On the mass-to-light ratio and the initial mass function in disc galaxies

Abstract

A low mass-to-light (M/L) ratio for the stellar component of spiral galaxies (M/L≲ 1 in the I band) is advocated by various dynamical arguments and by recent cosmological simulations of the formation of these systems. We discuss this possibility by means of chemo-photometric models for galactic discs, adopting different initial mass functions (IMFs). We show that a number of ‘bottom-light’ initial mass functions (namely, with less mass locked in low-mass stars than the standard Salpeter IMF), suggested independently in recent literature, do imply M/L ratios as low as mentioned above, at least for late-type spirals (Sbc/Sc). This conclusion still holds when the bulge contribution to mass and light is included. We also predict the typical stellar M/L ratio, and correspondingly the zero-point of the Tully–Fisher relation, to vary considerably with Hubble type (approximately 0.5–0.7 mag in the red bands, from Sa to Sc type). For some of the bottom-light IMFs considered, the efficiency of metal production tends to exceed what is typically estimated for spiral galaxies. Suitable tuning of the IMF mass limits, post-supernova fallback of metals on to black holes or metal outflows must then be invoked, to reproduce the observed chemical properties of disc galaxies. In the appendix we provide M/L–colour relations to estimate the stellar M/L ratio of a galaxy on the basis of its colours, for several IMFs.