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).
