The Wanderer: Charting WASP-77A b's Formation and Migration Using a System-Wide Inventory of Carbon and Oxygen Abundances

The elemental and isotopic abundances of volatiles like carbon, oxygen, and nitrogen may trace a planet's formation location relative to H$_2$O, CO$_2$, CO, NH$_3$, and N$_2$ "snowlines", or the distance from the star at which these volatile elements sublimate. By comparing the C/O and $^{12}$C/$^{13}$C ratios measured in giant exoplanet atmospheres to complementary measurements of their host stars, we can determine whether the planet inherited stellar abundances from formation inside the volatile snowlines, or non-stellar C/O and $^{13}$C enrichment characteristic of formation beyond the snowlines. To date, there are still only a handful of exoplanet systems where we can make a direct comparison of elemental and isotopic CNO abundances between an exoplanet and its host star. Here, we present a $^{12}$C/$^{13}$C abundance analysis for host star WASP-77A (whose hot Jupiter's $^{12}$C/$^{13}$C abundance was recently measured). We use MARCS stellar atmosphere models and the radiative transfer code TurboSpectrum to generate synthetic stellar spectra for isotopic abundance calculations. We find a $^{12}$C/$^{13}$C ratio of $51\pm 6$ for WASP-77A, which is sub-solar ($\sim 91$) but may still indicate $^{13}$C-enrichment in its companion planet WASP-77A b ($^{12}$C/$^{13}$C = 26 $\pm$ 16, previously reported). Together with the inventory of carbon and oxygen abundances in both the host and companion planet, these chemical constraints point to WASP-77A b's formation beyond the H$_2$O and CO$_2$ snowlines and provide chemical evidence for the planet's migration to its current location $\sim$0.024 AU from its host star.