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F. Gastaldello

Publications and source records attributed to F. Gastaldello.

At least 73 records · Page 4Linked to original sources

CHEX-MATE: Constraining the origin of the scatter in galaxy cluster radial X-ray surface brightness profiles

We investigate the statistical properties and the origin of the scatter within the spatially resolved surface brightness profiles of the CHEX-MATE sample, formed by 118 galaxy clusters selected via the SZ effect. These objects have been drawn from the Planck SZ catalogue and cover a wide range of masses, M$_{500}=[2-15] \times 10^{14} $M$_{\odot}$, and redshift, z=[0.05,0.6]. We derived the surface brightness and emission measure profiles and determined the statistical properties of the full sample. We found that there is a critical scale, R$\sim 0.4 R_{500}$, within which morphologically relaxed and disturbed object profiles diverge. The median of each sub-sample differs by a factor of $\sim 10$ at $0.05\,R_{500}$. There are no significant differences between mass- and redshift-selected sub-samples once proper scaling is applied. We compare CHEX-MATE with a sample of 115 clusters drawn from the The Three Hundred suite of cosmological simulations. We found that simulated emission measure profiles are systematically steeper than those of observations. For the first time, the simulations were used to break down the components causing the scatter between the profiles. We investigated the behaviour of the scatter due to object-by-object variation. We found that the high scatter, approximately 110%, at $R<0.4R_{500}$ is due to a genuine difference between the distribution of the gas in the core. The intermediate scale, $R_{500} =[0.4-0.8]$, is characterised by the minimum value of the scatter on the order of 0.56, indicating a region where cluster profiles are the closest to the self-similar regime. Larger scales are characterised by increasing scatter due to the complex spatial distribution of the gas. Also for the first time, we verify that the scatter due to projection effects is smaller than the scatter due to genuine object-by-object variation in all the considered scales. [abridged]

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The Planck clusters in the LOFAR sky: IV: LoTSS-DR2: statistics of radio halos and re-acceleration models

Diffuse cluster-scale synchrotron radio emission is discovered in an increasing number of galaxy clusters in the form of radio halos (RHs), probing the presence of relativistic electrons and magnetic fields in the intra-cluster medium. The favoured scenario to explain their origin is that they trace turbulent regions generated during cluster mergers where particles are re-accelerated. In this framework, RHs are expected to probe cluster dynamics and are predicted to be more frequent in massive systems. Statistical studies are important to study the connection of RHs with cluster dynamics and to constrain theoretical models. Furthermore, low-frequency surveys can shed light on the existence of RHs with very steep radio-spectra, a key prediction of turbulent models. We study the properties of RHs from clusters of the second catalog of Planck Sunyaev Zel'dovich detected sources that lie within the 5634 deg^2 covered by the second Data Release (DR2) of the LOFAR Two-meter Sky Survey. We find that the number of observed RHs, their radio flux density and redshift distributions are in line with what is expected in the framework of the re-acceleration scenario. In addition, the fraction of clusters with RHs increases with the cluster mass, confirming the leading role of the gravitational process of cluster formation in the generation of RHs. These models predict a large fraction of RHs with very steep spectrum in the DR2 Planck sample, this will be tested in future studies, yet a comparison of the occurrence of halos in GMRT and LOFAR samples indeed shows a larger occurrence of RHs at lower frequencies suggesting the presence of a number of very steep spectrum RH that is preferentially detected by LOFAR. Using morphological information we confirm that RHs are preferentially located in merging systems and that the fraction of newly LOFAR discovered RHs is larger in less disturbed systems.

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The Planck clusters in the LOFAR sky VI. LoTSS-DR2: Properties of radio relics

Context. It is well-established that shock waves in the intracluster medium launched by galaxy cluster mergers can produce synchrotron emission, which is visible to us at radio frequencies as radio relics. However, the particle acceleration mechanism producing these relics is still not fully understood. It is also unclear how relics relate to radio halos, which trace merger-induced turbulence in the intracluster medium. Aims. We aim to perform the first statistical analysis of radio relics in a mass-selected sample of galaxy clusters, using homogeneous observations. Methods. We analysed all relics observed by the Low Frequency Array Two Metre Sky Survey Data Release 2 (LoTSS DR2) at 144 MHz, hosted by galaxy clusters in the second Planck catalogue of SZ sources (PSZ2). We measured and compared the relic properties in a uniform, unbiased way. In particular, we developed a method to describe the characteristic downstream width in a statistical manner. Additionally, we searched for differences between radio relic-hosting clusters with and without radio halos. Results. We find that, in our sample, $\sim$ 10% of galaxy clusters host at least one radio relic. We confirm previous findings, at higher frequencies, of a correlation between the relic-cluster centre distance and the longest linear size, as well as the radio relic power and cluster mass. However, our findings suggest that we are still missing a population of low-power relics. We also find that relics are wider than theoretically expected, even with optimistic downstream conditions. Finally, we do not find evidence of a single property that separates relic-hosting clusters with and without radio halos.

