© E. Bulbul et al. 2022

1 Introduction

Galaxy clusters are located at the peaks in the cosmic density field and offer an independent and powerful probe of the growth of structure. Their overall abundance in the Universe is strongly dependent on the underlying cosmology. Extending the samples of known clusters of galaxies through ground-based and space-based observatories therefore is a way forward to place tight constraints on the cosmological parameters based on cluster counts (Kravtsov & Borgani 2012). Cluster surveys performed with ground-based optical telescopes relying on finding overdensities of red galaxies in the sky suffer from projection effects (Farahi et al. 2016; Zu et al. 2017; Busch & White 2017). Owing to the redshift-independent signal, cluster surveys based on the Sunyaev-Zeldovich (SZ) effect (Sunyaev & Zeldovich 1972) performed with the Planck Space Telescope, the South Pole Telescope (SPT), and the Atacama Cosmology Telescope (ACT) provide an advantage over detecting clusters out to high redshifts (Planck Collaboration XXIX 2014; Bleem et al. 2015; Hilton et al. 2021). However, their ability to detect nearby clusters of galaxies is limited by their beam size (Hincks et al. 2010; Planck Collaboration VIII 2011).

X-ray surveys are less sensitive to projection effects than optical surveys, and they have a better spatial resolution than the current SZ surveys. Therefore, they offer an efficient way for detecting clusters of galaxies. Despite these advantages, their selection function is crucial for further science exploitation (Clerc et al. 2018). Derivation of the selection function for extended X-ray surveys relies on the detection of the X-ray sources and their classification as extended objects. The first X-ray all-sky survey (RASS) was performed with the ROSAT telescope and provided the extensive cluster catalogs obtained in the soft X-ray band (Ebeling et al. 2001; Böhringer et al. 2000, 2004). Since the early 2010s, smaller but deeper X-ray surveys performed with XMM-Newton provided samples of clusters down to a flux limit of 10⁻¹⁵ erg s⁻¹ cm⁻² and allowed determining cosmological parameters through accurate modeling of the X-ray selection function (Pacaud et al. 2016; Adami et al. 2018). With the new availability of the extended ROentgen Survey with an Imaging Telescope Array (eROSITA) All-Sky Survey (eRASS, Predehl et al. 2021) in the full 0.2–10 keV X-ray band, we are on the verge of detecting 100,000 clusters and groups of galaxies down to the mass limit of 10¹³ M_sun, and we will be able to constrain cosmological parameters with a percent-level precision through cluster counts (Merloni et al. 2012).

Clusters of galaxies appear as extended sources in the X-ray sky mainly due to Bremsstrahlung emission from their diffuse intracluster medium (ICM). The source characterization strategy of the X-ray cluster surveys of eROSITA relies on the detection of extended sources based on their extent and detection likelihoods (Brunner et al. 2022; Liu et al. 2022a). Identification of the counterparts to these sources is then performed with multiple optical surveys and strategies (e.g., Klein et al. 2021; Salvato et al. 2022). Because of the sizable point spread functions (PSF) of X-ray telescopes, clusters of galaxies that host bright central active galactic nuclei (AGN) or peaked cool-core emission at high redshifts, or faint compact extended emission, can be missed by the selection cuts and misclassified as point sources (Green et al. 2017; Biffi et al. 2018; Clerc et al. 2018; Ghirardini et al. 2021b). We note that, in the context of this work, we define groups as halos with masses M₅₀₀ < 10¹⁴M_sun. For instance, it has been shown that very extended groups that have a central AGN may be missed by the extent selection in the ROSAT catalog because their surface brightness profiles are shallower than the beta model that is used as a template by the source detection algorithm (Xu et al. 2018). It is vital to understand the reasons for the misclassification and to determine the total number of these cases to understand the uncertainties in the selection function and the completeness of the eROSITA survey.

Beyond testing the selection function, clusters hosting bright AGN in their cores are also interesting targets for astrophysi-cal investigations and searches for dark matter. AGN outflows and jets play an important role in the formation and evolution of galaxies, in establishing the multiphase environment from group scales to clusters, and in regulating star formation and cooling flows in cluster cores (e.g., Rafferty et al. 2006; Gaspari et al. 2012; Gaspari & Sadowski 2017). In the local Universe, this feedback power is sufficient to offset the strong radiative cooling in the cores of clusters (McNamara & Nulsen 2007), although the details of this feedback process are still a matter of much debate (see Fabian 2012, for a review). It is vital to study feedback in groups and clusters with bright central AGN to understand how feedback influences the thermal history of the matter in these dense environments. Moreover, the mechanical output of radio feedback can be measured from the properties of the jet-inflated radio-plasma-filled cavities in the ICM (e.g., Churazov et al. 2000; Bîrzan et al. 2004), a joint analysis combining X-ray and radio data of these clusters is therefore important to complete the picture of AGN feedback. Clusters of galaxies that host bright central AGN can also be used to constrain the parameter space of axion-like particles, an ultralight theoretically well-motivated cold dark matter candidate (e.g., Burrage et al. 2009; Horns et al. 2012). Axion-like particles and photons interconvert in the presence of magnetic fields, leaving imprints on the X-ray spectra of sources. AGN embedded in large dark matter concentrations, such as galaxy clusters, provide an ideal environment with a magnetic field for this conversion to occur (Conlon et al. 2017; Berg et al. 2017; Reynolds et al. 2020).

One famous example in which a cluster is characterized as a point source in the ROSAT all-sky survey is the Phoenix cluster, which was later detected as an extended source through its significant SZ decrement in the millimeter-wave SPT data (McDonald et al. 2012). Previously known clusters that host a bright AGN include A1835 (z = 0.25; McNamara et al. 2006), NGC 5813 (z = 0.0065; Randall et al. 2015), MACS J1931.8-2634 (z = 0.35; Ehlert et al. 2011), and 3C 186 (z = 1.07 Siemiginowska et al. 2005). In recent years, great effort has been made to identify more clusters that are concealed by the hosting bright AGN and star-forming galaxies in the ROSAT all-sky survey point source catalog (Green et al. 2017; Donahue et al. 2020; Somboonpanyakul et al. 2021b). In these searches, a few remarkable clusters have been discovered, such as CHIPS 1356–3421 (z = 0.22) and CHIPS 1911+4455 (z = 0.48) (Somboonpanyakul et al. 2018, 2021a). Another 14 clusters hosting X-ray bright brightest cluster galaxies (BCGs) were identified in Donahue et al. (2020). The next logical step is to identify more of these extreme systems to extend feedback studies to groups with lower mass and clusters at higher redshifts, where we expect to see significant AGN activity, by pushing the flux limit down with the eROSITA all-sky survey.

The eROSITA Final Equatorial-Depth Survey (eFEDS), completed during the performance verification phase of eROSITA, is designed to demonstrate the survey science capabilities of the final all-sky survey (Predehl et al. 2021). The eFEDS field covers a 140 deg² area in the equatorial region of eRASS (126° < RA < 146° and −3° < Dec < +6°) and has a survey depth with a vignetted exposure time of 1.2 ks in the 0.5–2.0 keV energy band. The full X-ray source catalog including point and extended sources was presented in Brunner et al. (2022). Using the extent and detection likelihood selections, Liu et al. (2022a) compiled a sample of clusters of galaxies in the eFEDS field. The characterization and follow-up of the extended sources in this main catalog were presented in Liu et al. (2022a), Ghirardini et al. (2021a), and Klein et al. (2021). A point source catalog was also compiled based on the X-ray detection properties (Liu et al. 2022b), and the optical follow-up, characterization, and classification of these sources were presented in S21 and Nandra et al. (in prep.), respectively. Salvato et al. (2022, S21 hereafter) found that 346 of the 27369 point-like sources are secure clusters of galaxies with probabilities higher than 80%. This result is based on concentrations of red sequence galaxies around the X-ray position and on the comparison of photometric redshifts computed with two independent methods under different assumptions.

The primary goal of this paper is to characterize the properties of these candidate clusters and groups in the eFEDS point source sample, identified by S21, based on the multiwave-length data in X-ray, optical, and radio bands to understand the selection and completeness of the eROSITA cluster surveys. Another goal of this study is to identify clusters of galaxies or groups that have a central AGN, which are ideal targets for studying the AGN feedback cycle and constraining the parameter space for the axion-like particles. The eFEDS field has also been observed with a broad array of multiwavelength survey instruments through the LOw Frequency Array (LOFAR) in radio, optical photometric, and spectroscopic follow-up with the Dark Energy Camera Legacy Survey (DECaLS), Hyper Supreme Camera (HSC), the Sloan Digital Sky Survey (SDSS-IV and SDSS-V), and the Galaxy and Mass Assembly (GAMA), which offers a unique opportunity of finding these sources. In this work, we first summarize the S21 identification and classification method of 346 clusters of galaxies in disguise and further characterize the sample with SDSS follow-up observations in Sect. 2. The X-ray and radio properties and assessment of the selection and completeness are provided in Sect. 3. A cross-match exercise between eROSITA and other SZ surveys is presented in Sect. 3.4. In Sect. 4 we present galaxy clusters and groups that host bright AGN in their BCGs, which are ideal sources for further follow-up studies. Throughout this paper, we assume a flat ΛCDM cosmology with Ω_m = 0.3 and H₀ = 70 km s⁻¹ Mpc⁻¹ unless stated otherwise.

2 Sample, Source Classification, And Data Analysis

The eFEDS field was observed before the start of the eROSITA all-sky survey. Its location is optimized to take advantage of coverage by the other multiwavelength surveys, through LOFAR in the radio, the HSC Wide area Survey (Aihara et al. 2018), the KIDS-VIKING (Kuijken et al. 2019), the Dark Energy Spectro-scopic Instrument (DESI) Legacy Imaging Survey (Dey et al. 2019), GAMA (Driver et al. 2009), WIGGLEz (Drinkwater et al. 2018), The Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST) (Zhong et al. 2020), and SDSS (Gunn et al. 1998; Blanton et al. 2017; Smee et al. 2013) in the optical wavelengths. The depth of ~2.2 ks (~1.2 ks after taking the vignetting into account) of the survey slightly exceeds the depth that will be reached at the final eROSITA all-sky survey at the equatorial region.

The X-ray data processing for the eFEDS field was extensively described in Brunner et al. (2022). We here only provide the main steps. The analysis is performed with the latest eROSITA Standard Analysis Software System (eSASS, version eSSASusers_201009). The calibration, astrometric calibration, GTI, flare, and bad-pixel filtering are applied using the eSASS algorithms to obtain clean event files for each telescope module (TM). The main eFEDS catalog is constructed by running a sliding-cell detection algorithm using all telescope modules in the 0.2–2.3 keV band, where the eROSITA effective area is maximum (see Liu et al. 2022b, for details). The main source catalog, which is produced by applying a cut over the detection likelihood of 6 or higher, consists of 27 910 sources. A subsample of 542 extended sources is compiled by selecting sources with a source extent larger than zero, an extent likelihood higher than 6, and a detection likelihood higher than 5 (Liu et al. 2022a; Klein et al. 2021). We only use this sample for comparisons in this work, while the detailed analysis of these clusters is provided in Liu et al. (2022a), Ghirardini et al. (2021a), Bahar et al. (2022), and Pasini et al. (2022).

The point source catalog, on the other hand, is constructed from the main eFEDS catalog by applying a selection based on a detection likelihood higher than 6 and an extent likelihood of 0. This selection results in a total of 27 369 point-like sources in the eFEDS field. Some of the extended sources can be mixed in the point source catalog for various reasons, including a bright central AGN, bright cool-cores, and/or faint and compact extended emission. Our first goal is to understand this selection process using the eROSITA X-ray observations of these sources. To this end, we use the clusters identified in the point source catalog presented in S21, where the details of the optical identification and classification process are described extensively. The authors ran the red-sequence identifier code (MCMF) to find the concentrations of red galaxies around the detected point sources to locate the clusters of galaxies in the point source catalog (see Klein et al. 2019, 2021, for further information about MCMF). In this section, we summarize their point source identification and classification strategy, as well as the X-ray analysis of the detected extended sources.

