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Superclusters are the largest-scale environments where a number of galaxy clusters interact with each other through minor/major mergers and grow via accretion along cosmic filaments. We focus on the A3528 complex in the core of the Shapley Supercluster. This system includes three clusters, A3528 (composed itself by two sub-clusters, namely A3528N and A3528S), A3532 and A3530, and presents a mildly active dynamical state. We study how minor mergers affect the evolution of radio galaxies and whether they are able to re-accelerate relativistic electrons in the ICM. We used observations from the uGMRT (Band 3, 4 and 5) and MeerKAT (L-band) telescopes to obtain images and spectral index maps over a wide frequency band and spatial resolutions. We compare these data with those from the SRG/eROSITA X-ray telescope. We detect faint diffuse radio emission associated with the radio galaxies. The BCGs in A3528S and A3532 show filaments of diffuse radio emission which extend for $\sim200-400$ kpc out of the radio galaxy. The spectral index of these filaments is extremely steep and almost constant ($\alpha\sim -2, -2.5$). Contrary to the radio tails in A3528N, the spectral properties of these radio filaments are not consistent with standard models of plasma ageing. We also detect roundish diffuse radio emission around the BCG in A3528S which could be classified as a radio mini-halo. The radio tail in this cluster appears longer that in earlier detections, being $\sim300$ kpc long at all frequencies. We linked the presence of extended radio emission in the form of filaments and threads in the A3528 complex with the effect of minor mergers. This is reinforced by the increasing X-ray fluctuations in correspondence with the radio extended emission in A3528S. Despite the less energy involved, our findings support the hypothesis that these events can re-energise plasma originating from radio galaxies., Comment: 28 pages, 23 figures and 5 tables; accepted for publication in Astronomy & Astrophysics

A fraction of galaxy clusters harbor diffuse radio sources known as radio halos. The currently adopted scenario for their formation is based on second-order Fermi re-acceleration of seed electrons that is driven by merger-driven turbulence in the intra-cluster medium. This mechanism is expected to be inefficient, which implies that a significant fraction of halos should have very steep ($\alpha < -1.5$) energy spectra. We start investigating the potential and current limitations of the combination of the two surveys conducted by LOFAR, LoTSS (144 MHz) and LoLSS (54 MHz), to probe the origin of radio halos. We follow up the 20 radio halos detected in the DR1 of LoTSS, which covers the HETDEX field, with the LoLSS survey, and we study their spectral properties between 54 and 144 MHz. After the removal of compact sources, 9 halos were excluded due to unreliable halo flux density measurements at 54 MHz. Our main finding is that 7 out of 11 ($\sim$ 64%) exhibit an ultra-steep spectrum ($\alpha < -1.5$), which is a key prediction of turbulent re-acceleration models. We also note a tentative trend for more massive systems to host flatter halos, although the currently poor statistics does not allow for a deeper analysis. Our sample suffers from low angular resolution at 54 MHz, which limits the accuracy of the compact-sources subtraction. Nevertheless, this study is the first step towards providing compelling evidence for the existence of a large fraction of radio halos with very steep spectrum, which is a fundamental prediction of turbulent re-acceleration models. In this regard, the forthcoming second data release of LoLSS, along with the integration of LOFAR international stations and the instrumental upgrade to LOFAR2.0, will improve both the statistics and the low-frequency angular resolution, allowing to conclusively determine the origin of radio halos in galaxy clusters., Comment: A&A Letter; 11 pages, 12 figures

The evolution of Active Galactic Nuclei (AGN) is closely connected to their host galaxies and surroundings. Via feedback processes, AGN can counteract the cooling of the intracluster medium (ICM) and suppress star formation in their host galaxies. Radio observations at low frequencies provide a glimpse into the history of AGN activity. The Virgo cluster is a substantial reservoir of nearby galaxies and provides an ideal laboratory for the study of AGN as well as their feedback mechanisms. The aim of our work is to characterise the AGN population within the Virgo cluster down to low radio luminosities, constrain the AGN duty cycle and investigate environmental feedback in cluster member galaxies. We analyse 144 MHz and 1.3 GHz radio observations of early-type galaxies from the ACS Virgo Cluster Survey (ACSVCS) taken with LOFAR and MeerKAT. We detect 12 of these galaxies at 144 MHz, 5 of which show clearly extended radio emission. The radio luminosity shows a strong dependence on the stellar mass of the host galaxy, in agreement with previous results. As a notable outlier, the massive elliptical galaxy NGC 4365 ($M_* = 2.2 \times 10^{11} M_\odot$) is not detected as a compact source in the LOFAR observations. Instead, it is surrounded by diffuse, low-surface brightness emission, which hints towards a past phase of stronger nuclear activity. Furthermore, we find a cavity in NGC 4472 (= M 49) inflated by the wide-angle tail only visible in the LOFAR data, which implies that the cavity was created by a past outburst. The corresponding cavity power is of the same order of magnitude as the jet power in the present duty cycle of the AGN., Comment: 17 pages, 10 figures

