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The radiative cooling time of hot gas in the cool cores of many galaxy clusters and massive elliptical galaxies drops in the centre to below 100 million years. The mass cooling rates inferred from simple modelling of X-ray observations of these objects are very low, indicating that either AGN feedback is tightly balanced or that soft X-rays from cooling gas are somehow hidden from view. An intrinsic absorption model developed for application to galaxy clusters is used here to search for hidden cooling flows (HCFs) in seven nearby elliptical galaxies. Mass cooling rates of 0.5-8 solar masses per year are found in each galaxy. The absorbed cooling flow luminosity is in agreement with the observed Far Infrared (FIR) luminosity in each case, indicating absorbed emission is energetically capable of emerging in the FIR band. An observed lack of agreement between HCF rates and normal star formation rates suggests the cooled material must have an alternative fate, with low-mass star formation considered as the primary outcome., Comment: 17 pages, 14 figures, 7 tables. Accepted for publication in MNRAS

Cooling flows are common in galaxy clusters which have cool cores. The soft X-ray emission below 1 keV from the flows is mostly absorbed by cold dusty gas within the central cooling sites. Further evidence for this process is presented here through a more detailed analysis of the nearby Centaurus cluster and some additional clusters. Predictions of JWST near and mid-infrared spectra from cooling gas are presented. [NeVI] emission at 7.65 micron should be an important diagnostic of gas cooling between 6 and 1.5 times 10^5 K. The emerging overall picture of hidden cooling flows is explored. The efficiency of AGN feedback in reducing the total cooling rate in cool cores is shown to be above 50 percent for many clusters but is rarely above 90 per cent. The reduction is mostly in outer gas. Cooling dominates in elliptical galaxies and galaxy groups which have mass flow rates below about 15M/yr and in some massive clusters where rates can exceed 1000M/yr., Comment: 17 pages, 49 figures submitted to MNRAS

We present a detailed analysis of the velocity structure of the hot intracluster medium (ICM) within the A3266 galaxy cluster, including new observations taken between June and November 2023. Firstly, morphological structures within the galaxy cluster were examined using a Gaussian Gradient Magnitude (GGM) and adaptively smoothed GGM filter applied to the EPIC-pn X-ray image. Then, we applied a novel {\it XMM-Newton} EPIC-pn energy scale calibration, which uses instrumental Cu K$\alpha$ as reference for the line emission, to measure line-of-sight velocities of the hot gas within the system. This approach enabled us to create two-dimensional projected maps for velocity, temperature, and metallicity, showing that the hot gas displays a redshifted systemic velocity relative to the cluster redshift across all fields of view. Further analysis of the velocity distribution through non-overlapping circular regions demonstrated consistent redshifted velocities extending up to 1125 kpc from the cluster core. Additionally, the velocity distribution was assessed along regions following surface brightness discontinuities, where we observed redshifted velocities in all regions, with the largest velocities reaching $768 \pm 284$ km/s. Moreover, we computed the velocity Probability Density Function (PDF) from the velocity map. We applied a normality test, finding that the PDF adheres to an unimodal normal distribution consistent with theoretical predictions. Lastly, we computed a velocity structure function (VSF) for this system using the measured line-of-sight velocities. These insights advance our understanding of the dynamic processes within the A3266 galaxy cluster and contribute to our broader knowledge of ICM behavior in merging galaxy clusters., Comment: 12 pages, 15 figures, This paper is part of a series on the ICM velocity structure using XMM-Newton observations. Related series papers: arXiv:2109.06213, arXiv:2203.12635; doi:10.1093/mnras/stad1132; arXiv:2303.17556

High resolution X-ray spectra reveal hidden cooling flows depositing cold gas at the centres of massive nearby early-type galaxies with little sign of normal star formation. Optical observations are revealing that a bottom-heavy Initial Mass Function is common within the inner kpc of similar galaxies. We revive the possibility that a low-mass star formation mode is operating due to the high thermal pressure in the cooling flow, thus explaining the accumulation of low-mass stars. We further explore whether such a mode operated in early, high-redshift galaxies and has sporadically continued to the present day. The idea links observed distant galaxies with black holes which are ultramassive for their stellar mass, nearby red nuggets and massive early-type galaxies. Nearby elliptical galaxies may be red but they are not dead., Comment: 4 pages, 2 Figures, Accepted for publication in MNRAS

