HRS sample stellar, dust, gas mass functions

We discuss the results of the relationships between the K-band and stellar mass, far-infrared luminosities, star formation rate, dust and gas masses of nearby galaxies computing the bivariate K-band Luminosity Function (BLF) and bivariate K-band Mass Function (BMF) of the Herschel Reference Survey (HRS), a volume-limited sample with full wavelength coverage. We derive the BLFs and BMFs from the K-band and stellar mass, far-infrared luminosities, star formation rate, dust and gas masses cumulative distributions using a copula method which is outlined in detail.

The use of the bivariate computed taking into account the upper limits allows us to derive on a more solid statistical ground the relationship between the observed physical quantities. The analysis shows that the behaviour of the morphological (optically selected) subsamples is quite different. A statistically meaningful result can be obtained over the whole HRS sample only from the relationship between the K-band and the stellar mass, while for the remaining physical quantities (dust and gas masses, far-IR luminosity and star formation rate), the analysis is distinct for late-type (LT) and early-type galaxies (ETG).