  We identify the intrinsic dependence of star formation quenching on a variety
of galactic and environmental parameters, utilizing a machine learning approach
with Random Forest classification. We have previously demonstrated the power of
this technique to isolate causality, not mere correlation, in complex
astronomical data. First, we analyze three cosmological hydrodynamical
simulations (Eagle, Illustris, and IllustrisTNG), selecting snapshots spanning
the bulk of cosmic history from comic noon ($z \sim 2$) to the present epoch,
with stellar masses in the range $9 < \log(M_*/M_{\odot}) < 12$. In the
simulations, black hole mass is unanimously found to be the most predictive
parameter of central galaxy quenching at all epochs. Perhaps surprisingly,
black hole accretion rate (and hence the bolometric luminosity of active
galactic nuclei, AGN) is found to be of little predictive power over quenching.
This theoretical result is important for observational studies of galaxy
quenching as it cautions against using the current AGN state of a galaxy as a
useful proxy for the cumulative impact of AGN feedback on a galactic system.
The latter is traced by black hole mass not AGN luminosity. Additionally, we
explore a sub-set of 'observable' parameters, which can be readily measured in
extant wide-field galaxy surveys targeting $z = 0 - 2$, at $9 <
\log(M_*/M_{\odot}) < 12$. All three simulations predict that in lieu of black
hole mass, the stellar gravitational potential will outperform the other
parameters in predicting quenching. We confirm this theoretical prediction
observationally in the SDSS (at low redshifts) and in CANDELS (at intermediate
and high redshifts).
