A High-resolution Far-infrared Survey to Probe Black Hole-Galaxy Co-evolution

Far-infrared (FIR) surveys are critical to probing the co-evolution of black holes and galaxies, since of order half the light from accreting black holes and active star formation is emitted in the rest-frame infrared over $0.5\lesssim z \lesssim 10$. For deep fields with areas of 1 deg$^2$ or less, like the legacy surveys GOODS, COSMOS, and CANDELS, source crowding means that sub-arcsecond resolution is essential. In this paper, we show with a simulation of the FIR sky that observations made with a small telescope (2 m) at low angular resolution preferentially detect the brightest galaxies, and we demonstrate the scientific value of a space mission that would offer sub-arcsecond resolution. We envisage a facility that would provide high-resolution imaging and spectroscopy over the wavelength range $25-400\,\mu m$, and we present predictions for an extragalactic survey covering $0.5\,\hbox{deg}^2$. Such a survey is expected to detect tens of thousands of star-forming galaxies and thousands of Active Galactic Nuclei (AGN), in multiple FIR lines (e.g. [CII], [OI], [CI]) and continuum. At the longest wavelengths (200-400$\,\mu$m), it would probe beyond the reionization epoch, up to $z\sim 7$-8. A combination of spectral resolution, line sensitivity, and broad spectral coverage would allow us to learn about the physical conditions (temperature, density, metallicity) characterizing the interstellar medium of galaxies over the past $\sim 12$ billion years and to investigate galaxy-AGN co-evolution.