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Context. The degree of coupling between the gas and the magnetic field during the collapse of a core and the subsequent formation of a disk depends on the assumed dust size distribution. Aims. We study the impact of grain–grain coagulation on the evolution of magnetohydrodynamic (MHD) resistivities during the collapse of a prestellar core. Methods. We use a 1D model to follow the evolution of the dust size distribution, out-of-equilibrium ionisation state, and gas chemistry during the collapse of a prestellar core. To compute the grain–grain collisional rate, we consider models for both random and systematic, size-dependent, velocities. We include grain growth through grain–grain coagulation and ice accretion, but ignore grain fragmentation. Results. Starting with a Mathis-Rumpl-Nordsieck (MRN) size distribution (Mathis et al. 1977, ApJ, 217, 425), we find that coagulation in grain–grain collisions generated by hydrodynamical turbulence is not efficient at removing the smallest grains and, as a consequence, does not have a large effect on the evolution of the Hall and ambipolar diffusion MHD resistivities, which still drop significantly during the collapse like in models without coagulation. The inclusion of systematic velocities, possibly induced by the presence of ambipolar diffusion, increases the coagulation rate between small and large grains, removing small grains earlier in the collapse and therefore limiting the drop in the Hall and ambipolar diffusion resistivities. At intermediate densities ( n H ~ 10 8 cm −3 ), the Hall and ambipolar diffusion resistivities are found to be higher by 1 to 2 orders of magnitude in models with coagulation than in models where coagulation is ignored, and also higher than in a toy model without coagulation where all grains smaller than 0.1 μ m would have been removed in the parent cloud before the collapse. Conclusions. When grain drift velocities induced by ambipolar diffusion are included, dust coagulation happening during the collapse of a prestellar core starting from an initial MRN dust size distribution appears to be efficient enough to increase the MHD resistivities to the values necessary to strongly modify the magnetically regulated formation of a planet-forming disk. A consistent treatment of the competition between fragmentation and coagulation is, however, necessary before reaching firm conclusions. 

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.