The galaxy's gas content regulated by the dark matter halo mass results in a super-linear M${}_{\mathrm{BH}}$-M${}_{\star }$ relation

Abstract

Supermassive black holes (SMBHs) are tightly correlated with their hosts but the origin of such connection remains elusive. To explore the cosmic build-up of this scaling relation, we present an empirically-motivated model that tracks galaxy and SMBH growth down to z=0. Starting from a random mass seed distribution at z=10, we assume that each galaxy evolves on the star-forming "main sequence" (MS) and each BH follows the recently-derived stellar mass (M${}_{\star }$) dependent ratio between BH accretion rate and star formation rate, going as BHAR/SFR$\propto$M${}_{\star }^{0.73[+0.22,-0.29]}$. Our simple recipe naturally describes the BH-galaxy build-up in two stages. At first, the SMBH lags behind the host that evolves along the MS. Later, as the galaxy grows in M${}_{\star }$, our M${}_{\star }$-dependent BHAR/SFR induces a super-linear BH growth, as M${}_{\mathrm{BH}}$$\propto$M${}_{\star }^{1.7}$. According to this formalism, smaller BH seeds increase their relative mass faster and earlier than bigger BH seeds, at fixed M${}_{\star }$, thus setting along a gradually tighter M${}_{\mathrm{BH}}$-M${}_{\star }$ locus towards higher M${}_{\star }$. Assuming reasonable values of the radiative efficiency $\epsilon \sim$0.1, our empirical trend agrees with both high-redshift model predictions and intrinsic M${}_{\mathrm{BH}}$-M${}_{\star }$ relations of local BHs. We speculate that the observed non-linear BH-galaxy build-up is reflected in a twofold behavior with dark matter halo mass (M${}_{\mathrm{DM}}$), displaying a clear turnover at M${}_{\mathrm{DM}}\sim$2$\times$10${}^{12}$M${}_{\odot }$. While Supernovae-driven feedback suppresses BH growth in smaller halos (BHAR/SFR$\propto$M${}_{\mathrm{DM}}^{1.6}$), above the M${}_{\mathrm{DM}}$ threshold cold gas inflows possibly fuel both BH accretion and star formation in a similar fashion (BHAR/SFR$\propto$M${}_{\mathrm{DM}}^{0.3}$).

Accepted for publication in ApJ Letter. 8 pages, 5 figures

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