The eROSITA instrument aboard the Spectrum Roentgen Gamma (SRG) satellite has performed its first all-sky survey between December 2019 and June 2020. This paper presents the resulting hard X-ray (2.3-5 keV) sample, the first created from an all-sky imaging survey in the 2-8 keV band, for sources within western galactic sky. The 5466 hard X-ray selected sources detected with eROSITA are presented and discussed. The Bayesian statistics-based code NWAY is used to identify the counterparts for the X-ray sources. These sources are classified based on their multiwavelength properties, and the literature is searched to identify spectroscopic redshifts, which further inform the source classification. A total of 2547 sources are found to have good-quality counterparts, and 111 of these are detected only in the hard band. Comparing with other hard X-ray selected surveys, the eROSITA hard sample covers a larger redshift range and probes dimmer sources, providing a complementary and expanded sample as compared to Swift-BAT. Examining the column density distribution of missed and detected eROSITA sources present in the follow-up catalog of Swift BAT 70 month sources, it is demonstrated that eROSITA can detect obscured sources with column densities >10^24 cm^-2, but that the completeness drops rapidly after 10^23 cm^-2. A sample of hard-only sources, many of which are likely to be heavily obscured AGN, is also presented and discussed. X-ray spectral fitting reveals that these sources have extremely faint soft X-ray emission and their optical images suggest that they are found in more edge-on galaxies with lower b/a. The resulting X-ray catalog is demonstrated to be a powerful tool for understanding AGN, in particular heavily obscured AGN found in the hard-only sample.

Aims. By using eROSITA data in the eFEDS area, we provide a measure of the f(gas) - M-halo relation over the largest halo mass range, from Milky Way-sized halos to massive clusters, and to the largest radii (R-200) ever probed so far in local systems at z < 0.2. Methods. To cope with incompleteness and selection biases of the X-ray selection, we applied the stacking technique in eROSITA data of a highly complete and tested sample of optically selected groups. The method has been extensively tested on mock observations. Results. In massive clusters, the hot gas alone provides a baryon budget within R-200 consistent with Omega(b)/Omega(m), while at the group mass scale, it accounts only for 20-40% of the cosmic value. The f(gas) - M-halo relation is well fit by a power law with a consistent slope (within 1 sigma) at R-500 and R-200 and a normalization varying nearly by a factor of two. Such a relation is consistent with other works in the literature that consider X-ray survey data at the same depth as eFEDS, but it provides a lower average f(gas) in the group regime in comparison to works based on X-ray bright group samples. Comparison of the observed relation with the predictions of several hydrodynamical simulations (BAHAMAS, FLAMINGO, SIMBA, Illustris, IllustrisTNG, MillenniumTNG, and Magneticum) shows that all state-of-the-art simulations except Magneticum overpredict the gas fraction, with the largest discrepancy (up to a factor three) being in the 10(13.5) - 10(14.5) M-circle dot halo mass range. Conclusions. We emphasize the need for mechanisms that can effectively expel gas to larger radii in galaxy groups without excessively quenching star formation in their member galaxies. Current hydrodynamical simulations face a significant challenge in balancing their subgrid physics, as none can sufficiently evacuate gas from the halo virial region without negatively impacting the properties of the resident galaxy population.

Recently, we performed a systematic study of active galactic nucleus (AGN) feedback in a disk galaxy within the MACER framework. Various model predictions, including the AGN duty cycle, the correlation between black hole accretion rates and star formation rates, and the (cold) gas fraction, have been compared with observations and will be presented in a series of papers. As the second paper in this series, without adjusting any model parameters, we directly use the simulation data introduced in Paper I to compute the predicted X-ray surface brightness profile and compare it with eROSITA observations of circumgalactic medium emission around galaxies, which provide important constraints on AGN feedback models. For this comparison, we adopt two stacked eROSITA radial profiles of X-ray surface brightness: (1) distant galaxies with log(M*/M circle dot)=10.5-11.0 at z approximate to 0.02-0.10 from Y. Zhang et al. and (2) nearby L* galaxies within 50 Mpc from L. He & Z. Li. We find that the average simulated profile over time is in good agreement with the stacked measurements of Y. Zhang et al. over a broad radial range (out to similar to 100 kpc). Our model predictions also match the results of L. He & Z. Li at projected radii from similar to 20 to 120 kpc. While our simulations, which predict only thermal emission, are consistent with these recent X-ray observations, the limitations in our current model mean that this agreement does not preclude a potential contribution from nonthermal emission, e.g., from an extended halo of cosmic rays.

