For the last couple of weeks, we have been examining the Io-abstracts submitted for next month's Lunar and Planetary Science Conference. Today we take a look at a paper submitted by Giovanni Leone, Lionel Wilson, and Ashley Davies titled, "The Geothermal Gradient of Io: Consequences for Lithosphere Structure and Volcanic Eruptive activity." For this paper, the authors modeled the structure of Io's lithosphere by calculating how its temperature varies with depth. This research will be presented as a poster at the Igneous and Volcanic Processes session on Thursday, March 4.
Io's internal heat, generated by tidal stresses on Io's mantle, is released through volcanic activity in a process called advection. As opposed to convection or conduction, with advection, heat is transported from a system through a warm liquid, in this case, liquid hot magma. The model used by Leone and his colleagues was first developed in O'Reilly and Davies 1981 in order to explain how Io's lithosphere could be releasing so much heat (2.4 Watts per m2) yet still hold up Io's steep paterae walls and tall mountains. A conducting crust would be far too warm at shallow depths and too thin to hold up these structures. Thus, thanks to advection, all of the internal heat from the asthenosphere is released through volcanic eruptions and the lithosphere stays pretty cool except for the lower two to three kilometers of the 30-kilometer thick lithosphere, preventing viscous relaxation of Io's topography (see the craters of Saturn's moon Enceladus to see how viscous relaxation can distort topography).
For their model, Leone et al. used two equations from O'Reilly and Davies 1981 as well as improved knowledge about the chemistry and properties of Io's lithosphere to calculate the geothermal (or iothermal, if you will) gradient within the lithosphere, from the cold (100 K) surface to the lithosphere/asthenosphere interface at a depth of 30 kilometers and a temperature of 1500 K. Their inputs include estimates for the porosity of the lithosphere as a function of depth, the density of the magma, the globally-averaged, advected heat flux, radiogenic heatign rate, the magma specific heat, latent heat of crystallization, and thermal diffusivity. From these equations, the authors derived the lithospheric density, pressure, and temperature at different depths in Io's lithosphere. As expected, the lithosphere remains below the melting point of sulfur dioxide from the surface down to a depth of 21 kilometers. It remains below the melting point of sulfur until a depth of 26 kilometers. Much of the lithospheric heating takes place in the bottom few kilometers of the lithosphere.
The iothermal gradient generated by Leone's model does support the transport of magma all the way to the surface. Without any entrained volatiles, magma from the asthenosphere can rise to a depth of 23 kilometers before becoming negatively buoyant and forming magma reservoirs, assuming a pore-space fraction of 30% at the top of the lithosphere. As mentioned above, this is within the depth range of the melting point of the dominant volatiles on Io, sulfur and sulfur dioxide. These may then become entrained in the lava, allowing the magma to rise further to the surface. Leone et al. conclude that with volatile contents as low as 5% by mass, magma should be able to reach the surface using reasonable values for lithospheric porosity. With even more volatiles, such as the 10-30% suggested at some plume sites like Tvashtar, the modeled iothermal gradient would support the kinds of high eruption speeds observed at that volcano. They conclude "that there should be a positive correlation between mass eruption rate and volatile content." So it should not come as a surprise that major eruption on Io, like Tvashtar 1999/2001/2007, Thor 2001, Grian 1999, and Pillan 1997 all had volcanic plumes. Finally, they also place a limit on the porosity of Io's lithosphere at the surface at 38% as magma could not ascend into the lithosphere above that level, the crust would be too light.
Another factor that the authors examined was the effect that changes in the advected heat flow would have have on the lithosphere. Just as Kirchoff and McKinnon found last year, a decrease in volcanic activity but not a decrease in the amount of heat generated in the mantle (i.e. the temperature remains the same) would leading to a heating of the lower to mid-lithosphere, possibly leading to some melting. In Leone's model, the gradient changed from a steep curve at 2.4 W/m2 (remaining relatively cool until close to the lithosphere/asthenosphere boundary) to a much shallower one at 0.5 W/m2.
With this model of Io's geothermal gradient, Leone and his co-authors have placed limits on the amount of pore spaces are possible in Io's lithosphere. Their model is supported by their ability to replicate the ascent of magma to the surface, which is readily visible on Io's surface. Their model also helps support the argument that the volatiles in Io's lava are incorporated into its magma within reservoirs in the lithosphere. I would be interested to see how this model fits with the view that the upper 2-3 kilometers of Io's lithosphere maybe dominated by volatiles with silicates being predominant deeper into Io.
Link: The Geothermal Gradient of Io: Consequences for Lithosphere Structure and Volcanic Eruptive activity [www.lpi.usra.edu]