2.1 Counterparts to the point source catalog

The method adopted to identify multiwavelength counterparts to the point sources catalog was presented in detail in S21. In short, two independent methods (NWAY and Astromatch) were applied and the results were compared. Both methods (the first based on Bayesian statistics and the second based on maximum likelihood) used key features typical of X-ray emitters (regardless of their Galactic or extragalactic nature). While the key features (a mixture of fluxes, magnitudes, colors, and other properties) adopted by NWAY and Astromatch are different and identified by different algorithms, they were extracted from the multi wave length properties of the same training sample of about 23 000 XMM detected sources spanning the same X-ray flux of eFEDS and with reliable counterparts in the Legacy imaging survey supporting the Dark Energy Spectroscopic Instrument (DESI; Dey et al. 2019). Based on these features, both methods assign the probability of being the correct counterpart to each optical source within 30″ from the X-ray position. Then this probability is combined with the probability of a correct association based on the spatial distribution (separation, positional errors, number density). Both methods applied the procedure not only to the eFEDS sources, but also to a common validation sample of 3500 Chandra sources with secure counterparts that were made eROSITA-like in terms of positional accuracy.

Survey catalogs compiled by an automated source detection procedure can be characterized in terms of completeness and contamination because the catalogs may show spurious contaminating or missed sources. We determined the completeness level of the survey by a fraction of detected true sources in the simulations above a given flux threshold. Contamination is defined as the fraction of spurious sources, and purity is defined as the fraction of true sources in the catalog. Based on the results of the validation sample, we demonstrated that both methods perform very well. The purity and completeness exceed 95%. NWAY performs slightly better because it has a small number of sources with multiple possible associations. The counterparts assigned by the two methods are the same for 24 193 of the 27 369 sources in eFEDS (88.4%). The number of disagreements increases with decreasing X-ray detection threshold, which suggests that some of these sources might be spurious detections. Based on the comparison of the proposed counterparts and the probability value from the two methods, we graded the reliability of counterparts (CTP_QUALITY). Further details are given in S21, and we provide the CTP_QUALITY of our sources in the next section.

Fig. 1 Distribution of the 346 cluster candidates in eFEDS point source catalog. The color code represents the redshift of the cluster, provided by the MCMF (Klein et al. 2018, 2019). The radius of the circle corresponds to 3 R500 of each cluster.

2.2 MCMF Identification of Clusters

The multi component matched filter (MCMF; Klein et al. 2018, 2019) cluster confirmation tool is designed to identify ICM-selected clusters out of large samples candidates with a high degree of contamination. Its initial application on the ROSAT-based 2RXS catalog resulted in one of the largest X-ray-selected cluster catalogs to date without a selection based on source extent (Klein et al. 2018). At first glance, the application of MCMF on the eFEDS point source catalog is straightforward because the main difference is the much lower flux limit of the sample.

This impression turned out to be not true and forced changes to the default way of running MCMF, as well as to the selection of cluster candidates. In addition to the difference in flux limit, further differences complicate the correct identification of clusters in the point source sample. The first difference is related to the resolution and source measurement. In 2RXS, a fixed and large aperture of 5′ was used to measure the source flux, which essentially includes most of the flux for clusters with z > 0.2. In the case of eFEDS, a source that falls below the thresholds of being extended (add extent likelihood and extent thresholds) is measured with a point-like aperture (1′) that typically just contains a fraction of the total cluster flux. Furthermore, clusters showing more complex shapes can be split into multiple sources, each containing only a fraction of the cluster flux. Because of the selection criteria of the point source sample and the depth, the fraction of clusters in that sample is even smaller than in 2RXS. Finally, the low flux limit causes a very high source density of real point sources (e.g., AGN and stars), partially projected onto clusters.

These difficulties affect the MCMF confirmation in two ways. First, the X-ray flux from the source detection is not a good measure of the cluster flux. We therefore remeasured the richness of the candidates found by the default MCMF run using optical data alone. Second, we excluded all candidates and randoms within a radius from the extent-selected sources for the calibration of f_cont based on redshift and richness. This avoids biases caused by multiply counting the same extended cluster because of proximity to the cluster or overlaps with the cluster itself. The contamination fraction, f_cont, determines the probability for an optical concentration of red galaxies to be a chance alignment along the line of sight to the X-ray source. The randoms here are defined as randomized positions that exclude regions around the real cluster candidates (see Klein et al. 2018, 2021, for further details). Multiple counting of the same clusters just presented in the point-like sample remains unaccounted for in the derivation of f_cont. As these systems can be assumed to be smaller in extent because of the X-ray selection, the main reason for multiple counting of clusters is source splitting. Based on the additional information from the dedicated search for point-like counterparts of S21, we selected cluster candidates using the combined information of MCMF and the point-like candidates. With these selection criteria, we find 346 sources with a simultaneous concentration of red-sequence galaxies (see Salvato et al. 2022, for details). The locations of these clusters in the eFEDS field are shown in Fig. 1. The full MCMF catalogs typically include the information about the BCG positions, optical centroids, f_cont, an optical mass proxy, photometric red-shifts, and richness (see Klein et al. 2021, for details). In this catalog, we only provide MCMF redshifts and richness because the remaining sample properties are provided in Salvato et al. (2022).

In Fig. 2 we provide the redshift histogram of the full sample in the point source catalog. Compared to the extent-selected sample (z_med = 0.35), the median redshift of the sample is slightly higher (z_med = 0.40). This is expected because the apparent size of the cluster should be smaller than the sizes in the extent-selected sample for them to be missed by our selection criteria, which are based on the extent of the source. We identified an additional 18 clusters at high redshifts (z > 0.8), 10 of which lie at redshift z > 1. The middle and bottom panels of the same figure compares the richness and luminosity measurements of the clusters in the point source sample (in orange). The richness and luminosity of this sample is similar to the extent-selected sample, which is marked in blue.

The clusters and groups in the point source catalog are classified in S21 based on their counterparts in the optical data in the following scheme (in the order of cluster likelihood):

Class 5 marks the red-sequence galaxy concentration detected significantly with f_cont < 0.2 by MCMF in proximity of the X-ray position for which there is no secure point source counterpart in S21 (CTP_QUALITY ≤ 1). The probability of the source being in a cluster is f_cont < 0.2. These clusters could be missed by the extent of the likelihood cut. This category includes 120 clusters or groups in the catalog.

Class 4 sources are the clusters that have secure optical counterparts from S21 with CTP_QUALITY≥2 that the optical colors of the counterpart are consistent with a red galaxy member of the cluster identified by MCMF with a high f_cont < 0.2 probability at the same redshifts. The sources also lie in the elliptical locus in the z-W1 vs g-r plane; see figure 21 in S21. The BCGs identified by both MCMF and NWAY are the same passive red galaxy. We find 63 clusters that fall in this category.

Class 3 consists of clusters that correspond to a secure counterpart listed in S21 with CTP_QUALITY≥2 and MCMF with f_cont < 0.2. The redshift from LePhare of the identified point source counterparts and the redshift of the cluster found by MCMF agree. Unlike Class 4, the colors are more typical of AGNs, QSOs, or a hybrid (galaxy + AGN template; see Fig. 21 in S21). These clusters consist of AGN(s) in their vicinity that are associated with the X-ray detection. We find 96 cases in the catalog.

Class 2 point source candidate is identified by S21 with high probability (CTP_QUALITY≥2) and has a different redshift than the cluster identified by MCMF. The cluster red sequence is also detected with a very high probability of f_cont < 0.01. These cases can be interpreted as point sources that are in projection with clusters on the line of sight. We find 67 cases in total in this group. We note that the threshold likelihood applied to MCMF is more stringent than the classes above, and therefore there is a clear association with a cluster. For the point sources near the X-ray position, further analyses with instruments with high spatial angular resolution are required to determine the fraction of X-ray emission that is associated with the cluster or the point source counterpart.

The redshift and richness distribution of the sample shows no immediate correlation between these observables and the Cluster_Class (Class, hereafter). Because the clusters and groups in this sample have a relatively high probability (>80%; f_cont < 0.2) of being secure extended sources, we assume that they are all genuine clusters and groups throughout the paper.

We note that we applied a richness cut due to the optical cleaning applied (f_cont < 0.2) for both extended and point source samples. The clusters and groups in this sample have a relatively high probability (>80%) of being secure extended sources.

Fig. 2 Global properties of the 346 clusters and groups in the eFEDS point source catalog provided by MCMF. top panel: redshift distribution of the 346 clusters and groups in the eFEDS point source catalog provided by MCMF (blue). the median redshift of this sample is 0.40, i.e., slightly higher than the redshift distribution of the extent-selected clusters in Liu et al. (2022a) $(z_{\text{med}}^{\text{ext}}=0.35$ shown as gray bars). The redshift distribution of the extent-selected sample and clusters in the point source catalog is skewed toward the low redshifts, as expected. Middle panel: richness distribution of the clusters in the extent-selected sample (blue) with the clusters found in the eFEDS point source catalog (orange). Optical cleaning filtering of fcont < 0.2, recommended by Klein et al. (2021), was applied to both samples. Bottom panel: distribution of the soft-band (0.5–2 keV) luminosity as a function of redshift for the point source sample in orange, compared with the extent-selected sample in blue. The detections with <2σ are shown as upper limits. the dashed red line marks the flux limit 1.5 × 10−14 ergs s−1 cm−1 of the extended source sample reported in Liu et al. (2022a).

2.3 eROSITA X-ray data analysis

The method of X-ray analysis is very similar to the analysis of the extent-selected sample, and the details were already provided in Ghirardini et al. (2021a,a). We therefore only summarize the main steps of the X-ray analysis. The imaging analysis was performed in the soft 0.5–2 keV energy band using the eSASS (version eSASSusers_201009) tools evtool, and the exposure maps were created using expmap surrounding the centroid of the point sources. The images and exposure maps with 15′ at a side were created for further processing. The point sources within the field of view were either modeled or excised from images based on their flux (see Ghirardini et al. 2021a,a, for further details). The analysis procedure was applied to the extended source analysis, but in this sample, we did not excise the center from the analysis, neither do we provide core-excised properties in this work. We fit these images with a total image model after depro-jection of the model to the image plane. The model included a cluster component based on the Vikhlinin et al. (2006, V06, hereafter) formulation. Our background model consisted of vignetted Galactic soft thermal foreground model, an absorbed power-law model for the cosmic X-ray background component due to unresolved sources, and an unvignetted instrumental background model that was based on the best-fit model of the filter-wheel-closed data¹. We excluded the point sources within the fitting radius by modeling them as delta functions convolved with the point spread function (PSF) of eROSITA. The model gives the best-fit parameters of the V06 density model, which can be converted into a gas density by ρ_g = μ_en_em_p, where μ_e is the mean molecular weight, n_e is the number density of electrons, and m_p is the proton mass (Bulbul et al. 2010).

