On the Star Formation-AGN Connection at $z \lesssim 0.3$
  Using the spectra of a sample of $\sim$28,000 nearby obscured active galaxies
from Data Release 7 of the Sloan Digital Sky Survey (SDSS), we probe the
connection between AGN activity and star formation over a range of radial
scales in the host galaxy. We use the extinction-corrected luminosity of the
[OIII] 5007 \AA\ line as a proxy of intrinsic AGN power and supermassive black
hole (SMBH) accretion rate. The star formation rates (SFRs) are taken from the
MPA-JHU value-added catalog and are measured through the 3$^{\prime\prime}$
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 parametrize this relationship and find that the star
formation on radial scales $<$1.7 kpc, when including a constant disk
component, has a sub-linear dependence on SMBH accretion rate: $SFR \propto
\dot{M}^{0.36}$, suggesting that angular momentum transfer through the disk
limits accretion efficiency rather than the supply from stellar mass loss.
