Woven by the Whirls: The growth and entrainment of cold clouds in turbulent hot winds

TL;DR

This study addresses how external subsonic turbulence in a hot galactic wind influences the survival and entrainment of cold, dense clouds. Using 3D hydrodynamic simulations with radiative cooling and driven turbulence, the authors map outcomes across a range of $t_{\rm cool,mix}/t_{cc}$ and turbulent Mach numbers, and derive a modified survival criterion $t_{\rm cool,mix}/\tilde{t}_{cc} < 1$ with $\tilde{t}_{cc}= t_{cc} / \sqrt{1+\left(\mathcal{M}_{\rm turb}/\left(f_{\rm mix}\mathcal{M}_{\rm wind}\right)\right)^2}$, where $f_{\rm mix} \sim 0.6$. They find that in the fast cooling regime turbulence can boost cold gas growth by up to an order of magnitude due to increased surface area for mixing, and that clouds entrain more rapidly, with $t_{\rm ent} \sim 0.2\,t_{\rm drag}$ at high $\mathcal{M}_{\rm turb}$. The work also shows dramatic changes in cloud morphology from long tails to fluffed, orthogonally spread structures and predicts observable signatures in MgII absorption profiles. These results imply higher cold gas loading and altered observational diagnostics in galactic winds and CGM, and they highlight the need to incorporate wind turbulence in subgrid models and large-scale simulations.

Abstract

Galactic and intergalactic flows often exhibit relative motion between the cold dense gas and the hot diffuse medium. Such multiphase flows -- involving gas at different temperatures, densities, and ionization states -- for instance, galactic winds, are frequently turbulent. However, idealized simulations typically model the winds and driven turbulence separately, despite their intertwined roles in galaxy evolution. To address this, we investigate the survival of a dense cloud in a hot wind subject to continuous external turbulent forcing. We perform 3D hydrodynamic simulations across a range of turbulent Mach numbers in the hot phase $\mathcal{M}_{\rm turb}=v_{\rm turb}/c_{\rm s, wind}$ from 0.1 to 0.7 ($c_{\rm s, wind}$ and $v_{\rm turb}$ being the sound speed and the turbulent velocity in the hot phase, respectively). We find that in spite of the additional subsonic turbulence, cold clouds can survive if the cooling time of the mixed gas $t_{\rm cool, mix}$ is shorter than a modified destruction time $\tilde{t}_{\rm cc}$, i.e., $t_{\rm cool,mix}/\tilde{t}_{\rm cc}<1$ where $\tilde{t}_{\rm cc}=t_{\rm cc}/(1+\left(\mathcal{M}_{\rm turb}/\left(f_{\rm mix}\mathcal{M}_{\rm wind}\right)\right)^2)^{1/2}$, where $f_{\rm mix}\sim0.6$ is a fudge factor. Moreover, in the `survival regime', turbulence can enhance the growth of cold clouds by up to an order of magnitude because of more efficient stretching and an associated increase in the surface area. This increase in mass transfer between the phases leads to significantly faster entrainment of cold material in turbulent winds. In contrast to the narrow filamentary tails formed in laminar winds, turbulence stretches the cold gas orthogonally, dispersing it over a larger area and changing absorption line signatures.

Figures (15)

