Giant exoplanet composition: Why do the hydrogen-helium equation of state and interior structure matter?

Revealing the internal composition and structure of giant planets is fundamental for understanding planetary formation. However, the bulk composition can only be inferred through interior models. As a result, advancements in modelling aspects are essential to better characterise the interiors of giant planets. We investigate the effects of model assumptions such as the interior structure and the hydrogen-helium (H-He) equation of state (EOS) on the inferred interiors of giant exoplanets. We first assess these effects on a few test cases and compare H-He EOSs. We then calculate evolution models and infer the planetary bulk metallicity of 45 warm exoplanets, ranging from 0.1 to 10~$M_{\rm J}$. Planets with masses between about 0.2 and 0.6~$M_{\rm J}$ are most sensitive to the H-He EOS. Updating the H-He EOS reduces the inferred heavy-element mass, with an absolute difference in bulk metallicity of up to 13\%. Concentrating heavy elements in a core, rather than distributing them uniformly (and scaling opacities with metallicity), reduces the inferred metallicity (up to 17\%). The assumed internal structure, along with its effect on the envelope opacity, has the greatest effect on the inferred composition of massive planets ($M_{\rm p}>4~M_{\rm J}$). For $M_{\rm p}>0.6~M_{\rm J}$, the observational uncertainties on radii and ages lead to uncertainties in the inferred metallicity (up to 31\%) which are larger than the ones associated with the used H-He EOS and the assumed interior structure. However, for planets with $0.2<M_{\rm p}<0.6~M_{\rm J}$, the theoretical uncertainties are larger. Advancements in equations of state and our understanding of giant planet interior structures combined with accurate measurements of the planetary radius and age are crucial for characterising giant exoplanets.