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 covere
d by both surveys. We apply strategies of multivariate data analysis to a complete HI flux-limited subset of 1624 objects extracted from the control sample of HI emitters assembled by Toribio et al. (2011a) in order to: i) investigate the correlation structure of the space defined by an extensive set of observables describing gas-rich systems; ii) identify the intrinsic parameters that best define their HI 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 MHI are the diameter of the stellar disk, D25r, 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. The simplest and most accurate prescription is log(MHI/Msun)= 8.72 + 1.25*log(D25r/kpc). We find a slope of $-8.2 pm 0.5$ for the relation between optical magnitude and log rotation speed, in good agreement with Tully-Fisher studies, and a log slope of $1.55 pm 0.06$ for the HI mass-optical galaxy size relation. Given the homogeneity of the measurements and the completeness of our dataset, the latter outcome suggests that the constancy of the average (hybrid) HI surface density advocated by some authors for the spiral population is a crude approximation.
We report 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 two declination strips covering a total area of 9 hr X 16
deg. Our analysis seeks to assemble a control sample of galaxies suitable for providing absolute measures of the HI content of gaseous objects. From a database of ~15,000 HI detections, we have assembled three samples of gas-rich galaxies expected to show little or no evidence of interaction with their surroundings that could provide adequate HI standards. The most reliable results are obtained with a sample of 5647 sources found in low density environments, as defined by a nearest neighbor approach. The other two samples contain several hundred relatively isolated galaxies each, as determined from standard isolation algorithms. We find that isolated objects are not particularly gas-rich compared to their low-density-environment counterparts, while they suffer from selection bias and span a smaller dynamic range. All this makes them less suitable for defining a reference for HI content. We have explored the optical morphology of gaseous galaxies in quiet environments finding that, within the volume surveyed, the vast majority of them display unequivocal late-type galaxy features. In contrast, bona fide gas-rich early-type systems account only for a negligible fraction of the 21-cm detections. We argue that HI emission provides the most reliable way to determine the morphological population to which a galaxy belongs. We have also observed that the color distribution of flux-limited samples of optically-selected field HI emitters does not vary significantly with increasing distance, while that of non-detections becomes notably redder. This result suggests that the colors and HI masses of gas-rich galaxies cannot be very closely related.
We present an adaptation of the standard scenario of disk-galaxy formation to the concordant LCDM cosmology aimed to derive analytical expressions for the scale length and rotation speed of present-day disks that form within four different, cosmologi
cally motivated protogalactic dark matter halo-density profiles. We invoke a standard galaxy-formation model that includes virial equilibrium of spherical dark halos, specific angular momentum conservation during gas cooling, and adiabatic halo response to the gas inflow. The mean mass-fraction and mass-to-light ratio of the central stellar disk are treated as free parameters whose values are tuned to match the zero points of the observed size-luminosity and circular speed-luminosity relations of galaxies. We supply analytical formulas for the characteristic size and rotation speed of disks built inside Einasto r^{1/6}, Hernquist, Burkert, and Navarro-Frenk-White dark matter halos. These expressions match simultaneously the observed zero points and slopes of the different correlations that can be built in the RVL space of disk galaxies from plausible values of the galaxy- and star-formation efficiencies.