astro-ph.CO↗

Magnetic fields and relativistic electrons fill entire galaxy cluster

The hot plasma within merging galaxy clusters is predicted to be filled with shocks and turbulence that may convert part of their kinetic energy into relativistic electrons and magnetic fields generating synchrotron radiation. Analyzing Low Frequency Array (LOFAR) observations of the galaxy cluster Abell 2255, we show evidence of radio synchrotron emission distributed over very large scales of at least 5 megaparsec. The pervasive radio emission witnesses that shocks and turbulence efficiently transfer kinetic energy into relativistic particles and magnetic fields in a region that extends up to the cluster outskirts. The strength of the emission requires a magnetic field energy density at least 100 times higher than expected from a simple compression of primordial fields, presumably implying that dynamo operates efficiently also in the cluster periphery. It also suggests that nonthermal components may contribute substantially to the pressure of the intracluster medium in the cluster periphery.

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A Systematic Comparison of Galaxy Cluster Temperatures Measured with NuSTAR and Chandra

Temperature measurements of galaxy clusters are used to determine their masses, which in turn are used to determine cosmological parameters. However, systematic differences between the temperatures measured by different telescopes imply a significant source of systematic uncertainty on such mass estimates. We perform the first systematic comparison between cluster temperatures measured with Chandra and NuSTAR. This provides a useful contribution to the effort of cross-calibrating cluster temperatures due to the harder response of NuSTAR compared with most other observatories. We measure average temperatures for 8 clusters observed with NuSTAR and Chandra. We fit the NuSTAR spectra in a hard (3-10 keV) energy band, and the Chandra spectra in both the hard and a broad (0.6-9 keV) band. We fit a power-law cross-calibration model to the resulting temperatures. At a Chandra temperature of 10 keV, the average NuSTAR temperature was $(10.5 \pm 3.7)\%$ and $(15.7 \pm 4.6)\%$ lower than Chandra for the broad and hard band fits respectively. We explored the impact of systematics from background modelling and multiphase temperature structure of the clusters, and found that these did not affect our results. Our sample are primarily merging clusters with complex thermal structures so are not ideal calibration targets. However, given the harder response of NuSTAR it would be expected to measure a higher average temperature than Chandra for a non-isothermal cluster, so we interpret our measurement as a lower limit on the difference in temperatures between NuSTAR and Chandra.

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The evolving cluster cores: Putting together the pieces of the puzzle

In this work we address the issue of whether the division of clusters in cool cores (CCs) and non-cool cores (NCCs) is due to a primordial difference or to how clusters evolve across cosmic time. Our first goal is to establish if spectra from the central regions of a subclass of NCCs known as cool core remnants (CCRs) are consistent with having a small but significant amount of short cooling time gas, thereby allowing a transformation to CC systems on a timescale of a giga year. Our second goal is to determine if low ionization Fe lines emitted from this residual cool gas will be detectable by the calorimeters that will fly on board XRISM and ATHENA. We performed a spectral analysis of CCR systems with a multi temperature model and, assuming the different components to be in pressure equilibrium with one another, derived entropy and cooling time distributions for the X-ray emitting gas. We find that in most of our systems, the spectral model allows for a fraction of low entropy, short cooling time gas with a mass that is comparable to the one in CC systems. Moreover, simulations show that future spectrometers on board XRISM and ATHENA will have the power to directly resolve emission lines from the low temperature gas, thereby providing incontrovertible evidence for its presence. Within the scenario that we have explored, the constant fraction of CCs measured across cosmic time emerges from a dynamical equilibrium where CCs transformed in NCCs through mergers are balanced by NCCs that revert to CCs. Furthermore, CCs and NCCs should not be viewed as distinct sub classes, but as ``states" between which clusters can move.