The spectra and corresponding response files were extracted using the eSASS tool srctool within the over density radius R₅₀₀. The over density radius R₅₀₀ is the radius within which the local density of the cluster is 500 times the critical density of the Universe at the cluster redshift. The overdensity radii R₅₀₀ of these clusters were determined using the best-fit luminosity–mass scaling relations of the extent-selected sample based on the HSC weak-lensing observations (Chiu et al. 2022; Bahar et al. 2022). The background spectra were extracted between 4–6 R₅₀₀ surrounding the cluster centroid. We fit the spectra using the software package XSPEC version 12.11.1 (Arnaud 1996). The ICM emission was modeled with the soft thermal absorbed apec component (Smith et al. 2001; Foster et al. 2012), and the local background was modeled with two components for the emission from the Local Hot Bubble (or heliosphere); a cool unab-sorbed single-temperature thermal component (E ~ 0.1 keV), an absorbed thermal component (E ~ 0.2 keV) for the Galactic hotter halo and intergalactic medium, and a nonthermal component for the unresolved cosmic sources as described in Bulbul et al. (2012, 2019). The particle background is also added to the total background model. In this case, the model parameters were determined from the best-fit values of the shape parameters of the filter wheel closed data and are kept frozen (Freyberg et al. 2020), while the normalizations were left free in the fit. We adopted the Asplund et al. (2009) table for the abundances and the tbabs (Wilms et al. 2000) model with Willingale et al. (2013) for the column density n_H to account for the local absorption. Because most of the detected clusters lie are in the low-count regime, we strictly used C-statistics in our fits (Cash 1979; Kaastra 2017). In the fits, the temperature and normalization of the cluster model were left free, while the metallicity was fixed. Considering their smaller extent and low flux, it is not surprising that we cannot reliably measure the ICM temperature or abundance for most of these clusters. Additionally, because the PSF size of 26″, it is challenging to excise the central AGN when the spectra are extracted. When the central core is excised, we fail to measure the ICM temperature of the majority of these clusters because the count statistics are too low. We therefore adopted a uniform approach and fixed the abundance value to 0.3 solar abundance, and for the temperature, we assumed a probability distribution identical to the one observed in the eFEDS cluster catalog (Liu et al. 2022a). The temperature of a cluster was randomly drawn and allowed to vary smoothly around ${2.4}_{-0.9}^{+1.4}$ keV, where 2.4 keV is the median temperature, and 0.9 keV and 1.4 keV are the differences between the median and the 16th and 84th percentiles of the eFEDS cluster temperatures, respectively. These values of temperature and abundance were used in the conversion of the count-rate and surface brightness into the soft band 0.5–2 keV luminosity. To further calculate the masses of these clusters, we calculated the total masses based on the scaling relation of the luminosity to weak-lensing mass of the extent-selected sample presented in Chiu et al. (2022). The X-ray properties of the clusters and groups in this sample are available at the CDS.

3 Characterization of The Sample And Classification With Multiwavelength Observations

To be able to characterize the properties of the sample and understand the selection, completeness, and contamination of the extended sources in the point source sample, we furthermore used the eROSITA X-ray data, SDSS optical spectroscopy, and LOFAR radio observations of the eFEDS field. Our goal is to understand the reasons for the mischaracterization of the extended sources by the source detection algorithm and contamination in the sample, and to test the classification by comparison with the extended source catalog and through available multi-wavelength observations.

3.1 Characterization of The X-ray Selection Through eROSITA Observations

The luminosity measurements within R₅₀₀ of the full sample are shown in the left panel of Fig. 3. Because of the sizable PSF of eROSITA (≈26″ HEW FOV average; Predehl et al. 2021) and the small angular scales of the clusters in this sample, it is very challenging to excise the cluster core, in which the core emission dominates the overall emission in determining the core-excised luminosities. Therefore, when an AGN is present in the core or in projection (e.g., in Class 2 and 3 clusters), the flux and luminosity measurements reported in this work include the no-thermal X-ray emission from the central region and can be biased high. The measurements presented here should be taken as approximate upper limits of the luminosity. A follow-up study with deeper and higher spatial resolution X-ray observations with XMM-Newton and Chandra will help us to recover the unbiased ICM luminosity and temperatures of these clusters and groups. In Fig. 3 we present a comparison of luminosity measurements with a significance of >2σ. Figure 3 shows that a large fraction of the clusters (113, to be precise, corresponding to 33% of the sample) lie below the flux limit of 1.5 × 10⁻¹⁴ ergs s⁻¹ cm⁻² of the extent-selected sample (Liu et al. 2022a). X-ray emission from a subset of these clusters is also likely to be boosted by the AGN emission, where it is present. This boosting effect would push the luminosities above the detection limit of the eFEDS point source catalog. In the absence of the AGN (at the center or in projection), these sources would lie beyond the eFEDS survey detection limit and would only be detected with deeper surveys. The class distribution of the eFEDS point-like clusters does not show a clear trend with luminosity. Hence, we cannot make a firm conclusion about the nature of the sources and why the clusters in different classes are detected in the point source sample.

We also examined the richness and X-ray luminosity distribution of the clusters of the sample, shown in the right panel of Fig. 3. The clusters that have high X-ray luminosities for their richness may be those that host a bright quasar in their BCG. However, we note that optical richness alone is not a reliable proxy for the cluster luminosity because of the large scatter due to projection effects (Ge et al. 2019).

A consistent finding is also reflected in the total mass distribution of the sample, where the majority of these sources are in fact low-mass clusters or groups (see Fig. 4). Because the extent-selected clusters are a representative sample of clusters above the given flux limit, we used the Chiu et al. (2022) mass scaling relations, constructed from the soft-band X-ray luminosity and HSC weak-lensing mass measurements of the extent-selected clusters, to calculate the masses of the clusters of galaxies in the point source sample. The masses of most clusters lie between 1 × 10¹³ M_sun and 3 × 10¹⁴ M_sun, which is lower than the extent-selected sample. We note that the masses and luminosities reported here for Class 2 and 3 objects should be taken as upper limits as these clusters either have an AGN in projection or an AGN in their BCGs.

It is also possible that these clusters have a smaller extent and can just be missed by our extent selection as our detection algorithm sets the extent to zero if it is smaller than 6 (Brunner et al. 2022). Following the method presented in Ghirardini et al. (2021a), we estimated several dynamical properties of the clusters in the point source sample and compared them with the extent-selected sample presented in Ghirardini et al. (2021a). In Fig. 5 we compare the distributions of the core radii (R_core) constrained by the V06 model and the concentration parameter (c_SB) between these two samples. The concentration parameter is defined as the ratio of the surface brightness within 0.1 R₅₀₀ to the surface brightness within R₅₀₀ (Ghirardini et al. 2021a; Santos et al. 2008; Maughan et al. 2012). Intuitively, the expectation is that the smaller the core radius, the more compact the cluster. The left panel of Fig. 5 clearly shows that the clusters in the point source sample have relatively smaller core radii, hence the emission is more concentrated in a smaller area. Consistently, the concentration of the point source sample shows a clear excess in higher values than the extent-selected sample, indicating that a significantly larger fraction of cool-core clusters and clusters host a central AGN. We performed the same experiment by applying cuts in flux 1.5 × 10⁻¹⁴ ergs s⁻¹ cm⁻² and in detection likelihood to test whether the clusters are missed by the extent selection because they are fainter and/or more compact than the extent-selected clusters. The distribution of number density, core radius, and concentration parameter remains the same, indicating that the population of clusters in the point source catalog is more compact than the extent-selected sample. The extent-selected sample does not show a clear bias toward cool-core clusters or clusters with a central AGN, but contains the fraction of cool-cores is similar to that of SZ surveys (Ghirardini et al. 2021a). In this sample, we observe the opposite trend.

A comparison of the gas density of the clusters in the point source catalog and extent-selected clusters is shown in Fig. 6. The gas densities of the clusters in the extended source catalog in blue show an excess of X-ray emission at large radii R > 100 kpc compared to the clusters in the point source catalog. This result confirms our earlier finding that the clusters in the point source catalog are more compact than the extent-selected clusters. This is expected because the some clusters in the point source sample are expected to be dominated by the sources with a bright AGN or a cool-core at their centers. Regardless, it is important to note that we still detect the extended emission in the clusters and groups in the point source catalog beyond R > 100 kpc.

We also note that because AGNs are variable sources, the variability in AGN flux would also affect the detection and classification of the cluster. For instance, the decrease in the flux of the AGN in an AGN-dominated cluster would lead to a higher extent likelihood due to the relatively brighter ICM emission. The cluster is then likely to be classified as an extended source and would not be included in this sample. Moreover, the surface brightness concentration in this case decreases and becomes closer to the extent-selected sample shown in Fig. 5.

Fig. 3 Luminosity distribution of clusters with respect to redshift, class, and richness. Left panel: luminosity-redshift distribution of the clusters and groups identified in the point source sample based on their class. A 2σ detection limit is applied on the luminosities. The flux limit for the extent-selected sample of 1.5 × 10−14 ergs s−1 cm−2 is displayed as the dashed red line (Liu et al. 2022a). The luminosity of most clusters in the point source catalog is lower than that of the extent-selected sample, indicating that this sample is composed of clusters and groups that are smaller in extent and lower in mass, whose emission might be dominated by the central AGN. Right panel: X-ray luminosity as a function of the red-sequence richness. The blue data points show the extent-selected sample (Liu et al. 2022a; Klein et al. 2021). The orange points mark the clusters in the point source sample.

Fig. 4 Mass-redshift distribution of the clusters in the extent-selected sample (blue) and the clusters identified in the point source sample (orange). The clusters found in the point source sample are fainter than the extent-selected companions in the eFEDS field, suggesting that they are mostly missed due to our extent or detection likelihood selections.

Fig. 5 Distributions of the Rcore and cSB as a measure of compactness of the clusters in the point source catalog and the extent selected catalogs. The left panel shows the distribution of Rcore of the cluster sample in the point source catalog (orange) and the extent-selected (Lext > 12) cluster sample (blue). The right panel shows that the distribution of the cSB of the clusters in the point source catalog is smaller than in the extent-selected sample, indicating that the clusters in the point source catalog are more compact.

Fig. 6 Gas density of the clusters in the point source catalog (orange) compared with those in the extent-selected clusters (blue). The dashed curves display the median profiles of both samples. The shaded regions show the 68% confidence intervals around the median values of the radial profiles. The selection of an extent likelihood higher than 12 is applied to the extent-selected sample to reduce the AGN contamination in the sample (see Liu et al. 2022a; Ghirardini et al. 2021a). The median gas density of the clusters in the point source catalog is more compact than that in the extent-selected sample.

3.2 Characterization of The Source Classification And Contamination Through SDSS and GAMA Observations

We visually inspected the optical spectra of the counterparts, where available, for all classes of clusters to gain insights into the defined cluster classes (classes 2–5). The spectroscopic data from the GAMA DR3 or SDSS DR16 surveys (Baldry et al. 2018; Ahumada et al. 2020) were used. We additionally used spectra from special eFEDS plates acquired at the end of the SDSS-IV survey (Blanton et al. 2017; Merloni et al., in prep.). In this section, we describe the inspection of the optical spectra of these candidate clusters and groups and test our contamination level and classification.

All BCGs identified by MCMF for which a spectrum is available look like passive galaxies. The spectrum of one BCG (eFEDS J092121.7+033050, SRC_ID=15322) shows signs of recent star formation, that is, (weak) narrow emission lines possibly coming from HII regions. For a fraction of the BCGs identified by MCMF, stellar mass estimates are available (Taylor et al. 2011; Comparat et al. 2017), and all are above 10¹¹ M_⊙, which is consistent with massive galaxies. Overall, the galaxy population indicated by MCMF follows expectations (e.g., discussion by Clerc et al. 2020).

The counterparts identified by NWAY are more varied. Table 1 lists the counterparts for each class split into categories based on the optical spectra: red-sequence galaxy, galaxies with emission lines, type 1 and type 2 AGN, stars, or other (the signal-to-noise ratio of the spectra is too low to decide about a classification). After visual inspection of the images (in addition to the spectra), we found that in some cases, the sources targeted for spectros copy are a blend of a red compact object and an elliptical galaxy. These need more investigation to be classified in a clear way. We leave a detailed description of these cases for future studies. They are reported in the table below. We have optical spectra for a fraction of 13.4% (47.9, 65.1, and 7.5%) of sources from class 2 (classes 3, 4, and 5). Because of the optical selection function, this sample of spectra is not a fair sample in that it is biased toward the brighter objects. The completeness of the targeted objects is about 85% (50%) for an i-band magnitude of 21 (22).