Context: We present the first Cosmological Parameter inferences from eROSITA X-ray observations of galaxy clusters using a Machine Learning algorithm. Methods: We train a Random Forest using mock catalogs of clusters from Magneticum multi-cosmology hydrodynamical simulations. We apply the trained ML algorithm to observed X-ray features (gas luminosity, mass, and temperature) at different redshifts from the eROSITA eFEDS and eRASS1 catalogs. Results: We obtain cosmological constraints with precision comparable to those from standard analyses, such as weak lensing and cluster abundances. We infer Ω_ m=0.30^+0.03_-0.02, σ_8=0.81±0.01, and h_0=0.710±0.004. The recovered parameters show no tension in the Ω_ m-σ_8 space, but a significant deviation of h_0 from the Planck estimates. These inferences remain rather stable against variations of the input observable set and parameter space coverage. These results indicate that correlations among intracluster properties contain cosmological information beyond that encoded in the cluster abundance alone, which can be captured by machine learning trained on multi-cosmology simulations. Conclusions: ML algorithms trained on multi-cosmology hydrodynamical simulations can effectively infer cosmological parameters directly from galaxy cluster data. This is a change of paradigm in the context of cosmological parameter inferences. This approach complements traditional cluster-count analyses and is particularly suited to large upcoming surveys, where systematic uncertainties in mass calibration may otherwise dominate the error budget. It also highlights the potential of large-scale X-ray surveys to deliver independent tests of the standard cosmological model.

The mechanical feedback from the central active galactic nuclei (AGNs) can be crucial for balancing the radiative cooling of the intracluster medium (ICM) at the cluster centre. We aim to understand the relationship between the power of AGN feedback and the cooling of gas in the centres of galaxy clusters by correlating the radio properties of the brightest cluster galaxies (BCGs) with the X-ray properties of their host clusters. We used the catalogues from the first SRG/eROSITA All-Sky Survey (eRASS1) along with radio observations from the Australian SKA Pathfinder (ASKAP). In total, we identified 134 radio sources associated with BCGs of the 151 eRASS1 clusters located in the PS1, PS2, and SWAG-X ASKAP fields. Non-detections were treated as upper limits. We correlated the radio properties of the BCGs (radio luminosity, largest linear size/LLS, and BCG offset from the cluster centre) with the integrated X-ray luminosity of the host clusters. We utilised the concentration parameter, $c_{R_{500}}$ , to categorise the clusters into cool cores (CCs) and non-cool cores (NCCs). By combining $c_{R_{500}}$ with the BCG offset, we assessed the dynamical states of the clusters in our sample. Furthermore, we analysed the correlation between radio mechanical power and X-ray luminosity within the CC subsample. We observe a potential positive trend between LLS and BCG offset, which may hint at an environmental influence on the morphology of central radio sources. We find a weak trend suggesting that more luminous central radio galaxies are found in clusters with higher X-ray luminosity. Additionally, there is a positive but highly scattered relationship between the mechanical luminosity of AGN jets and the X-ray cooling luminosity within the CC subsample. This finding is supported by bootstrap resampling and flux-flux analyses. The correlation observed in our CC subsample indicates that AGN feedback is ineffective in high-luminosity (high-mass) clusters. At a cooling luminosity of $L_{\mathrm{X},\,r} \lt \mathrm{R}_{\mathrm{cool}}\approx 5.50\times10^{43}\,\mathrm{erg\,s^{-1}}$ , on average, AGN feedback appears to contribute only about $13\%-22\%$ of the energy needed to offset the radiative losses in the ICM.

