The HI Content of Spirals. I. Field-Galaxy HI Mass Functions and HI Mass-Optical Size Regression

A standard parametric maximum-likelihood technique is used to determine both the probability distribution over total HI mass $M_{\rm HI}$ and the regression of this quantity on the linear optical diameter $D_{\rm o}$ for field giant spirals (Sa-Sc) from a complete HI-flux-limited data set of these objects. Gaussian and Schechter parametrizations of the HI mass function are explored. We find that the available data are equally well described by both models, and that the different morphological classes of giant spirals have HI mass functions which, in general, agree well within the errors. The largest discrepancy corresponds to the Sb-type systems which exhibit a deficit of low HI-mass objects relative to the other types. Using a straightforward generalization of the gaussian model, we have also investigated the linear dependence of $M_{\rm HI}$ on $D_{\rm o}$. We confirm that the HI content of spirals is much better predicted by the size of their optical disks than by their morphological types alone. The inferred correlations imply a considerable decrease of the ratio $M_{\rm HI}/D_{\rm o}^2$ with increasing galaxy size for types earlier than Sc.