  The globular cluster 47~Tucanae (47~Tuc) is one of the most massive star
clusters in the Milky Way and is exceptionally rich in exotic stellar
populations. For several decades it has been a favorite target of observers,
and yet it is computationally very challenging to model because of its large
number of stars ($N\gtrsim 10^6$) and high density. Here we present detailed
and self-consistent 47~Tuc models computed with the \texttt{Cluster Monte
Carlo} code (\texttt{CMC}). The models include all relevant dynamical
interactions coupled to stellar and binary evolution, and reproduce various
observations, including the surface brightness and velocity dispersion
profiles, pulsar accelerations, and numbers of compact objects. We show that
the present properties of 47~Tuc are best reproduced by adopting an initial
stellar mass function that is both bottom-heavy and top-light relative to
standard assumptions \citep[as in, e.g.,][]{Kroupa2001}, and an initial Elson
profile \citep{Elson1987} that is overfilling the cluster's tidal radius. We
include new prescriptions in \texttt{CMC} for the formation of binaries through
giant star collisions and tidal captures, and we show that these mechanisms
play a crucial role in the formation of neutron star binaries and millisecond
pulsars in 47~Tuc; our best-fit model contains $\sim 50$ millisecond pulsars,
$70\%$ of which are formed through giant collisions and tidal captures. Our
models also suggest that 47~Tuc presently contains up to $\sim 200$
stellar-mass black holes, $\sim 5$ binary black holes, $\sim 15$ low-mass X-ray
binaries, and $\sim 300$ cataclysmic variables.