Aims. The hot circumgalactic medium (CGM), probed by X-ray observations, plays a central role in understanding gas flows that drive a galaxy's evolution. While CGM properties have been widely studied, the influence of a galaxy's large-scale cosmic environment on the hot gas content remains less explored. We investigate how the large-scale cosmic web affects the X-ray surface brightness (XSB) profiles of galaxies in the context of cosmological simulations. Methods. We used our novel IllustrisTNG-based lightcone, first developed in our previous work and spanning 0.03 <= z <= 0.3, to generate self-consistent mock X-ray observations, using intrinsic gas cell information. We applied the filament-finder DisPerSE on the galaxy distributions to identify cosmic filaments within the lightcone. We classified central galaxies into five distinct large-scale environment (LSE) categories: clusters and massive groups, cluster outskirts, filaments, filament-void transition regions, and voids and walls. Results. We find that the X-ray surface brightness profiles (XSB) of central galaxies of dark matter halos in filaments with M-200 m > 10(12) M-circle dot are X-ray brighter than those in voids and walls, with 20 - 45% deviations in the radial range of (0.3 - 0.5)& times;R-200 m. We investigated the source of this enhancement and found that filament galaxies have higher average gas densities, temperatures, and metallicities than void and wall galaxies. Conclusions. Our results demonstrate that the impact of the large-scale cosmic environment is imprinted on the hot CGM's X-ray emission. Future theoretical works studying the effects of assembly history, connectivity, and gas accretion on galaxies in filaments and voids would help further our understanding of the impact of the environment on X-ray observations.

Recent observations with SRG/eROSITA reveal the average X-ray surface brightness profile of the X-ray-emitting circumgalactic medium (CGM) around Milky Way (MW)-mass galaxies, offering valuable insights into the baryon budget in these systems. However, the estimation of the baryon mass depends critically on several assumptions regarding the gas density profile, temperature, metallicity, and the underlying halo mass distribution. Here, we assess how these assumptions affect the inferred baryon mass of the X-ray-emitting CGM in MW-mass galaxies, based on the stacked eROSITA signal. We find that variations in temperature profiles and uncertainties in the halo mass introduce the dominant sources of uncertainty, resulting in X-ray-emitting baryon mass estimates that vary by nearly a factor of four (0.8–3.5 × 1011 M⊙). Assumptions about metallicity contribute an additional uncertainty of approximately 50%. We emphasize that accurate X-ray spectral constraints on gas temperature and metallicity, along with careful modeling of halo mass uncertainty, are essential for accurately estimating the baryon mass for MW-mass galaxies. Future X-ray microcalorimeter missions will be crucial for determining the hot CGM properties and closing the baryon census at the MW-mass scale.

Mapping the local and distant Universe is key to our understanding of it. For decades, the Sloan Digital Sky Survey (SDSS) has made a concerted effort to map millions of celestial objects to constrain the physical processes that govern our Universe. The most recent and fifth generation of SDSS (SDSS-V) is organized into three scientific "mappers": the Milky Way Mapper, which aims to chart the various components of the Milky Way and constrain its formation and assembly; the Black Hole Mapper, which focuses on understanding supermassive black holes in distant galaxies across the Universe; and the Local Volume Mapper, which uses integral field spectroscopy to map the ionized interstellar medium in the Local Group. This paper describes the scope and content for the nineteenth data release (DR19) of SDSS, which is the most substantial to date in SDSS-V. DR19 is the first to contain data from all three mappers. Additionally, we also describe nine value-added catalogs that enhance the science that can be conducted with the SDSS-V data. Finally, we discuss how to access SDSS DR19 and provide illustrative examples and tutorials.

