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ABSTRACT In classical diffusion, particle step-sizes have a Gaussian distribution. However, in superdiffusion, they have power-law tails, with transport dominated by rare, long ‘Lévy flights’. Similarly, if the time interval between scattering events has power-law tails, subdiffusion occurs. Both forms of anomalous diffusion are seen in cosmic ray (CR) particle tracking simulations in turbulent magnetic fields. They also likely occur if CRs are scattered by discrete intermittent structures, as recently suggested. Anomalous diffusion mimics a scale-dependent diffusion coefficient, with potentially wide-ranging consequences. However, the finite size of galaxies implies an upper bound on step-sizes before CRs escape. This truncation results in eventual convergence to Gaussian statistics by the central limit theorem. Using Monte-Carlo simulations, we show that this occurs in both standard finite-thickness halo models, or when CR diffusion transitions to advection or streaming-dominated regimes. While optically thick intermittent structures produce power-law trapping times and thus subdiffusion, ‘Gaussianization’ also eventually occurs on time-scales longer than the maximum trapping time. Anomalous diffusion is a transient, and converges to standard diffusion on the (usually short) time-scale of particle escape, either from confining structures (subdiffusion), or the system as a whole (superdiffusion). Thus, standard assumptions of classical diffusion are physically justified in most applications, despite growing simulation evidence for anomalous diffusion. However, if escape times are long, this is no longer true. For instance, anomalous diffusion in the CGM or ICM would change CR pressure profiles. Finally, we show the standard diagnostic for anomalous diffusion, $$\langle d^2 \rangle \propto t^{\alpha }$$ with $$\alpha \ne 1$$, is not justified for truncated Lévy flights, and propose an alternative robust measure. 

ABSTRACT Radiative cooling can drive dynamics in multiphase gas. A dramatic example is hydrodynamic ‘shattering’, the violent pressure-driven fragmentation of a cooling cloud that falls drastically out of pressure balance with its surroundings. We run magnetohydrodynamic (MHD) simulations to understand how shattering is influenced by magnetic fields. In MHD, clouds do not ‘shatter’ chaotically. Instead, after initial fragmentation, both hot and cold phases coherently ‘stream’ in long-lived field-aligned self-sustaining gas flows, at high speed ($$\sim 100 \, {\rm km \, s^{-1}}$$). MHD thermal instability also produces such flows. They are due to the anisotropic nature of MHD pressure support, which only operates perpendicular to B-fields. Thus, even when $$P_{\rm B} + P_{\rm gas} \approx$$const, pressure balance only holds perpendicular to B-fields. Field-aligned gas pressure variations are unopposed, and results in gas velocities $$v \sim (2 \Delta P/\rho)^{1/2}$$ from Bernoulli’s principle. Strikingly, gas in adjacent flux tubes counter-stream in opposite directions. We show this arises from a cooling-induced MHD version of the thin shell instability. Magnetic tension is important both in enabling corrugational instability and modifying its non-linear evolution. Even in high $$\beta$$ hot gas, streaming can arise, since magnetic pressure support grows as gas cools and compresses. Thermal conduction increases the sizes and velocities of streaming cloudlets, but does not qualitatively modify dynamics. These results are relevant to the counter-streaming gas flows observed in solar coronal rain, as well as multiphase gas cooling and condensation in the interstellar medium, circumgalactic medium, and intracluster medium. 

Abstract The circumgalactic medium (CGM) is poorly constrained at the subparsec scales relevant to turbulent energy dissipation and regulation of multiphase structure. Fast radio bursts are sensitive to small-scale plasma density fluctuations, which can induce multipath propagation (scattering). The amount of scattering depends on the density fluctuation spectrum, including its amplitude $C_{\mathrm{n}}^2$, spectral indexβ, and dissipation scalel_i. We use quasar observations of CGM turbulence at ≳pc scales to infer $C_{\mathrm{n}}^2$, finding it to be $10^{-16}\lesssim C_{\mathrm{n}}^2\lesssim 10^{-9}$m^−20/3for hot (T> 10⁶K) gas and $10^{-8}\lesssim C_{\mathrm{n}}^2\lesssim 10^{-4}$m^−20/3for cool (10⁴≲T≲ 10⁵K) gas, depending on the gas sound speed and density. These values of $C_{\mathrm{n}}^2$are much smaller than those inferred in the interstellar medium at similar physical scales. The resulting scattering delays from the hot CGM are negligible (≪1μs at 1 GHz), but they are more detectable from the cool gas as either radio pulse broadening or scintillation, depending on the observing frequency and sightline geometry. Joint quasar-FRB observations of individual galaxies can yield lower limits onl_i, even if the CGM is not a significant scattering site. An initial comparison between quasar and FRB observations (albeit for different systems) suggestsl_i≳ 750 km in ∼10⁴K gas in order for the quasar and FRB constraints to be consistent. If a foreground CGM is completely ruled out as a source of scattering along an FRB sightline, thenl_imay be comparable to the smallest cloud sizes (≲pc) inferred from photoionization modeling of quasar absorption lines. 

