Letter to the Editor

The molecular mass function of the local Universe

¹ European Southern Observatory, Karl-Schwarzschild-Straße 2, 85748 Garching, Germany
e-mail: pandrean@eso.org
² National Astronomical Observatory of Japan, National Institutes of Natural Sciences, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
³ Nobeyama Radio Observatory, National Astronomical Observatory of Japan, National Institutes of Natural Sciences, 462-2 Nobeyama, Minamimaki, Minamisaku, Nagano 384-1305, Japan
⁴ Joetsu University of Education, Yamayashiki-machi, Joetsu, Niigata 943-8512, Japan
⁵ Aix Marseille Univ., CNRS, CNES, LAM, Marseille, France
⁶ Department of Astronomical Science, SOKENDAI (The Graduate University for Advanced Studies), 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
⁷ Department of Physics, Faculty of Science, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido 060-0810, Japan
⁸ Chip Computers Consulting s.r.l., Viale Don L. Sturzo 82, S. Liberale di Marcon, 30020 Venice, Italy

Received: 16 June 2020
Accepted: 6 October 2020

Abstract

Aims. We construct the molecular mass function using the bivariate K-band-mass function (BMF) of the Herschel Reference 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 the K-band and the gas mass cumulative distribution using a copula method, which is described in detail in our previous papers.

Results. The H₂ mass is relatively strongly correlated with the K-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 H₂ MF samples the molecular mass range from ∼4 × 10⁶ M_⊙ 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 between z = 0 and z = 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 redshift z = 0 for models aiming to predict the evolution of the molecular mass density.