We discuss the nature and physical properties of gas-mass selected galaxies in the ALMA spectroscopic survey (ASPECS) of the Hubble Ultra Deep Field (HUDF). We capitalize on the deep optical integral-field spectroscopy from the MUSE HUDF Survey and multi-wavelength data to uniquely associate all 16 line-emitters, detected in the ALMA data without preselection, with rotational transitions of carbon monoxide (CO). We identify ten as CO(2-1) at $1 < z < 2$, five as CO(3-2) at $2 < z < 3$ and one as CO(4-3) at $z = 3.6$. Using the MUSE data as a prior, we identify two additional CO(2-1)-emitters, increasing the total sample size to 18. We infer metallicities consistent with (super-)solar for the CO-detected galaxies at $z le 1.5$, motivating our choice of a Galactic conversion factor between CO luminosity and molecular gas mass for these galaxies. Using deep Chandra imaging of the HUDF, we determine an X-ray AGN fraction of 20% and 60% among the CO-emitters at $z sim 1.4$ and $z sim 2.6$, respectively. Being a CO-flux limited survey, ASPECS-LP detects molecular gas in galaxies on, above and below the main sequence (MS) at $z sim 1.4$. For stellar masses $ge 10^{10} (10^{10.5})$ M$_{odot}$, we detect about 40% (50%) of all galaxies in the HUDF at $1 < z < 2$ ($2 < z < 3$). The combination of ALMA and MUSE integral-field spectroscopy thus enables an unprecedented view on MS galaxies during the peak of galaxy formation.
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