Stellar and black hole feedback heat and disperse surrounding cold gas clouds, launching gas flows off circumnuclear and galactic disks and producing a dynamic interstellar medium. On large scales bordering the cosmic web, feedback drives enriched gas out of galaxies and groups, seeding the intergalactic medium with heavy elements. In this way, feedback shapes galaxy evolution by shutting down star formation and ultimately curtailing the growth of structure after the peak at redshift 2-3. To understand the complex interplay between gravity and feedback, we must resolve both the key physics within galaxies and map the impact of these processes over large scales, out into the cosmic web. The Advanced X-ray Imaging Satellite (AXIS) is a proposed X-ray probe mission for the 2030s with arcsecond spatial resolution, large effective area, and low background. AXIS will untangle the interactions of winds, radiation, jets, and supernovae with the surrounding ISM across the wide range of mass scales and large volumes driving galaxy evolution and trace the establishment of feedback back to the main event at cosmic noon., Comment: 29 pages, 18 figures; this white paper is part of a series commissioned for the AXIS Probe mission concept

The analysis of the elemental abundances in galaxy clusters offers valuable insights into the formation and evolution of galaxies. In this study, we explore the chemical enrichment of the intergalactic medium (ICM) in the Ophiuchus cluster by utilizing {\it XMM-Newton} EPIC-pn observations. We explore the radial profiles of Si, S, Ar, Ca, and Fe. Due to the high absorption of the system, we have obtained only upper limits for O, Ne, Mg, and Ni. We model the X/Fe ratio profiles with a linear combination of core-collapse supernovae (SNcc) and type~Ia supernovae (SNIa) models. We found a flat radial distribution of SNIa ratio over the total cluster enrichment $10-30\%$ for all radii. However, the absence of light $\alpha$-elements abundances may lead to over-estimation of the SNcc contribution., Comment: 9 pages, 8 figures. This paper is part of a series on the ICM chemical enrichment using galaxy clusters XMM-Newton observations for which the velocity structure has been measured. Related series papers: arXiv:2302.04286, arXiv:2309.02507

We examine deep {\it XMM-Newton} EPIC-pn observations of the Centaurus cluster to study the hot intracluster medium (ICM) and radial metal distributions within such an environment. We found that the best-fit spectral model corresponds to a log-normal temperature distribution, with discontinuities around $\sim10$~kpc, $\sim50$~kpc, and $\sim100$~kpc, also observed in the abundances distributions. We measured the radial profiles of O, Si, S, Ar, Ca, and Fe. These profiles reveal prominent negative gradients for distances $<90$~kpc, which then transition to flatter profiles. We modeled X/Fe ratio profiles with a linear combination of SNIcc and SNIa models. The best-fit model suggests a uniform SNIa percentage contribution to the total cluster enrichment, thus supporting an early enrichment of the ICM, with most of the metals present being produced before clustering., Comment: 8 pages, 9 figures. This paper is part of a series on the ICM chemical enrichment using galaxy clusters XMM-Newton observations for which the velocity structure has been measured. Related series papers: arXiv:2302.04286

Previous studies of the massive nearby galaxy cluster Abell 3558 reported a cold front around the cluster core, which is attributed to the sloshing of the core as it responds to the gravitational disturbance created by a past minor merger. Here, using XMM-Newton mosaic, we report the detection of two rare large-scale sloshing cold fronts far outside the cooling radius of Abell 3558. One of the detected cold fronts is located 600 kpc from the cluster core to the south-east, while the other is located 1.2 Mpc from the cluster core to the north-west. The latter cold front is one of the most distant cold fronts ever observed in a galaxy cluster. Our findings are in agreement with previous studies that sloshing can extend well beyond the cooling radius, on scales exceeding half the virial radius, suggesting that sloshing is a cluster-wide phenomenon and may affect the cluster's global properties., Comment: 5 pages, 4 figures. Accepted for publication in MNRAS Letters

This Technical Design Report presents a detailed description of all aspects of the LUXE (Laser Und XFEL Experiment), an experiment that will combine the high-quality and high-energy electron beam of the European XFEL with a high-intensity laser, to explore the uncharted terrain of strong-field quantum electrodynamics characterised by both high energy and high intensity, reaching the Schwinger field and beyond. The further implications for the search of physics beyond the Standard Model are also discussed.

