarray} N_{\rm F}\lesssim {}(1-P)\cdot {}\hat{N}_{\rm field} ~, \end{eqnarray}$$

    (D.7)
    where P = 0.8 is our threshold in the maximum probability (p_max). The idea behind formula (D.7) is simple. The subsample of detections in random fields with p_max > 0.8 and S > 20 contains more than |$P\times 100~{{\ \rm per\ cent}} = 80~{{\ \rm per\ cent}}$| of galaxy clusters. Thus, the number of false detections in this subsample can be estimated as |$\lt (1-P)\cdot {}\hat{N}_{\rm field}$|⁠. Based on the expressions (D.2) and (D.7) one can obtain

    $$\begin{eqnarray} Purity_{\rm high} = 1-(1 - P)\cdot \bigg (\cfrac{\hat{N}_{\rm field}}{N_{\rm {ComPACT}}}\bigg) ~. \end{eqnarray}$$

    (D8)