For Class 4, we find that almost all spectra are passive galaxies (one of them is an AGN, one has a low signal-to-noise ratio). The misclassification rate in this class therefore appears to be negligible. For Class 5, the situation is similar. For Class 2 and 3, the population of counterparts found by NWAY is more varied. In Class 2 (3), 1/9 = 11.1% (17/46 = 36.9%) are passive galaxies, while 7/9 = 77.7% (22/46 = 47.8%) of the total sources have an AGN counterpart. Only 10% of the AGN are located at the same redshift (within Δz/(1 + z) < 0.005) of host clusters. These results support the classification scheme used in S21. We extrapolated these percentages to the complete classes to obtain an estimate of the total number of clusters in the point source catalog as 120 + 63 × 0.95 + 96 × 0.37 + 67 × 0.11 = 222. This represents 1 ± 0.3% of the point sources (~27 000 point sources in total). With 2RXS/SPIDERS, Comparat et al. (2020b) found that the cluster contamination of the point source catalog was about 3%. With eROSITA, this figure improved by a factor of 3.

3.3 Characterization of The Source Classification Through Lofar Radio Properties

In this section, we summarize the LOFAR (van Haarlem et al. 2013) radio properties of the clusters and groups in the point source catalog and provide a comparison with the extent-selected sample. The details of the radio data analysis are already provided in detail in Pasini et al. (2022). We therefore omit them here and provide the results.

Pasini et al. (2022) (hereafter P21) performed a detailed study of the radio galaxies hosted in the BCG of the 542 eFEDS secure clusters (Liu et al. 2022a). We used the same radio source catalog, obtained from the LOFAR 120–168 MHz observations covering the entire eFEDS field, to carry out a similar analysis for the clusters in the point source catalog. A detailed explanation of the observations and related radio catalog is presented in P21. Here, we just provide a brief description. Radio sources are detected on a $\sim 135\mu \text{Jy}{\text{beam}}_{\left(8^{″}\times 9^{″}\right)}^{-1}$ -noise mosaic with a detection threshold of 5σ using PyBDSF² (Python Blob Detector and Source Finder). Flux densities of the LOFAR-detected sources are 10% higher on average than those in the TGSS-ADR1 (TIFR GMRT Sky Survey – Alternative Data Release 1) 150 MHz observations (Intema et al. 2017). The astrometric offsets in RA and Dec between the LOFAR and FIRST (Faint Images of the Radio Sky at Twenty-cm; Becker et al. 1995) detected sources are 0.13″ and 0.04″, respectively. The corresponding standard deviations are 0.70″ and 0.82″.

Similarly to P21, we cross-matched radio sources to the BCG positions of each candidate cluster by setting a sky threshold ~3θ, with θ being the synthesized beam of the interferometric radio observation. BCG positions were determined by selecting a massive red-sequence galaxy near the X-ray emission peak (see Klein et al. 2021, for further details). This matching method has a drawback in that we may not be able to associate the BCG with its radio emission in the case of very large sources if the radio coordinates lie farther away than 3θ from the galaxy. Nevertheless, using a looser threshold could produce false matches, and for this analysis, it is more convenient to lose some sources than to provide a large number of associations, some of which are insecure. After visual inspection of our results, we find 111 clusters that meet our criteria, while for 235 objects, we did not detect any radio source close to the BCG with the current sensitivity. Nondetections were treated as 3σ radio upper limits, with σ being the local rms of the LOFAR observation estimated at the position of each cluster. Table 2 summarizes the composition of detections and upper limits.

In Fig. 7 we show the correlation between the radio power of BCGs and the X-ray luminosity of the host cluster for the different classes. The radio luminosity spans from ~5 × 10²⁸ to ~ 10³⁴ W/Hz at 144 MHz. The range is the same as for the sample of BCG radio galaxies studied in P21. As also found in P21 and other similar works (e.g., Pasini et al. 2020, 2021), there is a trend for stronger radio galaxies to be hosted in more luminous (i.e., more massive) clusters. However, observational limitations, especially in the radio band, affect our results. This translates into a relevant number of upper limits. In P21, statistical tests were used to assess the correlation between X-ray and radio luminosities. Because each sub sample includes relatively few objects, we cannot perform the same tests here. Instead, we focused on the differences among the different cluster classes with respect to the relation.

Class 4 represents the objects that are most securely classified as clusters. The point source counterpart from S21 is coincident with a red passive galaxy, which in most of the cases is also the BCG identified by MCMF. This class therefore shows a higher radio detection fraction (~36%) than Classes 2, 3, and 5 (~34, ~31, and ~29%, respectively), as expected for BCGs at the center of galaxy clusters (e.g., Sabater et al. 2019). On the other hand, other classes are expected to include AGN, either in projection or in their BCGs. This is reflected in their radio detection fraction: in Class 2, for example, we searched for radio emission at the position of the best counterpart from S21 that is likely not a BCG, or at least not at the center of a cluster.

For this reason, we performed an alternative cross-matching. Instead of the BCG position from MCMF, we used the position of the NWAY counterpart. We expect the number of matches of Class 4 clusters that are detected with this alternative method (LOFAR-AGN) to be similar to the first method (LOFAR-BCG) because the class is defined through the AGN and the cluster redshifts are the same, and the AGN is consistent with a red, passive galaxy. On the other hand, we should observe significant differences for Classes 2 and 3 because we now searched for radio emission at the position of an AGN that is different from the MCMF identified BCG. The results of this second cross-matching, performed using the same criteria as the first, are presented in Table 2. We find 27 matches for class 4, compared to 23 with LOFAR-BCG. All results of the first method are in common with LOFAR-AGN, indicating that the second method found only four more matches. The number of Class 5 radio detections drops from 35 (LOFAR-BCG) to 17 (LOFAR-AGN), as expected because for these objects, NWAY was not able to locate any good counterpart. The number of detections for Class 2 decreases (from 23 to 15), while for Class 3, it is similar (from 30 to 33). Overall, these numbers are not easy to interpret because they are driven by numerous factors such as the BCG and AGN position, the sensitivity of the radio observation at these positions, and the chosen matching criteria, combined with the fact that radio emission is not guaranteed even in the case of a secure cluster (see also P21), let alone when the identification as a cluster is not reliable. For example, if Class 2 objects are in reality AGN, we would expect that they do not follow the same trend as we observe for clusters in the relation of X-ray luminosity to radio power. A different correlation has been observed for AGN (Vink et al. 2006; Sambruna et al. 1999). To this end, we show in the lower panels of Fig. 7 the distribution observed for Classes 2 and 3 with the second cross-matching method, LOFAR-AGN. Again, the low statistics does not allow us to derive conclusions from the correlation. Class 2 objects seem to stand out of the distribution observed for Class 4 clusters, suggesting that they might indeed represent different objects, but a larger sample is required to investigate this more accurately. In the near future, data from the eROSITA all-sky survey (eRASS, Bulbul et al. in prep.) will provide a significantly larger sample of clusters and AGN, which, combined with the LOFAR Two-Metre Sky Survey (LoTSS, Shimwell et al. 2017) as well as with the forthcoming LOFAR LBA Sky Survey (LoLSS, de Gasperin et al. 2021), will help us to shed more light on this.

3.4 Cross-matching the Sample With The Public SZ Surveys

We cross-matched the clusters in the point source catalog with the public cluster catalogs based on observations of the SZ effect that cover the eFEDS field. If the cluster hosts a bright BCG dominated by the AGN, these massive clusters at higher redshifts could easily be confused as point sources due to their compact size and bright core emission by the X-ray telescopes with sizable PSFs, as in the case of the Phoenix and El-Gordo clusters (McDonald et al. 2012; Menanteau et al. 2012). Because of their redshift-independent sensitivity, SZ surveys are less prone to this effect provided that the flux and mass limits of the surveys are comparable to X-ray surveys. In this paper, we propose a method that locates the high-redshift cool-core clusters that are missed by the extent selection and the wide PSF of eROSITA by carefully examining the point source catalog. To evaluate under which circumstances we miss high-redshift sources in the extent selection, we cross-matched our catalog with two independent public SZ surveys from the Planck and ACT telescopes that cover the eFEDS field.

Specifically, we cross-matched our catalog with the SZ effect-based catalogs with ACT (Hilton et al. 2021) and PLANCKSZ2 (Planck Collaboration XXVII 2016), which cover the entire eFEDS field.

Using a 2′ search radius around the positions of the eROSITA detected point sources, we find a total of five clusters that have counterparts in the ACT catalog. eFEDS J085635.7+014247 (ACT CLJ0856.5+0143) is the highest-redshift cluster at z = 0.72 in the matched sample. The cluster is marked as a Class 3 cluster in S21. The detection of this cluster in the point source catalog could be a case for a compact high-redshift cluster, and it would be misclassified as a point source by eROSITA. The X-ray centroid in the point source catalog is located 1.45′ southwest of the ACT centroid. Another cluster, eFEDS J085627.2+014217, is also detected to the southeast of the ACT centroid in the extent-selected catalog at a very similar redshift (Liu et al. 2022a). The cluster that is identified in this work by its red sequence and the cluster in the extent-selected sample probably belong to the same cluster system. Because we classify the cluster as a Class 3 object, that is, the point source identified here is in projection, this cluster in the point source catalog is either a merger and the point source in projection boosts the X-ray flux, or we detect the cluster outskirts in this case. In either case, the mass of this substructure or the subhalo is likely overestimated as a result of the point source flux. The ACT signal is likely to be associated with the more massive extended selected cluster with a mass of $M_{\text{SZ,WL}}={4.00}_{-0.77}^{+0.88}\times {10}^{14}{M}_{\text{sun}}$. The mass of the cluster eFEDS J085627.2+01421 in the extended catalog is ${6.58}_{-1.12}^{+1.42}\times {10}^{14}{M}_{\text{sun}}$ in Chiu et al. (2022) and is fully consistent with the mass reported in Hilton et al. (2021).

eFEDS J091129.5+052700 (ACT CLJ0911.6+0526) at a red-shift of 0.45, on the other hand, clearly hosts a bright core and could also be a merger as it shows an extended X-ray tail in the eROSITA image. Given that the richness of this source is 41 and it is classified into Class 5 (without a secure point source counterpart), it is likely that we missed this compact low-mass halo marked with a star in Fig. 8 because of the detection limit and extent likelihood cuts in the extent-selected sample. The ACT detection is located at 1.85′ west of our detection and has a mass of ${2.18}_{-0.43}^{+0.53}\times {10}^{14}{M}_{\text{sun}}$. Provided that the separation is greater than the beam size of ACT (1.4′ FWHM Aiola et al. 2020), the ACT and eROSITA detections are likely to be low-mass clusters undergoing a merger activity. Our weak-lensing inferred mass of the halo detected in X-rays is ${9.24}_{-3.81}^{+5.46}\times {10}^{13}{M}_{\text{sun}}$.

Similarly, the cluster eFEDS J092104.4-014813 (ACT CLJ0921.0-0148) at z = 0.59 with richness 85 in Class 5 is detected by both ACT and eROSITA. This is a clear case of a moderately massive galaxy cluster that was misclassified by our detection algorithm. The separation between the X-ray and the SZ centroid (0.39′) is within the beam size of ACT and within the spatial resolution of eROSITA. The reported mass of the cluster by the ACT collaboration is $M_{\text{SZ,WL}}={9.24}_{-0.67}^{+0.80}\times {10}^{14}{M}_{\text{sun}}$ while we obtain a weak-lensing inferred mass of $M_{\text{X,WL}}={2.05}_{-1.72}^{+1.09}\times {10}^{14}{M}_{\text{sun}}$ These measurements are consistent with each other within 1σ uncertainties.