• Figure 1: Projected column density of a cloud moving through a turbulent wind at various strengths of turbulent Mach number $\mathcal{M}_{\rm turb}$ (increasing from top to bottom). The [left column] shows the cloud evolution in the weak cooling regime ($t_{\rm cool,mix}/t_{\rm cc}=10^{-1}$), while the [right column] shows the state in the strong cooling regime ($t_{\rm cool,mix}/t_{\rm cc}=10^{-3}$). All the snapshots are taken at $8 t_{\rm cc}$, where $t_{\rm cc}\sim \chi^{1/2}R_{\rm cl}/v_{\rm rel}$ is the standard cloud crushing time and the cloud is moving towards right (along $\hat{x}$; as indicated by the arrow in bottom left panel) with velocity $v_{\rm rel}$ in a hot medium that is continuously stirred by external turbulent forcing. All panels show selected regions of the simulation domain, with a cyan cross marking the cloud’s initial position whenever visible. The turbulent Mach number in the hot medium $\mathcal{M}_{\rm turb}=v_{\rm turb} /c_{\rm s, wind}$ ($v_{\rm turb}$ and $c_{\rm s, wind}$ are the rms turbulent velocity and sound speed in the hot medium) is indicated on the left. Note that the morphology of tails of cold gas with and without turbulence is very different. Clouds in a turbulent wind are much more fluffier and stretched in the orthogonal direction, in comparison to the elongated streaks of cold mass when the cloud faces a uniform wind (top panels). Increased turbulent forcing enhances the cold gas mass (see $\overline{M}_{\rm cl}=M_{\rm cl}/M_{\rm cl,0}$ reported in each panel). The small relative velocity $\Delta v\sim |v_{\rm cl}-v_{\rm wind}|/v_{\rm rel}$ and displacement of the cloud $d$ observed at high $\mathcal{M}_{\rm turb}$, demonstrates that the cloud grows via a continuous accretion of mass and momentum from the increasing turbulent mixing layers in presence of stronger and stronger turbulent forcing. A curated playlist of videos illustrating the evolution of cold gas are available here: https://www.youtube.com/playlist?list=PLuwSozndVCNJzjKWqRO8u-GTCE0U8Zny2 .
• Figure 2: [Left panel]: Evolution of the cold mass $M_{\rm cl}$ (normalized by the initial cloud mass $M_{\rm cl,0}$) in units of cloud crushing time $t_{\rm cc}$ at various turbulent Mach numbers $\mathcal{M}_{\rm turb}=v_{\rm turb}/c_{\rm s, wind}$ and the ratio of the cooling time of the mixed gas to the cloud crushing time $t_{\rm cool, mix}/t_{\rm cc}$. [Right panel]: The relative velocity between the cloud and wind along the x-direction $v_{\rm cl}-v_{\rm wind}$ in units of the initial relative velocity $|v_{\rm cl,0}-v_{\rm wind,0}|$ plotted as a function of drag time $t_{\rm drag}\sim \chi R_{\rm cl}/v_{\rm wind}$. In both panels, the gray lines represent evolution in a laminar wind while the colored lines mark the evolution in a turbulent wind with strengths as indicated in the colorbar. In the left panel, the solid lines show how cold mass growth is enhanced in the fast cooling regime ($t_{\rm cool, mix}/t_{\rm cc} \sim 10^{-3}$). With increasing turbulence (higher $\mathcal{M}_{\rm turb}$ in magenta and cyan lines). Conversely, when cooling is weak ($t_{\rm cool, mix}/t_{\rm cc}\sim 1$), increasing turbulence hinders mass growth. This is demonstrated by the dashed colored lines, which show a reduced cold mass growth compared to the dashed gray line (without turbulence). As the turbulent forcing increases, it stretches and mixes the cold gas, leading the cloud to transition into the destruction regime (dashed cyan line ). Interestingly, in the right panel, the colored lines (with turbulence) fall steeply compared to the gray lines (without turbulence), suggesting a faster entrainment of clouds in winds with continuous turbulent forcing.
• Figure 3: The parameter space defined by the ratio $t_{\rm cool, mix}/t_{\rm cc}$ and the ratio of turbulent to wind Mach numbers $\mathcal{M}_{\rm turb}/\mathcal{M}_{\rm wind}$, illustrating the regimes for growth and destruction of clouds in cloud-crushing simulations with driven turbulence. Different markers represent various wind Mach numbers: circles, pentagons, squares and diamonds correspond to $\mathcal{M}_{\rm wind}=1.5, 0.65, 0.56,$ and $0.5$, respectively. Filled markers indicate growing clouds, while the hollow markers denote clouds that are eventually destroyed. We define a cloud as destroyed if the cold gas mass (see Fig. \ref{['fig:mass_growth']}) falls below 10% of the initial cloud mass $M_{\rm cl,0}$. Each point in the phase space is color-coded according to the cold gas mass growth rate $\dot{M}_{\rm cl}$ (in units of $M_{\rm cl,0}/t_{\rm cc}$) measured at $10\ t_{\rm cc}$, as indicated by the colormap. For clouds that are destroyed, the color reflects their destruction rate; if destruction occurs before $10\ t_{\rm cc}$, a fixed destruction rate of $\dot{M}_{\rm cl}=-0.7 M_{\rm cl,0}/t_{\rm cc}$ is used instead. As we move from left to right in the plot, the filled circles become progressively brighter green compared to the $\mathcal{M}_{\rm turb}=0$ case, indicating an enhancement of cold gas mass growth, especially at smaller values of $t_{\rm cool, mix}/t_{\rm cc}$. The modified criterion $t_{\rm cool, mix}/\tilde{t}_{\rm cc}<1$, where $\left.\tilde{t}_{\rm cc}= t_{\rm cc} \middle/\sqrt{1+\left(\mathcal{M}_{\rm turb}/f_{\rm mix}\mathcal{M}_{\rm wind}\right)^2}\right.$ with $f_{\rm mix}\sim0.6$, is shown in the solid gray line, which clearly separates the phase space into growth (shaded region in blue) and destruction (shaded region in pink) regimes.
• Figure 4: [Top panel]: Mass growth rate for the fast and moderate cooling regimes with different strengths of turbulent forcing. Different linestyles are for different $t_{\rm cool,mix}/t_{\rm cc}$. The line colors mark the evolution at different strengths of turbulent driving, as indicated in the colorbar. [Bottom panel]: area as a function of time for an isosurface considered at temperature threshold $T_{\rm thres}=2\times T_{\rm cl}$). Continuous turbulent forcing enhances dense mass growth in the growth regime, by an order of magnitude. Similarly, the surface area available for mixing is enhanced by an order of magnitude for most of the growing cases.
• Figure 5: Derived mixing velocity $v_{\rm mix}$ (in units of $c_{\rm s, cl}/(t_{\rm cool,cl}/t_{\rm sc,cl})^{-1/4}$) as a function of turbulent Mach number $\mathcal{M}_{\rm turb}$ in various cooling regimes $t_{\rm cool, mix}/t_{\rm cc}$ (indicated in the colormap). The triangles indicate the average mixing velocity between $10-20\ t_{\rm cc}$, with error bars showing its range within the specified time. The derived mixing velocity is therefore close to $\sim 0.2$, as found in standard cloud crushing simulations. Driven turbulence does not significantly affect the mixing velocity with which dense mass condenses onto the surface area available for cooling.