HI CONTENT AND OPTICAL PROPERTIES OF FIELD GALAXIES FROM THE ALFALFA SURVEY. II. MULTIVARIATE ANALYSIS OF A GALAXY SAMPLE IN LOW-DENSITY ENVIRONMENTS

This is the second paper of two reporting results from a study of the HI content and stellar properties of nearby galaxies detected by the Arecibo Legacy Fast ALFA blind 21 cm line survey and the Sloan Digital Sky Survey in a 2160 deg(2) region of high galactic latitude sky covered by both surveys, in the general Virgo direction. Here, we analyze a complete HI flux-limited subset of 1624 objects with homogeneously measured 21 cm and multi-wavelength optical attributes extracted from the control sample of HI emitters in environments of low local galactic density assembled by Toribio et al. (Paper I). Strategies of multivariate data analysis are applied to this data set in order to (i) investigate the correlation structure of the space defined by an extensive set of potentially independent observables describing gas-rich systems, (ii) identify the intrinsic parameters that best define their neutral gas content, and (iii) explore the scaling relations arising from the joint distributions of the quantities most strongly correlated with the HI mass. The principal component analysis performed over a set of five galaxy properties reveals that they are strongly interrelated, supporting previous claims that nearby HI emitters show a high degree of correlation. The best predictors for the expected value of M-HI are the diameter of the stellar disk, D-25,D-r, followed by the total luminosity (both in the r band), and the maximum rotation speed, while morphological proxies such as color show only a moderately strong correlation with the gaseous content attenuated by observational error. Among the various inferred prescriptions, the simplest and most accurate is log(M-HI/M-circle dot) = 8.72 + 1.25 log(D-25,D-r/kpc). We find a slope of -8.2 +/- 0.5 for the relation between optical magnitude and log rotation speed, in good agreement with Tully-Fisher studies, as well as a log slope of 1.55 +/- 0.06 for the HI mass-optical galaxy size relation. Given the homogeneity of the measurements and the completeness of our data set, the latter outcome suggests that the constancy of the average (hybrid) HI surface density advocated by some authors for the spiral population is just a crude approximation.