The relationship between the compositions of giant planets and their host stars is of fundamental interest in understanding planet formation. The solar system giant planets are enhanced above solar composition in metals, both in their visible atmospheres and bulk compositions. A key question is whether the metal enrichment of giant exoplanets is correlated with that of their host stars. Thorngren et al. (2016) showed that in cool (Teq < 1000 K) giant exoplanets, the total heavy-element mass increases with total Mp and the heavy element enrichment relative to the parent star decreases with total Mp. In their work, the host star metallicity was derived from literature [Fe/H] measurements. Here we conduct a more detailed and uniform study to determine whether different host star metals (C, O, Mg, Si, Fe, and Ni) correlate with the bulk metallicity of their planets, using correlation tests and Bayesian linear fits. We present new host star abundances of 19 cool giant planet systems, and combine these with existing host star data for a total of 22 cool giant planet systems (24 planets). Surprisingly, we find no clear correlation between stellar metallicity and planetary residual metallicity (the relative amount of metal versus that expected from the planet mass alone), which is in conflict with common predictions from formation models. We also find a potential correlation between residual planet metals and stellar volatile-to-refractory element ratios. These results provide intriguing new relationships between giant planet and host star compositions for future modeling studies of planet formation.
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