Another cross-matched cluster is eFEDS J094053.0+032250 (ACT CLJ0940.9+0322) at a redshift of 0.49, which is classified as a Class 4 cluster with richness 37. This cluster is located 1 5′ away from a very bright point source eFEDS J094057.2+032359 at z = 0.06 in S21. Because this is a lower-mass system, the influence from the very bright point source nearby might be another reason for the misclassification of this cluster. The eROSITA reported mass $M_{\text{X,WL}}={2.41}_{-0.76}^{+0.89}\times {10}^{14}{M}_{\text{sun}}$ and the ACT reported mass of ${2.76}_{-0.63}^{+0.77}\times {10}^{14}{M}_{\text{sun}}$ agree. The photo-z red-shift measurements of these clusters are consistent with each other within 1% in the two catalogs. The agreement of SZ and X-ray masses indicates that our X-ray postprocessing is able to remove the contamination from the northern point source well, but the large separation between the centroids (0 95′) could be due to the bias caused by the bright point source emission in X-rays and SZ during the detection run. One property in common for all these clusters is that they all have a low SZ signal-to-noise ratio of ~5 in the ACT catalog, suggesting that eROSITA probes the low-mass and low-luminosity cluster population with a low signal-to-noise ratio that is detected by SZ telescopes, as is the case of the extent-selected samples.

The last matched cluster is eFEDS J084615.7+050708 (ACT-CL J0846.2+0508). However, this cluster is located at the edge of the eFEDS field. We therefore do not discuss this case in detail.

We also cross-matched our sample with the PLANCKSZ2 catalog using a matching criterion of 2′ because the beam size of the Planck Telescope is larger (Planck Collaboration XXVII 2016). We find one cluster, eFEDS J094028.7+022838 (PSZ 2G232.84+38.13), at redshift z = 0.15, that is detected by both eROSITA and Planck. The Planck detection is 38″ away from the eROSITA X-ray center in the point source catalog. S21 flags this cluster as a Class 2 object because there are no nearby extent-selected clusters. This source is likely to be an AGN-dominated low-mass cluster with a richness of 73. However, this source is located at the border of the eFEDS field, which makes the luminosity and mass measurements challenging from the X-ray data. The eROSITA mass ${2.18}_{-0.45}^{+0.43}\times {10}^{14}{M}_{\text{sun}}$ of this cluster still agrees with the Planck measurement of 3.43 ± 0.3 × 10¹⁴ M_sun at about 2σ. Because of the large beam size of Planck, we extended our search criteria to 3′ and located two other clusters that were cross-matched with the eFEDS point source cluster sample. PSZ2 G232.79+31.48 is matched with eFEDS J091624.7–002432 (Class 3) in the point source catalog with a centroid separation of 2.71′ between Planck and eROSITA. We also find an extent-selected cluster nearby, eFEDS J091610.2–002348 in Liu et al. (2022a), located 3.4′ away to the east. The Planck detection is a better match to the extent-selected cluster eFEDS J091610.2–002348 considering the smaller separation of centroids. eFEDS J091610.2–002348 (PSZ2 G232.79+31.48) is detected in the extent-selected sample with a mass of ${5.4}_{-1.3}^{+2.8}\times {10}^{14}{M}_{\text{sun}}$ and is consistent with the Planck-reported mass of (4.86 ± 0.63 × 10¹⁴ M_sun). In this case, either our MCMF algorithm picked up the red galaxy distribution from the outskirts of the extent-selected cluster eFEDS J091610.2–002348, or we detected an infalling low-mass group onto the more massive cluster. As expected because of their small separation together with the large Planck beam size, individual clusters were not resolved by Planck. eROSITA, on the other hand, was able to resolve each, demonstrating the power of X-ray surveys in mapping large structures and locating a wide population of clusters of galaxies. Another similar case is eFEDS J093517.3+005144 (Class 3) at a redshift of 0.37 and richness of 98, which is matched with the nearby Planck cluster PSZ2 G233.68+36.14, but the SZ signal is 2.65′ away from the centroid of the X-ray source. We find two nearby clusters, one in the north (eFEDS J093500.7+005417) and the other in the south (eFEDS J093513.0+004757) in a pair at the same red-shift of ~0.35 in the extent-selected catalog in close proximity to this source. The Plank detection is a better match to the southern massive cluster. Our detection in the point source catalog could either be the outskirts of the massive southern cluster or a group infalling onto eFEDS J093513.0+004757 considering their very similar redshifts and proximity.

Although the beam size of Planck is large, the 3′ matching radius is already too large for cross-matches of the eROSITA and other SZ catalogs. It is important to note that all of the matched clusters presented here have a low signal-to-noise ratio <6 and low mass in both ACT and Planck catalogs. This shows that eROSITA detects rather low-mass systems that are just above the detection limit of the current SZ experiments.

Fig. 7 Radio properties of the clusters in the point source sample compared with the extent selected sample. Top and middle panels: radio power of BCGs versus X-ray luminosity of the host cluster for the PS sample (orange) and for the cluster sample studied in P21 (blue). Data are sized based on the detection likelihood, and arrows denote radio upper limits. From top left to bottom right: clusters of class 5, 4, 3 and 2. Bottom panel: radio power measured at the position of the AGN vs. X-ray luminosity for Class 3 (left) and 2 (right) objects.

Fig. 8 Images of eROSITA clusters identified in the point source catalog, matched with the public SZ catalogs (ACT and Planck; Hilton et al. 2021; Planck Collaboration XXVII 2016). Top panel: four matches (eFEDS J084615.7+050708 at the edge of the field is ignored) with ACT using a matching radius of 2 arcmin. Bottom panel: three matches with PLANCKSZ2 using a matching radius of 3 arcmin. Images are centered on the X-ray position of the cluster in the point source catalog, marked by the gray star. The diamond shows the location of the extended sources in the Liu et al. (2022a) catalog if there is any nearby. The SZ centroid from either the ACT or Planck catalog is shown as a cross.

4 Clusters Hosting Active Galactic Nuclei

Another goal of this study is to identify clusters and groups that host bright cool-cores and AGNs. In cooling-core clusters, bright X-ray emission and mid-IR emission is provided by the warm dust heated by the AGN or star formation, and radio emission from AGN jets is often observed together. Accretion of a central black hole that is fueled by the cooling gas can also produce radio emission in strong cooling-core clusters. Radio jets and lobes associated with the AGN may affect the surrounding ICM gas, creating deficits in the X-ray emission around the radio jets, which are called “cavities” in cluster centers (Blanton et al. 2010; Hlavacek-Larrondo et al. 2012). Several clusters show a clear association of a cooling flow in a cluster with the central galaxy (and AGN) that hosts radio sources. Examples are Abell 2052 (Blanton et al. 2001), Abell 2597 (McNamara et al. 2001), Abell 4059 (Heinz et al. 2002), Abell 262 (Blanton et al. 2004), and MS 0735.6+7321 (McNamara et al. 2005). Because of their compact and peaked X-ray emission, these clusters would be misclassified as point sources by the detection algorithm.

Our goal is to find these cool-core clusters with AGN in their BCGs using the multiwavelength data through eROSITA, LOFAR, WISE, and SDSS in the eFEDS point source catalog. Therefore, we searched for clusters that are bright in X-rays, radio, and mid-IR relative to the optical data in the eFEDS field. The catalog of clusters presented in this work was constructed by running the MCMF around the X-ray centroids. In general, MCMF and similar red-sequence galaxy concentration-finder algorithms such as red mapper (Rykoff et al. 2014) are based on finding red galaxies and generally identify a red galaxy as an optical counterpart. The BCG identified by MCMF is often a red galaxy because of the nature of the algorithm and is unlikely to be an AGN-hosting BCG. Therefore, MCMF would miss blue BCGs that might host a bright quasar at the center. On the other hand, our other algorithm NWAY, which was used to identify the counterparts of the point-like sources in S21, searches for all possible counterparts with a broader prior than only red-sequence features and would locate both the AGN and red galaxies as potential counterparts around the X-ray cen-troid. Therefore, a combination of the two methods, that is, using MCMF to find secure clusters through their red sequence with a probability f_cont > 0.2 and matching those with counterparts found through NWAY is the most powerful way to find potential BCG candidates that might host AGN. We then examined their optical, IR, and X-ray properties to construct a sample of BCG candidates. We summarize our procedure below to identify these special cases.

1. We constructed a secure cluster sample through red-sequence galaxy concentration in close proximity to an X-ray point source with MCMF.

2. We categorized the full sample with NWAY based on the redshift and proximity of the point source counterpart to construct cluster classes.

3. We built a sub sample of clusters that host a point source at the cluster redshift near the X-ray and optical centroids. These are the Class 3 clusters in the S21 classification scheme.

4. We applied a color selection cut to identify clusters that are outliers relative to the rest of the cluster population and bright in the IR band.

5. We examined the optical spectra and the X-ray, IR, and radio emission associated with the host cluster in this sub sample.

In this section, we describe the color-color diagrams, X-ray, radio, IR, and optical properties of these clusters. We note that we did not attempt to detect the cavities around the radio sources due to the PSF of eROSITA and the depth of the survey. Follow-up Chandra or XMM-Newton observations are required for detailed imaging observation measurements.

4.1 Selection Based on Color-Redshift Diagrams

One way to identify the AGN-dominated BCGs is through their colors in optical and IR bands. Specifically, we searched for clusters that deviate from the bulk of the cluster population in color-color diagrams. AGN can heat a larger fraction of their surrounding dust to higher temperatures and cause a relatively stronger emission at MIR wavelengths with respect to the apparent flux deficit at far-infrared (FIR) wavelengths (Mullaney et al. 2011; Lee et al. 2013). Moreover, the AGN activity should trigger the mid-IR (MIR) luminosities that are sensitive to star formation and AGN activity. Radio and infrared fluxes are also good diagnostics for locating the AGN that is “active”. Green et al. (2016) find that AGN-hosting BCGs appear redder than the passive populations in the W2 – W3 and W1 – W2 bands, whereas the star-forming BCGs appear red only in W2 – W3 (Green et al. 2016). We expect that BCGs that host AGN are redder than the passive galaxies, and this would be reflected in the g and r and WISE W1 and W2 colors of the source. In Fig. 9 we present the color-redshift diagrams in bands z – W1, g – r, W1 – W2, and W1 – W3 of the sample clusters and their NWAY- identified counterparts of the clusters in Class 2–4. Class 5 clusters were removed from the figure as they lack secure NWAY counterparts. The side color bars demonstrate the observed X-ray and radio luminosities of these clusters within R₅₀₀. Here we use the optical and infrared colors presented in S21.

We started with a sample of potential clusters and AGN at the same redshifts based on their class, that is, Class 3 clusters (112 clusters in total). We then examined their color-redshift distributions in the g – r, z – W1, W1 – W2, and W2 – W3 bands to identify clusters that are redder than the population of red galaxy members. In the redshift distributions of the g – r, W1 – W2, and z – W1 in Fig. 9, we see that the population of red galaxies mostly consists of Class 4 clusters, whose counterpart red galaxy is identified in NWAY and MCMF. We do not see any particular correlation in the W2 – W3 bands, therefore we excluded these bands from further selection. A sub sample of 46 clusters shows significant color offsets from the rest of the population with the selection criteria of g – r < 1.15, W1 – W2 > –0.3, and z – W1 > –0.5. These outlier clusters are all likely to host a radio-quiet or radio-loud AGN and would be interesting targets to examine further. We examine the clusters with central radio-loud AGN in the next section.

Fig. 9 Color redshift diagrams of the Class 2, 3, and 4 clusters, g-r, z-W1, W2-W3, and W1-W2 color diagrams of the counterparts identified by NWAY as a function of X-ray (panels on the left) and radio (panels on the right) luminosities of the host clusters in Classes 2, 3, and 4 with secure NWAY and MCMF counterparts. The outlier clusters are shown in black. They include the Class 3 clusters and groups with radio loud-AGN in their BCGs selected based on our color criteria. All these four cases have SDSS spectroscopy for further investigation.