The Sloan Digital Sky Survey V (SDSS-V) is pioneering panoptic spectroscopy: it is the first all-sky, multiepoch, optical-to-infrared spectroscopic survey. SDSS-V is mapping the sky with multiobject spectroscopy (MOS) at telescopes in both hemispheres (the 2.5 m Sloan Foundation Telescope at Apache Point Observatory and the 100-inch du Pont Telescope at Las Campanas Observatory), where 500 zonal robotic fiber positioners feed light from a wide-field focal plane to an optical (R similar to 2000, 500 fibers) and a near-infrared (R similar to 22,000, 300 fibers) spectrograph. In addition to these MOS capabilities, the survey is pioneering ultra-wide-field (similar to 4000 deg(2)) integral field spectroscopy enabled by a new dedicated facility (LVM-I) at Las Campanas Observatory, where an integral field spectrograph (IFS) with 1801 lenslet-coupled fibers arranged in a 0 degrees.5-diameter hexagon feeds multiple R similar to 4000 optical spectrographs that cover 3600-9800 angstrom. SDSS-V's hardware and multiyear survey strategy are designed to decode the chemodynamical history of the Milky Way and tackle fundamental open issues in stellar physics in its Milky Way Mapper program, trace the growth physics of supermassive black holes in its Black Hole Mapper program, and understand the self-regulation mechanisms and the chemical enrichment of galactic ecosystems at the energy injection scale in its Local Volume Mapper program. The survey is well timed to multiply the scientific output from major all-sky space missions. The SDSS-V MOS programs began robotic operations in 2021; IFS observations began in 2023 with the completion of the LVM-I facility. SDSS-V builds on decades of heritage of SDSS's pioneering advances in data analysis, collaboration spirit, infrastructure, and product deliverables in astronomy.

Context. In a hierarchical Lambda CDM Universe, cosmic filaments serve as the primary channels for matter accretion into galaxy clusters, influencing the shape of their dark matter halos. Aims. We investigate whether the elongation of galaxy clusters correlates with the orientation of surrounding filaments, providing the first observational test of this relationship in large supercluster regions. Methods. We identified and characterized cosmic filaments in two dimensions within the two superclusters that are part of the low-redshift sub-survey of the Chilean Cluster Galaxy Evolution Survey (CHANCES): the Shapley supercluster and the Horologium-Reticulum supercluster. We analyzed the alignment between filament directions-traced by galaxy distributions-and the triaxiality of cluster gravitational potentials-traced by X-ray emission-using publicly available optical and X-ray data. Results We have found that most (82%) of the X-ray clusters are associated with and interconnected by the optically detected filaments. The clusters-filaments alignment analysis shows that the elongation of most clusters is well aligned with nearby filaments, providing observational confirmation of theoretical predictions, with the alignment progressively reducing at larger cluster-centric distances (> 1.6r(200)). Conclusions. Overall, our results support the notion that filaments are the main source of galaxy accretion at redshift below 0.1, and additionally provide evidence that matter accretion through filaments shapes the gravitational potential of galaxy clusters. We propose this measurement as a simple observational proxy to determine the direction of accretion in clusters, which is key to understanding both galaxy evolution and the merger history of galaxy clusters.

We present the weak-lensing mass calibration and constrain the relation between the stellar mass of the brightest cluster galaxy (BCG), halo mass, and redshift (M-star,M- BCG-M-z) for a sample of 124 galaxy clusters and groups at redshift 0.1 < z < 0.8 from the first Data Release of the eROSITA All-Sky Survey (eRASS1), using data from the Hyper Suprime-Cam (HSC) Subaru Strategic Program. The cluster survey is conducted by the eROSITA X-ray telescope aboard the Spectrum-Roentgen-Gamma (SRG) space observatory. The cluster sample is X-ray-selected and optically confirmed with a negligibly low contamination rate (approximate to 5%). On the basis of individual clusters, the shear profiles g(+) of 96 clusters are derived using the HSC Three-Year (HSC-Y3) weak-lensing data, while the BCG stellar masses M-star,M- BCG of 101 clusters are estimated using the SED template fitting to the HSC five-band (grizY) photometry. The observed X-ray photon count rate C-R is used as the mass proxy, based on which individual halo masses M are obtained at the given C-R in a population modelling, while accounting for systematic uncertainties in the weak-lensing modelling through a simulation-calibrated weak-lensing mass-to-halo-mass (M-WL-M-z) relation. The count rate (C-R-M-z) and BCG stellar mass (M-star,M- BCG-M-z) relations are simultaneously constrained in forward modelling and population modelling. In agreement with the results based on the weak-lensing data from the DES and KiDS surveys, we obtain a C-R-M-z relation with a self-similar redshift scaling and a mass trend that is steeper than the self-similar prediction. We cannot simultaneously place stringent constraints on the power-law indices of the mass (B-BCG) and redshift (gamma(BCG)) trends, due to the parameter degeneracy arising from the sample selection and the limited sample size. By adopting an informative prior on gamma(BCG) to break the B-BCG-gamma(BCG) degeneracy, we obtain a M-star,M- BCG-M-z relation with the mass slope increasing to B-BCG = 0.38 +/- 0.11. Informed by the prior, our results suggest that the BCG stellar mass at a fixed halo mass has remained stable with a moderate increase at a level of (20 +/- 8)% since redshift z approximate to 0.8. This finding supports the picture of the rapid-then-slow BCG formation, where the majority of the stellar mass must have been assembled at a much earlier cosmic time.