It has been shown that the gas velocities within the intracluster medium (ICM) can be measured by applying novel XMM-Newton EPIC-pn energy scale calibration, which uses instrumental Cu Ka as reference for the line emission. Using this technique, we have measured the velocity distribution of the ICM for clusters involving AGN feedback and sloshing of the plasma within the gravitational well (Virgo and Centaurus) and a relaxed one (Ophiuchus). We present a detailed study of the kinematics of the hot ICM for these systems. First, we compute the velocity probability distribution functions (PDFs) from the velocity maps. We find that for all sources the PDF follows a normal distribution, with a hint for a multimodal distribution in the case of Ophiuchus. Then, we compute the velocity structure function (VSF) for all sources in order to study the variation with scale as well as the nature of turbulence in the ICM. We measure a turbulence driving scale of 10-20 kpc for the Virgo cluster, while the Ophiuchus cluster VSF reflects the absence of strong interaction between the ICM and a powerful Active Galactic Nucleus (AGN) at such spatial scales. For the former, we compute a dissipation time larger than the jet activity cycle, thus indicating that a more efficient heating process than turbulence is required to reach equilibrium. This is the first time that the VSF of the hot ICM has been computed using direct velocity measurements from X-ray astronomical observations., Comment: 10 pages, 9 Figures

Recently, we have uncovered Hidden Cooling Flows (HCF) in the X-ray spectra of the central Brightest Galaxies of 11 clusters, 1 group and 2 elliptical galaxies. Here we report such flows in a further 15 objects, consisting of 8 clusters, 3 groups, 3 ellipticals and 1 Red Nugget. The mass cooling rates are about 1 Msun/yr in the ellipticals, 2 to 20 Msun/yr in the groups and 20 to 100 Msun/yr in regular clusters. The Red Nugget, MRK1216, has an HCF of 10 Msun/yr. We review the fate of the cooled gas and investigate how some of it might accrete onto the central black hole. The gas is likely to be very cold and to have fragmented into low mass stars and smaller objects before being swallowed whole, with little luminous output. If such a scenario is correct and operates at a few Msun/yr then such objects may host the fastest growing black holes in the low redshift Universe. We briefly discuss the relevance of HCF to the growth of early galaxies and black holes., Comment: 15 pages, 18 Figures, accepted for publication in MNRAS

Cosmological simulations of structure formation predict that galaxy clusters continue to grow and evolve through ongoing mergers with group-scale systems. During these merging events, the ram pressure applied by the intracluster medium acts to strip the gas from the infalling groups, forming large tails of stripped gas, which eventually become part of the main cluster. In this work, we present a detailed analysis of our new deep Chandra observations of the NGC 4839 group falling into the nearby Coma cluster, providing a unique opportunity to explore the way galaxy clusters in the local universe continue to grow. Our analysis reveals a cold front feature at the leading head of the group, preceded by a bow shock of hot gas in front with a Mach number of $\sim\! 1.5$. The power spectrum of surface brightness fluctuations in the tail shows that the slope gets less steep as the distance from the leading head increases, changing from $-2.35_{-0.06}^{+0.07}$ at the inner part of the tail to $-1.37_{-0.07}^{+0.09}$ at the outermost part of the tail. These values are shallower than the slope of the Kolmogorov 2D power spectrum, indicating that thermal conduction is being suppressed throughout the tail, enabling long-lived small-scale turbulence, which would typically be washed out if thermal conduction was not inhibited. The characteristic amplitude of surface brightness fluctuations in the tail suggests a mild level of turbulence with a Mach number in the range of 0.1-0.5, agreeing with that found for the infalling group in Abell 2142., Comment: 10 pages, 10 figures, 3 tables. Accepted for publication in MNRAS

