Objective Classification of Spiral Galaxies Having Extended Rotation Curves Beyond the Optical Radius

We carry out an objective classification of four samples of spiral galaxies having extended rotation curves beyond the optical radius. A multivariate statistical analysis (viz., principal component analysis [PCA]) shows that about 96% of the total variation is due to two components, one being the combination of absolute blue magnitude and maximum rotational velocity beyond the optical region and the other being the central density of the halo. On the basis of PCA a fundamental plane has been constructed that reduces the scatter in the Tully-Fisher relation up to a maximum of 16%. A multiple stepwise regression analysis of the variation of the overall shape of the rotation curves shows that it is mainly determined by the central surface brightness, while the shape purely in the outer part of the galaxy (beyond the optical radius) is mainly determined by the size of the galactic disk.