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The Planck clusters in the LOFAR sky. III. LoTSS-DR2: Dynamic states and density fluctuations of the intracluster medium

The footprint of LoTSS-DR2 covers 309 PSZ2 galaxy clusters, 83 of which host a radio halo and 26 host a radio relic(s). It provides us an excellent opportunity to statistically study the properties of extended cluster radio sources, especially their connection with merging activities. We aim to quantify cluster dynamic states to investigate their relation with the occurrence of extended radio sources. We also search for connections between intracluster medium (ICM) turbulence and nonthermal characteristics of radio halos in the LoTSS-DR2. We analyzed XMM-Newton and Chandra archival X-ray data and computed concentration parameters and centroid shifts that indicate the dynamic states of the clusters. We also performed a power spectral analysis of the X-ray surface brightness (SB) fluctuations to investigate large-scale density perturbations and estimate the turbulent velocity dispersion. The power spectral analysis results in a large scatter density fluctuation amplitude. We therefore only found a marginal anticorrelation between density fluctuations and cluster relaxation state, and we did not find a correlation between density fluctuations and radio halo power. Nevertheless, the injected power for particle acceleration calculated from turbulent dissipation is correlated with the radio halo power, where the best-fit unity slope supports the turbulent (re)acceleration scenario. Two different acceleration models, transit-time damping and adiabatic stochastic acceleration, cannot be distinguished due to the large scatter of the estimated turbulent Mach number. We introduced a new quantity $[kT\cdot Y_X]_{r_\mathrm{RH}}$, which is proportional to the turbulent acceleration power assuming a constant Mach number. This quantity is strongly correlated with radio halo power, where the slope is also unity.

astro-ph.CO↗

Galaxy clusters enveloped by vast volumes of relativistic electrons

The central regions of galaxy clusters are permeated by magnetic fields and filled with relativistic electrons. When clusters merge, the magnetic fields are amplified and relativistic electrons are re-accelerated by turbulence in the intra cluster medium. These electrons reach energies of 1 -- 10 GeV and, in the presence of magnetic fields, produce diffuse radio halos that typically cover an area of ~1 square Mpc. Here we report observations of four clusters whose radio halos are embedded in much more extended, diffuse radio emission, filling a volume 30 times larger than that of radio halos. The emissivity in these larger features is about 20 times lower than the emissivity in radio halos. We conclude that relativistic electrons and magnetic fields extend far beyond radio halos, and that the physical conditions in the outer regions of the clusters are quite different from those in the radio halos.

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The galaxy group NGC 507: newly detected AGN remnant plasma transported by sloshing

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.

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Does the Fe L-shell blend bias abundance measurements in intermediate-temperature clusters?

In intermediate-temperature (T = 2.5 - 4.5 keV) galaxy clusters, abundance measurements are almost-equally driven by Fe K and L transitions, at $\sim$ 6.7 keV and 0.9 - 1.3 keV, respectively. While K-shell-derived measurements are considered reliable, the resolution of the currently available instrumentation, as well as our current knowledge of the atomic processes, makes the modelling of the L-line complex challenging, resulting in potential biases for abundance measurements. In this work, we study systematics related to the modelling of the Fe L-line complex that may influence iron-abundance measurements in the intermediate-temperature range. To this aim, we select a sample of three bright galaxy clusters, with long XMM-Newton observations available and temperature in the 2.5 - 4.5 keV range. We fit spectra extracted from concentric rings with APEC and APEC+APEC models, by alternatively excluding the L and K bands, and derive the fractional difference of the metal abundances, $ΔZ/Z$, as indication of the consistency between K- and L-shell-derived measurements. The $ΔZ/Z$ distribution is then studied as a function of the cluster radius, ring temperature and X-ray flux. The L-induced systematics, measured through an individual fit of each MOS and pn spectrum, remain constant at a 5 - 6% value in the whole 2.5 - 4.5 keV temperature range. Conversely, a joint fit of MOS and pn spectra leads to a slight excess of 1 - 2% in the above estimate. No significant dependence on the ring X-ray flux is highlighted. The measured 5 - 8% value indicates a modest contribution of the systematics to the derived iron abundances, giving confidence for future measurements. To date, these findings represent the best-achievable estimate of the systematics in analysis, while future microcalorimeters will significantly improve our understanding of the atomic processes underlying the Fe L emissions.

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Diffuse radio emission from non-Planck galaxy clusters in the LoTSS-DR2 fields

The presence of large-scale magnetic fields and ultra-relativistic electrons in the intra-cluster medium (ICM) is confirmed through the detection of diffuse radio synchrotron sources, so-called radio halos and relics. Due to their steep-spectrum nature, these sources are rarely detected at frequencies above a few GHz, especially in low-mass systems. The aim of this study is to discover and characterise diffuse radio sources in low-mass galaxy clusters in order to understand their origin and their scaling with host cluster properties. We searched for cluster-scale radio emission from low-mass galaxy clusters in the Low Frequency Array (LOFAR) Two-metre Sky Survey - Data Release 2 (LoTSS-DR2) fields. We made use of existing optical (Abell, DESI, WHL) and X-ray (comPRASS, MCXC) catalogues. The LoTSS-DR2 data were processed further to improve the quality of the images that are used to detect and characterize diffuse sources. We have detected diffuse radio emission in 28 galaxy clusters. The number of confirmed (candidates) halos and relics are six (seven) and 10 (three), respectively. Among these, 11 halos and 10 relics, including candidates, are newly discovered by LOFAR. Beside these, five diffuse sources are detected in tailed radio galaxies and are probably associated with mergers during the formation of the host clusters. We are unable to classify other 13 diffuse sources. We compare our newly detected, diffuse sources to known sources by placing them on the scaling relation between the radio power and the mass of the host clusters.

