  Multi-body dynamical interactions of binaries with other objects are one of
the main driving mechanisms for the evolution of star clusters. It is thus
important to bring our understanding of three-body interactions beyond the
commonly employed point-particle approximation. To this end we here investigate
the hydrodynamics of three-body encounters between star-black hole (BH)
binaries and single stars, focusing on the identification of final outcomes and
their long-term evolution and observational properties, using the moving-mesh
hydrodynamics code AREPO. This type of encounters produces five types of
outcomes: stellar disruption, stellar collision, weak perturbation of the
original binary, binary member exchange, and triple formation. The two decisive
parameters are the binary phase angle, which determines which two objects meet
at the first closest approach, and the impact parameter, which sets the
boundary between violent and non-violent interactions. When the impact
parameter is smaller than the semimajor axis of the binary, tidal disruptions
and star-BH collisions frequently occur when the BH and the incoming star first
meet, while the two stars mostly merge when the two stars meet first instead.
In both cases, the BHs accrete from an accretion disk at super-Eddington rates,
possibly generating flares luminous enough to be observed. The stellar
collision products either form a binary with the BH or remain unbound to the
BH. Upon collision, the merged stars are hotter and larger than main sequence
stars of the same mass at similar age. Even after recovering their thermal
equilibrium state, stellar collision products, if isolated, would remain hotter
and brighter than main sequence stars until becoming giants.
