The bivariate K-band-submillimetre luminosity functions of the local HRS galaxy sample

We study the relationship between the K-band and the sub-millimetre (submm) emissions of nearby galaxies by computing the bivariate K-band-submm luminosity function (BLF) of the Herschel Reference Survey (HRS), a volume-limited sample observed in submm with Herschel/SPIRE. We derive the BLF from the K-band and submm cumulative distributions using a copula method. Using the BLF allows us to derive the relationship between the luminosities on more solid statistical ground. The analysis shows that over the whole HRS sample, no statistically meaningful conclusion can be derived for any relationship between the K-band and the submm luminosity. However, a very tight relationship between these luminosities is highlighted, by restricting our analysis to late-type galaxies. The luminosity function of late-type galaxies computed in the K-band and in the submm are dependent and the dependence is caused by the link, between the stellar mass and the cold dust mass, which has been already observed.