Studying the flow of baryons into and out of galaxies is an important part of understanding the evolution of galaxies over time .
We present a detailed case study of the environment around an intervening Ly \alpha absorption line system at z _ { abs } = 0.633 , seen towards the quasar J0423 - 0130 ( z _ { QSO } = 0.915 ) .
We detect with ALMA the ^ { 12 } CO ( 2–1 ) , ^ { 12 } CO ( 3–2 ) and 1.2 mm continuum emission from a galaxy at the redshift of the Ly \alpha absorber at a projected distance of 135 kpc .
From the ALMA detections , we infer ISM conditions similar to those in low redshift Luminous Infrared Galaxies .
DDT MUSE integral field unit observations reveal the optical counterpart of the ^ { 12 } CO emission line source and three additional emission line galaxies at the absorber redshift , which together form a galaxy group .
The ^ { 12 } CO emission line detections originate from the most massive galaxy in this group .
While we can not exclude that we miss a fainter host , we reach a dust-uncorrected star-formation rate ( SFR ) limit of > 0.3 ~ { } \text { M } _ { \sun } \text { yr } ^ { -1 } within 100 kpc from the sightline to the background quasar .
We measure the dust-corrected SFR ( ranging from 3 to 50 M _ { \sun } yr ^ { -1 } ) , the morpho-kinematics and the metallicities of the four group galaxies to understand the relation between the group and the neutral gas probed in absorption .
We find that the Ly \alpha absorber traces either an outflow from the most massive galaxy or intra-group gas .
This case study illustrates the power of combining ALMA and MUSE to obtain a census of the cool baryons in a bounded structure at intermediate redshift .