Multivariate analysis of elliptical galaxies

We use principal components to investigate the properties of elliptical galaxies in the space of absolute magnitude, central velocity dispersion and central line strength. The analysis shows that elliptical galaxies are at least a two-parameter family and that, to a useful approximation, the data points define a plane in this space. We find that axial ratio is not correlated with the plane and therefore cannot be used to estimate the true shapes of elliptical galaxies. The correlation between mass-to-light ratio and the plane is highly significant, which may indicate that the stellar mass functions of elliptical galaxies are affected by their metallicities or by the depths of their potential wells. By minimizing residuals in the relation between absolute magnitude and velocity dispersion, we find a Virgocentric infall velocity of 230 ± 60 km s−1. Similar results are obtained when line strengths are included in the fits but the uncertainty is not reduced because the slope of the corrected relation is shallower.