A Simple Thermal Model for Lava Fountains: Application to Io

Introduction: The very high temperatures that have been reported for lavas on Io [e.g., 1-4] have proven to be difficult to explain [5,6]. Specifically, the estimates of lava temperatures ≥1600 °C require that the interior of Io either (1) have an extremely unusual chemistry or (2) be almost completely molten. Neither of these possibilities fits within our current understanding of the evolution of the Jovian system [7-12]. If Io has a broadly chondritic composition, then recent tidal heating models suggest that there should be no more than about 20% partial melting of the interior [e.g., 10,11]. This suggests a maximum magma temperature of about 1200 °C. There are three independent avenues of study that are bringing the interpreted eruption temperatures into line with the theoretical limits. Two of these were discussed by [12] where we showed that ascending Ionian magma could be superheated by 100-200 °C and that the uncertainties in the observations allow temperatures around 1300 °C. Together, this allows the observations to be consistent with the theoretical studies, but eruption temperatures in the range of 1400-1600 °C are not ruled out. Lava Fountain Thermal Model: The third avenue of study is to improve the models used to convert the observed temperatures to interpreted eruption temperatures. Specifically, earlier studies have used thermal models designed for lava flows. However, the locations where the highest temperatures have been observed (Tvashtar, Pillan, and Pele) all have extensive new dark pyroclastic deposits, indicating that these eruptions included spectacular lava fountains. In the case of Tvashtar, incandescent lava fountains 1-2 km tall were resolved in Galileo SSI images [13,14]. Similarly, the hottest resolved incandescent areas seen at Pele by the SSI camera imaging at night are interpreted to be lava fountains [4]. At Pillan, a 400-km diameter dark pyroclastic deposit formed contemporenously with the highest observed temperatures. The lava flow thermal models generally utilize assumptions only appropriate for effusive eruptions as discussed by [2,14]. The most serious problem with the thermal models that were used is that they assume that the lava is a semi-infinite half space. While [15] does look at the cooling of a lava flow after solidification, the geometry of a pyroclast is vastly different than that of a lava flow (~spherical vs. ~tabular). Small droplets of lava ejected as pyroclasts should cool much faster than these models would predict. Here we present a very simple thermal model for lava fountains, building upon work on lunar pyroclastics during the Apollo program [e.g., 16]. The eruption environments for the lunar and Ionian eruptions are remarkably similar in terms of gravity, atmospheric pressure, and likely magma composition. Therefore, it is reasonable to use the lunar data to constrain Ionian lava fountain models. Based on lunar pyroclastics, we expect the Ionian lava droplets to be 0.1-1 mm in radius [17]. Such small droplets can be adequately modeled as isothermal spheres that cool by thermal radiation. The details of radiative heat transfer within a fountain are beyond the scope of this work. Instead, we assume that the fountain is composed of three parts: a hidden optically thick core, an incandescent zone of cooling droplets, and dispersed cold pyroclasts. Only the middle portion is visible in thermal emission to a sensor. This visible part of the fountain will radiate to deep space, the surface of Io, the rest of the fountain, and sometimes Jupiter. We combine all these into a single “ambient” temperature (Ta). With these simplifying assumptions, the temperature T of a droplet as a function of time t is given by