astro-ph.CO↗

Particle re-acceleration and diffuse radio sources in the galaxy cluster Abell 1550

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 ($S_ν\propto ν^{-1.6}$) 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.

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The Planck clusters in the LOFAR sky. I. LoTSS-DR2: new detections and sample overview

Relativistic electrons and magnetic fields permeate the intra-cluster medium (ICM) and manifest themselves as diffuse sources of synchrotron emission observable at radio wavelengths, namely radio halos and radio relics. Although there is broad consensus that the formation of these sources is connected to turbulence and shocks in the ICM, the details of the required particle acceleration, the strength and morphology of the magnetic field in the cluster volume, and the influence of other sources of high-energy particles are poorly known. Sufficiently large samples of radio halos and relics, which would allow us to examine the variation among the source population and pinpoint their commonalities and differences, are still missing. At present, large numbers of these sources are easiest to detect at low radio frequencies, where they shine brightly. We examined the low-frequency radio emission from all 309 clusters in the second catalog of Planck Sunyaev Zel'dovich detected sources that lie within the 5634 deg$^2$ covered by the Second Data Release of the LOFAR Two-meter Sky Survey (LoTSS-DR2). We produced LOFAR images at different resolutions, with and without discrete sources subtracted, and created overlays with optical and X-ray images before classifying the diffuse sources in the ICM, guided by a decision tree. Overall, we found 83 clusters that host a radio halo and 26 that host one or more radio relics (including candidates). About half of them are new discoveries. The detection rate of clusters hosting a radio halo and one or more relics in our sample is $30\pm11$% and $10\pm6$%, respectively. Extrapolating these numbers, we anticipate that once LoTSS covers the entire northern sky it will provide the detection of $251\pm92$ clusters hosting a halo and $83\pm50$ clusters hosting at least one relic from Planck clusters alone.

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The XXL Survey: XLVIII; X-ray follow-up of distant XXL clusters: Masses, scaling relations and AGN contamination

We use deep follow-up XMM-Newton observations of 6 clusters discovered in the XXL Survey at $z>1$ to gain robust measurements of their X-ray properties and to investigate the extent to which scaling relations at low redshift are valid at $z>1$. This sample is unique as it has been investigated for AGN contamination, which ensures measurements are not undermined by systematic uncertainties, and pushes to lower mass at higher redshift than is usually possible, for example with Sunyaev-Zel'dovich (SZ) selected clusters. We determine the flux contribution of point sources to the XXL cluster flux in order to test for the presence of AGN in other high-redshift cluster candidates, and find 3XLSS J231626.8-533822 to be a point source misclassified as a cluster and 3XLSS J232737.3-541618 to be a genuine cluster. We present the first attempt to measure the hydrostatic masses in a bright subsample of $z>1$ X-ray selected galaxy clusters with a known selection function. Periods of high particle background significantly reduced the effective exposure times of observations (losing >50% in some cases) limiting the power of this study. When combined with complementary SZ selected cluster samples at higher masses, the data appear broadly consistent with the self-similar evolution of the low redshift scaling relations between ICM properties and cluster mass, suggesting that properties such as the X-ray temperature, gas mass and SZ signal remain reliable mass proxies even at high redshift.

astro-ph.CO↗

The Coma cluster at LOFAR frequencies II: the halo, relic, and a new accretion relic

We present LOw Frequency ARray observations of the Coma cluster field at 144\,MHz. The cluster hosts one of the most famous radio halos, a relic, and a low surface-brightness bridge. We detect new features that allow us to make a step forward in the understanding of particle acceleration in clusters. The radio halo extends for more than 2 Mpc, which is the largest extent ever reported. To the North-East of the cluster, beyond the Coma virial radius, we discover an arc-like radio source that could trace particles accelerated by an accretion shock. To the West of the halo, coincident with a shock detected in the X-rays, we confirm the presence of a radio front, with different spectral properties with respect to the rest of the halo. We detect a radial steepening of the radio halo spectral index between 144 MHz and 342 MHz, at $\sim 30^{\prime}$ from the cluster centre, that may indicate a non constant re-acceleration time throughout the volume. We also detect a mild steepening of the spectral index towards the cluster centre. For the first time, a radial change in the slope of the radio-X-ray correlation is found, and we show that such a change could indicate an increasing fraction of cosmic ray versus thermal energy density in the cluster outskirts. Finally, we investigate the origin of the emission between the relic and the source NGC 4789, and we argue that NGC4789 could have crossed the shock originating the radio emission visible between its tail and the relic.

