Bivariate luminosity-HI mass distribution function of galaxies based on the NIBLES survey

We present a new optical luminosity-HI mass bivariate luminosity function (BLF) based on HI line observations from the Nancay Interstellar Baryons Legacy Extragalactic Survey (NIBLES). NIBLES sources lie within the local universe (900 $\leq cz \leq$ 12,000 \kms) and were chosen from SDSS DR5 such that the optical luminosity function was sampled as uniformly as possible. The HI mass function (HIMF) derived from our raw-data BLF, which is based on HI detections only, is consistent with the HIMFs derived from other optically selected surveys in that the low-mass slope is flatter than those derived from blind HI surveys. However, spanning the entire luminosity range of NIBLES, we identify a highly consistent distribution of the HI gas mass to luminosity ratio (gas-to-light ratio) with a predictable progression in the mean MHI/Lr ratio as a function of Lr. This consistency allows us to construct plausible gas-to-light ratio distributions for very low-luminosity bins which lie outside the NIBLES sample. We also identify a $\sim$ 10% decrease in detection fraction for galaxies fainter than log(\Lr) = 9.25, consistent with the expected decrease due to distance and sensitivity effects. Accounting for these trends, we reconstruct plausible gas-to-light distributions spanning luminosity bins down to log(\Lr) = 5.25, thus producing a corrected BLF. This 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, lending credibility that this two dimensional optical luminosity-HI mass distribution is an accurate representation of the volume density distribution of galaxies in the local universe. We also note that our agreement with HIMFs from other surveys is dependent on accounting for all systematic differences such as selection method, Hubble constant and HI flux scale.