ABSTRACT The observed star formation and wind outflow rates in galaxies suggest cold gas must be continually replenished via infalling clouds or streams. Previous studies have highlighted the importance of cooling-induced condensation on such gas, which enables survival, mass growth, and a drag force which typically exceeds hydrodynamic drag. However, the combined effects of magnetic fields, cooling, and infall remain unexplored. We conduct 3D magnetohydrodynamic simulations of radiatively cooling infalling clouds and streams in uniform and stratified backgrounds. For infalling clouds, magnetic fields aligned with gravity do not impact cloud growth or dynamics significantly, although we see enhanced survival for stronger fields. In contrast, even weak transverse magnetic fields can significantly slow cloud infall via magnetic drag. This effect arises when strong ‘draped’ fields form at the cloud’s peak infall velocity, just before it decelerates. Besides enhancing survival, slow infall increases total cloud mass growth compared to the hydrodynamic case, even if reduced turbulent mixing lowers the mass growth rate. Streams often result in qualitatively different behaviour. Mass growth and hence accretion drag are generally much lower in hydrodynamic streams. Unlike in clouds, aligned magnetic fields suppress mixing and thus both mass growth or loss. Transverse fields do apply magnetic drag and allow streams to grow, when streams have a ‘head’ pushing through the medium. Overall, regardless of the efficacy of drag forces, streams are surprisingly robust in realistic potentials, as the destruction time when falling supersonically exceeds the infall time. We develop analytic models which reproduce cloud/stream trajectories. 

ABSTRACT Theory and observations reveal that the circumgalactic medium (CGM) and the cosmic web at high redshifts are multiphase, with small clouds of cold gas embedded in a hot, diffuse medium. We study the ‘shattering’ of large, thermally unstable clouds into tiny cloudlets of size $$\ell _{\rm shatter}\sim {\rm min}(c_{\rm s}t_{\rm cool})$$ using idealized numerical simulations. We expand upon previous works by exploring the effects of cloud geometry (spheres, streams, and sheets), metallicity, and an ionizing ultraviolet background. We find that ‘shattering’ is mainly triggered by clouds losing sonic contact and rapidly imploding, leading to a reflected shock that causes the cloud to re-expand and induces Richtmyer–Meshkov instabilities at its interface. The fragmented cloudlets experience a drag force from the surrounding hot gas, leading to recoagulation into larger clouds. We distinguish between ‘fast’ and ‘slow’ coagulation regimes. Sheets are always in the ‘fast’ coagulation regime, while streams and spheres transition to ‘slow’ coagulation above a critical overdensity, which is smallest for spheres. Surprisingly, $$\ell _\mathrm{shatter}$$ does not appear to be a characteristic clump size even if it is well resolved. Rather, fragmentation continues until the grid scale with a mass distribution of $$N(\gt m)\propto m^{-1}$$. We apply our results to cold streams feeding massive ($$M_{\rm v}\lower.5ex\rm{\,\, \buildrel\gt \over \sim \,\,}10^{12}\, {\rm M}_\odot$$) galaxies at $$z\lower.5ex\rm{\,\, \buildrel\gt \over \sim \,\,}2$$ from the cosmic web, finding that streams likely shatter upon entering the hot CGM through the virial shock. This could explain the large clumping factors and covering fractions of cold gas around such galaxies, and may be related to galaxy quenching by preventing cold streams from reaching the central galaxy. 

Abstract While it is well known that cosmic rays (CRs) can gain energy from turbulence via second-order Fermi acceleration, how this energy transfer affects the turbulent cascade remains largely unexplored. Here, we show that damping and steepening of the compressive turbulent power spectrum are expected once the damping time t damp ∼ ρ v 2 / E ̇ CR ∝ E CR − 1 becomes comparable to the turbulent cascade time. Magnetohydrodynamic simulations of stirred compressive turbulence in a gas-CR fluid with diffusive CR transport show clear imprints of CR-induced damping, saturating at E ̇ CR ∼ ϵ ˜ , where ϵ ˜ is the turbulent energy input rate. In that case, almost all of the energy in large-scale motions is absorbed by CRs and does not cascade down to grid scale. Through a Hodge–Helmholtz decomposition, we confirm that purely compressive forcing can generate significant solenoidal motions, and we find preferential CR damping of the compressive component in simulations with diffusion and streaming, rendering small-scale turbulence largely solenoidal, with implications for thermal instability and proposed resonant scattering of E ≳ 300 GeV CRs by fast modes. When CR transport is streaming dominated, CRs also damp large-scale motions, with kinetic energy reduced by up to 1 order of magnitude in realistic E CR ∼ E g scenarios, but turbulence (with a reduced amplitude) still cascades down to small scales with the same power spectrum. Such large-scale damping implies that turbulent velocities obtained from the observed velocity dispersion may significantly underestimate turbulent forcing rates, i.e., ϵ ˜ ≫ ρ v 3 / L . 

