Aims. The eROSITA Final Equatorial-Depth Survey has been carried out during the performance verification phase of the Spectrum-Roentgen-Gamma/eROSITA telescope and was completed in November 2019. This survey is designed to provide the first eROSITA-selected sample of clusters and groups and to test the predictions for the all-sky survey in the context of cosmological studies with clusters of galaxies. Methods. In the area of ∼140 square degrees covered by eFEDS, 542 candidate clusters and groups of galaxies were detected as extended X-ray sources with the eSASS source detection algorithm. We performed imaging and spectral analysis of the 542 cluster candidates with eROSITA X-ray data and studied the properties of the sample. Results. We provide the catalog of candidate galaxy clusters and groups detected by eROSITA in the eFEDS field down to a flux of ∼ 10 −14 erg s −1 cm −2 in the soft band (0.5-2 keV) within 1 . The clusters are distributed in the redshift range z =[0.01, 1.3] with a median redshift z median = 0.35. With eROSITA X-ray data, we measured the temperature of the intracluster medium within two radii, 300 kpc and 500 kpc, and constrained the temperature with > 2σ confidence level for ∼ 1/5 (102 out of 542) of the sample. The average temperature of these clusters is ∼2 keV. Radial profiles of flux, luminosity, electron density, and gas mass were measured from the precise modeling of the imaging data. The selection function, the purity, and the completeness of the catalog are examined and discussed in detail. The contamination fraction is ∼ 1/5 in this sample and is dominated by misidentified point sources. The X-ray luminosity function of the clusters agrees well with the results obtained from other recent X-ray surveys. We also find 19 supercluster candidates in this field, most of which are located at redshifts between 0.1 and 0.5, including one cluster at z ∼ 0.36 that was presented previously. Conclusions. The eFEDS cluster and group catalog at the final eRASS equatorial depth provides a benchmark proof of concept for the eROSITA All-Sky Survey extended source detection and characterization. We confirm the excellent performance of eROSITA for cluster science and expect no significant deviations from our pre-launch expectations for the final all-sky survey.

Context. Galaxy clusters are luminous tracers of the most massive dark matter haloes in the Universe. To use them as a cosmological probe, a detailed description of the properties of dark matter haloes is required. Aims. We characterize how the dynamical state of haloes impacts the dark matter halo mass function at the high-mass end (i.e., for haloes hosting clusters of galaxies). Methods. We used the dark matter-only MultiDark suite of simulations and the high-mass objects M > 2.7 × 1013 M⊙ h−1 therein. We measured the mean relations of concentration, offset, and spin as a function of dark matter halo mass and redshift. We investigated the distributions around the mean relations. We measured the dark matter halo mass function as a function of offset, spin, and redshift. We formulated a generalized mass function framework that accounts for the dynamical state of the dark matter haloes. Results. We confirm the recent discovery of the concentration upturn at high masses and provide a model that predicts the concentration for different values of mass and redshift with one single equation. We model the distributions around the mean values of concentration, offset, and spin with modified Schechter functions. We find that the concentration of low-mass haloes shows a faster redshift evolution compared to high-mass haloes, especially in the high-concentration regime. We find that the offset parameter is systematically smaller at low redshift, in agreement with the relaxation of structures at recent times. The peak of its distribution shifts by a factor of ∼1.5 from z = 1.4 to z = 0. The individual models are combined into a comprehensive mass function model, which predicts the mass function as a function of spin and offset. Our model recovers the fiducial mass function with ∼3% accuracy at redshift 0 and accounts for redshift evolution up to z ∼ 1.5. Results. This new approach accounts for the dynamical state of the halo when measuring the halo mass function. It offers a connection with dynamical selection effects in galaxy cluster observations. This is key toward precision cosmology using cluster counts as a probe.

