Equilibrium Star Formation In A Constant Q Disk: Model Optimisation 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.
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 Q_2f and therefore for
simplicity, we use the Wang&Silk(1994) approximation (Q_WS). We found that an
empirical scaling between the molecular to neutral ISM ratio (R_mol) 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. 2009) work better than the other prescriptions we tested. We
incorporate these relations into our `Constant Q disk' (CQ-disk) model.
