[C II] emission and star formation in late-type galaxies. II A model

We study the relationship between gas cooling via the [C II] (158 micron) line emission and dust cooling via the far-IR continuum emission on the global scale of a galaxy in normal (i.e. non-AGN dominated and non-starburst) late-type systems. It is known that the luminosity ratio of total gas and dust cooling, L(C II)/L(FIR), shows a non-linear behaviour with the equivalent width of the Halpha line emission, the ratio decreasing in galaxies of lower massive star-formation activity. This result holds despite the fact that known individual Galactic and extragalactic sources of the [C II] line emission show different [C II] line-to-far-IR continuum emission ratios. This non-linear behaviour is reproduced by a simple quantitative model of gas and dust heating from different stellar populations, assuming that the photoelectric effect on dust, induced by far-UV photons, is the dominant mechanism of gas heating in the general diffuse interstellar medium of the galaxies under investigation. According to the model, the global L(C II)/L(FIR) provides a direct measure of the fractional amount of non-ionizing UV light in the interstellar radiation field and not of the efficiency of the photoelectric heating. The model also defines a method to constrain the stellar initial mass function from measurements of L(C II) and L(FIR). A sample of 20 Virgo cluster galaxies observed in the [C II] line with the LWS on board ISO is used to illustrate the model. The limited statistics and the necessary assumptions behind the determination of the global [C II] luminosities from the spatially limited data do not allow us to establish definitive conclusions but data-sets available in the future will allow tests of both the reliability of the assumptions of our model and the statistical significance of our results.