The Anatomy of a Turbulent Radiative Mixing Layer: Insights from an Analytic Model with Turbulent Conduction and Viscosity

Turbulent Radiative Mixing Layers (TRMLs) form at the interface of cold, dense gas and hot, diffuse gas in motion with each other. TRMLs are ubiquitous in and around galaxies on a variety of scales, including galactic winds and the circumgalactic medium. They host the intermediate temperature gases that are efficient in radiative cooling, thus play a crucial role in controlling the cold gas supply, phase structure, and spectral features of galaxies. In this work, we introduce a simple parameterization of the effective turbulent conductivity and viscosity that enables us to develop a simple and intuitive analytic 1.5 dimensional model for TRMLs. Our analytic model reproduces the mass flux, total cooling, and phase structure of 3D simulations of TRMLs at a fraction of the computational cost. It also reveals essential insights into the physics of TRMLs, particularly the importance of the viscous dissipation of relative kinetic energy in balancing radiative cooling. This dissipation takes place both in the intermediate temperature phase, which offsets the enthalpy flux from the hot phase, and in the cold phase, which enhances radiative cooling. Additionally, our model provides a fast and easy way of computing the column density and surface brightness of TRMLs, which can be directly linked to observations.Comment: 32 pages, 22 figures. Submitted to Ap

Plasmoid Instability in the Multiphase Interstellar Medium

The processes controlling the complex clump structure, phase distribution, and magnetic field geometry that develops across a broad range of scales in the turbulent interstellar medium remains unclear. Using unprecedentedly high resolution three-dimensional magnetohydrodynamic simulations of thermally unstable turbulent systems, we show that large current sheets unstable to plasmoid-mediated reconnection form regularly throughout the volume. The plasmoids form in three distinct environments: (i) within cold clumps, (ii) at the asymmetric interface of the cold and warm phases, and (iii) within the warm, volume-filling phase. We then show that the complex magneto-thermal phase structure is characterized by a predominantly highly magnetized cold phase, but that regions of high magnetic curvature, which are the sites of reconnection, span a broad range in temperature. Furthermore, we show that thermal instabilities change the scale dependent anisotropy of the turbulent magnetic field, reducing the increase in eddy elongation at smaller scales. Finally, we show that most of the mass is contained in one contiguous cold structure surrounded by smaller clumps that follow a scale free mass distribution. These clumps tend to be highly elongated and exhibit a size versus internal velocity relation consistent with supersonic turbulence, and a relative clump distance-velocity scaling consistent with subsonic motion. We discuss the striking similarity of cold plasmoids to observed tiny scale atomic and ionized structures and HI fibers, and consider how the prevalence of plasmoids will modify the motion of charged particles thereby impacting cosmic ray transport and thermal conduction in the ISM and other similar systems.Comment: 19 pages, 10 figures. For associated movies, see https://dfielding14.github.io/movies

TuRMoiL of Survival: A Unified Survival Criterion for Cloud-Wind Interactions

Cloud-wind interactions play an important role in long-lived multiphase flows in many astrophysical contexts. When this interaction is primarily mediated by hydrodynamics and radiative cooling, the survival of clouds can be phrased in terms of the comparison between a timescale that dictates the evolution of the cloud-wind interaction, (the dynamical time-scale $\tau_{\rm dyn}$) and the relevant cooling timescale $\tau_{\rm cool}$. Previously proposed survival criteria, which can disagree by large factors about the size of the smallest surviving clouds, differ in both their choice of $\tau_{\rm cool}$ and (to a lesser extent) $\tau_{\rm dyn}$. Here we present a new criterion which agrees with a previously proposed empirical formulae but is based on simple physical principles. The key insight is that clouds can grow if they are able to mix and cool gas from the hot wind faster than it advects by the cloud. Whereas prior criteria associate $\tau_{\rm dyn}$ with the cloud crushing timescale, our new criterion links it to the characteristic cloud-crossing timescale of a hot-phase fluid element, making it more physically consistent with shear-layer studies. We develop this insight into a predictive expression and validate it with hydrodynamic ENZO-E simulations of ${\sim}10^4\, {\rm K}$, pressure-confined clouds in hot supersonic winds, exploring, in particular, high wind/cloud density contrasts, where disagreements are most pronounced. Finally, we illustrate how discrepancies among previous criteria primarily emerged due to different choices of simulation conditions and cooling properties, and discuss how they can be reconciled.Comment: 6.5 pages, 4 figures, submitted to ApJ

CloudFlex: A Flexible Parametric Model for the Small-Scale Structure of the Circumgalactic Medium

We present CloudFlex, a new open-source tool for predicting the absorption-line signatures of cool gas in galaxy halos with complex small-scale structure. Motivated by analyses of cool material in hydrodynamical simulations of turbulent, multiphase media, we model individual cool gas structures as assemblies of cloudlets with a power-law distribution of cloudlet mass $\propto m_{\rm cl}^{-\alpha}$ and relative velocities drawn from a turbulent velocity field. The user may specify $\alpha$, the lower limit of the cloudlet mass distribution ($m_{\rm cl,min}$), and several other parameters that set the total mass, size, and velocity distribution of the complex. We then calculate the MgII 2796 absorption profiles induced by the cloudlets along pencil-beam lines of sight. We demonstrate that at fixed metallicity, the covering fraction of sightlines with equivalent widths $W_{2796} < 0.3$ Ang increases significantly with decreasing $m_{\rm cl,min}$, cool cloudlet number density ($n_{\rm cl}$), and cloudlet complex size. We then present a first application, using this framework to predict the projected $W_{2796}$ distribution around ${\sim}L^*$ galaxies. We show that the observed incidences of $W_{2796}>0.3$ Ang sightlines within 10 kpc < $R_{\perp}$ < 50 kpc are consistent with our model over much of parameter space. However, they are underpredicted by models with $m_{\rm cl,min}\ge100M_{\odot}$ and $n_{\rm cl}\ge0.03$ $\rm cm^{-3}$, in keeping with a picture in which the inner cool circumgalactic medium (CGM) is dominated by numerous low-mass cloudlets ($m_{\rm cl}\lesssim100M_{\odot}$) with a volume filling factor ${\lesssim}1\%$. When used to simultaneously model absorption-line datasets built from multi-sightline and/or spatially-extended background probes, CloudFlex will enable detailed constraints on the size and velocity distributions of structures comprising the photoionized CGM.Comment: 22 pages, 7 figures. Submitted to AAS Journals, with minor modifications. Comments welcome. (1) Co-first authors who made equal contributions to this wor

