Chaotic star formation: error bars for the star formation efficiency and column density PDF

Simulations are very useful for testing our theoretical understanding of star formation by varying the initial conditions or treatment of various physical mechanisms. However, large, well resolved simulations including complex physics are computationally costly and therefore are normally only performed once. This leads to a crisis in modelling, because star formation is a chaotic system, where a small variation in initial conditions can be magnified to a large change in results. We create a suite of cluster-scale simulations with 30 different random realisations of the turbulent velocity field applied to the same initial conditions of an isolated spherical molecular cloud. We test commonly used metrics of star formation activity and cloud structure and measure the variance cause by this random variation in initial conditions, to quantify the error that should be applied to single-realisation simulations. We find that after 5 Myr the number of stars varies by 58 per cent of the mean, the star formation efficiency by 60 per cent of the mean ,and the shape of the column density PDF by 7 per cent of the mean. We provide a standard deviation at different times that should be applied as an error margin on all single realisation simulations to enable robust statistical comparison.