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Y. E. Bahar

Publications and source records attributed to Y. E. Bahar.

33 records · Page 2Linked to original sources

The Galaxy Group Merger Origin of the Cloverleaf Odd Radio Circle System

Odd radio circles (ORCs) are a newly discovered class of extended faint radio sources of unknown origin. We report the first detection of diffuse X-ray gas at the location of a low-redshift ORC (z=0.046) known as Cloverleaf ORC. This observation was performed with the XMM-Newton X-ray telescope. The physical extent of the diffuse X-ray emission corresponds to a region of approximately 230 kpc by 160 kpc, lying perpendicular to the radio emission detected by ASKAP. The X-ray spectrum shows characteristics of thermal multiphase gas with temperatures of 1.10+/-0.08 keV and 0.22+/-0.01 keV and a central density of $(4.9\pm0.6)\times10^{-4}$ cm$^{-3}$, indicating that the Cloverleaf ORC resides in a low-mass galaxy group. Using X-ray observations, with hydrostatic equilibrium and isothermal assumptions, we measure the galaxy group to have a gas mass and a total mass of $(7.7\pm 0.8) \times 10^{11}$ M$_{\rm sun}$ and $2.6\pm0.3\times10^{13}$~$M_{\rm sun}$ within the overdensity radius R$_{500}$. The presence of a high-velocity subgroup identified in optical data, the orientation of the brightest cluster galaxy, the disturbed morphologies of galaxies toward the east of the Cloverleaf ORC, and the irregular morphology of the X-ray emission suggest that this system is undergoing a galaxy group merger. The radio power of the ORC could be explained by the shock reacceleration of fossil cosmic rays generated by a previous episode of black hole activity in the central active galactic nucleus.

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The SRG/eROSITA All-Sky Survey: The first catalog of galaxy clusters and groups in the Western Galactic Hemisphere

Clusters of galaxies can be used as powerful probes to study astrophysical processes on large scales, test theories of the growth of structure, and constrain cosmological models. The driving science goal of the SRG/eROSITA All-Sky Survey (eRASS) is to assemble a large sample of X-ray-selected clusters with a well-defined selection function to determine the evolution of the mass function and, hence, the cosmological parameters. We present here a catalog of 12247 optically confirmed galaxy groups and clusters detected in the 0.2-2.3 keV as extended X-ray sources in a 13,116deg$^2$ region in the western Galactic hemisphere of the sky, which eROSITA surveyed in its first six months of operation. The clusters in the sample span the redshift range $0.003<z<1.32$. The majority (68%) of these clusters, 8361 sources, represent new discoveries without known counterparts in the literature. The mass range of the sample covers three orders of magnitude from $5\times10^{12}M_{\rm sun}$ to $2\times10^{15}M_{\rm sun}$. We construct a sample for cosmology with a higher purity level (~95%) than the primary sample, comprising 5259 securely detected and confirmed clusters in the 12791deg$^{2}$ common footprint with the DESI Legacy Survey DR10. We characterize the X-ray properties of each cluster, including their flux, luminosity and temperature, the total mass, gas mass, gas mass fraction, and mass proxy $Y_{X}$. These are determined within two apertures, 300 kpc, and the overdensity radius $R_{500}$, and are calculated by applying a forward modeling approach with a rigorous X-ray background treatment, K-factor, and the Galactic absorption corrections. Population studies utilizing LogN-LogS, the number of clusters detected above a given flux limit, and the luminosity function show overall agreement with the previous X-ray surveys after accounting for the survey completeness and purity (ABRIDGED)

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The SRG/eROSITA All-Sky Survey: First catalog of superclusters in the western Galactic hemisphere

