ERRATUM: "FAR-IR/SUBMILLIMETER SPECTROSCOPIC COSMOLOGICAL SURVEYS: PREDICTIONS OF INFRARED LINE LUMINOSITY FUNCTIONS FORz< 4 GALAXIES" (2012, ApJ, 745, 171)
In the published version of this article, an error was found in the computation of the total infrared (IR) luminosity. Using the formula from Sanders & Mirabel (1996) , we omitted the multiplication factor 1.8, which resulted in underestimations of the total luminosities. Therefore, we present here the corrected results for the line to continuum luminosity relations, the predicted number of sources that could be detected in spectroscopic cosmological surveys from the SPICA and CCAT telescopes,
... d CCAT telescopes, and the line luminosity functions. Because of the relatively small error, the impact on the conclusions of this article is minor. Moreover, Figure 3 of the original article, showing the IR luminosity function from the Valiante et al. (2009) paper, is incorrect due to a numerical artifact. Therefore, we have revised the figure and included it in this erratum. For better readability, we report here the whole of Sections 2.3 and 2.4, and the first three paragraphs of Section 3.1. Predicting Continuum Luminosity Functions with the Valiante et al. (2009) Model The third model that we used is the backward evolution model of Valiante et al. (2009) . It was developed using Spitzer and SCUBA observations, and it has been very successful in predicting Herschel results Altieri et al. 2010; Glenn et al. 2010; Oliver et al. 2010) . This model allows us to take into account galaxies that are not "pure" starburst or "pure" active galactic nuclei (AGNs), and for which the ratios between IR lines might not be the ones expected assuming "pure" spectral energy distributions. This is because the model considers all infrared galaxies as a single population, assuming that starbursts and AGNs coexist. It then uses an empirical relation to assign to each galaxy the fraction of the IR luminosity that is powered by the AGN for its given luminosity and redshift. This relation was derived using a complete sample of local IRAS galaxies, and extrapolated to high-z using Spitzer and SCUBA observations. Figure 1 shows the IR luminosity function predicted by this model for each z bin. Converting Continuum Luminosity Functions to Line or Feature Luminosity Functions The galaxy number counts per redshift and bolometric IR luminosity bin that are predicted by each model need to be converted into line luminosity functions, in order to estimate the number of objects that will be detectable in various lines, and to assess whether several of the open questions presented in Section 1 can be addressed. For this purpose, we derived correlations between line and continuum luminosities, including lines for which such correlations were not previously available in the literature, e.g., that of [Si ii] for both AGNs and star-forming galaxies. We examined the polycyclic aromatic hydrocarbon (PAH) feature at 11.25 μm, the purely rotational H 2 (0-0)S1 line at 17.03 μm, and the [Ne ii] 12.8 μm, [Ne v] 14.3 μm, [Ne iii] 15.5 μm, [S iii] 18.7 μm, [Ne v] 24.3 μm, [O iv] 26 μm, [Si ii] 34.8 μm, [O iii] 52 μm, [N iii] 57 μm, [O i] 63 μm, [O iii] 88 μm, [N ii] 121.90 μm, [O i] 145.52 μm, and [C ii] 157.74 μm fine-structure lines. These lines cover a wide parameter space of the critical density versus ionization potential diagram (see Figure 4 of the original article), tracing different astrophysical conditions: from photodissociation regions, to stellar/H ii regions, to the AGN, and coronal line regions (Spinoglio & Malkan 1992) . This makes the combination of their ratios useful for the creation of AGNs versus star formation diagnostic diagrams (e.g., Spinoglio & Malkan 1992; Genzel et al. 1998; Dale et al. 2006; Smith et al. 2007) . For lines at wavelengths shorter than 35 μm, we used the complete, 12 μm selected sample of local Seyfert galaxies (Tommasin et al. 2008 (Tommasin et al. , 2010 and the Bernard-Salas et al. (2009) sample of starburst galaxies to calibrate the line luminosities to L IR . These samples have been extensively observed in the mid-IR (MIR) with the Infrared Spectrometer (Houck et al. 2004) on board Spitzer (Werner et al. 2004) , and the Spitzer spectra have been reduced and analyzed in a consistent way. For the starburst galaxies, we excluded all objects for which there was evidence for the presence of an AGN from the literature or from the detection of [Ne v] (see Table 1 of Bernard-Salas et al. 2009 ). For the long-wavelength lines, we used the heterogeneous sample of local galaxies compiled by Brauher et al. (2008) containing all observations collected by the Long Wavelength Spectrometer (LWS; Clegg et al. 1996) on board Infrared Space Observatory (ISO; Kessler et al. 1996) . The IR luminosities of the galaxies of our sample have been computed from the IRAS fluxes, using the formula of L IR 7 representing the total mid-and far-infrared luminosity (Sanders & Mirabel 1996) . All luminosities are in units of 10 41 erg s −1 . 7 L IR is computed by fitting a single-temperature dust emissivity model ( ∝ ν −1 ) to the flux in all four IRAS bands, and should be accurate to ±5% for dust temperatures in the range 25-65 K. We notice that the IR luminosities, as defined above, are model dependent, and therefore could introduce some systematics. However, these do not affect the derived relations, as they are within the given errors.