Fading in the Flow: Suppression of cold gas growth in expanding galactic outflows

TL;DR

This study demonstrates that adiabatic expansion of starburst-driven winds, modelled by the CC85 solution, suppresses the growth of radiatively cooled cold clouds embedded within the flow. Through 3D hydrodynamic simulations with cooling and a novel cloud-tracking scheme, clouds remain in approximate local pressure equilibrium with the expanding wind, causing their density contrasts to erode downstream and their mass growth to slow compared with plane-parallel winds. The work reveals that cloud expansion drives differential tail growth, produces elongated cometary morphologies, and yields strong head-to-tail emission gradients that align better with observations such as those of M82, while also indicating a back-reaction on the wind that can alter large-scale multiphase outflow properties. These results underscore the need to revise single-cloud and multiphase wind models to account for background expansion when predicting mass loading and emission signatures in galactic winds.

Abstract

Multiphase outflows, revealed by multi-wavelength observations, are crucial in redistributing gas and metals within and around galaxies. These outflows are often modelled theoretically using wind tunnel simulations of a cold ($\sim 10^4$ K) cloud interacting with a uniform hot ($\sim 10^6$ K) wind. However, real outflows expand downstream, a feature overlooked in most idealised simulations. We study how an expanding wind affects the survival, morphology, and dynamics of a cloud. We conduct idealised hydrodynamic simulations with optically thin radiative cooling of a cloud in an expanding wind, modelled using the adiabatic Chevalier & Clegg (1985) solution. We find that clouds remain locally isobaric with the wind, leading to a steep decline in their density contrast and eventual dissolution downstream. Compared to a plane-parallel wind, this suppresses cold gas mass growth because as clouds travel downstream, the surrounding mixed boundary layer becomes diffuse and less radiative. Our analytical scaling arguments show that cloud expansion and local pressure equilibrium are the key regulators of cold mass growth. Unlike traditional simulations, our model accounts for the differential expansion experienced by the long cometary tails of clouds in wind tunnels. This creates a strong head-to-tail emission gradient in the filamentary cold gas, which is more consistent with observations. We also demonstrate that the dynamics of individual clouds can substantially alter the radial properties of their host multiphase outflows.

Figures (24)

• Figure 1: The initialisation of a cloud-crushing simulation with the choice of code units in Eqs. \ref{['eq:codeUnits']}. This simulation setup has translational symmetry because the background wind is uniform. Therefore, the cloud can, in principle, be placed anywhere. However, we choose to place it a few cloud radii from the left edge of the simulation domain as the wind blows from left to right. This ensures that the initial bow shock and the cloud tail are reliably captured within the simulation domain.
• Figure 2: The initialisation of a cloud-crushing simulation with the choice of code units in Eqs. \ref{['eq:codeUnitsCC85']}. Unlike 'vanilla' cloud-crushing, here the seed cloud is embedded in a Chevalier1985 wind. This introduces a background structure to the wind and breaks the translational symmetry of the initial condition of the 'vanilla' cloud-crushing setup. In addition, the wind is directed radially outward instead of being plane-parallel. Refer to Section \ref{['subsubsec:dedimensionalise-cc85']} for an explanation of each of the terms in this cartoon.
• Figure 3: Illustration of our novel 'cloud-tracking' algorithm. This algorithm is generic and can take into account a spatially varying background profile in any coordinate system. However, particular to our work, we use spherical coordinates which matches with the natural geometry of a Chevalier1985 wind. We track the centre of mass of the cloud material, marked by a passive tracer. Whenever this moves by more than $1$ cell length and the leftmost position of the tracer is more than $16\ R_{\rm cl}$ from the leftmost edge of the domain, we 'effectively' drop the cells from the left ( head), introduce an identical number of cells to the right ( tail) and fill them with the Chevalier1985 solution at their respective position. This procedure dynamically clips the simulation domain from the left (wind entry) and extends it to the right (wind exit) ensuring that a relatively small computational domain can follow a moving cloud and prevents its tail to quickly leak out of the simulation box.
• Figure 4: The temperature slices in the $z=0$ plane from our fiducial cloud-crushing simulation in a Chevalier1985 wind. The simulation parameters are $(\mathcal{M}, \chi, t_{\rm cool, mix}/t_{\rm cc}|_{\rm ini}) = (1.496, 100, 0.2)$; cf. Table \ref{['tab:CCinCC85_params']}. We show only a few selected snapshots that clearly demonstrate the formation of elongated cold structures starting from a spherical cloud (not shown here). Similar elongated structures of cold gas with cometary tails embedded in galactic winds have been recently observed in the M82 galaxy (Bolatto2024ApJFisher2024MNRAS). Unlike in a uniform wind, the cloud encounters different wind conditions along its tail as it moves downstream. The cold gas also expands orthogonal to the wind direction (see the attached scale). Follow the discussion in Section \ref{['subsubsec:GO_exp-box']} & Fig. \ref{['fig:cloud-spread']} for a quantitative estimate on cloud expansion. Use this https://youtu.be/c9lrGnPHgfI to see a video of the full evolution (also see the evolution of the corresponding density slice following https://youtu.be/SLNG99l_E6Y). Moving beyond qualitative visualisation, in Fig. \ref{['fig:cloud_profile']}, we make a detailed quantitative evaluation of the evolution of clouds in a Chevalier1985 wind. It is worth noting that we clip the slices in our visualisation to a smaller radial extent than in the simulation for clarity.
• Figure 5: The temporal evolution of cold gas mass (in units of solar mass in the left panel and initial cloud mass in the right panel) in our cloud-crushing simulations for clouds of different sizes initialised in a Chevalier1985 wind (solid lines) compared with identical simulations of cloud-crushing in a uniform wind ('vanilla' cloud-crushing in dashed lines of the same colour as their solid counterparts). We find that the growth of cold mass is significantly suppressed in an expanding background compared to 'vanilla' cloud-crushing. The background wind properties and the initial position of the cloud with respect to the wind remain the same in all these simulations. In this analysis, a cell is identified as being part of the cold cloud if they have a temperature less than $2 T_{\rm cl} = 8 \times 10^4\ {\rm K}$. The set of constant parameters chosen for these simulations is $(\mathcal{M}, \chi) = (1.496, 100)$ (cf. Table \ref{['tab:CCinCC85_params']}). Each line of different colour corresponds to different $t_{\rm cool, mix}/t_{\rm cc}|_{\rm ini} \propto R_{\rm thres}/R_{\rm cl}$, which translates to different cloud sizes. The time is in Myr in the left panel and normalised by the cloud-crushing time $t_{\rm cc, ini}=\sqrt{\chi} R_{\rm cl}/v_{\rm wind}$ evaluated at the initial position of the cloud (the right panel). The region of the simulation domain chosen for our analysis has wind temperatures greater than $9 \times 10^4 \ {\rm K}$, higher than the temperature below which we consider gas to be cold in our analysis. For the largest clouds ($t_{\rm cool, mix}/t_{\rm cc}|_{\rm ini} = 0.1, 0.2$), we truncate the evolution early after a significant portion of the initial tracer marking the cloud starts leaving our analysis domain. The largest clouds exhibit the greatest deviation in their cold mass content from their 'vanilla' cloud-crushing counterparts. The smallest cloud from our simulation shown in this figure ($t_{\rm cool, mix}/t_{\rm cc}|_{\rm ini} = 8$) gets destroyed in both the 'vanilla' cloud-crushing setup and cloud-crushing in a Chevalier1985 wind. It is relatively unaffected by an expanding wind and experiences a similar evolution in its cold mass content.