  A gas giant planet which survives the giant branch stages of evolution at a
distance of many au and then is subsequently perturbed sufficiently close to a
white dwarf will experience orbital shrinkage and circularization due to
star-planet tides. The circularization timescale, when combined with a known
white dwarf cooling age, can place coupled constraints on the scattering epoch
as well as the active tidal mechanisms. Here, we explore this coupling across
the entire plausible parameter phase space by computing orbit shrinkage and
potential self-disruption due to chaotic f-mode excitation and heating in
planets on orbits with eccentricities near unity, followed by weakly
dissipative equilibrium tides. We find that chaotic f-mode evolution activates
only for orbital pericentres which are within twice the white dwarf Roche
radius, and easily restructures or destroys ice giants but not gas giants. This
type of internal thermal destruction provides an additional potential source of
white dwarf metal pollution. Subsequent tidal evolution for the surviving
planets is dominated by non-chaotic equilibrium and dynamical tides which may
be well-constrained by observations of giant planets around white dwarfs at
early cooling ages.