Superclusters of galaxies mark the large-scale overdense regions in the Universe. Superclusters provide an ideal environment to study structure formation and to search for the emission of the intergalactic medium such as cosmic filaments and WHIM. In this work, we present the largest-to-date catalog of X-ray-selected superclusters identified in the first SRG/eROSITA All-Sky Survey (eRASS1). By applying the Friends-of-Friends method on the galaxy clusters detected in eRASS1, we identified 1338 supercluster systems in the western Galactic hemisphere up to redshift 0.8, including 818 cluster pairs and 520 rich superclusters with $\ge 3$ members. The most massive and richest supercluster system is the Shapley supercluster at redshift 0.05 with 45 members and a total mass of $2.58\pm0.51 \times10^{16} M_{\odot}$. The most extensive system has a projected length of 127~Mpc. The sizes of the superclusters we identified in this work are comparable to the structures found with galaxy survey data. We also found a good association between the eRASS1 superclusters and the large-scale structures formed by optical galaxies. 3948 clusters, corresponding to $45\%$ of the cluster sample, were identified as supercluster members. The reliability of each supercluster was estimated by considering the uncertainties in cluster redshifts and peculiar velocities. 63\% of the systems have a reliability larger than 0.7. The eRASS1 supercluster catalog provided in this work represents the most extensive sample of superclusters selected in the X-ray band in terms of the unprecedented sample volume, sky coverage, redshift range, the availability of X-ray properties, and the well-understood selection function of the parent cluster sample, which enables direct comparisons with numerical simulations. This legacy catalog will greatly advance our understanding of superclusters and the cosmic large-scale structure.

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The SRG/eROSITA All-Sky Survey: Dark Energy Survey Year 3 Weak Gravitational Lensing by eRASS1 selected Galaxy Clusters

Number counts of galaxy clusters across redshift are a powerful cosmological probe, if a precise and accurate reconstruction of the underlying mass distribution is performed -- a challenge called mass calibration. With the advent of wide and deep photometric surveys, weak gravitational lensing by clusters has become the method of choice to perform this measurement. We measure and validate the weak gravitational lensing (WL) signature in the shape of galaxies observed in the first 3 years of the DES Y3 caused by galaxy clusters selected in the first all-sky survey performed by SRG/eROSITA. These data are then used to determine the scaling between X-ray photon count rate of the clusters and their halo mass and redshift. We empirically determine the degree of cluster member contamination in our background source sample. The individual cluster shear profiles are then analysed with a Bayesian population model that self-consistently accounts for the lens sample selection and contamination, and includes marginalization over a host of instrumental and astrophysical systematics. To quantify the accuracy of the mass extraction of that model, we perform mass measurements on mock cluster catalogs with realistic synthetic shear profiles. This allows us to establish that hydro-dynamical modelling uncertainties at low lens redshifts ($z<0.6$) are the dominant systematic limitation. At high lens redshift the uncertainties of the sources' photometric redshift calibration dominate. With regard to the X-ray count rate to halo mass relation, we constrain all its parameters. This work sets the stage for a joint analysis with the number counts of eRASS1 clusters to constrain a host of cosmological parameters. We demonstrate that WL mass calibration of galaxy clusters can be performed successfully with source galaxies whose calibration was performed primarily for cosmic shear experiments.

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The SRG/eROSITA All-Sky Survey: Tracing the Large-Scale Structure with a clustering study of galaxy clusters

The spatial distribution of galaxy clusters provides a reliable tracer of the large-scale distribution of matter in the Universe. The clustering signal depends on intrinsic cluster properties and cosmological parameters. The ability of eROSITA onboard Spectrum-Roentgen-Gamma (SRG) to discover galaxy clusters allows probing the association of extended X-ray emission to dark matter haloes. We aim to measure the projected two-point correlation function to study the occupation of dark matter halos by clusters and groups detected by the first eROSITA all-sky survey (eRASS1). We create five volume-limited samples probing clusters with different redshift and X-ray luminosity. We interpret the correlation function with halo occupation distribution (HOD) and halo abundance matching (HAM) models. We simultaneously fit cosmological parameters and halo bias of a flux-limited sample of 6493 clusters with purity > 96%. Results. We obtain a detailed view of the halo occupation for eRASS1 clusters. The fainter population at low redshift (S0: LX = 4.63E43 erg/s, 0.1 < z < 0.2) is the least biased compared to dark matter, with b = 2.95 $\pm$ 0.21. The brightest clusters up to higher redshift (S4: LX = 1.77E44 erg/s , 0.1 < z < 0.6) exhibit a higher bias b = 4.34 $\pm$ 0.62. Satellite groups are rare, with a satellite fraction < 14.9% (8.1) for the S0 (S4) sample. We combine the HOD prediction with a HAM procedure to constrain the scaling relation between LX and mass in a new way and find a scatter of 0.36. We obtain cosmological constraints for the physical cold dark matter density 0.12+0.03-0.02 and an average halo bias b = 3.63+1.02-0.85. We model the clustering of galaxy clusters with a HOD approach for the first time, paving the way for future studies combining eROSITA with 4MOST, SDSS, Euclid, Rubin, and DESI to unravel the cluster distribution in the Universe.

