  To understand the physical origin of the close connection between
supermassive black holes and their host galaxies, it is vital to investigate
star formation properties in active galaxies. Using a large dataset of nearby
type 1 active galactic nuclei (AGNs) with detailed structural decomposition
based on high-resolution optical images obtained with the Hubble Space
Telescope, we study the correlation between black hole mass and bulge
luminosity and the (Kormendy) relation between bulge effective radius and
surface brightness. In both relations, the bulges of type 1 AGNs tend to be
more luminous than those of inactive galaxies with the same black hole mass or
the same bulge size. This suggests that the central regions of AGN host
galaxies have characteristically lower mass-to-light ratios than inactive
galaxies, most likely due to the presence of a younger stellar population in
active systems. In addition, the degree of luminosity excess appears to be
proportional to the accretion rate of the AGN, revealing a physical connection
between stellar growth and black hole growth. Adopting a simple toy model for
the increase of stellar mass and black hole mass, we show that the fraction of
young stellar population flattens out toward high accretion rates, possibly
reflecting the influence of AGN-driven feedback.