Recent low-frequency radio observations at 140 MHz discovered a 3 Mpc-long bridge of diffuse emission connecting the galaxy clusters Abell 0399 and Abell 0401. We present follow-up observations at 60 MHz to constrain the spectral index of the bridge, which so far has only been detected at 140 and 144 MHz. We analysed deep (~18 hours) LOw Frequency ARray (LOFAR) Low Band Antenna (LBA) data at 60 MHz to detect the bridge at very low frequencies. We then conducted a multi-frequency study with LOFAR HBA data at 144 MHz and uGMRT data at 400 MHz. Assuming second-order Fermi mechanisms for the re-acceleration of relativistic electrons driven by turbulence in the radio bridge regions, we compare the observed radio spectrum with theoretical synchrotron models. The bridge is detected in the 75'' resolution LOFAR image at 60 MHz and its emission fully connects the region between the two galaxy clusters. Between 60 MHz and 144 MHz we found an integrated spectral index value of -1.44 +\- 0.16 for the bridge emission. For the first time, we produced spectral index and related uncertainties maps for a radio bridge. We produce a radio spectrum, which show significant steepening between 144 and 400 MHz. This detection at low frequencies provides important information on the models of particle acceleration and magnetic field structure on very extended scales. The spectral index gives important clues to the origin of inter-cluster diffuse emission. The steepening of the spectrum above 144 MHz can be explained in a turbulent re-acceleration framework, assuming that the acceleration timescales are longer than ~200 Myr., Comment: Letter to the Editor: 7 pages, 4 figures, 2 tables; accepted for publication in Astronomy & Astrophysics (A&A)

Radio jets are present in a diverse sample of AGN. However, the mechanisms of jet powering are not fully understood, and it is yet unclear to what extent they obey mass-invariant scaling relations, similar to those found for the triggering and fuelling of X-ray selected AGN. We study the incidence of eROSITA/eFEDS X-ray and LOFAR radio AGN as a function of several stellar mass normalised AGN power indicators. A new sample of radio AGN from the LOFAR-eFEDS survey is defined and we publicly release this catalogue, including host galaxy counterparts from the Legacy Survey DR9, LOFAR radio morphologies and host galaxy properties from the complete, spectroscopic (z<0.4) GAMA09 survey. The fraction of GAMA09 galaxies hosting radio, X-ray and both radio and X-ray AGN are calculated as a function of the specific black hole kinetic ($\lambda_{\rm Jet}$) and radiative ($\lambda_{\rm Edd}$) power. The incidence of eFEDS X-ray AGN as a function of $\lambda_{\rm Edd}$ shows the same mass-invariance as found in past studies. Meanwhile, radio AGN, regardless of their morphology, are more likely to be hosted in more massive galaxies, at all $\lambda_{\rm Jet}$. Across the stellar mass range, the compact radio AGN incidence follows the same power-law distribution, showing that it is not only high mass galaxies that host high power radio AGN and vice versa. On the other hand, the incidence of compact and complex radio AGN is boosted at the highest jet powers, diverging from a simple power-law. Interestingly, this increased incidence cannot be explained by more powerful radio AGN lying in more dense environments which could naturally boost their radio luminosity. Overall, we show that statistical incidence studies are a powerful method to probe disk-jet coupling for different AGN accretion modes, although future work on a more reliable determination of jet power for diverse samples of radio AGN is needed., Comment: 30 pages, 32 figures, accepted for publication in A&A

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., Comment: 39 pages, 23 figures. Accepted for publication in A&A. Accompanying eROSITA-DE Data Release 1