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The SRG/eROSITA All-Sky Survey: X-ray selection function models for the eRASS1 galaxy cluster cosmology

Characterising galaxy cluster populations from catalog of sources selected in astronomical surveys requires knowledge of sample incompleteness, known as selection function. The first All-Sky Survey (eRASS1) by eROSITA onboard Spectrum Roentgen Gamma (SRG) has enabled the collection of large samples of galaxy clusters detected in the soft X-ray band over the Western Galactic hemisphere. The driving goal consists in constraining cosmological parameters, which puts stringent requirements on accuracy, flexibility and explainability of the selection function models. We use a large set of mock observations of the eRASS1 survey and we process simulated data identically to the real eRASS1 events. We match detected sources to simulated clusters and we associate detections to intrinsic cluster properties. We train a series of models to build selection functions depending only on observable surface brightness data. We develop a second series of models relying on global cluster characteristics such as X-ray luminosity, flux, and expected instrumental count-rate as well as on morphological properties. We validate our models using our simulations and we rank them according to selected performance metrics. We validate the models with datasets of clusters detected in X-rays and via the Sunyaev-Zeldovich effect. We present the complete Bayesian population modelling framework developed for this purpose. Our results reveal the surface brightness characteristics most relevant to cluster selection in the eRASS1 sample, in particular the ambiguous role of central surface brightness at the scale of the instrument resolution. We have produced a series of user-friendly selection function models and demonstrated their validity and their limitations. Our selection function for bright sources reproduces well the catalog matches with external datasets. (abridged)

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The SRG-eROSITA All-Sky Survey : Constraints on f(R) Gravity from Cluster Abundance

The evolution of the cluster mass function traces the growth of the linear density perturbations and can be utilized for constraining the parameters of cosmological and alternative gravity models. In this context, we present new constraints on potential deviations from general relativity by investigating the Hu-Sawicki parametrization of the f(R) gravity with the first SRG-eROSITA All-Sky Survey (eRASS1) cluster catalog in the Western Galactic Hemisphere in combination with the overlapping Dark Energy Survey Year 3, KiloDegree Survey and Hyper Supreme Camera data for weak lensing mass calibration. For the first time, we present constraints obtained from cluster abundances only. When we consider massless neutrinos, we find a strict upper limit of log |fR0| < -4.31 at 95% confidence level. Massive neutrinos suppress structure growth at small scales, and thus have the opposite effect of f(R) gravity. We consequently investigate the joint fit of the mass of the neutrinos with the modified gravity parameter. We obtain log |fR0| < -4.12 jointly with \sum m_ν< 0.44 e.V. at 95% confidence level, tighter than the limits in the literature utilizing cluster counts only. At log |fR0|= - 6, the number of clusters is not significantly changed by the theory. Consequently, we do not find any statistical deviation from general relativity from the study of eRASS1 cluster abundance. Deeper surveys with eROSITA, increasing the number of detected clusters, will further improve constraints on log |fR0| and investigate alternative gravity theories.

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The SRG/eROSITA all-sky survey: First X-ray catalogues and data release of the western Galactic hemisphere