Aims. The hot phase of the circumgalactic medium (CGM) allows us to probe the inflow and outflow of gas responsible for dictating the evolution of a galaxy's structure. Studying the hot CGM sheds light on the physical properties of the gas phase of the baryons, which is crucial to inform and constrain simulation models. With the recent advances in observational measurements probing the hot CGM in X-rays and thermal Sunyaev-Zeldovich (tSZ), we have a new avenue for widening our knowledge of gas physics and feedback. Methods. In this paper, we use the TNG300 hydrodynamical simulations to build a fully self-consistent forward model for the hot CGM. In order to do that, we construct a lightcone and generate mock X-ray observations of the large-scale structure. We quantify the main projection effects impacting CGM measurements, namely the locally correlated large-scale structure in X-rays and the effect due to satellite galaxies misclassified as centrals, which affect the measured hot CGM galactocentric profiles in stacking experiments. Results. We present an analytical model that describes the intrinsic X-ray surface brightness profiles of halos across the stellar and halo mass bins. The increasing stellar mass bins result in decreasing values of beta, the exponent quantifying the slope of the intrinsic galactocentric profiles. We measure the effect of misclassified centrals in stacking experiments for three stellar mass bins 10(10.5-11) M-circle dot, 10(11-11.25) M-circle dot, and 10(11.25-11.5) M-circle dot. We find that the contaminating effect of the misclassified centrals on the stacked profiles increases when the stellar mass decreases. When stacking galaxies of Milky-Way-like stellar mass, this effect is dominant already at a low level of contamination: in particular, misclassified centrals contributing 30%, 10%, or 1% of a sample dominate the measured surface brightness profile at radii >= 0.11xR(500c), >= 0.24xR(500c), and >= 1.04xR(500c), respectively.

We aim to participate in the calibration of the X-ray photon count rate to halo mass scaling relation of galaxy clusters selected in the first eROSITA All-Sky Survey on the Western Galactic Hemisphere (eRASS1) using KiDS-1000 weak-lensing (WL) data. We measure the radial shear profiles around eRASS1 galaxy clusters using background galaxies in KiDS-1000, as well as the cluster member contamination. Furthermore we provide consistency checks with the other stage-III WL surveys who take part in the eRASS1 mass calibration, DES Y3 and HSC-Y3. We determine the cluster member contamination of eRASS1 clusters present in KiDS-1000 based on source number density profiles, where we account for the obscuration caused by cluster galaxies. The extracted shear profiles, together with the contamination model and the lens sample selection, are then analysed through a Bayesian population model. We calibrate the WL mass bias parameter by analysing realistic synthetic shear profiles from mock cluster catalogues. Our consistency checks between KiDS-1000 and DES Y3 HSC-Y3 include the comparison of contamination-corrected density contrast profiles employing the union of background sources around common clusters, as well as the individual scaling relation results. We present a global contamination model for eRASS1 clusters in KiDS-1000 and the calibration results of the X-ray photon count rate to halo mass relation. The results of the WL mass bias parameter show that the uncertainty of the multiplicative shear bias dominates the systematic error budget at low clusters redshifts while the uncertainty of our contamination model does at high ones. The cross-checks between the three WL surveys show that they are statistically consistent with each other. This enables for the first time cosmological constraints from clusters calibrated by three state-of-the-art WL surveys. (abridged)

