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

What regulates star formation in different regions of the Galaxy is still debated and especially the role of turbulence is not fully understood. In this work, we explore the link between star formation, turbulence and the thermal state of the multi-phase interstellar medium (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 initial UV background weak, warm neutral gas naturally transitions to the cold phase, leading to high cold neutral medium (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 dramatically. In our simulations we see an increase from almost no CNM to up to a fraction of 15 % when including external turbulence driving; leading to an associated increase in the star formation rate. 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 M\({\mathstrut}_\odot\) pc\({\mathstrut}^{-2}\).