Constraining the Occurrence of ZLK-Induced White Dwarf Pollution with Dissipative Precession

Abstract

Von Zeipel-Lidov-Kozai (ZLK) oscillations, induced by bound, perturbative companions to white dwarfs, have been suggested as a dynamical mechanism that may contribute to white dwarf pollution. To trigger ZLK oscillations, however, a 3-body system must reach a sufficiently large mutual inclination between orbits. The occurrence of these high-mutual-inclination configurations can be curtailed by dissipative precession at the protoplanetary disk stage, which pushes exoplanet-hosting close binary systems toward preferential orbit-orbit alignment. In this work, we constrain the fraction of white dwarfs with binary companions that can undergo ZLK-driven pollution given the effects of dissipative precession. To accrete pollution via ZLK oscillations, a white dwarf binary system must be sufficiently inclined and the characteristic timescale of the oscillations must be sufficiently short to perturb material within the white dwarf's cooling age. Considering a sample of 4400 known white dwarf/main sequence binaries, we find that $50-70\%$ have favorable parameters for ZLK pollution, depending on the orbital separation of the polluting body. While the conditions for oscillations are favorable, the tendency for ZLK to result in massive but more infrequent polluters likely restricts the rates of ZLK-induced pollution among the observed population. In general, dissipative precession is a limiting factor in pollution rates for more closely separated binaries (initial separations $<500-800$~au), while ZLK timescale constraints are most limiting for wider binaries.