  Outflows driven by active galactic nuclei (AGN) are an important channel for
accreting supermassive black holes (SMBHs) to interact with their host galaxies
and clusters. Properties of the outflows are however poorly constrained due to
the lack of kinetically resolved data of the hot plasma that permeates the
circumgalactic and intracluster space. In this work, we use a single parameter,
outflow-to-accretion mass-loading factor $m=\dot{M}_{\rm out}/\dot{M}_{\rm
BH}$, to characterize the outflows that mediate the interaction between SMBHs
and their hosts. By modeling both M87 and Perseus, and comparing the simulated
thermal profiles with the X-ray observations of these two systems, we
demonstrate that $m$ can be constrained between $200-500$. This parameter
corresponds to a bulk flow speed between $4,000-7,000\,{\rm km\,s}^{-1}$ at
around 1 kpc, and a thermalized outflow temperature between
$10^{8.7}-10^{9}\,{\rm K}$. Our results indicate that the dominant outflow
speeds in giant elliptical galaxies and clusters are much lower than in the
close vicinity of the SMBH, signaling an efficient coupling with and
deceleration by the surrounding medium on length scales below 1 kpc.
Consequently, AGNs may be efficient at launching outflows $\sim10$ times more
massive than previously uncovered by measurements of cold, obscuring material.
We also examine the mass and velocity distribution of the cold gas, which
ultimately forms a rotationally supported disk in simulated clusters. The
rarity of such disks in observations indicates that further investigations are
needed to understand the evolution of the cold gas after it forms.
