The role of turbulence in setting the phase of the ISM and implications for the star formation rate

TL;DR

This paper investigates how turbulence and the thermal state of the multi-phase ISM regulate star formation, particularly addressing the KS relation in Milky Way–like environments. Using 1 kpc^3 stratified box simulations with SN-driven and large-scale external driving, plus constant and time-dependent UV backgrounds, the authors show that turbulence can either boost or suppress SFR depending on Σ and heating, yielding two regimes: CNM-formation–limited SF at low densities and dense-clump formation–limited SF at higher densities. They introduce an analytical model that combines a turbulence-generated density PDF with a cooling/heating curve to predict CNM fractions and connect these to the observed KS break near $9\,\mathrm{M}_{\odot}\,\mathrm{pc}^{-2}$. The results imply that environmental variation in CNM formation, influenced by UV heating and turbulent driving, can explain KS scatter and the knee, providing a framework to interpret SFRs in diverse galactic environments. Overall, the work advances our understanding of how turbulence and thermal bistability shape star formation in galaxies and offers a predictive CNM fraction model linked to KS phenomenology.

Abstract

In this work, we explore the link between star formation, turbulence and the thermal state of the multi-phase ISM. We analyse a suite of stratified box simulations modelling a realistic ISM that aims to probe environments similar to those found in the Milky Way. Turbulence is injected through stellar feedback and an external large-scale driving force. We find that star formation can be either boosted or reduced when increasing the external driving strength, depending on the environment. When the density is sufficiently high or the UV background weak, warm neutral gas naturally transitions to the cold phase, leading to high CNM fractions of around 30 -- 40\%. Under these conditions, excessive large-scale driving leads to a slight reduction of the CNM fraction and an increase in the amount of gas that is thermally unstable. What limits the star formation in this regime is a reduced fraction of dense gas due to additional turbulent support against collapse. For low density regions subject to significant external UV background, overdensities in which cooling is efficient are much rarer and we find that star formation is regulated by the formation of cold gas. In such cases, turbulence can significantly boost star formation by compressing gas in shocks and increasing the CNM fraction: we see an increase from almost no CNM to up to a fraction of 15 \%. We provide a model to quantify this behaviour and predict the CNM fraction by combining the standard ISM cooling/heating model with the density PDF generated by turbulence. The change in the dominant limiting process for star formation between low-density/externally heated and intermediate-density/feedback heated environments could provides a natural explanation for the observed break in the Kennicutt-Schmidt relation around column densities of 9\,\Msun\, pc$^{-2}$.

Figures (19)

• Figure 1: Comparison between the energy injection rate by SNe, assuming a 6% efficiency, and large-scale driving throughout the simulations averaged over bins of 5 Myr.
• Figure 2: Evolution of the mass-weighted 3D velocity dispersion in the different simulations, measured in a region between 100 pc above and 100 pc below the mid-plane.
• Figure 3: Gas surface density $\Sigma$ for edge-on and face-on projections of the final snapshot of each simulation. The field of view is 1 kpc $\times$ 0.5 kpc and 1 kpc $\times$ 1 kpc respectively, each with a depth of 1 kpc. The green dots indicate the location of the sink particles. Top: low-$\Sigma$ runs with $\Sigma = 10.2$$\mathrm{M}_{\odot}$ pc$^{-2}$. Bottom: high-$\Sigma$ runs with $\Sigma = 19.1$$\mathrm{M}_{\odot}$ pc$^{-2}$.
• Figure 4: The star formation history in each simulation. Left: low-$\Sigma$. Right: high-$\Sigma$. Top: evolution of the star formation rate, smoothed over a time scale of 7.5 Myr for low-$\Sigma$ and 0.5 Myr for high-$\Sigma$. Bottom: evolution of star formation efficiency. The grey lines show the fits to estimate the global SFR of the simulation. The labels indicate the average SFR value found from these fits.
• Figure 5: An example of a phase diagram, which show the relation between pressure $P$ or temperature $T$ and number density $n$ in the simulations. The colour corresponds to the mass fraction, on a logarithmic scale, with dark being high and light being low. We also show the mass-weighted histograms of each quantity. The dashed black line shows the theoretical cooling model, while the dotted lines indicate the temperature thresholds we adopts for the definition of WNM and CNM in this work.