Equilibrium star formation in a constant Q disc: Model optimization and initial tests
We develop a model for the distribution of the ISM and star formation in galaxies based on recent studies that indicate that galactic disks stabilise to a constant stability parameter, which we combine with prescriptions of how the phases of the ISM are determined and for the Star Formation Law (SFL). The model predicts the gas surface mass density and star formation intensity of a galaxy given its rotation curve, stellar surface mass density and the gas velocity dispersion. This model is tested on radial profiles of neutral and molecular ISM surface mass density and star formation intensity of 12 galaxies selected from the THINGS sample. Our tests focus on intermediate radii (0.3 to 1 times the optical radius) because there are insufficient data to test the outer disks and the fits are less accurate in detail in the centre. Nevertheless, the model produces reasonable agreement with ISM mass and star formation rate integrated over the central region in all but one case. To optimise the model, we evaluate four recipes for the stability parameter, three recipes for apportioning the ISM into molecular and neutral components, and eight versions of the SFL. We find no clear-cut best prescription for the two-fluid (gas and stars) stability parameter Q2f and therefore for simplicity, we use the Wang & Silk (1994) approximation (QWS). We found that an empirical scaling between the molecular to neutral ISM ratio (Rmol) and the stellar surface mass density proposed by Leroy et al. (2008) works marginally better than the other two prescriptions for this ratio in predicting the ISM profiles, and noticeably better in predicting star formation intensity from the ISM profiles produced by our model with the SFLs we tested. Thus in the context of our modeled ISM profiles, the linear molecular SFL and the two-component SFL (Krumholz et al. 2009b) work better than the other prescriptions we tested. We incorporate these relations into our ‘Constant Q disk’ (CQ-disk) model.