While I was away, a new paper was published in the journal Nature on astrometric measurements of Io's orbit, looking at changes of that orbit (as well as Ganymede and Europa) over a period of 116 years, the number of years covered by the observations used. This paper is authored by Valéry Lainey, Jean-Eudes Arlot, Özgür Karatekin, and Tim Van Hoolst and is titled "Strong tidal dissipation in Io and Jupiter from astrometric observations."
The authors "numerically integrated the full equations of motion for the three satellites' center of mass" and fitted their model to astronomical observations of the Jupiter system acquired between 1891 and 2003. This allowed them to more accurately determine long-period terms in the interaction between the three satellites and Jupiter. For example, one goal of these types of models is to determine whether these three satellites are moving away or toward Jupiter. In other words, are the periods and semi-major axes of these satellites' orbits increasing or decreasing? Previous models gave often drastically different results based on fewer observations. Using this longer time-span of astrometric observations and fitting for the rate of tidal dissipation within Io and Jupiter, Lainey et al. determined that Io is slowly spirally in toward Jupiter (decrease of 55 kilometers in the semi-major axis of Io's orbit in 116 years), while Europa and Ganymede are spirally outward from Jupiter (an increase of 125 km and 365 km, respectively).
This change in the orbital and rotational periods of these satellites shows that Io, Europa, and Ganymede are slowly leaving a state of Laplace Resonance, where Europa's orbital period is twice that of Io and Ganymede's is four times that of Io. It is this resonance that helps prevent Io's orbit from circularizing. Because Io's orbit is eccentric (non-circular), the gravitational pull of the tidal bulge Io creates on Jupiter varies depending on the position of Io in its orbit. This varying gravitational pull causes friction within Io's interior, which is dissipated as heat. If Europa and Ganymede's orbits increase in size and Io's orbit decreases in size, then eventually this resonance will be broken. Once this happens, Io's orbit will slowly circularize and reduce the amount of tidal energy that is dissipated as heat, causing Io to become dormant.
While much of this part of the paper has been discussed quite a bit in the popular press (see articles from Ars Technica and New Scientist), another result from Lainey et al. is that the current rate of tidal dissipation is consistent with estimates of Io's global heat flow. Previously, it was suspected that Io was emitting more heat that was supported by the current tidal dissipation rate, suggesting that Io's interior was being heated up more in the past and it is now cooling down from that more intense period of tidal heating. Another theory suggested that the Laplace resonance between Io, Europa, and Ganymede goes through a cycles extreme tidal heating and dormancy. With the rate of tidal heating and the global heat flow being consistent with each other, such non-steady state heating models are not needed. However, as noted earlier, it still looks like these three satellites are slowly moving out of exact resonance. It was not shown whether a cyclical resonance system might still be possible.
Link: Strong tidal dissipation in Io and Jupiter from astrometric observations [nature.com]