Developing a turbulence-regulated star formation theory in a medium with non-lognormal gas density statistics.

Star formation happens within cold molecular clouds which are subject to supersonic turbulent motions and strong magnetic fields. The gas density PDF of such a medium has been previously used to predict the star formation rate potential that a cold gas cloud has, e.g., Krumholz & McKee (2005), Federrath & Klessen (2012) and Burkhart & Mocz (2018). Critical to these theories is the lognormal gas density probability density function, which connects the underlying statistics of the medium to the star formation rate in these models. However, foundational works from Hopkins (2013a), Mocz & Burkhart (2018) and Beattie et al (2022a) indicate that (global) lognormal models violate mass conservation, and are theoretically and empirically incorrect for the gas density probability density function of a supersonic medium. In this project, we aim to utilise computational and analytical techniques to modify the Federrath & Klessen (2012)-type turbulence-regulated star formation theories to include underlying Hopkins (2013a) gas density statistics, exploring how higher-order moments of the PDF influence the theoretical star formation rate. Furthermore, we will calibrate our theoretical models with star formation rates predicted by detailed numerical star-formation simulations, which may be used directly as sub-grid star formation models in global galaxy simulations.