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Galaxy evolution through infrared and submillimeter spectroscopy: Measuring star formation and black hole accretion with JWST and ALMA

Rest-frame mid- to far-infrared spectroscopy is a powerful tool to study how galaxies formed and evolved, because a major part of their evolution occurs in heavily dust enshrouded environments, especially at the so-called Cosmic Noon. Using the calibrations of IR lines we predict the expected fluxes of lines and features, with the aim to measure the star formation rate and the Black Hole Accretion rate in intermediate to high redshift galaxies. The launch of the James Webb Space Telescope will allow us a deep investigation of both the SF and the BHA obscured processes as a function of cosmic time. We assess the spectral lines and features that can be detected by JWST-MIRI in galaxies and Active Galactic Nuclei up to redshift z= 3. We confirm the fine-structure lines of [MgIV]4.49um and [ArVI]4.53um as good BHA rate tracers for the 1<z<3 range, and we propose the [NeVI]7.65um line as the best tracer for redshifts of z<1.5. We suggest the use of the [ArII]6.98um and [ArIII]8.99um lines to measure the SF rate, for z<3 and z<2. At higher redshifts, the PAH features at 6.2um and 7.7um can be observed at z<3 and z<2.7 respectively. Rest-frame far-IR spectroscopy is currently being collected in high redshift galaxies (z>3) with the Atacama Large Millimeter Array. We confirm that the [CII]158um line is a good tracer of the SF rate and can in most cases (0.9<z<2 and 3<z<9) be observed, and we propose the use of the combination of [OIII]88um and [OI]145um lines as an alternative SF rate tracer, that can be detected above z>3. We conclude, however, that the current and foreseen facilities will not be able to cover properly the peak of the obscured SF and BHA activities at the Cosmic Noon of galaxy evolution and a new IR space telescope, actively cooled to obtain very good sensitivities, covering the full IR spectral range from about 10um to 300um, will be needed.