Deblending the MIGHTEE-COSMOS survey with XID+: the resolved radio source counts to S 1.4 ≈ 5μJy

Deep radio continuum surveys provide fundamental constraints on galaxy evolution, but source confusion limits sensitivity to the faintest sources. We present a complete framework for producing high-fidelity deblended radio catalogues from the confused MIGHTEE maps using the probabilistic deblending framework XID+ and prior positions from deep multi-wavelength data in the COSMOS field. To assess performance, we construct MIGHTEE-like simulations based on the Tiered Radio Extragalactic Continuum Simulation radio source population, ensuring a realistic distribution of star-forming galaxies and active galactic nuclei for validation. Through these simulations, we show that prior catalogue purity is the dominant factor controlling deblending accuracy: a high-purity prior, containing only sources with a high likelihood of radio detection, recovers accurate flux densities and reproduces input source counts down to ~ 3σ (where σ = thermal noise). On the other hand, a complete prior overestimates the source counts due to spurious detections. Our optimal strategy combines the high-purity prior with a mask that removes sources detected above 50µy. Applied to the ~1.3 deg² area of the MIGHTEE-COSMOS field defined by overlapping multi-wavelength data, this procedure yields a deblended catalogue of 89 562 sources. The derived 1.4 GHz source counts agree with independent P(D) analyses and indicate that we resolve the radio background to ~ 4.8 µJy. We also define a recommended high-fidelity sample of 20 757 sources, based on detection significance, flux density, and goodness-of-fit, which provides reliable flux densities for individual sources in the confusion-limited regime.