4.2 Clusters Bright in X-rays, IR, and Radio

To construct a sample of blue BCG candidates, we searched for clusters with significant, radio, X-ray, and IR emission while hosting an AGN in their vicinity at the same redshift, and show significant color offset from the rest of the red sequence galaxies. Out of these 46 clusters in the Class 3 group, we find that 33 of them have a LOFAR radio detection within their R₅₀₀ and show significant color offset in the g – r, z – W1, and W1 – W2 planes. We identified a sub sample of eight BCG candidates with a significant LOFAR radio detection (>5σ significance) in close proximity to the X-ray detection, within the positional accuracy of eROSITA (~5″, see Brunner et al. 2022). These candidates are shown in the color-color diagrams in Fig. 9 and are marked with diamonds with black corners. Only five of these eight clusters have SDSS spectra (see Merloni et al., in prep, for spectral targeting). We describe their multi wavelength properties through eROSITA X-ray, LOFAR radio, DECALS optical data, and SDSS-V spectra below and provide their multi wavelength images in Fig. 10. The SDSS-IV spectra of the five counterparts show clear signatures of AGN and absorption lines from the host galaxy. In five cases, we detect emission lines from the AGN and absorption lines in their SDSS spectra. This confirms our classification scheme. The remaining three clusters were not targeted with SDSS, but we still provide their images in the X-ray, optical, and radio band passes in Fig. 11.

1. eFEDS J091437.8+024558 is the most spectacular cluster identified in this sub sample with a mass of ${3.61}_{-0.36}^{+0.47}\times {10}^{14}{M}_{\text{sun}}$ Significant radio emission is associated with the central AGN, as shown in Fig. 10. The X-ray and radio luminosities are ${8.42}_{-1.24}^{+1.40}\times {10}^{43}\text{erg}{\text{s}}^{-1}$ and 0.913 ± 0.003 Jy. The colors of the counterpart show IR excess emission with g−r = 0.45, z − W1 = 1.88, and W1 − W2 = 0.52. The bright radio source is detected at 1.6″ away from the X-ray detection. The optical spectrum shows significantly bright and broad Hα and β lines from the central AGN.

2. eFEDS J083520.1+012516 is a low-mass cluster located at a redshift of z = 0.30 with a mass of ${1.15}_{-0.18}^{+0.25}\times {10}^{14}{M}_{\text{sun}}$. The X-ray luminosity inferred from the scaling relations is ${1.52}_{-0.30}^{+0.47}\times {10}^{43}\text{erg}{\text{s}}^{-1}$ and the radio luminosity is 0.47 ± 0.05 × 10⁻² Jy. Very extended AGN radio emission with an elongated filament (~800 kpc) to the northwest of the system is shown in Fig. 10. The colors of the counterpart, g − r = 0.43, z − W1 = 1.31, and W1 − W2 = −0.05, show excess in the infrared bands. The SDSS spectra of this system show broad Hα lines from the central QSO and Ca-H and Ca-K emission lines from the host galaxy.

3. eFEDS J085749.8+013530 is most likely a group with richness 26 at a redshift of 0.29. The soft-band X-ray luminosity is ${6.97}_{-1.54}^{+2.04}\times {10}^{42}\text{ergs}{\text{s}}^{-1}$ and the mass is ${6.46}_{-1.04}^{+1.38}\pm {10}^{13}{M}_{\text{sun}}$ The colors also show departures from the main sequence with g − r = 0.84, z − W1 = 1.16, and W1 − W2 = 0.02, The radio luminosity of the central radio source is 0.14 ± 0.002 Jy. The AGN emission in the center with filaments of radio emission extends to the south for ~500 kpc. This source was also targeted with the SDSS-IV. The spectrum of the counterpart shows a clear sign of Hα emission from the central AGN, as well as absorption features from the host galaxy.

4. eFEDS J085545.0–003342 is a clear case of a nearby group with a radio-loud central AGN. The red galaxy BCG identified by MCMF and the AGN identified by NWAY are located at the same redshift, z = 0.28. The total mass inferred from the scaling relations is ${1.95}_{-0.69}^{+1.11}\pm {10}^{13}{M}_{\text{sun}}$ The soft-band X-ray luminosity is ${1.33}_{-0.64}^{+1.05}\times {10}^{42}\text{erg}{\text{s}}^{-1}$. The colors show mild excess in the infrared with g − r = 1.12, z − W1 = 0.17, and W1 − W2 = −0.29. We kept it in the list for completeness. We also find significant radio emission associated with the AGN with a LOFAR luminosity of 5.81 ± 0.15 × 10⁻² Jy. The optical spectrum shows clear absorption lines from the host galaxy, as well as a weak broad Hα line from the obscured AGN.

5. eFEDS J084659.6+014947 is another low-mass group with a richness of 19 at a redshift of 0.35. The soft-band X-ray luminosity is ${6.04}_{-1.75}^{+2.98}\times {10}^{42}\text{ergs}{\text{s}}^{-1}$. The total mass is estimated to be ${5.66}_{-1.25}^{+1.92}\times {10}^{13}{M}_{\text{sun}}$. The colors show mild infrared excess with g − r = 0.96, z − W1 = 1.17, and W1 − W2 = 0.22. The source has a weak radio source with a luminosity of 0.14 ± 0.02 Jy at the location of the X-ray detection. The optical spectra show a bright Hα line from the central AGN.

6. eFEDS J091451.0+000851 is a high-redshift (z = 0.5) low-mass group with a richness of 29. The soft-band X-ray luminosity is ${2.55}_{-2.42}^{+4.59}\times {10}^{42}\text{ergs}{\text{s}}^{-1}$, and the estimated mass is ${3.17}_{-2.79}^{+3.37}\times {10}^{13}{M}_{\text{sun}}$. The counterpart has colors of g − r = 0.76, z − W1 = 0.80, and W1 − W2 = 0.73 with brighter emission in the infrared than the red member galaxies. The radio source with a luminosity of 0.82 ± 0.04 ×10⁻² Jy is significantly detected at the >22σ confidence level. This source is not observed by SDSS-IV, therefore it is not possible to confirm the classification of this source.

7. eFEDS J092227.1+043339 is another low-mass group with a richness of 15 at a redshift of 0.33. The soft-band X-ray luminosity is ${6.55}_{-1.63}^{+2.53}\times {10}^{42}\text{ergs}{\text{s}}^{-1}$, and the estimate total mass inferred from the eFEDS scaling relations is ${6.55}_{-1.63}^{+2.53}\times {10}^{13}{M}_{\text{sun}}$. The counterpart shows the brightest IR emission with colors g − r = 0.45, z − W1 = 3.41, and W1 − W2 = 0.28. The bright radio source detected 1.7″ away from the X-ray detection is significantly detected at a luminosity of 0.16 ± 0.002 Jy, but this source lacks optical spectroscopy.

8. eFEDS J093447.6+021513 is another low-mass group at a redshift of 0.50. The soft-band luminosity is ${6.49}_{-3.47}^{+4.41}\times {10}^{43}\text{erg}{\text{s}}^{-1}$ The group has an estimated total mass of ${5.43}_{-2.32}^{+2.58}\times {10}^{13}{M}_{\text{sun}}$. The colors show bright IR emission with g − r = 0.26, z − W1 = 2.54, and W1 − W2 = 0.18. The LOFAR-detected radio source located 5″ away from the X-ray detection has a luminosity of 3.63 ± 0.08 × 10⁻² Jy. No SDSS spectroscopy is available for this source.

In our visual inspection, we identified several other promising candidates, but they are not as strong radio and X-ray emitters as the candidates above. They include eFEDS J091218.7+022924, eFEDS J093833.0+025017, eFEDS J085902.4–005150, and eFEDS J091649.2+000033, which show an AGN with clearly visible Ca-H and Ca-K and broad Hα lines, as well as emission from the red galaxy in their optical spectra.

For completeness, we examined LOFAR radio and optical data of the Class 4 clusters to confirm that we did not miss any AGN-dominated BCGs in Class 4 clusters, where the counterpart finders NWAY and MCMF agree on the reddest passive galaxy as the counterpart. We identified several interesting radio features in this class. In some of these clusters, we observe radio emission from an AGN, radio galaxy, and diffuse sources, such as halos and relics, associated with the cluster itself. These clusters are presented in Figs. 12 and A.1. We describe the properties of the diffuse sources that could be radio halos or relics in the text below.

1. eFEDS J083826.4+015607 (z = 0.45): the LOFAR observations detect a diffuse source with a projected size of 40 arcsec, located 2′ to the north of the cluster center (Fig. 12, left). The diffuse source does not have an optical counterpart in the DECaLS image. If the diffuse source is part of the cluster, its projected size is 270 kpc, and it can be classified as a candidate radio relic.

2. eFEDS J084149.8+014717 (z = 0.38): a diffuse source is detected with LOFAR roughly 2.5′ to the north of the cluster center (Fig. 12, middle). It has a projected size of 1.2 × 0.5′². Its major axis is elongated in the NE-SW direction and is roughly perpendicular to the line to the cluster center. The diffuse source is not entirely associated with any radio galaxies. It has a flux density of 21.3 ± 2.2 mJy and a radio power of (12.3 ± 1.3) × 10²⁴ W Hz⁻¹ (k-corrected) if it is located at the cluster redshift of z = 0.387. The properties of the diffuse source are consistent with those of a radio relic. Future studies are required to confirm the nature of the source.

3. eFEDS J092600.8+040849 (z = 0.31): diffuse radio emission is detected in the central region of the cluster with LOFAR (Fig. 12, right). The diffuse source with a projected size of 40 × 20 arcsec² is elongated in the NE–SW direction, which is roughly similar to the major axis of the X-ray emission seen with eROSITA. The flux density of the radio source is 5.0 ± 0.7 mJy, which corresponds to a radio power of (1.78 ± 0.25) × 10²⁴ WHz⁻¹. The diffuse radio source is not associated with the BCG and could be the brightest part of a radio halo. This requires deeper observations for confirmation.

Fig. 10 0.5–2 keV soft-band images of the AGN-hosting clusters and groups in Class 3. The soft-band eROSITA images are shown in the leftmost panel. In the two middle panels, we provide DECaLS images in the optical band and LOFAR images in the radio band of the same clusters. The red- sequence galaxies are shown in the DECALS images. The overlaid LOFAR contours in green show the location of the radio source associated with the identified BCGs from NWAY. Rightmost panels: SDSS spectra of the counterpart identified by the NWAY. Green lines show the significantly detected emission lines, whereas orange lines show the absorption lines on the optical SDSS spectra displayed in the right panels. The continuous line in red shows the best-fit model to the spectra.

Fig. 11 0.5–2 keV soft-band images of the candidates of clusters and groups hosting radio-loud AGNs in their BCG in Class 3. The soft-band eROSITA images are shown in the leftmost panel. The two middle panels show DECaLS images in the optical band and LOFAR images in the radio band of the same clusters. The red-sequence galaxies are shown in the DECALS images. The overlaid LOFAR contours in green show the location of the radio source associated with the cluster.

5 Results and Discussion

We presented the X-ray, optical, and radio properties of the clusters and groups of galaxies identified and classified in the eFEDS point source catalog presented in S21. These clusters or groups are misclassified as point-like sources by the eROSITA source detection algorithm with an extent likelihood of zero. Our goal is to characterize this sample, to understand the selection of the eFEDS survey, and to find AGN-dominated clusters that are worth further follow-up investigations. The clusters in the eFEDS point source catalog were identified by running the red-sequence finder algorithm MCMF around the X-ray centroids. In total, S21 found 346 clusters and groups in the eFEDS point source sample, spanning a high-redshift range from 0.1 to 1.3. The overall distribution of the redshifts of the sample is similar to the extent-selected sample, but the median redshift of 0.40 is slightly higher than that of the extended sample. Additionally, 10 new high-z clusters at redshifts z > 0.8 are identified in this new sample. In addition to 433 clusters in the Liu et al. (2022a) extent-selected catalog (taking into account the 20% contamination), this brings the total number of clusters to 779 in the eFEDS field with a source density of 5.6 clusters per square degree. We note that the selection of this catalog and the extent-selected sample are quite different and should be treated with care. This catalog of clusters should not be combined with the extent-selected sample for studies involving the sample properties and the X-ray selection function provided in Liu et al. (2022a).

