The Leaky Moon: Why Io’s Atmosphere is Always Trying to Escape | HackerNoon

Escape takes place mostly above a certain level in the upper atmosphere known as the exobase where the transition from a collisional gas to a collisionless gas occurs (Figure 10). Below the exobase the atmosphere can be treated as a fluid, because the average distance a molecule or atom travels before making a collision – the mean free path – is shorter than the smallest macroscopic length scale. The latter is usually defined by the pressure scale height H which characterizes the exponential decay of pressure with altitude.

Above the exobase is a quasi-collisionless region known as the exosphere where the mean free path exceeds the atmospheric scale height. Collisions are sufficiently infrequent that neutral atoms and molecules execute dynamical trajectories that are influenced by mostly Io’s and Jupiter’s gravitational field.

The exobase is defined for the hydrostatic equilibrium state and, moreover, for a single species represented by a single temperature. A similar definition of a corresponding altitude in a dynamic plume with bulk flow velocity is not possible. McDoniel et al. (2017) showed that plume particles elevated above the exobase of a purely-sublimated atmosphere may bounce off the sublimated atmosphere near the exobase when falling back towards the surface (Figure 11, right). In large plumes, the level where upward-moving sufficiently fast particles could escape without collisions is likely above the canopy shock, which is expected to be higher than exobase altitudes found in simulations of the sublimated atmosphere (Summers and Strobel, 1996; McDoniel et al., 2017).

We also note that the top of Io’s atmosphere is not in local thermodynamic equilibrium (LTE) and thus different classes of molecules or atoms may have different temperatures and thus exobase altitudes.

Generally, ejected plume gases do not have sufficient velocities to escape Io’s gravity directly. Under ballistic (collisionless) conditions, to reach an altitude of 400 km as inferred for the highest plumes, an ejection velocity of 1.2 km/s is needed. This is still well below Io’s escape velocity of 2.56 km/s or the velocity to reach the distance of the Hill radius (the radius where Io’s gravity is equal to Jupiter’s, near 5.8 RIo) of 2.33 km/s. Assuming a Maxwellian velocity distribution with a high core temperature of 800 K around an upward bulk velocity of 1.2 km/s, only less than 10-5 of the intact SO2 molecules reach the escape velocity. Even with an optimistic SO2 plume gas source rate of 105 kg/s, this yields an escape rate of ~1 kg/s, three orders lower than the canonical number. Ejection velocity, gas temperatures and SO2 source rates commonly assumed for simulating large plumes like the Pele plume are lower than our assumptions here (Zhang et al., 2003; 2004; McDoniel et al., 2017) and our approximation likely overestimates the escaping fraction. In addition, simulations revealed that the ejected plume gas is effectively slowed by falling gases in the canopy shocks, likely further reducing the escaping fraction (Zhang et al., 2003).

This situation is vastly different from the Enceladus plume, where the surface gravity is 6% of Io’s surface gravity and the fraction of escaping molecules is two orders of magnitude higher than those returning to the surface (e.g., Tian et al., 2007; Villanueava et al., 2023). We note, however, that there might be potential pathways for direct volcanic escape that have not yet been explored, such as the dynamical behavior of volatiles originating from hot surface lavas with temperatures of 1200 K or higher.

In a gravitationally-bound atmosphere with an exosphere, the key non-dimensional parameter governing escape is the Jeans parameter λ, which is defined as