A New Window into Planet Formation and Migration: Refractory-to-Volatile Elemental Ratios in Ultra-hot Jupiters

A primary goal of exoplanet characterization is to use a planet's current composition to understand how that planet formed. For example, the C/O ratio has long been recognized as carrying important information on the chemistry of volatile species. Refractory elements, like Fe, Mg, and Si, are usually not considered in this conversation because they condense into solids like Fe(s) or MgSiO$_3$ and would be removed from the observable, gaseous atmosphere in exoplanets cooler than about 2000~K. However, planets hotter than about 2000~K, called ultra-hot Jupiters (UHJs), are warm enough to largely avoid the condensation of refractory species. In this paper, we explore the insight that the measurement of refractory abundances can provide into a planet's origins. Through refractory-to-volatile elemental abundance ratios, we can estimate a planet's atmospheric rock-to-ice fraction and constrain planet formation and migration scenarios. We first relate a planet's present-day refractory-to-volatile ratio to its rock-to-ice ratio from formation using various compositional models for the rocky and icy components of the protoplanetary disk. We discuss potential confounding factors like the sequestration of heavy metals in the core and condensation. We then show such a measurement using atmospheric retrievals of the low-resolution UV-IR transmission spectrum of WASP-121b with PETRA, from which we estimate a refractory-to-volatile ratio of 5.0$^{+6.0}_{-2.7}\times$ solar and a rock-to-ice ratio greater than 2/3. This result is consistent with significant atmospheric enrichment by rocky planetismals. Lastly, we discuss the rich future potential for measuring refractory-to-volatile ratios in ultra-hot Jupiters with the arrival of JWST and by combining observations at low- and high-resolution.