Our first goal was to understand the reason for the mis-classification of these clusters in the point source catalog by using the multi wavelength follow-up data in optical, X-ray, and radio bands. The reasons for this misclassification may include that this particular population of clusters is fainter, more compact, and hosts a cool-core or central AGN that dominates the overall X-ray emission compared to the extent-selected companions. The richness distribution of the clusters in the point source sample (after a similar optical cleaning was applied) implies that this sample may represent a similar population of clusters and groups as the extent-selected sample in terms of their optical properties. We were able to measure the luminosity within R₅₀₀ of 193 clusters with a detection confidence of 2σ or higher from the eROSITA imaging analysis. Figure 3 shows that 113 clusters lie below the flux limit of the eFEDS extent-selected clusters (1.5 × 10⁻¹⁴ ergs s⁻¹ cm⁻²). The luminosity and mass distribution of the sample shows that this sample is mostly dominated by low-mass groups and clusters that are under luminous and compact compared to the clusters in the extended source catalog. The comparison of gas density profiles out to R₅₀₀ (Fig. 6) with the extent-selected clusters indicates that this sample is dominated by centrally bright clusters, either with an AGN at the core, or with bright cool cores. Comparing the distribution of their R_core measurements and concentration parameters with the extent-selected sample, we can conclude that the majority of these clusters are indeed compact. The Kolmogorov-Smirnov test probability of the R_core of the extent- and point-source-selected distributions to be drawn from the identical parent distribution is very low, P ~ 10¹⁵. Assuming the spectroscopic follow-up observations with SDSS (45% of the total sources) are representative of the full sample, we find that AGNs (associated with clusters or in projection) constitute 10% of the sample. In the few cases that AGNs or cool-cores dominate the ICM emission, it is possible that the overall flux is magnified by the central AGN and boosted above the detection limit. In these cases, the measured X-ray luminosities of the host clusters are biased high and should be treated as upper limits. Because of the PSF size of eROSITA and the small extent of these clusters, we were not able to excise the core when we extracted X-ray properties. Although we find only a few cases like this, a follow-up study of these clusters with X-ray telescopes with better spatial resolution, for example, XMM-Newton and Chandra, is required to distinguish the AGN emission from the cluster emission. Examining the correlation of their class, assigned based on the assigned counterparts, with luminosity and richness, we cannot pinpoint an isolated dominating effect, other than being compact and under-luminous as the reason for the misclassification of these extended sources. Many factors seem to play a role in their selection.

To understand the selection and completeness of the extent-selected sample better, we compared the fraction of clusters detected as point sources with our simulations. These simulations were derived from the eROSITA mock observations based on the Multi Dark and UNIT N-body realizations of dark matter halos and the observed ICM models (Comparat et al. 2020a). We ran our detection algorithm with the same set of settings applied to the data on the simulations at the full depth of the all-sky survey. The full depth was preferred because of its similarity to the depth of the eFEDS survey, but we note that the eFEDS survey is slightly deeper than the final eROSITA all-sky survey at the same location. In Fig. 13 we compare the fraction of sources detected in the extent-selected sample as a function of the detection counts (ML_CTS in ermdet outputs) calculated within the extent parameter, which is related at the R_core of the beta model (see Brunner et al. 2022, for details). Overall, the fraction of detected clusters in the observed eFEDS extent-selected sample (shaded regions) and simulations (dashed lines) agrees within the uncertainties. The clusters that are misclassi-fied as point sources have a lower detection flux (or counts) than the extent-selected sample. The majority of the clusters (>50%) are detected as point sources below a detection count limit of ~40 or lower. This may mean that if a cluster has 40 counts or more in the core region, it is more likely to be detected as an extended source. If the cluster has 100 counts or more in the core, it has a >90% chance to be detected as an extended source. The rest, a small fraction of bright sources with 100 counts or more, may be detected as a point source if they are compact and at high redshift. The clusters below the flux limit may either have a bright cool core or AGN in their centers and/or have a very compact extended emission that is confused with a point source and is still detected by the boosted X-ray emission. The remaining clusters are fainter than the eFEDS extent-selected sample with a minimum flux of ~2.7 × 10⁻¹⁴ ergs s⁻¹ cm⁻¹ in the sample. These clusters are misclassified because of their lower fluxes, while their compactness, the central AGN, and their cool core might also play a minor role. The number of clusters below the detection flux limit of 2.7 × 10⁻¹⁴ within R_core is 56 in the point source sample. When we take the contamination of the 20% level in the extended sample into account, the total number of genuine clusters increases to 489 (433+56) in the eFEDS field (Liu et al. 2022a). From these numbers, we find that the extent selection finds roughly 88% of the clusters. The simulations (see Fig. 13 right-hand panel) predict this level to be ~80%, which agrees with our measurements at the 2σ level. The small difference between the observations and simulations is expected and can be due to the spatially varying depth of the all-sky survey simulations used here. We recall that the eFEDS survey has a slightly higher and uniform depth. The scatter in the true versus observed flux may also cause this small departure from the expectations.

We further examined this sample using the classification introduced by S21 and used our multi-wavelength observations. Based on the assigned optical counterparts by confirmation algorithms (NWAY and MCMF), S21 classified the full sample into four categories. In Class 4, NWAY and MCMF agree about the most probable optical counterpart, which is a red passive galaxy. On the other hand, in Class 3, NWAY finds an AGN as the potential counterpart near the X-ray position. This class is more likely to host a bright AGN at the core of the host cluster. We exploited a LOFAR 144 MHz observation of eFEDS to search for radio counterparts at the position of the BCG for the different classes of objects. We find that the radio detection fraction of Class 4 is higher (~47%) than for other classes, as expected because this class represents secure clusters with an AGN at the position of the BCG. A second run of the algorithm was used to search for radio emission at the position of the AGN provided by NWAY. The results for Class 4 are the same as in the first run, and the results for other classes are hard to interpret because of the relatively small statistics.

Another goal of this study was to identify clusters with AGN-dominated BCGs or cool-core clusters at high redshifts because X-ray surveys have often been criticized for missing high-redshift clusters and AGN-dominated groups in their extended source catalogs. We here established a new method for determining these sources in the point source catalog using their multi wavelength observations. To assess the cases in which extended sources were misclassified, we cross-matched the point source sample with the ACT and Planck SZ survey. Five clusters matched the ACT DR5 catalog at higher redshifts of 0.5–0.7, and one cluster matched the Planck PSZ2 catalog at a lower red-shift (z = 0.15). The measured photo-zs are consistent with the reported values in the SZ catalogs. The common properties of the matched clusters are that they all have a) a low signal-to-noise ratio SZ signal-to-noise ratio <6 and b) low luminosities and masses. This indicates that we probe high-z galaxy clusters and group populations with lower mass and lower luminosity with eROSITA, close to the detection limit of ACT and Planck surveys. The majority of the clusters that we identified using our method are below the detection limit of the current public SZ surveys. Using this method, we would find not only massive high-redshift clusters, but also AGN-dominated compact galaxy groups at low redshift that are beyond the reach of the public data of the current SZ surveys. This demonstrates the power of eROSITA over current public SZ surveys.

The method we established here to find groups and clusters that host bright AGN in their BCGs makes use of the cluster classification of S21. Starting from Class 3 objects, that is, the class of clusters or groups that have NWAY- identified AGN at the same redshift as the host cluster, we down selected a sample of 46 clusters and groups that were brighter in the g band than in the r band, brighter in z band than in W1 band, and brighter in W1 band than in W2 band in their optical data than the rest of the cluster population. These clusters and groups are interesting targets in which to study AGN feedback in dense environments. We find that the radio detections of 33 of these clusters and groups are associated with the cluster itself within R₅₀₀ using the complementary LOFAR eFEDS data. The radio and infrared emission associated with these clusters indicates that the central super massive black hole is indeed active and heats the surrounding medium to IR luminosities. Eight of these 33 clusters have radio emission in close proximity to the X-ray detection within ~5″ (source localization accuracy of eROSITA). The targeted by SDSS-V spectroscopic observations are available for five clusters and groups. These SDSS data provide the necessary high spectral resolution observations to characterize these sources in more detail and to test our classification method. The inspected spectra of these sources indeed show broad line signatures from the central AGN as well as the emission from the cluster galaxy, confirming that our selection method is successful in identifying these extraordinary clusters and groups. These populations of clusters and groups represent excellent targets for further astrophysical investigations and cosmology, for instance, studying the AGN feedback cycle in galaxy groups and clusters and constraining ultralight dark matter particles. One target we find through the search is a remarkable cluster and group, eFEDS J091437.8+024558 (z=0.40, M₅₀₀ = ${3.61}_{-0.36}^{+0.47}\times {10}^{14}{M}_{\text{sun}}),$ eFEDS $\text{J083520}\text{.1+012516(}z=0.30,M_{500}={1.15}_{-0.18}^{+0.25}\times {10}^{14}{M}_{\text{sun}}),$ and eFEDS $\text{J092227}\text{.1+043339(}z=0.33,M_{500}={6.55}_{-1.63}^{+2.53}\times {10}^{13}{M}_{\text{sun}}).$ This group of clusters is particularly bright in all the bands from X-rays and radio to infrared. It is a BCG candidate, and could be an ideal target for studying AGN feedback. It might also be used to constrain the parameter space of axion-like particles.

Fig. 12 Clusters that host diffuse emission in the ICM. The background are DECaLS optical band-grz images. The LOFAR (green) and eROSITA (magenta) first contours are drawn at 3σ. The subsequent contours are multiplied by a factor of 2. The cross at the center of the images indicates the location of the clusters.

Fig. 13 Comparisons of the number of clusters in point source and extent selected catalogs with eROSITA simulations. Left panel: the fraction of clusters detected in the extent-selected sample vs. the clusters in the point source sample as a function of the counts in Rcore (specified as a ML_CTS in the ermldet detection runs) in simulations. Right panel: the cumulative number of clusters in the extended and point source catalogs above a detection flux (ML_Flux in the ermldet runs) limit of 2.7 × 10−14 ergs s−1 cm−2 measured within Rcore (EXT parameter in ermldet outputs).

6 Conclusions

Several studies (e.g., the Phoenix cluster) have shown that clusters of galaxies with compact cores and/or hosting a star-burst galaxy and a strong point source at the center can be misclassified as point sources in the extent-selected X-ray surveys because their PSF is finite (Green et al. 2017; McDonald et al. 2012; Somboonpanyakul et al. 2018). As a pilot study, we examined the point sources in the benchmark eROSITA Final Equatorial-Depth Survey (eFEDS) point source catalog. eFEDS is unique because the majority of the sources have spectroscopic data from the SDSS and GAMA surveys and deep radio data through LOFAR. We examined 346 clusters and groups identified via their red sequence by S21 through their multi wavelength observations in the optical, IR, radio, and X-ray bands in detail. We used these observations to understand the selection effects and the completeness of the eFEDS cluster sample. We find that the majority of the sources are under luminous and below the flux limit of the extended sources. Their faint fluxes and compact sizes cause them to be mischaracterized as point sources by our detection algorithm. Overall, the sample includes a small fraction (≈10%) of clusters and groups hosting AGN at their centers, but this is not the main reason that these clusters are missed in the eFEDS extent-selected catalog. In the current version of the detection algorithm of eSASS, a detected source with an extent likelihood parameter lower than 6 is set to have an extent likelihood of zero. Lowering the detection likelihood limit and allowing the extent likelihood parameter to be lower than 6 would help to classify these clusters as extended sources in future eROSITA All Sky-survey catalogs. However, we note that this would also increase the contamination fraction in the extent-selected sample.

