The Bivariate Luminosity-HI Distribution Function of Galaxies

To investigate the correlation between optical luminosity and Hi mass, we obtained 21cm Hi line observations from the 100m class Nanç ay Radio Telescope of 2600 galaxies in the local universe (900 ≤ cz ≤ 12000 km s−1 ). We first present the observations and basic results of the Nanc¸ay Interstellar Baryons Legacy Extragalactic Survey (NIBLES), followed by Arecibo follow-up Hi line observations of 305 Nanç ay Hi undetected galaxies. Analysis of the low-luminosity follow-up sources indicates that they may have, on average, a more concentrated stellar mass distribution than the Nanc¸ay detected galaxies of corresponding luminosity. Using the data from NIBLES, we derive a bivariate optical luminosity-Hi mass distribution function (BLF), using initially the Nanc¸ay data, and later by incorporating the Arecibo follow-up observations. Our initial, uncorrected BLF can be summed over luminosity to produce an Hi mass function (HIMF) with a flat low-mass slope, in agreement with other optically selected Hi studies. However, we also identify a highly consistent distribution in the Hi gas mass-to-luminosity ratio (gas-to-light ratio) with predictable progressive offset as a function of luminosity which allows us to construct plausible gas-to-light distributions for very low-luminosity bins that lie outside the NIBLES sample, thus producing a corrected BLF. The corrected BLF is in good qualitative agreement with optical luminosity-Hi mass distributions from the ALFALFA survey and is able to accurately reproduce blind survey HIMFs. Incorporating the more sensitive Arecibo observations into our BLF analysis yields a density increase of about 10% for low gas-to-light ratio sources of low luminosity, resulting in a HIMF that is slightly shallower than values obtained by recent blind Hi surveys. However, when applying an extrapolated Arecibo-based gas-to-light distribution to the corrected BLF, the very lowest luminosity bins (log(Lr) ≤ 6.25) show a density increase of ∼0.5 - 1 dex but have a minimal impact on the resulting HIMF low-mass slope. This small impact on the resulting HIMF illustrates the importance of understanding the two-dimensional density distribution of galaxies: the one-dimensional HIMF is incapable of being sensitive to evolutionary differences within a given galaxy luminosity bin, but those differences can manifest themselves in a two-dimensional distribution