  The elemental compositions of planet hosting stars serve as proxies for the
primordial compositions of the protoplanetary disks within which the planets
form. The temperature profile of the disk governs the condensation fronts of
various compounds, and although these chemically distinct regions migrate and
mix during the disk lifetime, they can still leave an imprint on the
compositions of the forming planets. Observable atmospheric compositions of hot
Jupiters when compared against their host stars could potentially constrain
their formation and migration processes. We compared the measured planetary and
stellar abundances of carbon and oxygen for ten systems with hot Jupiters. If
the planets formed by core accretion with significant planetesimal accretion
and migrated through the disk, the hot Jupiter atmospheres should be
substantially super-stellar in O/H and sub-stellar in C/O. On the contrary,
however, we find that currently reported abundances of hot Jupiters have
generally super-stellar C/O ratios, though present uncertainties on the
reported O/H and C/O ratios are too large to reach a firm conclusion. In one
case however, HD 209458b, the elevated C/O and depleted O/H of the planet
compared to the host star is significant enough to suggest an origin far beyond
the ice line, with predominantly gas accretion, and subsequent disk-free
migration. Improved measurements from the James Webb Space Telescope will
enable more precise measurements for more hot Jupiters and we predict, based on
the current marginal trend, that a sizable fraction of hot Jupiters will show
enrichment of C/O and lower O/H than their hosts, similar to HD 209458b.