We present the discovery of a very extended (550 kpc) and low-surface-brightness ($ 3.3 \mu \mathrm{Jy} \, arcsec^{-2} $ at 144 MHz) radio emission region in Abell 1318. These properties are consistent with its characterisation as an active galactic nucleus (AGN) remnant radio plasma, based on its morphology and radio spectral properties. We performed a broad-band (54 - 1400 MHz) radio spectral index and curvature analysis using LOFAR, uGMRT, and WSRT-APERTIF data. We also derived the radiative age of the detected emission, estimating a maximum age of 250 Myr. The morphology of the source is remarkably intriguing, with two larger, oval-shaped components and a thinner, elongated, and filamentary structure in between, plausibly reminiscent of two aged lobes and a jet. Based on archival {\it Swift} as well as SDSS data we performed an X-ray and optical characterisation of the system, whose virial mass was estimated to be $ \sim 7.4 \times 10^{13} \, \mathrm{M} _{\odot}$. This places A1318 in the galaxy group regime. Interestingly, the radio source does not have a clear optical counterpart embedded in it, thus, we propose that it is most likely an unusual AGN remnant of previous episode(s) of activity of the AGN hosted by the brightest group galaxy ($ \sim 2.6 \times 10^{12} \, \mathrm{M} _{\odot}$), which is located at a projected distance of $\sim$170 kpc in the current epoch. This relatively high offset may be a result of IGrM sloshing sourced by a minor merger. The filamentary morphology of the source may suggest that the remnant plasma has been perturbed by the system dynamics, however, only future deeper X-ray observations will be able to address this question., Comment: 16 pages, 9 figures, accepted by A&A; edited some affiliations

Cosmological simulations predict the presence of warm hot thermal gas in the cosmic filaments that connect galaxy clusters. This gas is thought to constitute an important part of the missing baryons in the Universe. In addition to the thermal gas, cosmic filaments could contain a population of relativistic particles and magnetic fields. A detection of magnetic fields in filaments can constrain early magnetogenesis in the cosmos. So far, the resulting diffuse synchrotron emission has only been indirectly detected. We present our search for thermal and non-thermal diffuse emission from inter-cluster regions of 106 paired galaxy clusters by stacking the $0.6-2.3$~keV X-ray and 144~MHz radio data obtained with the eROSITA telescope on board the Spectrum-Roentgen-Gamma (SRG) observatory and LOw Frequency ARray (LOFAR), respectively. The stacked data do not show the presence of X-ray and radio diffuse emission in the inter-cluster regions. This could be due to the sensitivity of the data sets and/or the limited number of cluster pairs used in this study. Assuming a constant radio emissivity in the filaments, we find that the mean radio emissivity is not higher than $1.2\times10^{-44}\,{\rm erg \, s^{-1} \, cm^{-3} \, Hz^{-1}}$. Under equipartition conditions, our upper limit on the mean emissivity translates to an upper limit of $\sim75\,{\rm nG}$ for the mean magnetic field strength in the filaments, depending on the spectral index and the minimum energy cutoff. We discuss the constraint for the magnetic field strength in the context of the models for the formation of magnetic fields in cosmic filaments., Comment: Accepted for publication on MNRAS on June 5, 2023

Many galaxy clusters show diffuse cluster-scale emission in the form of radio halos, showing that magnetic fields and relativistic electrons are mixed in with the intra-cluster medium (ICM). There is general agreement that the origin of radio halos is connected to turbulence, generated during cluster mergers. Statistical studies of large samples of galaxy clusters in the radio band have the potential to unveil the connection between the properties of radio halos and the mass and dynamics of the host clusters. Previous studies have been limited to massive clusters and based on a small number of radio halos. The aim of this paper is to investigate the scaling relation between the radio power of radio halos and the mass of the host clusters at low frequencies and down to lower cluster masses. We analysed the clusters from the second catalogue of Planck Sunyaev Zel'dovich sources that lie within the 5634 sq deg covered by the second Data Release of the LOFAR Two-meter Sky Survey. We derived the correlation between the radio power and the mass of the host clusters and we investigated the distribution of clusters without radio halos with respect to the correlation. We use X-ray observations to classify the dynamical state of clusters and investigate its role on the power of radio halos. We found a correlation between the power of radio halos at 150 MHz and the mass of the host clusters down to 3e14 Msun. This correlation has a large scatter, part of which can be attributed to the different dynamical states of host clusters. We used two statistical test to show that the distribution of clusters with and without (upper limits) radio halos in the mass-radio power diagram is not compatible with a single correlation and that it is also not compatible with clusters being uniformly distributed below an upper envelope constituted by the correlation., Comment: 12 pages, 7 figures, submitted to A&A

