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Exploring the relationship between black hole accretion and star formation with blind mid-/far-infrared spectroscopic surveys

We present new estimates of redshift-dependent luminosity functions of IR lines detectable by SPICA/SAFARI and excited both by star formation and by AGN activity. The new estimates improve over previous work by using updated evolutionary models and dealing in a self consistent way with emission of galaxies as a whole, including both the starburst and the AGN component. New relationships between line and AGN bolometric luminosity have been derived and those between line and IR luminosities of the starburst component have been updated. These ingredients were used to work out predictions for the source counts in 11 mid/far-IR emission lines partially or entirely excited by AGN activity. We find that the statistics of the emission line detection of galaxies as a whole is mainly determined by the star formation rate, because of the rarity of bright AGNs. We also find that the slope of the line integral number counts is flatter than 2 implying that the number of detections at fixed observing time increases more by extending the survey area than by going deeper. We thus propose a wide spectroscopic survey of 1 hour integration per field-of-view over an area of 5 deg$^{2}$ to detect (at 5$σ$) $\sim$760 AGNs in [OIV]25.89$μ$m $-$ the brightest AGN mid-infrared line $-$ out to $z\sim2$. Pointed observations of strongly lensed or hyper-luminous galaxies previously detected by large area surveys such as those by Herschel and by the SPT can provide key information on the galaxy-AGN co-evolution out to higher redshifts.