The ViSta method for stacking in the Fourier domain and its application to the dusty star-forming galaxies in the ALMA Science Archive

We present ViSta, a Visibility Stacking method to combine interferometric observations in the Fourier domain at radio to sub-millimeter wavelengths for galaxies. The goal of our method is to maximize the exploitation of available archival interferometric data. By stacking visibilities of galaxies with secure spectroscopic redshifts directly in the Fourier domain and transforming them into the rest-frame, we can enhance the stacked signal, suppress noise, and improve image reconstruction thanks to an extended coverage of the visibility domain. The ViSta method is highly flexible, allowing stacking of visibilities regardless of the array configuration or spectral setup. It is effective for both targeted sources and spurious detections offset from the phase center, whether unresolved or extended, within the field of view of the telescope. We validated the method using simulated interferometric datasets. For point-like sources, we can reconstruct the true emission with approximately 90% accuracy, obtaining similar results to classical image-plane stacking. In contrast, for faint and extended sources below the noise level, our method can provide a more accurate estimate of the signal compared to traditional image-based approaches. Finally, we applied ViSta to a sample of dusty star-forming galaxies observed with the Atacama Large Millimeter/sub-millimeter Array to detect the CO(3-2) emission line. As for the simulated case, we demonstrated that our tool performs better than image-plane stacking when the signal from individual sources is no longer easily detectable, achieving higher SNR. Finally, we outline potential future applications of this stacking approach.