We simulate the evolution of relativistic electrons injected into the medium of a small galaxy cluster by a central radio galaxy, studying how the initial jet power affects the dispersal and the emission properties of radio plasma. By coupling passive tracer particles to adaptive-mesh cosmological MHD simulations, we study how cosmic-ray electrons are dispersed as a function of the input jet power. We also investigate how the latter affects the thermal and non-thermal properties of the intracluster medium, with differences discernible up to $\sim$ Gyr after the start of the jet. We evolved the energy spectra of cosmic-ray electrons, subject to energy losses that are dominated by synchrotron and inverse Compton emission as well as energy gains via re-acceleration by shock waves and turbulence. We find that in the absence of major mergers the amount of re-acceleration experienced by cosmic-ray electrons is not enough to produce long-lived detectable radio emissions. However, for all simulations the role of re-acceleration processes is crucial to maintain a significant and volume-filling reservoir of fossil electrons ($\gamma \sim 10^3$) for several Gyrs after the first injection by jets. This is important to possibly explain recent discoveries of cluster-wide emission and other radio phenomena in galaxy clusters., Comment: 25 pages, 24 figures. A & A accepted, in press

We study diffuse radio emission in the galaxy cluster A1550, with the aim of constraining particle re-acceleration in the intra-cluster medium. We exploit observations at four different frequencies: 54, 144, 400 and 1400 MHz. To complement our analysis, we make use of archival Chandra X-ray data. At all frequencies we detect an ultra-steep spectrum radio halo ($S_\nu \propto \nu^{-1.6}$) with an extent of 1.2 Mpc at 54 MHz. Its morphology follows the distribution of the thermal intra-cluster medium inferred from the Chandra observation. West of the centrally located head-tail radio galaxy, we detect a radio relic with projected extent of 500 kpc. From the relic, a 600 kpc long bridge departs and connect it to the halo. Between the relic and the radio galaxy, we observe what is most likely a radio phoenix, given its curved spectrum. The phoenix is connected to the tail of the radio galaxy through two arms, which show a nearly constant spectral index for 300 kpc. The halo could be produced by turbulence induced by a major merger, with its axis lying in the NE-SW direction. This is supported by the position of the relic, whose origin could be attributed to a shock propagating along the merger axis. It is possible that the same shock has also produced the phoenix through adiabatic compression, while the bridge could be generated by electrons which were pre-accelerated by the shock, and then re-accelerated by turbulence. Finally, we detect hints of gentle re-energisation in the two arms which depart from the tail of the radio galaxy., Comment: 16 pages, 10 figures

In this data release from the LOFAR Two-metre Sky Survey (LoTSS) we present 120-168MHz images covering 27% of the northern sky. Our coverage is split into two regions centred at approximately 12h45m +44$^\circ$30' and 1h00m +28$^\circ$00' and spanning 4178 and 1457 square degrees respectively. The images were derived from 3,451hrs (7.6PB) of LOFAR High Band Antenna data which were corrected for the direction-independent instrumental properties as well as direction-dependent ionospheric distortions during extensive, but fully automated, data processing. A catalogue of 4,396,228 radio sources is derived from our total intensity (Stokes I) maps, where the majority of these have never been detected at radio wavelengths before. At 6" resolution, our full bandwidth Stokes I continuum maps with a central frequency of 144MHz have: a median rms sensitivity of 83$\mu$Jy/beam; a flux density scale accuracy of approximately 10%; an astrometric accuracy of 0.2"; and we estimate the point-source completeness to be 90% at a peak brightness of 0.8mJy/beam. By creating three 16MHz bandwidth images across the band we are able to measure the in-band spectral index of many sources, albeit with an error on the derived spectral index of +/-0.2 which is a consequence of our flux-density scale accuracy and small fractional bandwidth. Our circular polarisation (Stokes V) 20" resolution 120-168MHz continuum images have a median rms sensitivity of 95$\mu$Jy/beam, and we estimate a Stokes I to Stokes V leakage of 0.056%. Our linear polarisation (Stokes Q and Stokes U) image cubes consist of 480 x 97.6 kHz wide planes and have a median rms sensitivity per plane of 10.8mJy/beam at 4' and 2.2mJy/beam at 20"; we estimate the Stokes I to Stokes Q/U leakage to be approximately 0.2%. Here we characterise and publicly release our Stokes I, Q, U and V images in addition to the calibrated uv-data., Comment: 23 figures, 1 table and 29 pages. The catalogues, images and uv-data associated with this data release are publicly available via https://lofar-surveys.org/

