Black-Hole Growth is Mainly Linked to Host-Galaxy Stellar Mass rather than Star Formation Rate

We investigate the dependence of black-hole accretion rate (BHAR) on host-galaxy star formation rate (SFR) and stellar mass ($M_*$) in the CANDELS/GOODS-South field in the redshift range of $0.5\leq z < 2.0$. Our sample consists of $\approx 18000$ galaxies, allowing us to probe galaxies with $0.1 \lesssim \mathrm{SFR} \lesssim 100\ M_\odot\ \mathrm{yr}^{-1}$ and/or $10^8 \lesssim M_* \lesssim 10^{11}\ M_{\odot}$. We use sample-mean BHAR to approximate long-term average BHAR. Our sample-mean BHARs are derived from the $Chandra$ Deep Field-South 7 Ms observations, while the SFRs and $M_*$ have been estimated by the CANDELS team through SED fitting. The average BHAR is correlated positively with both SFR and $M_*$, and the BHAR-SFR and BHAR-$M_*$ relations can both be described acceptably by linear models with a slope of unity. However, BHAR appears to be correlated more strongly with $M_*$ than SFR. This result indicates that $M_*$ is the primary host-galaxy property related to black-hole growth, and the apparent BHAR-SFR relation is largely a secondary effect due to the star-forming main sequence. Among our sources, massive galaxies ($M_* \gtrsim 10^{10} M_{\odot}$) have significantly higher BHAR/SFR ratios than less-massive galaxies, indicating the former have higher black-hole fueling efficiency and/or higher SMBH occupation fraction than the latter. Our results can naturally explain the observed proportionality between $M_{\rm BH}$ and $M_*$ for local giant ellipticals, and suggest their $M_{\rm BH}/M_*$ is higher than that of local star-forming galaxies. Among local star-forming galaxies, massive systems might have higher $M_{\rm BH}/M_*$ compared to dwarfs.