The mechanical feedback from the central AGNs can be crucial for balancing the radiative cooling of the intracluster medium at the cluster centre. We aim to understand the relationship between the power of AGN feedback and the cooling of gas in the centres of galaxy clusters by correlating the radio properties of the brightest cluster galaxies (BCGs) with the X-ray properties of their host clusters. We used catalogues from the first SRG/eROSITA All-Sky Survey (eRASS1) along with ASKAP radio data. In total, we identified 134 radio sources associated with BCGs of the 151 eRASS1 clusters located in the PS1, PS2, and SWAG-X ASKAP fields. Non-detections were treated as upper limits. We correlated BCG radio luminosity, largest linear size (LLS), and BCG offset with the integrated X-ray luminosity of their host clusters. To characterise cool cores (CCs) and non-cool cores (NCCs), we used the concentration parameter c_R_500 and combined it with the BCG offset to assess cluster dynamical state. We analysed the correlation between radio mechanical power and X-ray luminosity within the CC subsample. We observe a potential positive trend between LLS and BCG offset, suggesting an environmental effect on radio-source morphology. We find a weak trend where more luminous central radio galaxies are found in clusters with higher X-ray luminosity. Within the CC subsample, there is a positive but highly scattered relationship between the mechanical luminosity of AGN jets and the X-ray cooling luminosity. This finding is supported by bootstrap resampling and flux-flux analyses. The correlation indicates that AGN feedback is ineffective in high-luminosity (high-mass) clusters. At a cooling luminosity of L_X, r<R_cool≈ 5.50×10^43 erg/s, on average, AGN feedback appears to contribute only about 13

This study examines the average X-ray properties of massive halos at z< 0.2, covering the largest halo mass range to date, from Milky Way-like halos to massive clusters. The analysis is based on stacking in the eFEDS area of the GAMA galaxy group sample, validated with synthetic data that mimic observed eROSITA X-ray and GAMA optical data using Magneticum lightcones. Stacking was conducted in halo mass bins and tested for AGN and X-ray binary contamination, systematics in the halo mass proxy, and uncertainties in optical group centers. The study provides average X-ray surface brightness profiles in six mass bins, spanning Milky Way-like systems to poor clusters. The scatter in the X-ray luminosity-mass (LX-M) relation is attributed to gas concentration: low X-ray luminosity systems at fixed halo mass exhibit lower central gas concentrations than high-luminosity systems, consistent with Magneticum predictions. However, discrepancies in dark matter concentration arise, with Magneticum predicting undetected groups as older and more relaxed, while observations suggest the opposite. New LX-M relations are presented covering three decades of halo mass. These relations fit a single power law, aligning with previous studies. Magneticum matches observed gas distributions across all masses, whereas IllustrisTNG, EAGLE, Simba, and FLAMINGO exhibit significant discrepancies at various mass scales. Simulations calibrated on local galaxy properties accurately reproduce central galaxies but fail to capture gas properties. Conversely, simulations like Magneticum excel in gas predictions but produce overly massive central galaxies. Further exploration of gas and dark matter distributions and their effects on galaxy properties is critical to comprehending the role of gravitational forces and feedback in shaping large-scale structure and galaxy evolution.

We present the weak-lensing mass calibration of 124 galaxy clusters and groups at redshift $0.1

