Visibility stacking of ALMA archival data: unveiling the molecular ISM of dusty star-forming galaxies at cosmic noon

Dusty star-forming galaxies (DSFGs) host some of the most intense episodes of star formation in cosmic history, dominating the cosmic star formation rate density at z ~ 2–3, during the cosmic noon. Characterising the state of their molecular gas is an essential step towards understanding how galaxies assembled their stellar mass across cosmic time. Submillimetre spectral lines observed with interferometers such as ALMA provide the ideal diagnostic of these physical conditions. However, individual transitions are often faint, making stacking techniques essential to recover weak signals buried in noise and to build reliable statistical studies using public archives. Because these galaxies have been targeted across numerous independent programs, archival datasets are deeply heterogeneous in angular resolution, spectral setup, sensitivity, and redshift. Combining such data via post-processed images introduces severe artifacts and beam discrepancies, highlighting the need for a novel methodology capable of handling disparate datasets across broad redshift ranges. In this thesis, we address this challenge by presenting ViSta, a stacking framework that operates natively in the Fourier domain. By combining data directly on a common rest-frame uv plane and spectral grid, ViSta preserves native noise statistics and eliminates image-plane artifacts. Validated on simulated and real observations, ViSta reliably recovers faint line signals buried in noise. Notably, the noisier the data, the greater the gain over traditional image-plane methods. Although an initial version tailored for ALMA demonstrated the validity of this approach, poor computational scaling limited its application to large archival samples. We therefore re-engineered the framework using high-performance computing, achieving over an order-of-magnitude speedup and enabling joint stacking across multiple interferometers. We then apply ViSta to a sample of 104 DSFGs observed with ALMA to reconstruct their average CO Spectral Line Energy Distribution, constrain excitation conditions, and evaluate gravitational lensing biases. The LIR-normalised ladder peaks at mid-J transitions, tracing warm, moderately dense gas. Confirmed lensed and unconfirmed systems yield consistent ladders and excitation parameters with no evidence for differential lensing, supporting strongly lensed galaxies as proxies for the broader population. Finally, non-LTE modelling confirms that a two-component ISM combining warm and cool gas best reproduces the observed emission, yielding physical conditions aligned with previous studies. These findings establish a benchmark for high-redshift ISM studies and demonstrate the power of uv-stacking for archival science in the SKAO era.