We have found evidence of bulk velocities following active galactic nucleus (AGN) bubbles in the Virgo cluster and galaxy motions in the Centaurus cluster. In order to increase the sample and improve our understanding of the intracluster medium (ICM), we present the results of a detailed mapping of the Ophiuchus cluster with {\it XMM-Newton} to measure bulk flows through very accurate Fe~K measurements. To measure the gas velocities we use a novel EPIC-pn energy scale calibration, which uses the Cu K$\alpha$ instrumental line as reference for the line emission. We created 2D spectral maps for the velocity, metallicity, temperature, density, entropy and pressure with a spatial resolution of 0.25$'$ ($\sim 26$~kpc). The ICM velocities in the central regions where AGN feedback is most important are similar to the velocity of the brightest cluster galaxy (BCG). We have found a large interface region where the velocity changes abruptly from blueshifted to redshifted gas which follows a sharp surface brightness discontinuity. We also found that the metallicities and temperatures do not change as we move outwards from the giant radio fossil previously identified in radio observations of the cluster. Finally, we have found a contribution from the kinetic component of $<25\%$to the total energy budget for large distances., Comment: 15 pages, 20 figures. This paper is part of a series on the ICM velocity structure using XMM-Newton observations. Related series papers: arXiv:2109.06213, arXiv:2203.12635

We present a detailed analysis of the elemental abundances distribution of the Virgo cluster using {\it XMM-Newton} observations. We included in the analysis a new EPIC-pn energy scale calibration which allow us to measure velocities with uncertainties down to $\Delta v \sim 150$ km/s. We investigate the radial distribution of O, Ne, Mg, Si, Ar, S, Ca, Ni and Fe. We found that the best-fit model is close to a single-temperature component for distances $>80$~kpc and the cooler gas is more metal-rich. Discontinuities in temperature are found around $\sim30$~kpc and $\sim90$~kpc, which correspond to the radius of the cold fronts. We modeled elemental X/Fe ratio profiles with a linear combination of SNIa and SNcc models. We found a flat radial distribution of SNIa ratio over the total cluster enrichment, which supports an early ICM enrichment scenario, with most of the metals present being produced prior to clustering., Comment: 9 pages, 10 figures

The extremely rapid assembly of the earliest galaxies during the first billion years of cosmic history is a major challenge for our understanding of galaxy formation physics. The advent of JWST has exacerbated this issue by confirming the existence of galaxies in significant numbers as early as the first few hundred million years. Perhaps even more surprisingly, in some galaxies, this initial highly efficient star formation rapidly shuts down, or quenches, giving rise to massive quiescent galaxies as little as 1.5 billion years after the Big Bang. However, due to their faintness and red colour, it has proven extremely challenging to learn about these extreme quiescent galaxies, or to confirm whether any exist at earlier times. Here we report the spectroscopic confirmation of a massive quiescent galaxy, GS-9209, at redshift $z=4.658$, just 1.25 billion years after the Big Bang, using JWST NIRSpec. From these data we infer a stellar mass of $M_* = 3.8\pm0.2\times10^{10}\ M_\odot$, which formed over a $\simeq200$ Myr period before this galaxy quenched its star formation activity at $z=6.5^{+0.2}_{-0.5}$, when the Universe was $\simeq800$ million years old. Based on the presence of broad H$\alpha$ in the spectrum and a high narrow-line [NII]/H$\alpha$ ratio, we infer the presence of an accreting supermassive black hole, with a mass of $M_\bullet = 5\pm1\times10^{8}\ M_\odot$. This large black hole mass relative to the stellar mass suggests that active galactic nucleus (AGN) feedback may have been responsible for quenching this galaxy. GS-9209 is also extremely compact, with an effective radius, $r_e=215\pm20$ parsecs. This galaxy is both a likely descendent of the highest-redshift submillimetre galaxies and quasars, and a likely progenitor for the dense, ancient cores of the most massive local galaxies., Comment: 23 pages, 6 figures, 2 tables, accepted for publication in Nature

We have recently uncovered Hidden Cooling Flows (HCFs) in the XMM RGS spectra of 3 clusters of galaxies, Centaurus, Perseus and A1835. Here we search for them in a wider sample of objects: the X-ray brightest group NGC5044; 4 moderate X-ray luminosity clusters Sersic 159, A262, A2052 and RXJ0821; and 3 high X-ray luminosity clusters RXJ1532, MACS 1931 and the Phoenix cluster. Finally we examine two Virgo elliptical galaxies, M49 and M84. All statistically allow the addition of an HCF. We find a significant detection of an HCF in 6 clusters and 2 elliptical galaxies. The hidden mass cooling rates are 5 to 40 Solar masses per year for the normal clusters, 1000 Solar masses per year or more for the extreme clusters and 1 to 2 Solar masses per year for the elliptical galaxies. We discuss the implications of the results for the composition of the innermost parts of the massive host galaxies and look forward to future observations., Comment: 10 Pages, 13 figures, 3 tables, MNRAS submitted