ABSTRACT Astrophysical gases such as the interstellar-, circumgalactic-, or intracluster-medium are commonly multiphase, which poses the question of the structure of these systems. While there are many known processes leading to fragmentation of cold gas embedded in a (turbulent) hot medium, in this work, we focus on the reverse process: coagulation. This is often seen in wind-tunnel and shearing layer simulations, where cold gas fragments spontaneously coalesce. Using 2D and 3D hydrodynamical simulations, we find that sufficiently large (≫cstcool), perturbed cold gas clouds develop pulsations which ensure cold gas mass growth over an extended period of time (≫r/cs). This mass growth efficiently accelerates hot gas which in turn can entrain cold droplets, leading to coagulation. The attractive inverse square force between cold gas droplets has interesting parallels with gravity; the ‘monopole’ is surface area rather than mass. We develop a simple analytic model which reproduces our numerical findings. 

Abstract We investigate how cosmic rays (CRs) affect thermal and hydrostatic stability of circumgalactic (CGM) gas, in simulations with both CR streaming and diffusion. Local thermal instability can be suppressed by CR-driven entropy mode propagation, in accordance with previous analytic work. However, there is only a narrow parameter regime where this operates, before CRs overheat the background gas. As mass dropout from thermal instability causes the background density and hence plasma β ≡ Pg/PB to fall, the CGM becomes globally unstable. At the cool disk to hot halo interface, a sharp drop in density boosts Alfven speeds and CR gradients, driving a transition from diffusive to streaming transport. CR forces and heating strengthen, while countervailing gravitational forces and radiative cooling weaken, resulting in a loss of both hydrostatic and thermal equilibrium. In lower β halos, CR heating drives a hot, single-phase diffuse wind with velocities v∝(theat/tff)−1, which exceeds the escape velocity when theat/tff ≲ 0.4. In higher β halos, where the Alfven Mach number is higher, CR forces drive multi-phase winds with cool, dense fountain flows and significant turbulence. These flows are CR dominated due to ‘trapping’ of CRs by weak transverse B-fields, and have the highest mass loading factors. Thus, local thermal instability can result in winds or fountain flows where either the heat or momentum input of CRs dominates. 

Spurred by rich, multiwavelength observations and enabled by new simulations, ranging from cosmological to subparsec scales, the past decade has seen major theoretical progress in our understanding of the circumgalactic medium (CGM). We review key physical processes in the CGM. Our conclusions include the following: ▪ The properties of the CGM depend on a competition between gravity-driven infall and gas cooling. When cooling is slow relative to free fall, the gas is hot (roughly virial temperature), whereas the gas is cold ( T ∼ 10⁴K) when cooling is rapid. ▪ Gas inflows and outflows play crucial roles, as does the cosmological environment. Large-scale structure collimates cold streams and provides angular momentum. Satellite galaxies contribute to the CGM through winds and gas stripping. ▪ In multiphase gas, the hot and cold phases continuously exchange mass, energy, and momentum. The interaction between turbulent mixing and radiative cooling is critical. A broad spectrum of cold gas structures, going down to subparsec scales, arises from fragmentation, coagulation, and condensation onto gas clouds. ▪ Magnetic fields, thermal conduction, and cosmic rays can substantially modify how the cold and hot phases interact, although microphysical uncertainties are presently large. Key open questions for future work include the mutual interplay between small-scale structure and large-scale dynamics, and how the CGM affects the evolution of galaxies. 

ABSTRACT Understanding the survival, growth, and dynamics of cold gas is fundamental to galaxy formation. While there has been a plethora of work on ‘wind tunnel’ simulations that study such cold gas in winds, the infall of this gas under gravity is at least equally important, and fundamentally different since cold gas can never entrain. Instead, velocity shear increases and remains unrelenting. If these clouds are growing, they can experience a drag force due to the accretion of low-momentum gas, which dominates over ram pressure drag. This leads to subvirial terminal velocities, in line with observations. We develop simple analytic theory and predictions based on turbulent radiative mixing layers. We test these scalings in 3D hydrodynamic simulations, both for an artificial constant background and a more realistic stratified background. We find that the survival criterion for infalling gas is more stringent than in a wind, requiring that clouds grow faster than they are destroyed ($$t_{\rm grow} \lt 4\, t_{\rm cc}$$). This can be translated to a critical pressure, which for Milky Way-like conditions is $$P \sim 3000 \, {k}_\mathrm{ B} \, {\rm K}\, {\rm cm}^{-3}$$. Cold gas that forms via linear thermal instability (tcool/tff < 1) in planar geometry meets the survival threshold. In stratified environments, larger clouds need only survive infall until cooling becomes effective. We discuss applications to high-velocity clouds and filaments in galaxy clusters.