Spectral Stacking of Radio-Interferometric Data

Mapping molecular line emission beyond the bright low-J CO transitions is still challenging in extragalactic studies, even with the latest generation of (sub-)mm interferometers, such as ALMA and NOEMA. 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. 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 use imaged simulated interferometric and total power observations at different signal-to-noise levels, based on real CO observations. 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. 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.