Prior-based Source Extraction below the Confusion Limit with XID+ in the Herschel-SPIRE Dark Field

Source detection and photometry with Herschel-SPIRE is fundamentally limited by confusion rather than instrumental noise, with 1 σ confusion noises of ∼5–7 mJy across the 250–500 μ m bands. We apply XID+, a probabilistic Bayesian deblender, to the Herschel-SPIRE Dark Field, the deepest SPIRE image obtained, using positional priors from a Spitzer-MIPS 24 μ m catalog of 2625 sources over a 225 arcmin 2 overlap region. Euclidean-normalized differential number counts are recovered at 250, 350, and 500 μ m and compared against an independent P ( D ) fluctuation analysis of the same field, the SIDES+uchuu simulation, and published literature counts. XID+ recovers counts below the 1 σ confusion noise in all three bands, in good agreement with P ( D ) and HerMES+stacking to ∼2 mJy. These results validate prior-based deblending and motivate its adoption for next-generation far-infrared surveys with NASA’s PRIMA.