ABSTRACT UV-FIR spectral energy distribution (SED) modelling is an effective way to disentangle emission between star formation (SF) and active galactic nuclei (AGNs) in galaxies; however, this approach becomes uncertain for composite AGNs/SF galaxies that comprise 50–70 per cent of IR-samples. Cosmic X-ray background (XRB) models require a large fraction of obscured AGNs to reproduce the observed XRB peak, motivating reliable SED analyses in objects where the AGNs may be ‘buried’ in the galaxy and in the mid-IR to far-IR SED. In this paper, we study a 24 $\mu$m-selected (S24 > 100 $\mu$Jy) sample of 95 galaxies with $0~{{\ \rm per\ cent}} \lt f_{\mathrm{ MIR},\mathrm{ AGN}} \lt 100~{{\ \rm per\ cent}}$, 0.4 < z < 2.7, and 1011L⊙ < LIR < 1013L⊙. We test the performance of AGN models ranging in torus optical depth via SED fitting, comparing results with Spitzer mid-infrared spectroscopy and X-ray observations. The best-fitting torus optical depth can shed light on whether these galaxies host a luminous obscured AGN population. We find that permitting a broader AGN SED parameter space results in improved fit quality with higher optical depths, higher FIR AGN contributions, and higher LBol, impacting the bright end of the LBol luminosity function. Our results suggest there may be a population of dust-obscured composites that are bolometrically significant but have their AGNs mostly hidden in the mid-IR SED. If so, literature applications of SED fitting that often simplify AGN models or omit optically thick tori may largely underestimate AGN contribution from composite sources, as these sources are both numerous and have solutions sensitive to the assumed range of AGN models.
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