Constraining Ongoing Volcanic Outgassing Rates and Interior Compositions of Extrasolar Planets with Mass Measurements of Plasma Tori

We present a novel method of constraining volcanic activity on extrasolar terrestrial worlds via characterization of circumstellar plasma tori. Our work generalizes the physics of the Io plasma torus to propose a hypothetical circumstellar plasma torus generated by exoplanetary volcanism. The quasi-steady torus mass is determined by a balance between material injection and ejection rates from volcanic activity and corotating magnetospheric convection, respectively. By estimating the Alfvén surfaces of planet-hosting stars, we calculate the torus mass-removal timescale for a number of exoplanets with properties amenable to plasma torus construction. Assuming a uniform toroidal geometry comparable to Io's "warm" torus, we calculate quasi-steady torus masses inferable from the optical depth of atomic spectral features in torus-contaminated stellar spectra. The calculated quasi-steady masses can be used to constrain the volcanic outgassing rates of each species detected in the torus, providing quantitative estimates of bulk volcanic activity and interior composition with minimal assumptions. Such insight into the interior state of an exoplanet is otherwise accessible only after destruction via tidal forces. We demonstrate the feasibility of our method by showcasing known exoplanets which are susceptible to tidal heating and could generate readily-detectable tori with realistic outgassing rates of order 1 ton s$^{-1}$, comparable to the Io plasma torus mass injection rate. This methodology may be applied to stellar spectra measured with ultraviolet instruments with sufficient resolution to detect atomic lines and sensitivity to recover the ultraviolet continuum of GKM dwarf stars. This further motivates the need for ultraviolet instrumentation above Earth's atmosphere.