Jets from supermassive black holes in the centres of galaxy clusters are a potential candidate for moderating gas cooling and subsequent star formation through depositing energy in the intra-cluster gas. In this work, we simulate the jet-intra-cluster medium interaction using the moving-mesh magnetohydrodynamics code Arepo. Our model injects supersonic, low density, collimated and magnetised outflows in cluster centres, which are then stopped by the surrounding gas, thermalise and inflate low-density cavities filled with cosmic-rays. We perform high-resolution, non-radiative simulations of the lobe creation, expansion and disruption, and find that its dynamical evolution is in qualitative agreement with simulations of idealised low-density cavities that are dominated by a large-scale Rayleigh-Taylor instability. The buoyant rising of the lobe does not create energetically significant small-scale chaotic motion in a volume-filling fashion, but rather a systematic upward motion in the wake of the lobe and a corresponding back-flow perpendicular to it. We find that, overall, 50 per cent of the injected energy ends up in material which is not part of the lobe, and about 25 per cent remains in the inner 100 kpc. We conclude that jet-inflated, buoyantly rising cavities drive systematic gas motions which play an important role in heating the central regions, while mixing of lobe material is sub-dominant. Encouragingly, the main mechanisms responsible for this energy deposition can be modelled already at resolutions within reach in future, high-resolution cosmological simulations of galaxy clusters.

Multiphase galaxy winds, the accretion of cold gas through galaxy haloes, and gas stripping from jellyfish galaxies are examples of interactions between cold and hot gaseous phases. There are two important regimes in such systems. A sufficiently small cold cloud is destroyed by the hot wind as a result of Kelvin-Helmholtz instabilities, which shatter the cloud into small pieces that eventually mix and dissolve in the hot wind. On the contrary, stripped cold gas from a large cloud mixes with the hot wind to intermediate temperatures, and then becomes thermally unstable and cools, causing a net accretion of hot gas to the cold tail. Using the magneto-hydrodynamical code arepo, we perform cloud crushing simulations and test analytical criteria for the transition between the growth and destruction regimes to clarify a current debate in the literature. We find that the hot-wind cooling time sets the transition radius and not the cooling time of the mixed phase. Magnetic fields modify the wind-cloud interaction. Draping of wind magnetic field enhances the field upstream of the cloud and fluid instabilities are suppressed by a turbulently magnetised wind beyond what is seen for a wind with a uniform magnetic field. We furthermore predict jellyfish galaxies to have ordered magnetic fields aligned with their tails. We finally discuss how the results of idealised simulations can be used to provide input to subgrid models in cosmological (magneto-)hydrodynamical simulations, which cannot resolve the detailed small-scale structure of cold gas clouds in the circum-galactic medium.

Feedback processes by active galactic nuclei in the centres of galaxy clusters appear to prevent large-scale cooling flows and impede star formation. However, the detailed heating mechanism remains uncertain. One promising heating scenario invokes the dissipation of Alfvén waves that are generated by streaming cosmic rays (CRs). In order to study this idea, we use three-dimensional magneto-hydrodynamical simulations with the arepo code that follow the evolution of jet-inflated bubbles that are filled with CRs in a turbulent cluster atmosphere. We find that a single injection event produces the CR distribution and heating rate required for a successful CR heating model. As a bubble rises buoyantly, cluster magnetic fields drape around the leading interface and are amplified to strengths that balance the ram pressure. Together with helical magnetic fields in the bubble, this initially confines the CRs and suppresses the formation of interface instabilities. But as the bubble continues to rise, bubble-scale eddies significantly amplify radial magnetic filaments in its wake and enable CR transport from the bubble to the cooling intracluster medium. By varying the jet parameters, we obtain a rich and diverse set of jet and bubble morphologies ranging from Fanaroff-Riley type I-like (FRI) to FRII-like jets. We identify jet energy as the leading order parameter (keeping the ambient density profiles fixed), whereas jet luminosity is primarily responsible for setting the Mach numbers of shocks around FRII-like sources. Our simulations also produce FRI-like jets that inflate bubbles without detectable shocks and show morphologies consistent with cluster observations.

Non-relativistic shocks accelerate ions to highly relativistic energies provided that the orientation of the magnetic field is closely aligned with the shock normal (quasiparallel shock configuration). In contrast, quasi-perpendicular shocks do not efficiently accelerate ions. We model this obliquity-dependent acceleration process in a spherically expanding blast wave setup with the moving-mesh code arepo for different magnetic field morphologies, ranging from homogeneous to turbulent configurations. A Sedov-Taylor explosion in a homogeneous magnetic field generates an oblate ellipsoidal shock surface due to the slower propagating blast wave in the direction of the magnetic field. This is because of the efficient cosmic ray (CR) production in the quasi-parallel polar cap regions, which softens the equation of state and increases the compressibility of the post-shock gas. We find that the solution remains self-similar because the ellipticity of the propagating blast wave stays constant in time. This enables us to derive an effective ratio of specific heats for a composite of thermal gas and CRs as a function of the maximum acceleration efficiency. We finally discuss the behavior of supernova remnants expanding into a turbulent magnetic field with varying coherence lengths. For a maximum CR acceleration efficiency of about 15 per cent at quasi-parallel shocks (as suggested by kinetic plasma simulations), we find an average efficiency of about 5 per cent, independent of the assumed magnetic coherence length.

Radio relics in galaxy clusters are extended synchrotron sources produced by cosmic-ray electrons in the microgauss magnetic field. Many relics are found in the cluster periphery and have a cluster-centric, narrow arc-like shape, which suggests that the electrons are accelerated or reaccelerated by merger shock fronts propagating outward in the intracluster plasma. In the X-ray, some relics do exhibit such shocks at the location of the relic, but many do not. We explore the possibility that radio relics trace not the shock fronts but the shape of the underlying distribution of seed relativistic electrons, lit up by a recent shock passage. We use magnetohydrodynamic simulations of cluster mergers and include bubbles of relativistic electrons injected by jets from the central active galactic nucleus or from an off-center radio galaxy. We show that the merger-driven gas motions (a) can advect the bubble cosmic rays to very large radii and (b) spread the relativistic seed electrons preferentially in the tangential direction—along the gravitational equipotential surfaces—producing extended, filamentary, or sheet-like regions of intracluster plasma enriched with aged cosmic rays, which resemble radio relics. Once a shock front passes across such a region, the sharp radio emission edges would trace the sharp boundaries of these enriched regions rather than the front. We also show that these elongated cosmic-ray features are naturally associated with magnetic fields stretched tangentially along their long axis, which could help explain the high polarization of relics.