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Abstract We analyze the cooling and feedback properties of 48 galaxy clusters at redshifts 0.4 < z < 1.3 selected from the South Pole Telescope (SPT) catalogs to evolve like the progenitors of massive and well-studied systems at z ∼ 0. We estimate the radio power at the brightest cluster galaxy (BCG) location of each cluster from an analysis of Australia Telescope Compact Array data. Assuming that the scaling relation between the radio power and active galactic nucleus (AGN) cavity power P cav observed at low redshift does not evolve with redshift, we use these measurements in order to estimate the expected AGN cavity power in the core of each system. We estimate the X-ray luminosity within the cooling radius L cool of each cluster from a joint analysis of the available Chandra X-ray and SPT Sunyaev–Zel’dovich (SZ) data. This allows us to characterize the redshift evolution of the P cav / L cool ratio. When combined with low-redshift results, these constraints enable investigations of the properties of the feedback–cooling cycle across 9 Gyr of cluster growth. We model the redshift evolution of this ratio measured for cool-core clusters by a log-normal distribution Log -  ( α + β z , σ 2 ) and constrain the slope of the mean evolution to β = −0.05 ± 0.47. This analysis improves the constraints on the slope of this relation by a factor of two. We find no evidence of redshift evolution of the feedback–cooling equilibrium in these clusters, which suggests that the onset of radio-mode feedback took place at an early stage of cluster formation. High values of P cav / L cool are found at the BCG location of noncool-core clusters, which might suggest that the timescales of the AGN feedback cycle and the cool core–noncool core transition are different. This work demonstrates that the joint analysis of radio, SZ, and X-ray data solidifies the investigation of AGN feedback at high redshifts. 

Context. The excitation of the filamentary gas structures surrounding giant elliptical galaxies at the center of cool-core clusters, also known as brightest cluster galaxies (BCGs), is key to our understanding of active galactic nucleus (AGN) feedback, and of the impact of environmental and local effects on star formation. Aims. We investigate the contribution of thermal radiation from the cooling flow surrounding BCGs to the excitation of the filaments. We explore the effects of small levels of extra heating (turbulence), and of metallicity, on the optical and infrared lines. Methods. Using the C LOUDY code, we modeled the photoionization and photodissociation of a slab of gas of optical depth A V  ≤ 30 mag at constant pressure in order to calculate self-consistently all of the gas phases, from ionized gas to molecular gas. The ionizing source is the extreme ultraviolet (EUV) and soft X-ray radiation emitted by the cooling gas. We tested these models comparing their predictions to the rich multi-wavelength observations from optical to submillimeter, now achieved in cool core clusters. Results. Such models of self-irradiated clouds, when reaching sufficiently large A V , lead to a cloud structure with ionized, atomic, and molecular gas phases. These models reproduce most of the multi-wavelength spectra observed in the nebulae surrounding the BCGs, not only the low-ionization nuclear emission region like optical diagnostics, [O  III ] λ 5007 Å/H β , [N  II ] λ 6583 Å/H α , and ([S  II ] λ 6716 Å+[S  II ] λ 6731 Å)/H α , but also the infrared emission lines from the atomic gas. [O  I ] λ 6300 Å/H α , instead, is overestimated across the full parameter space, except for very low A V . The modeled ro-vibrational H 2 lines also match observations, which indicates that near- and mid-infrared H 2 lines are mostly excited by collisions between H 2 molecules and secondary electrons produced naturally inside the cloud by the interaction between the X-rays and the cold gas in the filament. However, there is still some tension between ionized and molecular line tracers (i.e., CO), which requires optimization of the cloud structure and the density of the molecular zone. The limited range of parameters over which predictions match observations allows us to constrain, in spite of degeneracies in the parameter space, the intensity of X-ray radiation bathing filaments, as well as some of their physical properties like A V or the level of turbulent heating rate. Conclusions. The reprocessing of the EUV and X-ray radiation from the plasma cooling is an important powering source of line emission from filaments surrounding BCGs. C LOUDY self-irradiated X-ray excitation models coupled with a small level of turbulent heating manage to simultaneously reproduce a large number of optical-to-infrared line ratios when all the gas phases (from ionized to molecular) are modeled self-consistently. Releasing some of the simplifications of our model, like the constant pressure, or adding the radiation fields from the AGN and stars, as well as a combination of matter- and radiation-bounded cloud distribution, should improve the predictions of line emission from the different gas phases. 

ABSTRACT We present Atacama Large Millimetre/submillimetre Array observations of the brightest cluster galaxy Hydra-A, a nearby (z = 0.054) giant elliptical galaxy with powerful and extended radio jets. The observations reveal CO(1−0), CO(2–1), 13CO(2–1), CN(2–1), SiO(5–4), HCO+(1–0), HCO+(2–1), HCN(1–0), HCN(2–1), HNC(1–0), and H2CO(3–2) absorption lines against the galaxy’s bright and compact active galactic nucleus. These absorption features are due to at least 12 individual molecular clouds that lie close to the centre of the galaxy and have velocities of approximately −50 to +10 km s−1 relative to its recession velocity, where positive values correspond to inward motion. The absorption profiles are evidence of a clumpy interstellar medium within brightest cluster galaxies composed of clouds with similar column densities, velocity dispersions, and excitation temperatures to those found at radii of several kpc in the Milky Way. We also show potential variation in a ∼10 km s−1 wide section of the absorption profile over a 2 yr time-scale, most likely caused by relativistic motions in the hot spots of the continuum source that change the background illumination of the absorbing clouds.