The molecular mass function of the local Universe

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Abstract
Aims.We construct the molecular mass function using the bivariateK-band-mass function (BMF) of theHerschelReference Survey (HRS), which is a volume-limited sample that has already been widely studied at the entire electromagnetic spectrum.Methods.The molecular mass function was derived from theK-band and the gas mass cumulative distribution using a copula method, which is described in detail in our previous papers.Results.The H2mass is relatively strongly correlated with theK-band luminosity because of the tight relation between the stellar mass and the molecular gas mass within the sample with a scatter, which is likely due to those galaxies which have lost their molecular content because of environmental effects or because of a larger gas consumption due to past star formation processes. The derived H2MF samples the molecular mass range from ∼4 × 106M⊙to ∼1010 M⊙, and when compared with theoretical models, it agrees well with the theoretical predictions at the lower end of the mass values; whereas at masses larger than 1010 M⊙, the HRS sample may miss galaxies with a large content of molecular hydrogen and the outcomes are not conclusive. The value of the local density of the molecular gas mass inferred from our analysis is ∼1.5 × 107 M⊙Mpc−3, and it is compared with the results at larger redshifts, confirming the lack of strong evolution for the molecular mass density betweenz= 0 andz= 4.Conclusions.This is the first molecular mass function that has been derived on a complete sample in the local Universe, which can be used as a reliable calibration at redshiftz= 0 for models aiming to predict the evolution of the molecular mass density.

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