The Activation of Galactic Nuclei and Their Accretion Rates are Linked to the Star Formation Rates and Bulge-types of Their Host Galaxies

We use bulge-type classifications of 809 representative SDSS galaxies by Gadotti (2009) to classify a large sample of galaxies into real bulges (classical or elliptical) and pseudobulges using Random Forest. We use structural and stellar population predictors that can easily be measured without image decomposition. Multiple parameters such as the central mass density with 1 kpc, concentration index, S\'{e}rsic index and velocity dispersion do result in accurate bulge classifications when combined together. We classify $\sim 44,500$ face-on galaxies above stellar mass of 10$^{10}$ M$_\odot$ and redshift $ 0.02 < z < 0.07$ into real bulges or pseudobulges with $93 \pm 2$\% accuracy. We show that $\sim 75 - 90\%$ of AGNs identified by the optical line ratio diagnostic are hosted by real bulges. The pseudobulge fraction significantly decreases with AGN signature as the line ratios change from indicating pure star formation ($\sim 54 \pm 4$ \%), to composite of star formation and AGN ($\sim 18 \pm 3$\%), and to AGN-dominated galaxies ($\sim 5 \pm 3$\%). Using the dust-corrected [\ion{O}{3}] luminosity as an AGN accretion indicator, and the stellar mass and radius as proxies for a black hole mass, we find that AGNs in real bulges have lower Eddington ratios than AGNs in pseudobulges. Real bulges have a wide range of AGN and star formation activities, although most of them are weak AGNs. For both bulge-types, their Eddington ratios are correlated with specific star formation rates (SSFR). Real bulges have lower specific accretion rate but higher AGN fraction than pseudobulges do at similar SSFRs.