Modelling Mechanical Heating in Star-Forming Galaxies: CO and 13CO Line Ratios as Sensitive Probes

We apply photo-dissociation region (PDR) molecular line emission models, that have varying degrees of enhanced mechanical heating rates, to the gaseous component of simulations of star-forming galaxies taken from the literature. Snapshots of these simulations are used to produce line emission maps for the rotational transitions of the CO molecule and its 13CO isotope up to J = 4-3. We consider two galaxy models: a small disk galaxy of solar metallicity and a lighter dwarf galaxy with 0.2 \zsun metallicity. Elevated excitation temperatures for CO(1 - 0) correlate positively with mechanical feedback, that is enhanced towards the central region of both model galaxies. The emission maps of these model galaxies are used to compute line ratios of CO and 13CO transitions. These line ratios are used as diagnostics where we attempt to match them These line ratios are used as diagnostics where we attempt to match them to mechanically heated single component (i.e. uniform density, Far-UV flux, visual extinction and velocity gradient) equilibrium PDR models. We find that PDRs ignoring mechanical feedback in the heating budget over-estimate the gas density by a factor of 100 and the far-UV flux by factors of ~10 - 1000. In contrast, PDRs that take mechanical feedback into account are able to fit all the line ratios for the central < 2 kpc of the fiducial disk galaxy quite well. The mean mechanical heating rate per H atom that we recover from the line ratio fits of this region varies between $10^{-27}$ -- $10^{-26}$~erg s$^{-1}$.