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

TL;DR

ViSta tackles the challenge of extracting faint spectral lines from heterogeneous interferometric archives by performing stacking directly in the uv-domain. It coherently aligns visibilities to the rest-frame using $\lambda_{\rm RF}=\lambda/(1+z)$ and applies related spectral and flux corrections via $\Delta\lambda_{\rm RF}=\Delta\lambda/(1+z)$ and $L_{\rm RF}=S_{\rm obs}\,4\pi D_{\rm L}^2/(1+z)$, then concatenates data across observations. In simulations, ViSta recovers point-like emission with about 90% accuracy and yields substantial SNR gains for faint extended sources, with reported improvements of roughly 39% at high sensitivity and 53% at lower sensitivity for spectral lines, plus ~18% gain for continuum extraction. Applied to real ALMA CO(3-2) data, ViSta produces results consistent with image-domain stacking when morphologies are well constrained and demonstrates clear advantages in low-SNR or sparse-uv regimes; the authors also release public code and outline future scalable, cross-facility implementations for the SKA era.

Abstract

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 (DSFGs) observed with the Atacama Large Millimeter/sub-millimeter Array (ALMA) 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.

Figures (16)

• Figure 1: The ViSta method general workflow. We also provide specifics for ALMA Measurement Sets, listing the functions from CASA or other astronomical libraries and the tables that have been manually modified. The blue color cells refers to the input data editing phase, while the red color cells represents the output extraction steps.
• Figure 2: Example of the image and uv-plane coverage in units of meters for one of the uncorrupted simulated sources at redshift 2.9, observed with ALMA configuration 4. The left panels (1 and 2) shows the image and uv-plane coverage in the observed frame, while the right panels (3 and 4) shows the resulting image after rest-framing.
• Figure 3: uv-plane coverage of the stacked simulated source. Visibilities from different array configurations have been centered on the phase center and shifted to the rest frame using the ViSta method applied to the ALMA data. The left panel shows the rest-framed visibilities position in the uv-plane for all the 50 mock observation, color-coded according to the observing configuration. The right panel shows the difference in uv-plane coverage for the same configuration (5 sources at configuration 4, with max baseline at 780m ) observed at different redshifts.
• Figure 4: Comparison between the peak channel image of a single mock source before stacking, where the source signal is below the noise level (left panel), and the result after stacking 50 mock sources using the ViSta method (right panel).
• Figure 5: Top panel: Spectral line profiles recovered using the ViSta-ImFit method for different numbers of stacked point-like mock sources ($N = 1$, 5, 10, 25, 50), compared to the true emission profile (green solid line). Bottom panel: measured RMS noise of the corresponding stacked spectra as a function of $N$. The dashed line represents the expected $1/\sqrt{N}$ scaling, corresponding to the theoretical noise reduction with ideal stacking. The agreement between the measured and expected values confirms the statistical robustness of the method.