Using the spectra of a sample of approximately 28,000 nearby obscured active galaxies from Data Release 7 of the Sloan Digital Sky Survey (SDSS), we probe the connection between active galactic nucleus (AGN) activity and star formation over a range of radial scales in the host galaxy. We use the extinction-corrected luminosity of the [O iii] 5007A line as a proxy of intrinsic AGN power and supermassive black hole (SMBH) accretion rate. The star formation rates (SFRs) are taken from the MPA-JHU value-added catalog and are measured through the 3 inch SDSS aperture. We construct matched samples of galaxies covering a range in redshifts. With increasing redshift, the projected aperture size encompasses increasing amounts of the host galaxy. This allows us to trace the radial distribution of star formation as a function of AGN luminosity. We find that the star formation becomes more centrally concentrated with increasing AGN luminosity and Eddington ratio. This implies that such circumnuclear star formation is associated with AGN activity, and that it increasingly dominates over omnipresent disk star formation at higher AGN luminosities, placing critical constraints on theoretical models that link host galaxy star formation and SMBH fueling. We parameterize this relationship and find that the star formation on radial scales (is) less than 1.7 kpc, when including a constant disk component, has a sub-linear dependence on SMBH accretion rate: SFR in proportion to solar mass(sup 0.36), suggesting that angular momentum transfer through the disk limits accretion efficiency rather than the supply from stellar mass loss