Jets from active galactic nuclei (AGN) are known to recurrently enrich their surrounding medium with mildly-relativistic particles and magnetic fields. Here, we present a detailed multi-frequency analysis of the nearby (z=0.01646) galaxy group NGC 507. In particular, we present new high-sensitivity and high spatial resolution radio images in the frequency range 144-675 MHz obtained using LOFAR and uGMRT observations. These reveal the presence of previously undetected diffuse radio emission with complex, filamentary morphology, likely related to a previous outburst of the central galaxy. Based on spectral ageing considerations, we derived that the plasma was first injected by the AGN 240-380 Myr ago and is now cooling. Our analysis of deep archival XMM-Newton data confirms that the system is dynamically disturbed, as previously suggested. We detect two discontinuities in the X-ray surface brightness distribution (in East and South direction) tracing a spiral pattern, which we interpret as cold fronts produced by sloshing motions. The remarkable spatial coincidence observed between the newly-detected arc-like radio filament and the southern concave X-ray discontinuity strongly suggests that the remnant plasma has been displaced by the sloshing motions on large scales. Overall, NGC 507 represents one of the clearest examples known to date in which a direct interaction between old AGN remnant plasma and the external medium is observed in a galaxy group. Our results are consistent with simulations, which suggest that filamentary emission can be created by the cluster/group weather disrupting AGN lobes and spreading their relativistic content into the surrounding medium., Comment: 21 pages, 15 figures, 3 tables, A&A accepted

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., Comment: 16 pages, 13 figures. To appear on A&A, Special Issue: The Early Data Release of eROSITA and Mikhail Pavlinsky ART-XC on the SRG Mission

We investigate the kinematic properties of a large (N=998) sample of COSMOS spectroscopic galaxy members distributed among 79 groups. We identify the Brightest Group Galaxies (BGGs) and cross-match our data with the VLA-COSMOS Deep survey at 1.4 GHz, classifying our parent sample into radio/non-radio BGGs and radio/non-radio satellites. The radio luminosity distribution spans from $L_R\sim2\times10^{21}$ W Hz$^{-1}$ to $L_R\sim3\times$10$^{25}$ W Hz$^{-1}$. A phase-space analysis, performed by comparing the velocity ratio (line-of-sight velocity divided by the group velocity dispersion) with the galaxy-group centre offset, reveals that BGGs (radio and non-radio) are mostly ($\sim$80\%) ancient infallers. Furthermore, the strongest ($L_R>10^{23}$ W Hz$^{-1}$) radio galaxies are always found within 0.2$R_{\rm vir}$ from the group centre. Comparing our samples with HORIZON-AGN, we find that the velocities and offsets of simulated galaxies are more similar to radio BGGs than to non-radio BGGs, albeit statistical tests still highlight significant differences between simulated and real objects. We find that radio BGGs are more likely to be hosted in high-mass groups. Finally, we observe correlations between the powers of BGG radio galaxies and the X-ray temperatures, $T_{\rm x}$, and X-ray luminosities, $L_{\rm x}$, of the host groups. This supports the existence of a link between the intragroup medium and the central radio source. The occurrence of powerful radio galaxies at group centres can be explained by Chaotic Cold Accretion, as the AGN can feed from both the galactic and intragroup condensation, leading to the observed positive $L_{\rm R}-T_{\rm x}$ correlation., Comment: 11 pages, 8 figures

Our understanding of how AGN feedback operates in galaxy clusters has improved in recent years owing to large efforts in multi-wavelength observations and hydrodynamical simulations. However, it is much less clear how feedback operates in galaxy groups, which have shallower gravitational potentials. In this work, using very deep VLA and new MeerKAT observations from the MIGHTEE survey, we compiled a sample of 247 X-ray selected galaxy groups detected in the COSMOS field. We have studied the relation between the X-ray emission of the intra-group medium and the 1.4 GHz radio emission of the central radio galaxy. For comparison, we have also built a control sample of 142 galaxy clusters using ROSAT and NVSS data. We find that clusters and groups follow the same correlation between X-ray and radio emission. Large radio galaxies hosted in the centres of groups and merging clusters increase the scatter of the distribution. Using statistical tests and Monte-Carlo simulations, we show that the correlation is not dominated by biases or selection effects. We also find that galaxy groups are more likely than clusters to host large radio galaxies, perhaps owing to the lower ambient gas density or a more efficient accretion mode. In these groups, radiative cooling of the ICM could be less suppressed by AGN heating. We conclude that the feedback processes that operate in galaxy clusters are also effective in groups., Comment: 15 pages, 14 figures