  Differences in the elemental abundances of planet hosting stars in binary
systems can give important clues and constraints about planet formation and
evolution. In this study we performed a high-precision, differential elemental
abundance analysis of a wide binary system, HD 80606/80607, based on
high-resolution, high signal-to-noise ratio Keck/HIRES spectra. HD 80606 is
known to host a four Jupiter mass giant planet while no planet has yet been
detected around HD 80607. We determined stellar parameters as well as
abundances for 23 elements for these two stars with extremely high precision.
Our main results are: (i) we confirmed that the two components share very
similar chemical compositions, but HD 80606 is marginally more metal-rich than
HD 80607 with an average difference of +0.013 $\pm$ 0.002 dex ($\sigma$ = 0.009
dex) and (ii) there is no obvious trend between abundance differences and
condensation temperature. Assuming this binary formed from material with the
same chemical composition, it is difficult to understand how giant planet
formation could produce the present-day photospheric abundances of the elements
we measure. We can not exclude the possibility that HD 80606 might have
accreted about 2.5 to 5 $M_{\rm Earth}$ material onto its surface, possibly
from a planet destabilised by the known highly-eccentric giant.

Solar and Stellar Astrophysics;Earth and Planetary Astrophysics