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

We study the relations between the mass of the central black hole (BH) MBH, the dark matter halo mass Mh, and the stellar-to-halo mass fraction f⋆ ?M⋆/Mh in a sample of 55 nearby galaxies with dynamically measured $M_{m BH}gt 10^6, {m M}_odot$ and $M_{m h}gt 5 times 10^{11}, {m M}_odot$. The main improvement with respect to previous studies is that we consider both early- and late-type systems for which Mh 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 MBH-Mh-f⋆ space. We find that: (i) Mh and MBH strongly correlate with each other and anticorrelate with f⋆; (ii) there is a break in the slope of the MBH-Mh relation at Mh of $10^{12}, { m M}_odot$, and in the f⋆-MBH relation at MBH of $sim 10^7!-!10^8, { m M}_odot$; (iii) at a fixed MBH, galaxies with a larger f⋆ tend to occupy lighter haloes and to have later morphological types. We show that the observed trends can be reproduced by a simple equilibrium model in the ΛCDM framework where galaxies smoothly accrete dark and baryonic matter at a cosmological rate, having their stellar and BH build-up regulated both by the cooling of the available gas reservoir and by the negative feedback from star formation and active galactic nuclei (AGNs). 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).