XID+PRIMA, II: Stepping Through Hyperspectral Imaging to Deblend PRIMAger Beyond the Extragalactic Confusion Limit
The PRIMA mission concept aims to map large areas with spectral coverage and sensitivities inaccessible to previous FIR space telescopes, covering 25-235 $μ$m. We synthesise images representing a deep imaging survey, with realistic instrumental and confusion noise, reflecting the latest PRIMAger specifications. We present a new Bayesian modelling approach XID+stepwise that exploits PRIMAger's hyperspectral imaging to derive self-consistent, informative flux priors by sequentially propagating constraints from short to long wavelengths. With Euclid-like prior source positions, this method recovers fluxes to within 20% down to 0.2-0.7 mJy across 45-84 $μ$m, which correspond to factors of 1.3-3.5 fainter than the confusion limit. For the most confusion-dominated channels, accurate fluxes are measured down to 0.8, 2.7, 9.3, and 23.4 mJy at 92, 126, 183, and 235 $μ$m, respectively, which are factors of 2-5 better than the confusion limit. Using a deeper Euclid-based prior catalogue and weak ancillary flux priors at 25 $μ$m yields further improvements, reaching up to a factor 5 fainter than the confusion limit at 96 $μ$m. Additionally, we demonstrate that positional priors from blind source detection followed by deblending via XID+ enables PRIMAger to achieve sensitivity beyond the confusion limits using PRIMAger data alone. We show that IR-luminous galaxies at $z \sim 2$ are robustly detected in a large fraction of the PRIMAger channels (>98% in 12 out of the 16 considered channels), providing dense sampling of the FIR SED even for sources several factors below the classical confusion limit. We explore the impact on our results for a range of systematic effects, including cirrus contamination, optical degradation, and calibration uncertainties. These findings indicate that confusion noise will not limit the key science from PRIMA extragalactic imaging surveys when employing XID+.