We study the interplay among cooling, heating, conduction and magnetic fields in gravitationally stratified plasmas using simplified, plane‐parallel numerical simulations. Since the physical heating mechanism remains uncertain in massive haloes such as groups or clusters, we adopt a simple, phenomenological prescription which enforces global thermal equilibrium and prevents a cooling flow. The plasma remains susceptible to local thermal instability, however, and cooling drives an inward flow of material. For physically plausible heating mechanisms in clusters, the thermal stability of the plasma is independent of its convective stability. We find that the ratio of the cooling time‐scale to the dynamical time‐scale tcool/tff controls the non‐linear evolution and saturation of the thermal instability: when tcool/tff≲ 1, the plasma develops extended multiphase structure, whereas when tcool/tff≳ 1 it does not. (In a companion paper, we show that the criterion for thermal instability in a more realistic, spherical potential is somewhat less stringent, tcool/tff≲ 10.) When thermal conduction is anisotropic with respect to the magnetic field, the criterion for multiphase gas is essentially independent of the thermal conductivity of the plasma. Our criterion for local thermal instability to produce multiphase structure is an extension of the cold versus hot accretion modes in galaxy formation that applies at all radii in hot haloes, not just to the virial shock. We show that this criterion is consistent with data on multiphase gas in galaxy groups and clusters; in addition, when tcool/tff≳ 1, the net cooling rate to low temperatures and the mass flux to small radii are suppressed enough relative to models without heating to be qualitatively consistent with star formation rates and X‐ray line emission in groups and clusters.

We present global multidimensional numerical simulations of the plasma that pervades the dark matter haloes of clusters, groups and massive galaxies (the 'intracluster medium'; ICM). Observations of clusters and groups imply that such haloes are roughly in global thermal equilibrium, with heating balancing cooling when averaged over sufficiently long time-and length-scales; the ICM is, however, very likely to be locally thermally unstable. Using simple observationally motivated heating prescriptions, we show that local thermal instability (TI) can produce a multiphase medium -with ∼10 4 K cold filaments condensing out of the hot ICMonly when the ratio of the TI time-scale in the hot plasma (t TI ) to the free-fall time-scale (t ff ) satisfies t TI /t ff 10. This criterion quantitatively explains why cold gas and star formation are preferentially observed in low-entropy clusters and groups. In addition, the interplay among heating, cooling and TI reduces the net cooling rate and the mass accretion rate at small radii by factors of ∼100 relative to cooling-flow models. This dramatic reduction is in line with observations. The feedback efficiency required to prevent a cooling flow is ∼10 −3 for clusters and decreases for lower mass haloes; supernova heating may be energetically sufficient to balance cooling in galactic haloes. We further argue that the ICM self-adjusts so that t TI /t ff 10 at all radii. When this criterion is not satisfied, cold filaments condense out of the hot phase and reduce the density of the ICM. These cold filaments can power the black hole and/or stellar feedback required for global thermal balance, which drives t TI /t ff 10. In comparison to clusters, groups have central cores with lower densities and larger radii. This can account for the deviations from self-similarity in the X-ray luminosity-temperature (L X -T X ) relation. The high-velocity clouds observed in the Galactic halo can be due to local TI producing multiphase gas close to the virial radius if the density of the hot plasma in the Galactic halo is 10 −5 cm −3 at large radii.

We find that clouds of optically-thin, pressure-confined gas are prone to fragmentation as they cool below ∼ 10 6 K. This fragmentation follows the lengthscale ∼ c s t cool , ultimately reaching very small scales (∼ 0.1 pc/n) as they reach the temperature ∼ 10 4 K at which hydrogen recombines. While this lengthscale depends on the ambient pressure confining the clouds, we find that the column density through an individual fragment N cloudlet ∼ 10 17 cm −3 is essentially independent of environment; this column density represents a characteristic scale for atomic gas at 10 4 K. We therefore suggest that "clouds" of cold, atomic gas may in fact have the structure of a mist or a fog, composed of tiny fragments dispersed throughout the ambient medium. We show that this scale emerges in hydrodynamic simulations, and that the corresponding increase in the surface area may imply rapid entrainment of cold gas. We also apply it to a number of observational puzzles, including the large covering fraction of diffuse gas in galaxy halos, the broad line widths seen in quasar and AGN spectra, and the entrainment of cold gas in galactic winds. While our simulations make a number of assumptions and thus have associated uncertainties, we show that this characteristic scale is consistent with a number of observations, across a wide range of astrophysical environments. We discuss future steps for testing, improving, and extending our model.

We present three-dimensional magnetohydrodynamic simulations of magnetized gas clouds accelerated by hot winds. We initialize gas clouds with tangled internal magnetic fields and show that this field suppresses the disruption of the cloud: rather than mixing into the hot wind as found in hydrodynamic simulations, cloud fragments end up co-moving and in pressure equilibrium with their surroundings. We also show that a magnetic field in the hot wind enhances the drag force on the cloud by a factor ∼ (1 + v 2 A /v 2 wind ), where v A is the Alfven speed in the wind and v wind measures the relative speed between the cloud and the wind. We apply this result to gas clouds in several astrophysical contexts, including galaxy clusters, galactic winds, the Galactic center, and the outskirts of the Galactic halo. Our results can explain the prevalence of cool gas in galactic winds and galactic halos and how such cool gas survives in spite of its interaction with hot wind/halo gas. We also predict that drag forces can lead to a deviation from Keplerian orbits for the G2 cloud in the galactic center.