Insight into the Formation of $\beta$ Pic b through the Composition of Its Parent Protoplanetary Disk as Revealed by the $\beta$ Pic Moving Group Member HD 181327

It has been suggested that $\beta$ Pic b has a supersolar metallicity and subsolar C/O ratio. Assuming solar carbon and oxygen abundances for the star $\beta$ Pic and therefore the planet's parent protoplanetary disk, $\beta$ Pic b's C/O ratio suggests that it formed via core accretion between its parent protoplanteary disk's H$_{2}$O and CO$_{2}$ ice lines. $\beta$ Pic b's high metallicity is difficult to reconcile with its mass $M_{\text{p}}~=~11.7~M_{\text{Jup}}$ though. Massive stars can present peculiar photospheric abundances that are unlikely to record the abundances of their former protoplanetary disks. This issue can be overcome for early-type stars in moving groups by infering the elemental abundances of the FGK stars in the same moving group that formed in the same molecular cloud and presumably share the same composition. We infer the photospheric abundances of the F dwarf HD 181327, a $\beta$ Pic moving group member that is the best available proxy for the composition of $\beta$ Pic b's parent protoplanetary disk. In parallel, we infer updated atmospheric abundances for $\beta$ Pic b. As expected for a planet of its mass formed via core-accretion beyond its parent protoplanetary disk's H$_{2}$O ice line, we find that $\beta$ Pic b's atmosphere is consistent with stellar metallicity and confirm that is has superstellar carbon and oxygen abundances with a substellar C/O ratio. We propose that the elemental abundances of FGK dwarfs in moving groups can be used as proxies for the otherwise difficult-to-infer elemental abundances of early-type and late-type members of the same moving groups.