Tracing the history of recent bulge star formation in Active Galactic Nuclei

We examine the relation between black hole accretion and bulge star formation as a function of look-back time (τ) in 20 541 obscured active galactic nuclei (AGNs; with redshifts z̄ ~ 0.1 and bolometric luminosities L_Bol ~ 10⁴³-10⁴⁵ erg s^-1) optically selected from the Sloan Digital Sky Survey (SDSS). To quantify the most recently formed stars with ages less than typical AGN lifetimes, we estimate the differentiated specific star formation rate (SSFRτ) based on population synthesis analysis. The Eddington ratio (λ) is inferred using [O III] λ5007 luminosity and stellar velocity dispersion as proxies for L_Bol and black hole mass, respectively. We find that when τ < τ ₀, SDSS AGNs follow a power law λ ∝ SSFR^1.0-1.1_τ the relation flattens out when τ > τ ₀. The threshold time-scale τ₀ is ~0.1 (~1) Gyr in young (old) bulges. The scatter in the power laws is dominated by observational uncertainties. These results may provide useful constraints on models explaining the correlations between AGN activity and bulge star formation.