Geometrical tests of cosmological models - II. Calibration of rotational widths and disc scaling relations

This is the second in a series of three papers dedicated to a new technique to select galaxies that can act as standard rods and standard candles in order to perform geometrical tests on large samples of high redshift galaxies to constrain different cosmological parameters. The goals of this paper are (1) to compare different rotation indicators in order to understand the relation between rotation velocities extracted from observations of the H alpha lambda 6563 angstrom line and the [OII]lambda 3727 angstrom line; and (2) to determine the scaling relations between physical size, surface brightness and magnitude of disc galaxies and their rotation velocity using the SFI++, a large catalog of nearby galaxies observed at I-band. A good correlation is observed between the rotation curve-derived velocities of the H alpha and [OII] observations, as well as between those calculated from velocity histograms, justifying the direct comparison of velocities measured from Ha rotation curves in nearby galaxies and from [OII] line widths at higher redshifts. To provide calibration for the geometrical tests, we give expressions for the different scaling relations between properties of galaxies (size, surface brightness, magnitude) and their rotation speeds. We use Malmquist bias-corrected distances from the SFI++ template Tully-Fisher relation to generate a size-rotation velocity relation with unprecedentedly small scatter. We show how the best size-rotation velocity relation is derived when size is estimated not from disc scale lengths but from the isophotal diameter r(23.5), once these have been corrected for inclination and extinction effects.