How stellar feedback reshapes the turbulence driving parameter of molecular clouds in disc galaxies

The turbulence driving parameter $b$ measures the ratio of compressive to solenoidal modes in supersonic interstellar turbulence and directly controls the density fluctuations — and hence the star formation rate — predicted by turbulent models of star formation. Galaxy-scale simulations have measured $b$ for an ensemble of molecular clouds only in gravity-only discs; Körtgen (2020) found ensemble-averaged $b\sim0.5$–$0.7$ with rapid, collision-driven fluctuations per cloud, but omitted stellar feedback and sink particles, using an artificial pressure floor and optically thin heating/cooling instead of radiative transfer. The open problem is to determine, in a self-consistently evolving disc-galaxy simulation that includes stellar feedback (supernovae, radiative feedback), the statistics and time evolution of $b$ for the molecular-cloud ensemble: whether feedback adds compressive pulses or drives solenoidal motions (e.g. via baroclinic vorticity production in supernova remnants), how the result depends on galactic environment and field geometry, and how the rapid collision-driven changes in $b$ translate into the star-formation histories of individual clouds. As of August 2026 the warm-neutral-medium, shearing-box analogue has been treated (Gerrard & Federrath 2026), but the molecular-cloud ensemble in a full disc with feedback remains untreated.

Background

Molecular clouds — the cold, dense gas phase of the interstellar medium (ISM) out of which stars form — are permeated by supersonic turbulence, i.e. chaotic motions whose speed exceeds the sound speed. This turbulence is a mixture of compressive modes (curl-free motions that converge and build up density contrasts) and solenoidal modes (divergence-free, rotational motions that stir the gas without directly compressing it). The mixture is quantified by the turbulence driving parameter $b$: for isothermal gas, $b=\sigma_{\rho/\rho_0}/\mathcal{M}$, the ratio of the density dispersion to the turbulent Mach number $\mathcal{M}$, with $b=1/3$ for purely solenoidal driving, $b\approx0.4$ for a natural mixture, and $b=1$ for purely compressive driving (Federrath et al. 2010); $b$ can equivalently be extracted from the compressive ratio of the velocity field, i.e. the fraction of turbulent power in compressive modes. The two routes coincide for isothermal gas under Fourier (large-scale) driving, but the density-variance calibration is not guaranteed under point-source (supernova-like) driving, so the two diagnostics can return different values of $b$ in feedback-driven regimes. The value matters because compressive driving produces roughly three times larger density dispersions and up to an order of magnitude higher star formation rates than solenoidal driving, so $b$ is a key input to analytical and simulation-based star formation laws.

What physically sets $b$ in real galaxies is poorly constrained. Idealized box simulations show that supernova (SN) explosions — the death events of massive stars, which inject momentum and energy into the ISM — produce turbulence with a compressive ratio below the natural-mixture equilibrium, because baroclinic vorticity generation (rotation produced when pressure and density gradients are misaligned across shocks) converts compressive SN energy into solenoidal motions (Pan et al. 2016). Photoionization feedback from massive stars, by contrast, drives strongly compressive turbulence in cloud pillars (Menon et al. 2020). In disc-galaxy simulations without feedback, molecular clouds forming by gravitational fragmentation show broadly distributed, fluctuating $b$ (Jin et al. 2017; Körtgen, Federrath & Banerjee 2017). Körtgen (2020) extended this to an ensemble of tracked clouds in self-gravitating, magnetized disc galaxies with the mass of the Large Magellanic Cloud (LMC), simulated with the FLASH magnetohydrodynamics code using adaptive mesh refinement (automatic grid refinement in dense regions) at peak resolution $\Delta x=19.5$ pc, starting from Toomre-$Q=2$ initial discs in a fixed external potential with a purely toroidal magnetic field (the Toomre $Q$ parameter measures gravitational stability of a rotating disc). Gravity-only driving gave ensemble-averaged $b\sim0.5$–$0.7$, with individual clouds swinging from fully solenoidal to fully compressive within a few Myr, driven by cloud–cloud collisions and tidal shear; the ensemble statistics agreed with the observational range $b\in[0.4,0.7]$ for solar-neighbourhood clouds (Kainulainen & Federrath 2017). Those simulations included neither stellar feedback nor sink particles (localized point-mass star particles that accrete gas) — the study introduced an artificial pressure term on the highest level of refinement and treated the gas thermodynamics by optically thin heating and cooling instead of radiative transfer — so the question of how feedback processes reshape $b$ — whether supernovae add compressive pulses or instead drive solenoidal motions through baroclinic instability — remains open. The paper's scope limitations are: the density-variance–Mach-number relation did not emerge at $\Delta x=19.5$ pc, which the paper attributed primarily to the lack of numerical resolution, with full convergence expected only at sub-parsec resolution; the cloud-tracking algorithm did not search for newly formed clouds and thus traced only the firstly identified ensemble; and the setup used a fixed external potential, constant initial Toomre $Q=2$, and a purely toroidal initial magnetic field. The paper itself remarks that the compressive tendency found under gravity-only driving may change once stellar feedback is included, and that the highly fluctuating per-cloud driving parameter would strongly affect the cloud's star formation rate. Meanwhile, spatially resolved observations now measure $b$ across entire nearby galaxies (the LMC star-forming region N159E with $b\approx0.9$, Sharda et al. 2021; the Small Magellanic Cloud with median $b\sim0.51$, Gerrard et al. 2023; NGC 7793 and NGC 1313, predominantly solenoidal on average with localized compressive regions, Miller, Grasha & Federrath 2026), so a simulation prediction for feedback-regulated cloud-ensemble $b$ is directly testable.

Problem Statement

In self-consistently evolving disc-galaxy simulations that include stellar feedback — supernova explosions and radiative feedback from massive stars, together with sink particles and the corresponding star-formation prescription — determine the statistics and time evolution of the turbulence driving parameter $b$ of the molecular-cloud ensemble, as the feedback counterpart of the gravity-only measurement of Körtgen (2020). Specifically: (1) how does feedback reshape the ensemble-averaged and per-cloud $b$ relative to gravity-only discs — does it add compressive pulses or drive solenoidal motions through baroclinic vorticity production in supernova remnants — and do the collision-driven, few-Myr $b$ swings found without feedback persist, dampen, or amplify; (2) how do the ensemble statistics of $b$ depend on the galactic environment (i.e. galactocentric position, external gravitational potential, and initial magnetic-field geometry); (3) whether, and at what resolution, the density-variance–Mach-number diagnostic of $b$ becomes usable in a self-consistent disc; and (4) how do the rapid, collision-driven changes in $b$ translate into the star-formation histories of individual clouds once stellar feedback and sink-particle star formation are included? The four parts are jointly required — they are the components of the determination of the statistics and time evolution of $b$ sought here — and no single part alone resolves the problem.

References

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