Stellar Mass-to-Light Ratios and the Tully-Fisher relation

We use spiral galaxy evolution models to argue that there are substantial variations in stellar mass-to-light ratio (M/L) within and among galaxies. Our models show a strong correlation between stellar M/L and galaxy color. We compare the colors and maximum-disk M/L values of a sample of galaxies to the model color-M/L relation, finding that a Salpeter IMF is too massive but that an IMF with fewer low mass stars fits the observations well. Applying our color-M/L relation to the Tully-Fisher (TF) relation, we find a stellar mass TF-relation that is independent of originating passband. Adding the HI gas mass, we find that the maximum slope of the baryonic TF-relation is 3.5. 1. Galaxy Evolution Models and Mass-to-Light Ratios We have used the galaxy evolution models described by Bell & Bower (2000) to investigate stellar M/L ratios of galaxies. These models were tuned to fit the observed trends between the colors and the structural parameters of spiral galaxies (Bell & de Jong 2000). Using a local gas density dependent star formation law, the photometric evolution is calculated, taking chemical evolution into account. As well as a closed box model we have models with gas infall and outflow, mass dependent formation epochs and star bursts. All models show large variations in M/L, amounting from a factor 8 in B to 2 in K, but in all models we find a strong correlation between M/L and optical color (e.g. Fig. 1a). The slope of the color-M/L relation is very robust against the particular stellar population synthesis model and against the exact details of the galaxy evolution model. The main uncertainty in the correlation is the zero-point, which is determined by the assumed IMF; most notably by the relative amount of low mass stars, which contribute to the mass but not to the luminosity and color. A constraint on the color-M/L correlation zero-point can be obtained from galaxy rotation curves. The stellar disk in a galaxy cannot be more massive than allowed by its rotation curve, resulting in a maximum-disk M/L. In Fig. 1b we show the maximum-disk M/L values versus the extinction corrected B–R color for the Verheijen (1998) galaxy sample. These M/L values are truly upper limits: any mass not accounted for in the rotation curve decompositions will push the stellar M/L even lower. The solid line in Fig. 1b shows the fit to the color-M/L relation for our best model using a standard Salpeter IMF. Clearly