Mass-to-light ratios from the fundamental plane of spiral galaxy disks

Abstract

The best-fitting 2-dimensional plane within the 3-dimensional space of spiral galaxy disk observables (rotational velocity v_{rot}, central disk surface brightness μ_0 = -2.5log I_0, and disk scale-length h) has been constructed. Applying a three-dimensional bisector method of regression analysis to a sample of ~100 spiral galaxy disks that span more than four mag arcsec^{-2} in central disk surface brightness yields v_{rot} ~ I_0^{0.50+/-0.05}h^{0.77+/-0.07} (B-band) and v_{rot} ~ I_0^{0.43+/-0.04}h^{0.69+/-0.07} (R-band). Contrary to popular belief, these results suggest that in the B-band, the dynamical mass-to- light ratio (within 4 disk scale-lengths) is largely independent of surface brightness, varying as I_0^{0.00+/-0.10}h^{0.54+/-0.14}. Consistent results were obtained when the expanse of the analysis was truncated by excluding the low surface brightness galaxies. Previous claims that M/L_B varies with I_0^{-1/2} are shown to be misleading and/or due to galaxy selection effects. Not all low-surface-brightness disk galaxies are dark matter dominated. The situation is however different in the near-infrared where L_{K'} \~ v^4 and M/L_{K'} is shown to vary as I_0^{-1/2}. Theoretical studies of spiral galaxy disks should not assume a constant M/L ratio within any given passband. The B-band dynamical mass-to-light ratio (within 4 disk scale-lengths) has no obvious correlation with (B-R) disk colour, while in the K'-band it varies as -1.25+/-0.28(B-R). Combining the present observational data with recent galaxy model predictions implies that the logarithm of the stellar-to-dynamical mass ratio is not a constant value, but increases as disks become redder, varying as 1 .70+/-0.28(B-R).