Non-thermal emission from clusters of galaxies at the high-energy X-ray regime has been searched with various instruments, but the detection significance of this emission has yet been found to be either marginal or controversial. Taking advantage of NuSTAR's unique capability to focus X-rays in the hard energy band, we present a detailed analysis of 238 ks NuSTAR observations of the merging galaxy cluster SPT-CL J2031-4037, searching for non-thermal inverse Compton emission. Our spectral analysis of SPT-CL J2031-4037 shows a possibility that the hard X-ray emission of the cluster can be described by a non-thermal component, though we cannot completely rule out a purely thermal origin for this hard emission. Including the statistical and systematic uncertainties, our best model fit yields a 20-80 keV non-thermal flux of $3.93_{-1.10}^{+1.24} \times 10^{-12}$ erg s$^{-1}$ cm$^{-2}$. The estimated non-thermal flux is comparable to those found in other galaxy clusters using NuSTAR and other X-ray instruments. Using this non-thermal flux with the existing radio data of the cluster, we estimate a volume-averaged magnetic field strength in the range of around 0.1-0.2 $\mu$G., Comment: 10 pages, 10 figures, 4 tables. Accepted for publication in MNRAS

The pooling of prior opinions is an important area of research and has been for a number of decades. The idea is to obtain a single belief probability distribution from a set of expert opinion belief distributions. The paper proposes a new way to provide a resultant prior opinion based on a minimization of information principle. This is done in the square-root density space, which is identified with the positive orthant of Hilbert unit sphere of differentiable functions. It can be shown that the optimal prior is easily identified as an extrinsic mean in the sphere. For distributions belonging to the exponential family, the necessary calculations are exact, and so can be directly applied. The idea can also be adopted for any neighbourhood of a chosen base prior and spanned by a finite set of ``contaminating" directions.

The radiative cooling time of the hot gas at the centres of cool cores in clusters of galaxies drops down to 10 million years and below. The observed mass cooling rate of such gas is very low, suggesting that AGN feedback is very tightly balanced or that the soft X-ray emission from cooling is somehow hidden from view. We use an intrinsic absorption model in which the cooling and coolest gas are closely interleaved to search for hidden cooling flows in the Centaurus, Perseus and A1835 clusters of galaxies. We find hidden mass cooling rates of between 10 to 500 Msunpyr as the cluster mass increases, with the absorbed emission emerging in the Far Infrared band. Good agreement is found between the hidden cooling rate and observed FIR luminosity in the Centaurus Cluster. The limits on the other two clusters allow for considerable hidden cooling. The implied total mass of cooled gas is much larger than the observed molecular masses. We discuss its fate including possible further cooling and collapse into undetected very cold clouds, low mass stars and substellar objects, Comment: 11 pages. 7 figures, 2 tables MNRAS in press

This paper provides a new analysis of ROSAT observations of the Coma cluster, to determine the amount of soft X--ray radiation in excess of the contribution from the hot intra--cluster medium. The re--analysis is made possible by a high--resolution study of the hot intra--cluster medium with the XMM-Newton and Planck telescopes out to the cluster's virial radius. The analysis confirms the original findings of a strong excess of soft X--ray radiation, which is likely to be of thermal origin. We find quantitative agreement between the detected soft excess and the physical characteristics of warm--hot intergalactic medium (WHIM) filaments seen in hydrodynamical simulations. We conclude that the most plausible explanation for the soft excess is the presence of $\sim 10$~Mpc--long filaments at $\log T(K)\simeq 6$, with a baryon overdensity $\sim 300$, converging towards the Coma cluster. This interpretation therefore provides support for the identification of the missing low--redshift baryons with WHIM filaments, as predicted by numerical simulations., Comment: MNRAS accepted