Multiphase Gas and the Fractal Nature of Radiative Turbulent Mixing Layers

A common situation in galactic and intergalactic gas involves cold dense gas in motion relative to hot diffuse gas. Kelvin-Helmholtz instability creates a turbulent mixing layer and populates the intermediate-temperature phase, which often cools rapidly. The energy lost to cooling is balanced by the advection of hot high enthalpy gas into the mixing layer, resulting in growth and acceleration of the cold phase. This process may play a major role in determining the interstellar medium and circumgalactic medium phase structure, and accelerating cold gas in galactic winds and cosmic filaments. Cooling in these mixing layers occurs in a thin corrugated sheet, which we argue has an area with fractal dimension $D=5/2$ and a thickness that adjusts to match the hot phase mixing time to the cooling time. These cooling sheet properties form the basis of a new model for how the cooling rate and hot gas inflow velocity depend on the size $L$, cooling time $t_{\rm cool}$, relative velocity $v_{\rm rel}$, and density contrast $\rho_{\rm cold}/\rho_{\rm hot}$ of the system. Entrainment is expected to be enhanced in environments with short $t_{\rm cool}$, large $v_{\rm rel}$, and large $\rho_{\rm cold}/\rho_{\rm hot}$. Using a large suite of three dimensional hydrodynamic simulations, we demonstrate that this fractal cooling layer model accurately captures the energetics and evolution of turbulent interfaces and can therefore be used as a foundation for understanding multiphase mixing with strong radiative cooling.Comment: 11 pages, 5 figures, submitted to ApJL. Movies can be found here https://dfielding14.github.io/movies

Regulation of Star Formation by a Hot Circumgalactic Medium

Galactic outflows driven by supernovae (SNe) are thought to be a powerful regulator of a galaxy's star-forming efficiency. Mass, energy, and metal outflows ($\eta_M$, $\eta_E$, and $\eta_Z$, here normalized by the star formation rate, the SNe energy and metal production rates, respectively) shape galaxy properties by both ejecting gas and metals out of the galaxy and by heating the circumgalactic medium (CGM), preventing future accretion. Traditionally, models have assumed that galaxies self-regulate by ejecting a large fraction of the gas which enters the interstellar medium (ISM), even though such high mass-loadings are in growing tension with observations. To better understand how the relative importance of ejective (i.e. high mass-loading) vs preventative (i.e. high energy-loading) feedback affects the present-day properties of galaxies, we develop a simple gas-regulator model of galaxy evolution, where the stellar mass, ISM, and CGM are modeled as distinct reservoirs which exchange mass, metals, and energy at different rates within a growing halo. Focusing on the halo mass range from $10^{10}$ to $10^{12} M_{\odot}$, we demonstrate that, with reasonable parameter choices, we can reproduce the stellar-to-halo mass relation and the ISM-to-stellar mass relation with low mass-loaded ($\eta_M \sim 0.1-10$) but high energy-loaded ($\eta_E \sim 0.1-1$) winds, with self-regulation occurring primarily through heating and cooling of the CGM. We show that the model predictions are robust against changes to the mass-loading of outflows but are quite sensitive to our choice of the energy-loading, preferring $\eta_E \sim 1$ for the lowest mass halos and $\sim 0.1$ for Milky Way-like halos.Comment: 19 pages, 9 Figures, submitted to Ap

Impact of Cosmic Rays on Thermal Instability in the Circumgalactic Medium

Large reservoirs of cold (~10⁴ K) gas exist out to and beyond the virial radius in the circumgalactic medium (CGM) of all types of galaxies. Photoionization modeling suggests that cold CGM gas has significantly lower densities than expected by theoretical predictions based on thermal pressure equilibrium with hot CGM gas. In this work, we investigate the impact of cosmic-ray physics on the formation of cold gas via thermal instability. We use idealized three-dimensional magnetohydrodynamic simulations to follow the evolution of thermally unstable gas in a gravitationally stratified medium. We find that cosmic-ray pressure lowers the density and increases the size of cold gas clouds formed through thermal instability. We develop a simple model for how the cold cloud sizes and the relative densities of cold and hot gas depend on cosmic-ray pressure. Cosmic-ray pressure can help counteract gravity to keep cold gas in the CGM for longer, thereby increasing the predicted cold mass fraction and decreasing the predicted cold gas inflow rates. Efficient cosmic-ray transport, by streaming or diffusion, redistributes cosmic-ray pressure from the cold gas to the background medium, resulting in cold gas properties that are in between those predicted by simulations with inefficient transport and simulations without cosmic rays. We show that cosmic rays can significantly reduce galactic accretion rates and resolve the tension between theoretical models and observational constraints on the properties of cold CGM gas