Connecting planet formation and astrochemistry: Refractory carbon depletion leading to super-stellar C/O in giant planetary atmospheres

[Abridged] Combining a time-dependent astrochemical model with a model of planet formation and migration, we compute the carbon-to-oxygen ratio (C/O) of a range of planetary embryos starting their formation in the inner solar system (1-3 AU). The volatile and ice abundance of relevant carbon and oxygen bearing molecular species are determined through a complex chemical kinetic code which includes both gas and grain surface chemistry. This is combined with a model for the abundance of the refractory dust grains to compute the total carbon and oxygen abundance in the protoplanetary disk available for incorporation into a planetary atmosphere. We include the effects of the refractory carbon depletion that has been observed in our solar system, and posit two models that would put this missing carbon back into the gas phase. This excess gaseous carbon then becomes important in determining the final planetary C/O because the gas disk now becomes more carbon rich relative to oxygen (high gaseous C/O). One model, where the carbon excess is maintained throughout the lifetime of the disk results in Hot Jupiters that have super-stellar C/O. The other model deposits the excess carbon early in the disk life and allows it to advect with the bulk gas. In this model the excess carbon disappears into the host star within 0.8 Myr, returning the gas disk to its original (sub-stellar) C/O, so the Hot Jupiters all exclusively have sub-stellar C/O. This shows that while the solids will tend to be oxygen rich, Hot Jupiters can have super-stellar C/O if a carbon excess can be maintained by some chemical processing of the dust grains. Whether the carbon and oxygen content of the atmosphere was accreted primarily by gas or solid accretion is heavily dependent on the mass of the atmosphere and where in the disk the growing planet accreted.