The eROSITA telescope array aboard the Spektrum Roentgen Gamma (SRG) satellite began surveying the sky in December 2019, with the aim of producing all-sky X-ray source lists and sky maps of an unprecedented depth. Here we present catalogues of both point-like and extended sources using the data acquired in the first six months of survey operations (eRASS1; completed June 2020) over the half sky whose proprietary data rights lie with the German eROSITA Consortium. We describe the observation process, the data analysis pipelines, and the characteristics of the X-ray sources. With nearly 930000 entries detected in the most sensitive 0.2-2.3 keV energy range, the eRASS1 main catalogue presented here increases the number of known X-ray sources in the published literature by more than 60%, and provides a comprehensive inventory of all classes of X-ray celestial objects, covering a wide range of physical processes. A smaller catalogue of 5466 sources detected in the less sensitive but harder 2.3-5 keV band is the result of the first true imaging survey of the entire sky above 2 keV. We show that the number counts of X-ray sources in eRASS1 are consistent with those derived over narrower fields by past X-ray surveys of a similar depth, and we explore the number counts variation as a function of the location in the sky. Adopting a uniform all-sky flux limit (at 50% completeness) of F_{0.5-2 keV} > 5 \times 10^{-14}$ erg\,s$^{-1}$\,cm$^{-2}$, we estimate that the eROSITA all-sky survey resolves into individual sources about 20% of the cosmic X-ray background in the 1-2 keV range. The catalogues presented here form part of the first data release (DR1) of the SRG/eROSITA all-sky survey. Beyond the X-ray catalogues, DR1 contains all detected and calibrated event files, source products (light curves and spectra), and all-sky maps. Illustrative examples of these are provided.

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The X-ray invisible Universe. A look into the halos undetected by eROSITA

The paper presents the analysis of optically selected GAMA groups and clusters in the SRG/eROSITA X-ray map of eFEDS (eROSITA Final Equatorial Depth Survey), in the halo mass range $10^{13}-5{\times}10^{14}$ $M_{\odot}$ and at $z < 0.2$. All X-ray detections have a clear GAMA counterpart, but most of the GAMA groups in the halo mass range $10^{13}-10^{14}$ $M_{\odot}$ remain undetected. We compare the X-ray surface brightness profiles of the eROSITA detected groups with the mean stacked profile of the undetected low-mass halos at fixed halo mass. Overall, we find that the undetected groups exhibit less concentrated X-ray surface brightness, dark matter, and galaxy distributions with respect to the X-ray detected halos. The mean gas mass fraction profiles are consistent in the two samples within 1.5$σ$, indicating that the gas follows the dark matter profile. The low mass concentration and the magnitude gap indicate that these systems are young. They reside with a higher probability in filaments while X-ray detected groups favor the nodes of the Cosmic Web. Because of the lower central emission, the undetected systems tend to be X-ray under-luminous at fixed halo mass and to lie below the $L_X-M_{halo}$ relation. Interestingly, the X-ray detected systems inhabiting the nodes scatter the less around the relation, while those in filaments tend to lie below it. We do not observe any strong relationship between the system X-ray appearance and the AGN activity. We cannot exclude the role of the past AGN feedback in affecting the gas distribution over the halo lifetime. However, the data suggests that the observed differences might be related to the halo assembly bias.

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Central radio galaxies in galaxy clusters: Joint surveys by eROSITA and ASKAP

The extended ROentgen Survey with an Imaging Telescope Array (eROSITA) telescope onboard the Spectrum-Roentgen-Gamma (SRG) mission has finished the first eROSITA All-Sky Survey (eRASS:1), and detected 10$^4$ galaxy clusters in the western Galactic hemisphere. In the radio band, the Australian Square Kilometre Array Pathfinder (ASKAP) telescope finished its pilot 1 phase of the project 'Evolutionary Map of the Universe' (EMU) with 220.000 sources in a 270 deg$^2$ field overlapping with eRASS:1. These two surveys are used to study radio-mode Active Galactic Nuclei (AGN) in clusters. In order to understand the efficiency of radio-mode feedback at the centers of galaxy clusters, we relate the radio properties of brightest cluster galaxies (BCG) to the X-ray properties of the host clusters. We identify the central radio sources in eRASS:1 clusters or calculate corresponding upper limits on the radio luminosity. Then, we derive relations between the X-ray properties of the clusters and the radio properties of the corresponding central radio source. We also apply a mid-infrared color criterion using WISE colors to identify AGN. In total we investigate a sample of 75 clusters. We find a statistically significant correlation between the X-ray luminosity of the cluster and the 944 MHz radio luminosity of the corresponding central radio galaxy. There is also a positive trend between the radio power and the largest linear size (LLS) of the radio source. The density and the LLS do not show any correlation. We find that in high luminosity clusters with L_X > $10^{43}$ erg s$^{-1}$ the kinetic luminosity of the radio jets is not longer correlated with the X-ray luminosity and discuss various reasons. We find an anti-correlation between the central cooling time t_cool and the radio luminosity L_R indicating a need for more powerful AGN in clusters with short central cooling times.

