  Fomalhaut is a nearby stellar system and has been found to be a triple based
on astrometric observations. With new radial velocity and astrometric data, we
study the association between Fomalhaut A, B, and C in a Bayesian framework
finding that the system is gravitationally bound or at least associated. Based
on simulations of the system, we find that Fomalhaut C can be easily
destabilized through combined perturbations from the Galactic tide and stellar
encounters. Considering that observing the disruption of a triple is probably
rare in the solar neighbourhood, we conclude that Fomalhaut C is a so-called
"gravitational pair" of Fomalhaut A and B. Like the Cooper pair mechanism in
superconductors, this phenomena only appears once the orbital energy of a
component becomes comparable with the energy fluctuations caused by the
environment. Based on our simulations we find (1) an upper limit of 8 km/s
velocity difference is appropriate when selecting binary candidates and (2) an
empirical formula for the escape radius, which is more appropriate than tidal
radius when measuring the stability of wide binaries.
