Comparing SCUBA-2 and ALMA Selections of Faint DSFGs in Abell 2744

We make a comparison of deep SCUBA-2 450 $\mu$m and 850 $\mu$m imaging on the massive lensing cluster field Abell 2744 with Atacama Large Millimeter/submillimeter Array (ALMA) 1.2 mm data. Our primary goal is to assess how effective the wider-field SCUBA-2 sample, in combination with red JWST priors, is for finding faint dusty star-forming galaxies (DSFGs) compared to the much more expensive mosaicked ALMA observations. We cross-match our previously reported direct ($>5\sigma$) SCUBA-2 sample and red JWST NIRCam prior-selected ($>3\sigma$) SCUBA-2 sample to direct ALMA sources from the DUALZ survey. We find that roughly 95% are confirmed by ALMA. The red priors also allow us to probe deeper in the ALMA image. Next, by measuring the 450 $\mu$m and 850 $\mu$m properties of the full ALMA sample, we show that 46/69 of the ALMA sources are detected at 850 $\mu$m and 24/69 are detected at 450 $\mu$m in the SCUBA-2 images, with a total detection fraction of nearly 75%. All of the robust ($>5\sigma$) ALMA sources that are not detected in at least one SCUBA-2 band lie at 1.2 mm fluxes $\lesssim$ 0.6 mJy and are undetected primarily due to the higher SCUBA-2 flux limits. We also find that the SCUBA-2 detection fraction drops slightly beyond $z=3$, which we attribute to the increasing 1.2 mm to 850 $\mu$m and 1.2 mm to 450 $\mu$m flux ratios combined with the ALMA selection. The results emphasize the power of combining SCUBA-2 data with JWST colors to map the faint DSFG population.