Local luminous infrared (IR) galaxies (LIRGs) have both high star formation rates (SFR) and a high AGN (Seyfert and AGN/starburst composite) incidence. Therefore, they are ideal candidates to explore the co-evolution of black hole (BH) growth and star formation (SF) activity, not necessarily associated with major mergers. Here, we use Spitzer/IRS spectroscopy of a complete volume-limited sample of local LIRGs (distances of <78Mpc). We estimate typical BH masses of 3x10^7 M_sun using [NeIII]15.56micron and optical [OIII]5007A gas velocity dispersions and literature stellar velocity dispersions. We find that in a large fraction of local LIRGs the current SFR is taking place not only in the inner nuclear ~1.5kpc region, as estimated from the nuclear 11.3micron PAH luminosities, but also in the host galaxy. We next use the ratios between the SFRs and BH accretion rates (BHAR) to study whether the SF activity and BH growth are contemporaneous in local LIRGs. On average, local LIRGs have SFR to BHAR ratios higher than those of optically selected Seyferts of similar AGN luminosities. However, the majority of the IR-bright galaxies in the RSA Seyfert sample behave like local LIRGs. Moreover, the AGN incidence tends to be higher in local LIRGs with the lowest SFRs. All this suggests that in local LIRGs there is a distinct IR-bright star forming phase taking place prior to the bulk of the current BH growth (i.e., AGN phase). The latter is reflected first as a composite and then as a Seyfert, and later as a non-LIRG optically identified Seyfert nucleus with moderate SF in its host galaxy.
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