This paper presents the construction and validation of complete stellar mass-selected, volume-limited galaxy samples using the Legacy Survey (data release 10) galaxy catalogs, covering similar to 16 800 deg(2) of extra-galactic sky and extending to redshifts of z < 0.35. We used companion mock catalogs to ensure a controlled galaxy selection. We measured the two-point correlation function of these galaxies with tiny statistical uncertainties at the percent level and systematic uncertainties up to 5%. We fitted a four-parameter halo occupation distribution (HOD) model to retrieve the population of host halos, yielding results on the stellar to halo mass relation that are consistent with the current models of galaxy formation and evolution. Using these complete galaxy samples, we measured and analyzed the cross-correlation between galaxies and all soft X-ray photons observed by SRG/eROSITA in the 0.5-2 keV band over similar to 13 000 deg(2). The cross-correlation measurements have an unprecedented sub-percent statistical uncertainty and 5-10% systematic uncertainty. We introduced a novel extension to the halo model to interpret the cross-correlation, decomposing contributions from X-ray point sources, hot gas, satellites, and the two-halo term. The model offers a new comprehensive view of the relation between the complete 0.5-2 keV X-ray photon field and complete sets of galaxies at low redshift and their host halos. For low stellar mass thresholds (log M*/M-circle dot > 10, 10.25, 10.5), we find that the point source emission dominates the cross-correlation at small separation (r < 80 kpc). Then, in the range of 80 < r < 2 Mpc, the emission from large halos hosting satellite galaxies dominates. Finally, on scales beyond those considered here (r > 2 Mpc), the two-halo term becomes dominant. Interestingly, there is no scale at which the hot gas dominates. In the range (20 < r < 200 kpc), the hot gas contributes to more than 10% of the signal. Progressively, with the minimum stellar mass increasing, the hot gas emission increases. For the log M*/M-circle dot > 10.75 sample, in the range 50-60 kpc, the three components contribute each the same surface brightness. For the log M*/M-circle dot > 11 sample, the hot gas is the dominating emission source over the range of 30-200 kpc. Finally, for the log M*/M-circle dot > 11.25 and (11.5) samples, the hot gas emission dominates over other components until 400 (700) kpc. We constrained the slope of the scaling relation between halo mass and X-ray luminosity (over three orders of magnitude in mass) at the 5% level, using the samples with the lowest mass threshold. We find a slope of 1.629(-0.089)(+0.091). Additional analyses explore the energy dependence of the cross-correlation and differences between red sequence and blue cloud galaxies, revealing sensitivity to galaxy quiescent fractions and opening avenues for a more complex, unified modeling of galaxies, active galactic nuclei (AGNs), and hot gas in the optical and X-rays.

Context. During its calibration and performance verification phase, the eROSITA instrument aboard the Spectrum-RG satellite performed a uniform wide-area X-ray survey of approximately 140 deg(2), known as the eROSITA Final Equatorial Depth Survey (eFEDS). Aims. The primary aim of eFEDS is to demonstrate the scientific performance to be expected at the end of the eight-pass eROSITA all-sky survey. This survey will provide the first focussed image of the whole sky in the hard X-ray (>2 keV) bandpass. The expected source population in this energy range is thus of great interest, particularly for AGN studies. Methods. We used a 2.3-5 keV selection to construct a sample of 246 point-like hard X-ray sources for further study and characterisation. These sources are classified as either extragalactic (similar to 90%) or Galactic (similar to 10%), with the former consisting overwhelmingly of AGN and the latter active stars. We concentrated our further analysis on the extragalactic AGN sample, describing their X-ray and multi-wavelength properties and comparing them to the eFEDS main AGN sample selected in the softer 0.2-2.3 keV band. Results. The eROSITA hard band selects a subsample of sources that is a factor of more than ten brighter than the eFEDS main sample. The AGN within the hard population reach up to z = 3.2 but on the whole, they are relatively nearby, with median z = 0.34 compared to z = 0.94 for the main sample. The hard survey probes typical luminosities in the range log L-X = 43-46. The X-ray spectral analysis shows significant intrinsic absorption (with log N-H > 21) in similar to 20% of the sources, with a hard X-ray power law continuum with mean < Gamma >= 1.83 +/- 0.04, which is typical of AGN, but slightly harder than the soft-selected eROSITA sample. Around 10% of the hard sample show a significant 'soft excess' component. The sampled black hole mass distribution in the eFEDS broad-line AGN population is consistent with that of the deeper COSMOS survey that probes a higher redshift population. On the other hand, the Eddington ratios appear systematically lower, which is consistent with the idea that the decline in SMBH activity since z similar to 1 is due to a reduction in the typical accretion rate, rather than a shift towards activity in lower-mass black holes. Conclusions. The eFEDS hard sample provides a preview of what can be expected from the eRASS final survey in terms of data quality. This pilot survey indicates the power of eROSITA to shed new light on the demographics and evolution of AGN, and the potential for discovery of new and rare populations.