astro-ph.HE↗

Radio footprints of a minor merger in the Shapley Supercluster: From supercluster down to galactic scales

The Shapley Supercluster ($\langle z \rangle\approx0.048$) contains several tens of gravitationally bound clusters and groups, making it it is an ideal subject for radio studies of cluster mergers. We used new high sensitivity radio observations to investigate the less energetic events of mass assembly in the Shapley Supercluster from supercluster down to galactic scales. We created total intensity images of the full region between A 3558 and A 3562, from $\sim 230$ to $\sim 1650$ MHz, using ASKAP, MeerKAT and the GMRT, with sensitivities ranging from $\sim 6$ to $\sim 100$ $μ$Jy beam$^{-1}$. We performed a detailed morphological and spectral study of the extended emission features, complemented with ESO-VST optical imaging and X-ray data from XMM-Newton. We report the first GHz frequency detection of extremely low brightness intercluster diffuse emission on a $\sim 1$ Mpc scale connecting a cluster and a group, namely: A 3562 and the group SC 1329--313. It is morphologically similar to the X-ray emission in the region. We also found (1) a radio tail generated by ram pressure stripping in the galaxy SOS 61086 in SC 1329-313; (2) a head-tail radio galaxy, whose tail is broken and culminates in a misaligned bar; (3) ultrasteep diffuse emission at the centre of A 3558. Finally (4), we confirm the ultra-steep spectrum nature of the radio halo in A 3562. Our study strongly supports the scenario of a flyby of SC 1329-313 north of A 3562 into the supercluster core. [abridged...]

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X-ray characterisation of the massive galaxy clusterClG-J104803.7+313843 at z=0.76 with XMM-Newton

We present the characterisation of the massive cluster ClG-J$104803.7+313843$ at $z=0.76$ performed using a serendipitous XMM-Newton observation. High redshift and massive objects represent an ideal laboratory to benchmark our understanding of how cluster form and assembly formation driven mainly by gravity.Leveraging the high throughput of XMM-Newton we were firstly able to determine the redshift of the object, shedding light on ambiguous photometric redshift associations. We investigated the morphology of this cluster which shows signs of merging activities in the outskirts and a flat core. We also measured the radial density profile up to $R_{500}$. With these quantities in hand, we were able to determine the mass, $M_{500}=5.64^{+0.79}_{-0.62} \times 10^{14}M_{\odot}$, using the YX proxy. This quantity improves previous measurement of the mass of this object by a factor of $\sim 3.5$. The characterisation of one cluster at such mass and redshift regime is fundamental as these objects are intrinsically rare, the number of objects discovered so far being less than $\sim 25$. Our study highlights the importance of using X-ray observations in combination with ancillary multi-wavelength data to improve our understanding of high-z and massive clusters

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A snapshot of the oldest AGN feedback phases

Active Galactic Nuclei (AGN) inject large amounts of energy into their host galaxies and surrounding environment, shaping their properties and evolution. In particular, AGN jets inflate cosmic-ray lobes, which can rise buoyantly as light `bubbles' in the surrounding medium, displacing and heating the encountered thermal gas and thus halting its spontaneous cooling. These bubbles have been identified in a wide range of systems. However, due to the short synchrotron lifetime of electrons, the most advanced phases of their evolution have remained observationally unconstrained, preventing us to fully understand their coupling with the external medium, and thus AGN feedback. Simple subsonic hydrodynamic models predict that the pressure gradients, naturally present around the buoyantly rising bubbles, transform them into toroidal structures, resembling mushroom clouds in a stratified atmosphere. The way and timescales on which these tori will eventually disrupt depend on various factors including magnetic fields and plasma viscosity. Here we report LOFAR observations below 200 MHz, sensitive to the oldest radio-emitting particles, showing the late evolution of multiple generations of cosmic-ray AGN bubbles in a galaxy group with unprecedented level of detail. The bubbles' buoyancy power can efficiently offset the radiative cooling of the intragroup medium. However, the bubbles have still not thoroughly mixed with the thermal gas, after hundreds of million years, likely under the action of magnetic fields.

astro-ph.HE↗