Context. The extended ROentgen Survey with an Imaging Telescope Array (eROSITA) onboard the Spectrum-Roentgen-Gamma (SRG) observatory is revolutionizing X-ray astronomy. The mission provides unprecedented samples of active galactic nuclei (AGN) and clusters of galaxies, with the potential of studying astrophysical properties of X-ray sources and measuring cosmological parameters using X-ray-selected samples with higher precision than ever before. Aims. We aim to study the detection, and the selection of AGN and clusters of galaxies in the first eROSITA all-sky survey, and to characterize the properties of the source catalog. Methods. We produced a half-sky simulation at the depth of the first eROSITA survey (eRASS1), by combining models that truthfully represent the population of clusters and AGN. In total, we simulated 1 116 758 clusters and 225 583 320 AGN. We ran the standard eROSITA detection algorithm, optimized for extragalactic sources. We matched the input and the source catalogs with a photon-based matching algorithm. Results. We perfectly recovered the bright AGN and clusters. We detected half of the simulated AGN with flux larger than 2×10 −14 erg/s/cm 2 as point sources and half of the simulated clusters with flux larger than 3×10 −13 erg/s/cm 2 as extended sources in the 0.5 -2.0 keV band. We quantified the detection performance in terms of completeness, false detection rate, and contamination. We studied the population in the source catalog according to multiple cuts of source detection and extension likelihood. We find that the latter is suitable for removing contamination, and the former is very efficient in minimizing the false detection rate. We find that the detection of clusters of galaxies is mainly driven by flux and exposure time. It additionally depends on secondary effects, such as the size of the clusters on the sky plane and their dynamical state. The cool core bias mostly affects faint clusters classified as point sources, while its impact on the extent-selected sample is small. We measured the fraction of the area covered by our simulation as a function of limiting flux. We measured the X-ray luminosity of the detected clusters and find that it is compatible with the simulated values. Conclusions. We discuss how to best build samples of galaxy clusters for cosmological purposes, accounting for the nonuniform depth of eROSITA. This simulation provides a digital twin of the real eRASS1.

Aims. The eROSITA Final Equatorial-Depth Survey (eFEDS), executed during the performance verification phase of the Spectrum-Roentgen-Gamma (SRG)/eROSITA telescope, was completed in November 2019. One of the science goals of this survey is to demonstrate the ability of eROSITA to detect samples of clusters and groups at the final depth of the eROSITA all-sky survey. Methods. Because of the sizeable (≈26″ HEW FOV average) point-spread function of eROSITA, high-redshift clusters of galaxies or compact nearby groups hosting bright active galactic nuclei (AGN) can be misclassified as point sources by the source detection algorithms. A total of 346 galaxy clusters and groups in the redshift range of 0.1 < z < 1.3 were identified based on their red sequenc in the eFEDS point source catalog. Results. We examine the multiwavelength properties of these clusters and groups to understand the potential biases in our selection process and the completeness of the extent-selected sample. We find that the majority of the clusters and groups in the point source sample are indeed underluminous and compact compared to the extent-selected sample. Their faint X-ray emission, well below the flux limit of the extent-selected eFEDS clusters, and their compact X-ray emission are likely to be the main reason for this misclassification. In the sample, we confirm that 10% of the sources host AGN in their brightest cluster galaxies (BCGs) through optical spectroscopy and visual inspection. By studying their X-ray, optical, infrared, and radio properties, we establish a method for identifying clusters and groups that host AGN in their BCGs. We successfully test this method on the current point source catalog through the Sloan Digital Sky Survey optical spectroscopy and find eight low-mass clusters and groups with active radio-loud AGN that are particularly bright in the infrared. They include eFEDS J091437.8+024558, eFEDS J083520.1+012516, and eFEDS J092227.1+043339 at redshifts 0.3−0.4. Conclusions. This study helps us to characterize and understand our selection process and assess the completeness of the eROSITA extent-selected samples. The method we developed will be used to identify high-redshift clusters, AGN-dominated groups, and low-mass clusters that are misclassified in the future eROSITA all-sky survey point source catalogs.

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