Revealing the relation between black-hole growth and host-galaxy compactness among star-forming galaxies

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.