We examine the relation between black hole accretion and bulge star formation as a function of look-back time ( \tau ) in 20,541 obscured AGNs ( with redshifts \bar { z } \sim 0.1 and bolometric luminosities L _ { { Bol } } \sim 10 ^ { 43 } – 10 ^ { 45 } 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 ( SSFR _ { \tau } ) based on population synthesis analysis .
Eddington ratio ( \lambda ) is inferred using [ O III ] \lambda 5007 luminosity and stellar velocity dispersion as proxies for L _ { { Bol } } and black hole mass respectively .
We find that when \tau < \tau _ { 0 } , SDSS AGNs follow a power law \lambda \propto SSFR _ { \tau } ^ { 1.0 - 1.1 } ; the relation flattens out when \tau > \tau _ { 0 } .
The threshold timescale \tau _ { 0 } is \sim 0.1 ( \sim 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 .