  Recent studies show that a universal relation between black-hole (BH) growth
and stellar mass ($M_\bigstar$) or star formation rate (SFR) is an
oversimplification of BH-galaxy co-evolution, and that morphological and
structural properties of host galaxies must also be considered. Particularly, a
possible connection between BH growth and host-galaxy compactness was
identified among star-forming (SF) galaxies. Utilizing $\approx 6300$ massive
galaxies with $I_{\rm 814W}~<~24$ at $z$ $<$ 1.2 in the COSMOS field, we
perform systematic partial-correlation analyses to investigate how
sample-averaged BH accretion rate ($\rm \overline{BHAR}$) depends on
host-galaxy compactness among SF galaxies, when controlling for morphology and
$M_\bigstar$ (or SFR). The projected central surface-mass density within 1 kpc,
$\Sigma_{1}$, is utilized to represent host-galaxy compactness in our study. We
find that the $\rm \overline{BHAR}$-$\Sigma_{1}$ relation is stronger than
either the $\rm \overline{BHAR}$-$M_\bigstar$ or $\rm \overline{BHAR}$-SFR
relation among SF galaxies, and this $\rm \overline{BHAR}$-$\Sigma_{1}$
relation applies to both bulge-dominated galaxies and galaxies that are not
dominated by bulges. This $\rm \overline{BHAR}$-$\Sigma_{1}$ relation among SF
galaxies suggests a link between BH growth and the central gas density of host
galaxies on the kpc scale, which may further imply a common origin of the gas
in the vicinity of the BH and in the central $\sim$ kpc of the galaxy. This
$\rm \overline{BHAR}$-$\Sigma_{1}$ relation can also be interpreted as the
relation between BH growth and the central velocity dispersion of host galaxies
at a given gas content, indicating the role of the host-galaxy potential well
in regulating accretion onto the BH.
