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Appendix A: Optical spectra of nine galaxies

We present the optical spectra of nine galaxies in our sample without a previously published [N ii]/Hα ratio, to best of our knowledge. Their reduced spectra were available through the Smithsonian Astrophysical Observatory Telescope Data Center. They were obtained between 1998 and 2006 with the FAST Spectrograph (Tokarz & Roll 1997) on the Mount Hopkins Tillinghast 1.5 m reflector. The slit width was 3′′  and the spectra cover the spectral range between 3700 and 7500 Å with a dispersion of 1.5 Å per pixel. The integration times were between 600 and 1500 s. The spectra are not flux-calibrated, but they can be used to measure line ratios between transitions close in wavelength.

In the spectra shown in FigureA.1, we measured the fluxes of the Hβ, [O iii]λ5007 Å, Hα, and [N ii]λ6584 Å emission lines using a single-component Gaussian fit, except for CGCG 468-002 NED01, which shows a blue-shifted broad Hα component. The FWHM of the narrow component in this galaxy is ~500 km s^-1 (Alonso-Herrero et al. 2013), whereas the broad Hα component has a FWHM of 3100 ± 190 km s^-1 and is blue-shifted by 180 ± 60 km s^-1. The observed line ratios are listed in Table A.1. Hβ is not corrected for stellar absorption.

We used the standard optical diagnostic diagram [N ii]/Hα vs. [O iii]/Hβ (Baldwin et al. 1981) to determine the nuclear activity classification. We used the boundary limits between H ii, composite and AGN galaxies proposed by Kewley et al. (2006). Figure A.2 shows that four of the galaxies lie in the composite region of the diagram, one in the H ii region, although close to the H ii-composite border, and one galaxy, CGCG 468-002 NED01, is classified as AGN. Since in this object we only detect a broad component in Hα, we classify it as Sy1.9. For UGC 03405 and NGC 7753, the Hβ and [O iii]λ5007 Å transitions were not detected so we excluded these objects from the diagram. However, the high [N ii]/Hα ratio in these two sources, together with the absence of [O iii] detections, which is bright in AGNs, suggests that these are composite galaxies.

Appendix B: Likelihood with detections and upper limits

In this appendix we briefly describe how the upper limits are included in our Bayesian analysis (see, e.g., Gregory 2005; Bohm & Zech 2010, for a general description of the Bayesian approach). We let F_i and σ_i be the flux and 1σ uncertainty

measured for a galaxy in the band i. If the galaxy is not detected, we measure the nσ_i upper limit. Likewise, the prediction of the model k for the flux of band i is M_i(k). The likelihood is defined as (B.1)For the detections we assume that f_i follows a normal distribution (B.2)On the other hand, to obtain the likelihood for the upper limits, , we first calculate the probability for the flux to have an arbitrary value R_i. The unknown background in the aperture used to measure the flux is B_i. The standard deviation of the background is σ_i, and for simplicity we assume that the mean background of the image is zero. That the galaxy flux is R_i but we do not detect it on the image at a nσ_i level is because R_i + B_i<nσ_i. If the background follows a normal distribution the probability of this is (B.3)where Φ is the cumulative distribution function of the standard normal distribution. Therefore the likelihood value for the upper limits is (B.4)Then when substituting Eqs. (B.3) and (B.4) into Eq. (B.1), (B.5)where i₁ and i₂ are the subindices for the detections and non-detections, respectively. The logarithm of Eq. (B.5) is (B.6)Thus, we assign the following probability to model k in the parameter inference process (B.7)

Appendix C: Multi-wavelength imaging of the LIRGs

Appendix D: Best fitting model results to the SED

© ESO, 2015