A universal relation between the properties of supermassive black holes, galaxies, and dark matter halos

We study the relations between the mass of the central black hole (BH) $M_{\rm BH}$, the dark matter halo mass $M_{\rm h}$, and the stellar-to-halo mass fraction $f_\star\propto M_\star/M_{\rm h}$ in a sample of $55$ nearby galaxies with dynamically measured $M_{\rm BH}>10^6\,{\rm M}_\odot$ and $M_{\rm h}>5\times10^{11}\,{\rm M}_\odot$. The main improvement with respect to previous studies is that we consider both early- and late-type systems for which $M_{\rm h}$ is determined either from globular cluster dynamics or from spatially resolved rotation curves. Independently of their structural properties, galaxies in our sample build a well defined sequence in the $M_{\rm BH}$-$M_{\rm h}$-$f_\star$ space. We find that: (i) $M_{\rm h}$ and $M_{\rm BH}$ strongly correlate with each other and anti-correlate with $f_\star$; (ii) there is a break in the slope of the $M_{\rm BH}$-$M_{\rm h}$ relation at $M_{\rm h}$ of $10^{12}\,{\rm M}_\odot$, and in the $f_\star$-$M_{\rm BH}$ relation at $M_{\rm BH}$ of $\sim10^7\!-\!10^8\,{\rm M}_\odot$; (iii) at a fixed $M_{\rm BH}$, galaxies with a larger $f_\star$ tend to occupy lighter halos and to have later morphological types. We show that the observed trends can be reproduced by a simple equilibrium model in the $\Lambda$CDM framework where galaxies smoothly accrete dark and baryonic matter at a cosmological rate, having their stellar and black hole build-up regulated both by the cooling of the available gas reservoir and by the negative feedback from star formation and active galactic nuclei (AGN). Feature (ii) arises as the BH population transits from a rapidly accreting phase to a more gentle and self-regulated growth, while scatter in the AGN feedback efficiency can account for feature (iii).