Furthermore, by combining the cluster classification of S21, the optical spectra through SDSS and GAMA, the radio emission from LOFAR, infrared from the WISE survey, and X-ray data from eROSITA, we developed a method for searching for groups and clusters with BCGs dominated by central AGN at their cores. This method was successfully tested in this work and resulted in the identification of eight low-mass groups and clusters that host AGN in their BCGs. Three of these are a promising low-mass cluster at z = 0.3–0.4 for in-depth studies of AGN feedback. Most of these low-mass groups and clusters we identified are below the detection limit of the current SZ surveys and are undetected in their public catalogs. This highlights the power of eROSITA in detecting this unique nearby low-mass, low-luminosity groups and high-redshift cool-core clusters, and verifies the validity of our method in identifying them in the point source catalog.

In the first eROSITA All-Sky Survey (eRASS) in the German half of the sky, we expect to detect ~ 10 000 extended sources and ~500 000 point-like sources. With a simple scaling from eFEDS, we predict that ~6000 clusters and groups will be found in the point source catalog. Of these, 400 candidate clusters and groups will likely have an AGN in their BCGs. This sample will include not only high-redshift clusters, but also low-mass clusters and groups. Somboonpanyakul et al. (2021a) predicted a 2 ± 1% occurrence rate for the clusters that appear as point sources and are bright in mid-IR and radio wavelengths and 1% occurrence rates for Phoenix-like clusters with a rapidly cooling core at high redshift. According to these rates, we expect to detect about 40–80 high-redshift clusters of galaxies in this sample. A large sample with this size will allow studying cooling and feedback cycles and their evolution with redshift, discovering the new star burst-BCG clusters, and enabling searches for ultralight dark matter candidates, axion-like particles. However, identifying AGN in BCGs relies on the availability of large-area optical, radio, and IR surveys covering a significant fraction of the eRASS area. The large and uniform coverage with Legacy Survey DR10 in the g, r, z, and W bands, a dedicated follow-up program with SDSS (see Black Hole Mapper pro-gram³), and large coverage with radio surveys such as MeerKAT and ASKAP, eROSITA will provide a significant leap forward in the southern eRASS sky in identifying these clusters.

Acknowledgements

Authors thank the anonymous referee, Nicolas Clerc and Susanne Friedrich for helpful discussions and comments on the draft. E.B. acknowledges financial support from the European Research Council (ERC) Consolidator Grant under the European Union’s Horizon 2020 research and innovation programme (grant agreement CoG DarkQuest No 101002585). D.N.H. acknowledges support from the ERC through the grant ERC-Stg DRANOEL n. 714245. J.W. acknowledges support by the Deutsche For schungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2094 -390783311. This work is based on data from eROSITA, the soft X- ray instrument aboard SRG, a joint Russian-German science mission supported by the Russian Space Agency (Roskosmos), in the interests of the Russian Academy of Sciences represented by its Space Research Institute (IKI), and the Deutsches Zentrum für Luft und Raumfahrt (DLR). The SRG spacecraft was built by Lavochkin Association (NPOL) and its subcontractors, and is operated by NPOL with support from the Max Planck Institute for Extraterrestrial Physics (MPE). The development and construction of the eROSITA X-ray instrument was led by MPE, with contributions from the Dr. Karl Remeis Observatory Bamberg & ECAP (FAU Erlangen-Nuernberg), the University of Hamburg Observatory, the Leibniz Institute for Astrophysics Potsdam (AIP), and the Institute for Astronomy and Astrophysics of the University of Tübin–gen, with the support of DLR and the Max Planck Society. The Argelander Institute for Astronomy of the University of Bonn and the Ludwig Maximilians Universität Munich also participated in the science preparation for eROSITA. The eROSITA data shown here were processed using the eSASS software system developed by the German eROSITA consortium. Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS-IV acknowledges support and resources from the Center for High Performance Computing at the University of Utah. The SDSS website is www.sdss.org. SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, Center for Astrophysics ∣ Harvard & Smithsonian, the Chilean Participation Group, the French Participation Group, Instituto de Astrofisica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU)/University of Tokyo, the Korean Participation Group, Lawrence Berkeley National Laboratory, Leibniz Institut für Astro-physik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatário Nacional/MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University. This work made use of SciPy (Jones et al. 2001), matplotlib, a Python library for publication quality graphics (Hunter 2007), Astropy, a community-developed core Python package for Astronomy (Astropy Collaboration 2013), NumPy (Van Der Walt et al. 2011).

Appendix A Multiwavelength images of clusters with radio emission

Fig. A.1 Left panel: Soft-band 0.5 – 2 keV eROSITA images of the clusters that shown significant radio emission associated with the BCG. The overlaid green contours mark the radio emission from LOFAR data. Middle panel: DECALS images of the same clusters. Right panel: LOFAR images.

References

All Tables

All Figures

	Fig. 1 Distribution of the 346 cluster candidates in eFEDS point source catalog. The color code represents the redshift of the cluster, provided by the MCMF (Klein et al. 2018, 2019). The radius of the circle corresponds to 3 R500 of each cluster.
In the text

Fig. 2 Global properties of the 346 clusters and groups in the eFEDS point source catalog provided by MCMF. top panel: redshift distribution of the 346 clusters and groups in the eFEDS point source catalog provided by MCMF (blue). the median redshift of this sample is 0.40, i.e., slightly higher than the redshift distribution of the extent-selected clusters in Liu et al. (2022a) $(z_{\text{med}}^{\text{ext}}=0.35$ shown as gray bars). The redshift distribution of the extent-selected sample and clusters in the point source catalog is skewed toward the low redshifts, as expected. Middle panel: richness distribution of the clusters in the extent-selected sample (blue) with the clusters found in the eFEDS point source catalog (orange). Optical cleaning filtering of fcont < 0.2, recommended by Klein et al. (2021), was applied to both samples. Bottom panel: distribution of the soft-band (0.5–2 keV) luminosity as a function of redshift for the point source sample in orange, compared with the extent-selected sample in blue. The detections with <2σ are shown as upper limits. the dashed red line marks the flux limit 1.5 × 10−14 ergs s−1 cm−1 of the extended source sample reported in Liu et al. (2022a).

In the text

Fig. 3 Luminosity distribution of clusters with respect to redshift, class, and richness. Left panel: luminosity-redshift distribution of the clusters and groups identified in the point source sample based on their class. A 2σ detection limit is applied on the luminosities. The flux limit for the extent-selected sample of 1.5 × 10−14 ergs s−1 cm−2 is displayed as the dashed red line (Liu et al. 2022a). The luminosity of most clusters in the point source catalog is lower than that of the extent-selected sample, indicating that this sample is composed of clusters and groups that are smaller in extent and lower in mass, whose emission might be dominated by the central AGN. Right panel: X-ray luminosity as a function of the red-sequence richness. The blue data points show the extent-selected sample (Liu et al. 2022a; Klein et al. 2021). The orange points mark the clusters in the point source sample.

In the text

	Fig. 4 Mass-redshift distribution of the clusters in the extent-selected sample (blue) and the clusters identified in the point source sample (orange). The clusters found in the point source sample are fainter than the extent-selected companions in the eFEDS field, suggesting that they are mostly missed due to our extent or detection likelihood selections.
In the text

Fig. 5 Distributions of the Rcore and cSB as a measure of compactness of the clusters in the point source catalog and the extent selected catalogs. The left panel shows the distribution of Rcore of the cluster sample in the point source catalog (orange) and the extent-selected (Lext > 12) cluster sample (blue). The right panel shows that the distribution of the cSB of the clusters in the point source catalog is smaller than in the extent-selected sample, indicating that the clusters in the point source catalog are more compact.

In the text

Fig. 6 Gas density of the clusters in the point source catalog (orange) compared with those in the extent-selected clusters (blue). The dashed curves display the median profiles of both samples. The shaded regions show the 68% confidence intervals around the median values of the radial profiles. The selection of an extent likelihood higher than 12 is applied to the extent-selected sample to reduce the AGN contamination in the sample (see Liu et al. 2022a; Ghirardini et al. 2021a). The median gas density of the clusters in the point source catalog is more compact than that in the extent-selected sample.

In the text

Fig. 7 Radio properties of the clusters in the point source sample compared with the extent selected sample. Top and middle panels: radio power of BCGs versus X-ray luminosity of the host cluster for the PS sample (orange) and for the cluster sample studied in P21 (blue). Data are sized based on the detection likelihood, and arrows denote radio upper limits. From top left to bottom right: clusters of class 5, 4, 3 and 2. Bottom panel: radio power measured at the position of the AGN vs. X-ray luminosity for Class 3 (left) and 2 (right) objects.

In the text

Fig. 8 Images of eROSITA clusters identified in the point source catalog, matched with the public SZ catalogs (ACT and Planck; Hilton et al. 2021; Planck Collaboration XXVII 2016). Top panel: four matches (eFEDS J084615.7+050708 at the edge of the field is ignored) with ACT using a matching radius of 2 arcmin. Bottom panel: three matches with PLANCKSZ2 using a matching radius of 3 arcmin. Images are centered on the X-ray position of the cluster in the point source catalog, marked by the gray star. The diamond shows the location of the extended sources in the Liu et al. (2022a) catalog if there is any nearby. The SZ centroid from either the ACT or Planck catalog is shown as a cross.

In the text

Fig. 9 Color redshift diagrams of the Class 2, 3, and 4 clusters, g-r, z-W1, W2-W3, and W1-W2 color diagrams of the counterparts identified by NWAY as a function of X-ray (panels on the left) and radio (panels on the right) luminosities of the host clusters in Classes 2, 3, and 4 with secure NWAY and MCMF counterparts. The outlier clusters are shown in black. They include the Class 3 clusters and groups with radio loud-AGN in their BCGs selected based on our color criteria. All these four cases have SDSS spectroscopy for further investigation.

In the text

Fig. 10 0.5–2 keV soft-band images of the AGN-hosting clusters and groups in Class 3. The soft-band eROSITA images are shown in the leftmost panel. In the two middle panels, we provide DECaLS images in the optical band and LOFAR images in the radio band of the same clusters. The red- sequence galaxies are shown in the DECALS images. The overlaid LOFAR contours in green show the location of the radio source associated with the identified BCGs from NWAY. Rightmost panels: SDSS spectra of the counterpart identified by the NWAY. Green lines show the significantly detected emission lines, whereas orange lines show the absorption lines on the optical SDSS spectra displayed in the right panels. The continuous line in red shows the best-fit model to the spectra.

In the text

Fig. 11 0.5–2 keV soft-band images of the candidates of clusters and groups hosting radio-loud AGNs in their BCG in Class 3. The soft-band eROSITA images are shown in the leftmost panel. The two middle panels show DECaLS images in the optical band and LOFAR images in the radio band of the same clusters. The red-sequence galaxies are shown in the DECALS images. The overlaid LOFAR contours in green show the location of the radio source associated with the cluster.

In the text

	Fig. 12 Clusters that host diffuse emission in the ICM. The background are DECaLS optical band-grz images. The LOFAR (green) and eROSITA (magenta) first contours are drawn at 3σ. The subsequent contours are multiplied by a factor of 2. The cross at the center of the images indicates the location of the clusters.
In the text

Fig. 13 Comparisons of the number of clusters in point source and extent selected catalogs with eROSITA simulations. Left panel: the fraction of clusters detected in the extent-selected sample vs. the clusters in the point source sample as a function of the counts in Rcore (specified as a ML_CTS in the ermldet detection runs) in simulations. Right panel: the cumulative number of clusters in the extended and point source catalogs above a detection flux (ML_Flux in the ermldet runs) limit of 2.7 × 10−14 ergs s−1 cm−2 measured within Rcore (EXT parameter in ermldet outputs).

In the text

	Fig. A.1 Left panel: Soft-band 0.5 – 2 keV eROSITA images of the clusters that shown significant radio emission associated with the BCG. The overlaid green contours mark the radio emission from LOFAR data. Middle panel: DECALS images of the same clusters. Right panel: LOFAR images.
In the text