The NIBLES bivariate luminosity--HI mass distribution function revised using Arecibo follow-up observations

We present a modified optical luminosity--HI mass bivariate luminosity function (BLF) based on HI line observations from the Nan\c{c}ay Interstellar Baryons Legacy Extragalactic Survey (NIBLES), including data from our new, four times more sensitive follow-up HI line observations obtained with the Arecibo radio telescope. The follow-up observations were designed to probe the underlying HI mass distribution of the NIBLES galaxies that were undetected or marginally detected in HI at the Nan\c{c}ay Radio Telescope. Our total follow-up sample consists of 234 galaxies, and it spans the entire luminosity and color range of the parent NIBLES sample of 2600 nearby (900 $< cz <$ 12,000 kms$^{-1}$) SDSS galaxies. We incorporated the follow-up data into the bivariate analysis by scaling the NIBLES undetected fraction by an Arecibo-only distribution. We find the resulting increase in low HI mass-to-light ratio densities to be about 10\% for the bins $-1.0 \le$ log($\frac{M_{\rm HI}/M_{\odot}}{ L_{\rm r}/L_{\odot}}$) $\le -0.5$, which produces an increased HI mass function (HIMF) low mass slope of $\alpha = -1.14 \pm 0.07$, being slightly shallower than the values of $-1.35 \pm 0.05$ obtained by recent blind HI surveys. Applying the same correction to the optically corrected bivariate luminosity function from our previous paper produces a larger density increase of about 0.5 to 1 dex in the lowest HI mass-to-light ratio bins for a given luminosity while having a minimal effect on the resulting HIMF low mass slope, which still agrees with blind survey HIMFs. This indicates that while low HI-mass-to-light ratio galaxies do not contribute much to the one-dimensional HIMF, their inclusion has a significant impact on the densities in the two-dimensional distribution.