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Effects of Multiphase Gas and Projection on X-ray Observables in Simulated Galaxy Clusters as Seen by eROSITA

The number density of galaxy clusters as a function of mass and redshift is a sensitive function of the cosmological parameters. To use clusters for cosmological parameter studies, it is necessary to determine their masses as accurately as possible, which is typically done via mass-observable scaling relations. X-ray observables can be biased by multiphase gas and projection effects, especially in the case where cluster temperatures and luminosities are estimated from single-model fits to all of the emission with a given radius. Using simulated galaxy clusters from a realistic cosmological simulation, we seek to determine the importance of these biases in the context of Spectrum-Roentgen-Gamma/eROSITA observations of clusters. We extract clusters from the Magneticum suite, and simulate eROSITA observations of these clusters using PHOX and SIXTE. We compare the fitted observables from these observations to those derived from the simulations. We fitted an intrinsically scattered $L_{\rm X}-T$ scaling relation to these measurements following a Bayesian approach with which we fully took into account the selection effects and the mass function. The largest biases on the cluster observables come from the inadequacy of single-temperature model fits to represent emission from multiphase gas, as well as a bias arising from cluster emission within the projected $r_{500c}$ along the line of sight but outside of the spherical $r_{500c}$. We find that the biases on temperature and luminosity due to the projection of emission from other clusters within $r_{500c}$ is small. We find that our simulated clusters follow a $L_{\rm X}-T$ scaling relation that has a broadly consistent but slightly shallower slope compared to the literature, and that the intrinsic scatter of $L_{\rm X}$ at given T is lower compared to the recent observational results where the selection effects are fully considered.

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X-ray analysis of JWST's first galaxy cluster lens SMACS J0723.3-7327

SMACS~J0723.3-7327 is the first galaxy cluster lens observed by JWST. Based on the ERO data from JWST, several groups have reported the results on strong lensing analysis and mass distribution of this cluster. However, limited by the angular coverage of the JWST data, the strong lensing models only cover the central region. X-ray analysis on the hot ICM is necessary to obtain a more complete constraint on the mass distribution in this very massive cluster. In this work, we aim to perform a comprehensive X-ray analysis of J0723 to obtain accurate ICM hydrostatic mass measurements, using the X-ray data from SRG/eROSITA and Chandra X-ray observatories. By comparing the hydrostatic mass profile with the strong lensing model, we aim to provide the most reliable constraint on the distribution of mass up to R500. Thanks to the eROSITA all-sky survey and Chandra data, which provide high S/N and high angular resolution respectively, we are able to constrain the ICM gas density profile and temperature profile with good accuracy both in the core and to the outskirts. With the density and temperature profiles, we compute the hydrostatic mass profile, which is then projected along the line of sight to compare with the mass distribution obtained from the recent strong lensing analysis based on JWST data. We also deproject the strong lensing mass distribution using the hydrostatic mass profile we obtained in this work. The X-ray results obtained from eROSITA and Chandra agree very well with each other. The hydrostatic mass profiles we measured in this work, both projected and deprojected, are in good agreement with recent strong lensing results based on JWST data, at all radii. We also find that the radial acceleration relation in J0723 is inconsistent with the RAR for spiral galaxies, implying that the latter is not a universal property of gravity across all mass scales.

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The eROSITA Final Equatorial-Depth Survey (eFEDS): A complete census of X-ray properties of Subaru Hyper Suprime-Cam weak lensing shear-selected clusters in the eFEDS footprint