We performed individual weak-lensing (WL) mass measurements for 78 eROSITA's first All-Sky Survey (eRASS1) clusters in the footprint of Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) S19A. We did not adopt priors on the eRASS1 X-ray quantities or assumption of the mass and concentration relation. In the sample, we found three clusters are misassociated with optical counterparts and 12 clusters are poorly fitted with an NFW profile. The average mass for the 12 poor-fit clusters changes from similar to 10(14) h(70)(-1) M-circle dot to similar to 2 x 10(13) h(70)(-1) M-circle dot when lensing contamination from surrounding mass structures is taken into account. The scaling relations between the true mass and cluster richness and X-ray count-rate agree well with the results of the eRASS1 western Galactic hemisphere region based on count-rate-inferred masses, which were calibrated with the HSC-SSP, DES, and KiDS surveys. We developed a Bayesian framework for inferring the mass-concentration relation of the cluster sample, explicitly incorporating the effects of weak-lensing mass calibration in the mass-concentration parameter space. The redshift-dependent mass and concentration relation is in excellent agreement with predictions of dark-matter-only numerical simulations and previous studies using X-ray-selected clusters. Based on the two-dimensional (2D) WL analysis, the offsets between the WL-determined centers and the X-ray centroids for 36 eRASS1 clusters with high WL S/N can be described by two Gaussian components. We find that the miscentering effect with X-ray centroids is smaller than that involving peaks in the galaxy maps. Stacked mass maps support a small miscentering effect, even for clusters with a low WL S/N. The projected halo ellipticity is = 0.45 at M-200 similar to 4 x 10(14) h(70)(-1) M-circle dot, which is in agreement with the results of numerical simulations and previous studies of clusters characterized by masses greater than twice the mass treated here.

Aims. Recent eROSITA measurements of the radial profiles of the hot circumgalactic medium (CGM) in the Milky Way stellar mass (MW-mass) regime provide us with a new benchmark to constrain the hot gas around MW-mass central and satellite galaxies and their halo mass distributions. Modeling this rich data set with state-of-the-art hydrodynamical simulations is required to further our understanding of the shortcomings in the current paradigm of galaxy formation and evolution models. Methods. We developed forward models for the stacked X-ray radial surface brightness profile measured by eROSITA around MW-mass galaxies. Our model contains two emitting components: hot gas (around central galaxies and around satellite galaxies hosted by more massive halos) and X-ray point sources (X-ray binaries (XRBs) and active galactic nuclei (AGNs)). We modeled the hot gas profile using the TNG300-based products. We generated mock observations with our TNG300-based model (matching stellar mass and redshift with observations) with different underlying halo mass distributions. Therefore, we tested the CGM properties as a function of their host halo mass distribution. The point sources are described by a simple point spread function of eROSITA, and we fit their normalization in this work. In total, we fit the X-ray surface brightness profile with two free parameters: the normalization of satellites in more massive host halos and the normalization of the mean point source emission. Results. We show that for the same mean stellar mass, a factor similar to 2x increase in the mean value of the underlying halo mass distribution results in similar to 4x increase in the stacked X-ray luminosity from the hot CGM. Using empirical models to derive a permissible range of AGN and XRB luminosities in the MW-mass X-ray galaxy stack, we choose our forward model that best describes the hot CGM for the eROSITA observations. Our chosen model in the MW stellar mass bin is in good agreement with previous literature results. We find that at less than or similar to 40 kpc from the galaxy center, the hot CGM from central galaxies and the X-ray point sources emission (from XRBs and AGNs) each account for 40 - 50% of the total X-ray emission budget. Beyond similar to 40 kpc, we find that the hot CGM around satellites (probing their more massive host halos with mean M-200m similar to 10(14) M circle dot) dominates the stacked X-ray surface brightness profile. Conclusions. The gas physics driving the shape of the observed hot CGM (in stellar-mass-selected X-ray stacking experiments) is tightly correlated with the underlying halo-mass distribution. This work provides a novel technique to constrain the AGN X-ray luminosity jointly with the radial hot CGM gas distribution within the halo using measurements from X-ray galaxy stacking experiments. Implementing this technique on other state-of-the-art simulations will provide a new ground for testing different galaxy formation models with observations.