  The accretion of tidally disrupted planetary bodies is the current consensus
model for the presence of photospheric metals commonly detected in white
dwarfs. While most dynamical studies have considered a single star and
associated planetary instabilities, several investigations have instead
considered the influence of widely-bound stellar companions as potential
drivers of white dwarf pollution. This study examines the prevalence of wide
binaries among polluted white dwarfs using Gaia Data Release 3 astrometry,
where three samples are investigated: 71 DAZ stars with metals detected in the
ultraviolet using the Hubble Space Telescope, and two groups of DZ stars
identified via Sloan Digital Sky Survey spectroscopy, comprised of 116 warmer
and 101 cooler sources. Each sample was searched for spatially-resolved,
co-moving companions, and compared to the same analysis of thousands of field
white dwarfs within overlapping regions of the Gaia Hertzsprung-Russell
diagram. The wide binary fraction of the DAZ sample is $10.6_{-3.2}^{+3.9}$ per
cent, and within $1 \sigma$ of the corresponding field. However, the search
yields wide binary fractions of less than 1.8 per cent for the two independent
DZ star catalogues, which are each distinct from their fields by more than $3
\sigma$. Both sets of results support that pollution in white dwarfs is not the
result of stellar companions, and the delivery of metals to white dwarf
surfaces is caused by major planets. The discrepancy between the DAZ and DZ
star wide binary fractions cannot be caused by white dwarf spectral evolution,
suggesting these two populations may have distinct planetary architectures.