The eFEDS survey is a proof-of-concept mini-survey designed to demonstrate the survey science capabilities of SRG/eROSITA. It covers an area of 140 square degrees where 542 galaxy clusters have been detected out to a redshift of 1.3. The eFEDS field is partly embedded in the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) S19A data release, which covers 510 square degrees, containing approximately 36 million galaxies. This galaxy catalogue is used to construct a sample of 180 shear-selected galaxy clusters. In the common area to both surveys, about 90 square degrees, we investigate the effects of selection methods in the galaxy cluster detection by comparing the X-ray selected, eFEDS, and the shear-selected, HSC-SSP S19A, galaxy cluster samples. There are 25 shear-selected clusters in the eFEDS footprint. The relation between X-ray bolometric luminosity and weak-lensing mass is investigated, and it is found that the normalization of the bolometric luminosity and mass relation of the X-ray selected and shear-selected samples is consistent within $1σ$. Moreover, we found that the dynamical state and merger fraction of the shear-selected clusters is not different from the X-ray selected ones. Four shear-selected clusters are undetected in X-rays. A close inspection reveals that one is the result of projection effects, while the other three have an X-ray flux below the ultimate eROSITA detection limit. Finally, 43% of the shear-selected clusters lie in superclusters. Our results indicate that the scaling relation between X-ray bolometric luminosity and true cluster mass of the shear-selected cluster sample is consistent with the eFEDS sample. There is no significant population of X-ray underluminous clusters, indicating that X-ray selected cluster samples are complete and can be used as an accurate cosmological probe.

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The eROSITA Final Equatorial-Depth Survey (eFEDS): Catalog of galaxy clusters and groups

The eROSITA Final Equatorial-Depth Survey has been carried out during the PV phase of the SRG/eROSITA telescope and completed in November 2019. This survey is designed to provide the first eROSITA-selected sample of galaxy clusters and groups and to test the predictions for the all-sky survey in the context of cosmological studies with clusters. In the 140 deg$^2$ area covered by eFEDS, 542 candidate clusters and groups are detected as extended X-ray sources, down to a flux of $\sim10^{-14} $erg/s/cm$^2$ in the soft band (0.5-2 keV) within 1'. In this work, we provide the catalog of candidate galaxy clusters and groups in eFEDS. We perform imaging and spectral analysis on the eFEDS clusters with eROSITA X-ray data, and study the properties of the sample. The clusters are distributed in the redshift range [0.01, 1.3], with the median redshift at 0.35. We obtain the ICM temperature measurement with $>2σ$ c.l. for $\sim$1/5 (102/542) of the sample. The average temperature of these clusters is $\sim$2 keV. Radial profiles of flux, luminosity, electron density, and gas mass are measured from the precise modeling of the imaging data. The selection function, the purity and completeness of the catalog are examined and discussed in detail. The contamination fraction is $\sim1/5$ in this sample, 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 eFEDS, most of which are located at redshifts between 0.1 and 0.5. The eFEDS cluster and group catalog 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.

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The eROSITA Final Equatorial-Depth Survey (eFEDS): LOFAR view of brightest cluster galaxies and AGN feedback

During the performance verification phase of the SRG/eROSITA telescope, the eROSITA Final Equatorial-Depth Survey (eFEDS) has been carried out. It covers a 140 deg$^2$ field located at 126$^\circ <$ R.A. $< 146^\circ$ and -3$^\circ <$ Dec. $< +6^\circ$ with a nominal exposure over the field of 2.2 ks. 542 candidate clusters were detected in this field, down to a flux limit $F_X \sim 10^{-14}$ erg s$^{-1}$ cm$^{-2}$ in the 0.5-2 keV band. In order to understand radio-mode feedback in galaxy clusters, we study the radio emission of brightest cluster galaxies of eFEDS clusters, and we relate it to the X-ray properties of the host cluster. Using LOFAR we identify 227 radio galaxies hosted in the BCGs of the 542 galaxy clusters and groups detected in eFEDS. We treat non-detections as radio upper limits. We analyse the properties of radio galaxies, such as redshift and luminosity distribution, offset from the cluster centre, largest linear size and radio power. We study their relation to the intracluster medium of the host cluster. We perform statistical tests to deal with upper limits on the radio luminosities. BCGs with radio-loud AGN are more likely to lie close to the cluster centre than radio-quiet BCGs. There is a clear relation between the cluster's X-ray luminosity and the radio power of the BCG. Statistical tests indicate that this correlation is not produced by selection effects in the radio band. We see no apparent link between largest linear size of the radio galaxy and central density of the host cluster. Converting the radio luminosity to kinetic luminosity, we find that radiative losses of the intracluster medium are in an overall balance with the heating provided by the central AGN. Finally, we tentatively classify our objects into disturbed and relaxed, and we show that the link between the AGN and the ICM apparently holds regardless of the dynamical state of the cluster.

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