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Unveiling the 3D structure of the central molecular zone from stellar kinematics and photometry: The 50 and 20 km/s clouds

The central molecular zone (CMZ), surrounding the Galactic centre, is the largest reservoir of dense molecular gas in the Galaxy. Despite its relative proximity, the 3D structure of the CMZ remains poorly constrained, primarily due to projection effects. We aim to constrain the line-of-sight location of two molecular clouds in the CMZ -- the 50 and 20 km/s clouds -- and to investigate their possible physical connection using stellar kinematics and photometry. This study serves as a pilot for future applications across the full CMZ. We estimated the line-of-sight position of the clouds by analysing stellar kinematics, stellar densities, and stellar populations towards the cloud regions and a control field. We find an absence of westward moving stars in the cloud regions, which indicates that they lie on the near side of the CMZ. This interpretation is supported by the stellar density distributions. The similar behaviour observed in the two clouds, as well as in the region between them (the ridge), suggests that they are located at comparable distances and are physically linked. We also identified an intermediate-age stellar population (2-7 Gyr) in both regions, consistent with that observed on the near side of the CMZ. We estimated the line-of-sight distances at which the clouds and the ridge become kinematically detectable (i.e. where the proper motion component parallel to the Galactic plane differs from that of the control field at the 3 sigma level) by converting their measured proper motions parallel to the Galactic plane using a theoretical model of the stellar distribution. We find that the 50 and 20 km/s clouds are located at $43\pm8$ pc and $56\pm11$ pc from Sgr A*, respectively, and that the ridge lies at $56\pm11$ pc; this supports the idea that the clouds are physically connected through the ridge.