There are few direct measurements of ICM velocity structure, despite its importance for understanding clusters. We present a detailed analysis of the velocity structure of the Centaurus cluster using XMM-Newton observations. Using a new EPIC-pn energy scale calibration, which uses the Cu Ka instrumental line as reference, we are able to obtain velocity measurements with uncertainties down to $\Delta v \sim 79$ km/s. We create 2D spectral maps for the velocity, metallicity, temperature, density, entropy and pressure with an spatial resolution of 0.25'. We have found that the velocity structure of the ICM is similar to the velocity structure of the main galaxies while the cold fronts are likely moving in a plane perpendicular to our line of sight with low velocity. Finally, we have found a contribution from the kinetic component of <25\% to the total energetic budget for radius $>30$ kpc., Comment: 16 pages, 23 figures. This paper is part of a series on the ICM velocity structure using XMM-Newton observations. Related series papers: arXiv:2109.06213, arXiv:2303.17556

We investigate the properties of the dark matter (DM) halo surrounding the nearby galaxy group NGC 1600. Through the use of deep (252 ks) Chandra observations and 64.3 ks of XMM-Newton observations, we construct surface brightness profiles in multiple energy bands in order to perform hydrostatic equilibrium analysis of the hot plasma within NGC 1600. Regardless of the DM model profile assumed, we measure a halo concentration (c$_{200}$) that is an extreme, positive outlier of the $\Lambda$CDM c$_{200}$-M$_{200}$ relation. For a typical NFW DM profile, we measure c$_{200}\!=\!26.7\pm1.4$ and M$_{200}\!=\!(2.0\pm0.2)\times10^{13}$ M$_\odot$; assuming a similar halo mass, the average concentration expected is c$_{200}=6-7$ for the theoretical $\Lambda$CDM c-M relation. Such a high concentration is similar to that of well-known fossil groups MRK 1216 and NGC 6482. While NGC 1600 exhibits some properties of a fossil group, it fails to meet the X-ray luminosity threshold of L$_X>5\times10^{41}$ erg s$^{-1}$. Whether or not it is considered a fossil group, the high concentration value makes it part of a select group of galaxy groups., Comment: 7 pages, 5 figures. Accepted for publication in MNRAS

We examine Suzaku, XMM-Newton, and Chandra observations of the Abell 2029/2033 system to investigate the nature of a bridge of X-ray emission joining the two galaxy clusters. By modelling the contributions from the outskirts of the two clusters, and excluding the emission from the southern infalling group and the background group LOS9, we find a significant excess of X-ray emission between the two clusters at the level of 6.5-7.0$\sigma$, depending on the choice of model, that cannot be explained by the overlap of the clusters. This excess component to the surface brightness is consistent with being emission from a filament with roughly 1.0 Mpc wide. The derived emission measure for the gas associated with the filament yields an average gas density of $3.7^{+1.0}_{-0.7} \times 10^{-5}$ cm$^{-3}$, corresponding roughly to 160 times the mean baryon density of the Universe. The Suzaku X-ray spectrum of the excess emission indicates that it is significantly colder ($1.4_{-0.5}^{+0.7}$ keV) than the cluster outskirts emission from the two clusters ($\sim$ 5 keV), statistically consistent with the temperature expected from the hottest and densest parts of the warm-hot intergalactic medium (WHIM). The geometry, density, and temperature are similar to those found from X-ray studies of the Abell 222/223 filament., Comment: 10 pages, 6 figures, 3 tables. Accepted for publication in MNRAS

We present a detailed analysis of the velocity structure of the Virgo cluster using {\it XMM-Newton} observations. Using a novel technique which uses uses the Cu K$\alpha$ instrumental line to calibrate the EPIC-pn energy scale, we are able to obtain velocity measurements with uncertainties down to $\Delta v \sim 100$ km/s. We created 2D projected maps for the velocity, temperature, metallicity, density, pressure and entropy with an spatial resolution of 0.25$'$. We have found that in the innermost gas there is a high velocity structure, most likely indicating the presence of an outflow from the AGN while our analysis of the cluster cool core using RGS data indicates that the velocity of the gas agrees with the M87 optical redshift. An overall gradient in the velocity is seen, with larger values as we move away from the cluster core. The hot gas located within the western radio flow is redshifted, moving with a velocity $\sim 331$ km/s while the hot gas located within the eastern radio flow is blueshifted, with a velocity $\sim 258$ km/s, suggesting the presence of backflows. Our results reveal the effects of both AGN outflows and gas sloshing, in the complex velocity field of the Virgo cluster., Comment: 19 pages, 21 figures; This paper is part of a series on the ICM velocity structure using XMM-Newton observations. Related series papers: arXiv:2203.12635, arXiv:2303.17556