Spectral stacking of radio-interferometric data

Context. Mapping molecular line emission beyond the bright low-J CO transitions is still challenging in extragalactic studies, even with the latest generation of (sub-)millimetre interferometers, such as ALMA and NOEMA.
Aims: We summarise and test a spectral stacking method that has been used in the literature to recover low-intensity molecular line emission, such as HCN(1−0), HCO⁺(1−0), and even fainter lines in external galaxies. The goal is to study the capabilities and limitations of the stacking technique when applied to imaged interferometric observations.
Methods: The core idea of spectral stacking is to align spectra of the low S/N spectral lines to a known velocity field calculated from a higher S/N line expected to share the kinematics of the fainter line (e.g. CO(1−0) or 21 cm emission). Then these aligned spectra can be coherently averaged to produce potentially high S/N spectral stacks. Here we used imaged simulated interferometric and total power observations at different S/N levels, based on real CO observations.
Results: For the combined interferometric and total power data, we find that the spectral stacking technique is capable of recovering the integrated intensities even at low S/N levels across most of the region where the high S/N prior is detected. However, when stacking interferometer-only data for low S/N emission, the stacks can miss up to 50% of the emission from the fainter line.
Conclusions: A key result of this analysis is that the spectral stacking method is able to recover the true mean line intensities in low S/N cubes and to accurately measure the statistical significance of the recovered lines. To facilitate the application of this technique we provide a public Python package, called PYSTACKER.