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The most active phases of star formation and black hole accretion are strongly affected by dust extinction, making far-infrared (FIR) observations the best way to disentangle and study the co-evolution of galaxies and super massive black holes. The plethora of fine-structure lines and emission features from dust and ionised and neutral atomic and warm molecular gas in the rest-frame mid-infrared (MIR) and FIR provide unmatched diagnostic opportunities to determine the properties of gas and dust, measure gas-phase metallicities, and map cold galactic outflows in even the most obscured galaxies. By combining multi-band photometric surveys with low- and high-resolution FIR spectroscopy, the PRobe far-Infrared Mission for Astrophysics (PRIMA), a 1.8 m diameter, cryogenically cooled FIR observatory currently at the conception stage, will revolutionise the field of galaxy evolution by taking advantage of this IR toolkit to find and study dusty galaxies across galactic time. In this work, we make use of the phenomenological simulation SPRITZand the Santa Cruz semi-analytical model to describe how a moderately deep multi-band PRIMA photometric survey can easily reach beyond previous IR missions to detect and study galaxies down to 10¹¹ L_⊙beyond cosmic noon and at least up toz = 4, even in the absence of gravitational lensing. By decomposing the spectral energy distribution (SED) of these photometrically selected galaxies, we show that PRIMA can be used to accurately measure the relative AGN power, the mass fraction contributed by polycyclic aromatic hydrocarbons (PAHs), and the total IR luminosity. At the same time, spectroscopic follow up with PRIMA will allow us to trace both the star formation and black hole accretion rates (SFRs and BHARs), the gas-phase metallicities, and the mass-outflow rates of cold gas in hundreds to thousands of individual galaxies toz = 2. 

ABSTRACT The PRobe far-Infrared Mission for Astrophysics (PRIMA) concept aims to perform mapping with spectral coverage and sensitivities inaccessible to previous FIR space telescopes. PRIMA’s imaging instrument, PRIMAger, provides unique hyperspectral imaging simultaneously covering 25–235 µm. We synthesize images representing a deep, 1500 h deg−2 PRIMAger survey, with realistic instrumental and confusion noise. We demonstrate that we can construct catalogues of galaxies with a high purity (>95 per cent) at a source density of 42 k deg−2 using PRIMAger data alone. Using the XID+ deblending tool, we show that we measure fluxes with an accuracy better than 20 per cent to flux levels of 0.16, 0.80, 9.7, and 15 mJy at 47.4, 79.7, 172, and 235 µm, respectively. These are a factor of ∼2 and ∼3 fainter than the classical confusion limits for 72–96 and 126–235 µm, respectively. At $$1.5 \le z \le 2$$, we detect and accurately measure fluxes in 8–10 of the 10 channels covering 47–235 µm for sources with $$2 \lesssim \log ({\rm SFR}) \lesssim 2.5$$, a 0.5 dex improvement on what might be expected from the classical confusion limit. Recognizing that PRIMager will operate in a context where high-quality data will be available at other wavelengths, we investigate the benefits of introducing additional prior information. We show that by introducing even weak prior flux information when employing a higher source density catalogue (more than one source per beam), we can obtain accurate fluxes an order of magnitude below the classical confusion limit for 96–235 µm.