Averaged spectral energy distributions (SEDs) of active and starburst galaxies, from the 12 μm sample in the local universe, and QSOs, from an optically selected sample at a mean redshift (z) = 0.7, are built from optical, near-IR, and far-IR (FIR; IRAS and Infrared Space Observatory) photometric observations. These SEDs are then used to predict at various redshifts the number of Seyfert type 1 and type 2, starburst, and normal galaxies and QSOs that will be detected by future space missions dedicated to FIR and submillimeter astronomy, such as SIRTF and Herschel. These predictions are then compared with the expected capabilities and detection limits of future deep FIR surveys. Possible ways to identify active galactic nucleus candidates on FIR color-color plots for follow-up observations are then explored.

New far-infrared photometry with ISOPHOT aboard the Infrared Space Observatory (ISO) is presented for 58 galaxies with homogeneous published data for another 32 galaxies, all belonging to the 12 μm galaxy sample - in total, 29 Seyfert 1 galaxies, 35 Seyfert 2 galaxies, and 12 starburst galaxies, or about half of the 12 μm active galaxy sample, plus 14 normal galaxies for comparison. ISO and Infrared Astronomical Satellite (IRAS) data are used to define color-color diagrams and spectral energy distributions (SEDs). Thermal dust emission at two temperatures (one cold at 15-30 K and one warm at 50-70 K) can fit the 60-200 μm SED, with a dust emissivity law proportional to the inverse square of the wavelength. Seyfert 1 galaxies and Seyfert 2 galaxies are indistinguishable longward of 100 μm, while, as already seen by IRAS, the former have flatter SEDs shortward of 60 μm. A mild anticorrelation is found between the [200-100] color and the "60 μm excess." We infer that this is due to the fact that galaxies with a strong starburst component and thus a strong 60 μm flux have a steeper far-infrared turnover. In non-Seyfert galaxies, increasing the luminosity corresponds to increasing the star formation rate, which enhances the 25 and 60 μm emission. This shifts the peak emission from around 150 μm in the most quiescent spirals to shorter than 60 μm in the strongest starburst galaxies. To quantify these trends further, we identified with the IRAS colors three idealized infrared SEDs: pure quiescent disk emission, pure starburst emission, and pure Seyfert nucleus emission. Even between 100 and 200 μm, the quiescent disk emission remains much cooler than the starburst component. Seyfert galaxies have 100-200 μm SEDs ranging from pure disks to pure starbursts, with no apparent contribution from their active nuclei at those wavelengths.

We present a coherent database of spectroscopic observations of far-IR fine-structure lines from the Herschel/PACS archive for a sample of 170 local AGN, plus a comparison sample of 20 starburst galaxies and 43 dwarf galaxies. Published Spitzer/IRS and Herschel/SPIRE line fluxes are included to extend our database to the full 10-600 $\mu m$ spectral range. The observations are compared to a set of CLOUDY photoionisation models to estimate the above physical quantities through different diagnostic diagrams. We confirm the presence of a stratification of gas density in the emission regions of the galaxies, which increases with the ionisation potential of the emission lines. The new [OIV]25.9$\mu m$/[OIII]88$\mu m$ vs [NeIII]15.6$\mu m$/[NeII]12.8$\mu m$ diagram is proposed as the best diagnostic to separate: $i)$ AGN activity from any kind of star formation; and $ii)$ low-metallicity dwarf galaxies from starburst galaxies. Current stellar atmosphere models fail to reproduce the observed [OIV]25.9$\mu m$/[OIII]88$\mu m$ ratios, which are much higher when compared to the predicted values. Finally, the ([NeIII]15.6$\mu m$ + [NeII]12.8$\mu m$)/([SIV]10.5$\mu m$ + [SIII]18.7$\mu m$) ratio is proposed as a promising metallicity tracer to be used in obscured objects, where optical lines fail to accurately measure the metallicity. The diagnostic power of mid- to far-infrared spectroscopy shown here for local galaxies will be of crucial importance to study galaxy evolution during the dust-obscured phase at the peak of the star formation and black-hole accretion activity ($1 < z < 4$). This study will be addressed by future deep spectroscopic surveys with present and forthcoming facilities such as JWST, ALMA, and SPICA.