Stoddard, P. R., and D. M. Jurdy, Distribution of Io's Volcanoes: Possible influence on spin axis, Geophys. Res. Lett., 29(9), 10.1029/2001GL014539, 2002.

Department of Geology and Environmental Geosciences, Northern Illinois University

Department of Geological Sciences, Northwestern University

Abstract. We examine the potential effect of volcanic distribution on the orientation of Io's spin axis. Volcanoes dominate Io's surface and the massive outpourings documented in short intervals could cause instability in Io's rotation and a corresponding reorientation of its spin axis. Currently, the volcanoes and mountains exhibit a complementary distribution, with the maximum principal axis for the set of 351 volcanoes close to the position of the rotation axis. Assuming an otherwise homogeneous body, a changing mass distribution on its surface could control the location of the spin axis. In models changing the location of as few as three volcanoes is sufficient to cause dramatic shifts of the principal axis positions, and hence the spin axis orientation. This result, although somewhat diminished, still prevails even when a strong influence of Io's tidal bulge is included in the model.

Io, the innermost and third largest (r ~ 1815 km) of Jupiter's Galilean satellites, is the most volcanically active body yet encountered. Buffeted by tidal forces from Jupiter and the other Galilean moons, Io is being constantly resurfaced by 100's of silicate volcanoes (Howell, 1997). The resulting redistribution of mass, from depth to the surface (Carr et al., 1998), may cause rotational instability on Io, and extreme episodes of true polar wander (up to 90º) in a geologically short time frame, termed inertial interchange true polar wander by Kirschvink et al. (1997). Similar instability has been proposed for both Pluto and Triton (Rubincam, 2000, 2001).

Io undergoes synchronous rotation about Jupiter, orbiting and rotating once every 42.46 hours. Gravity and moment of inertia studies indicate a metallic core for Io, and its density of 3500 kg m^-³ is consistent with a silicate mantle. Io's fresh surface bears no evidence of impact craters, indicating a surface age of no more than 10 million years. Io also hosts over 100 mountains (Carr et al., 1998) whose distribution complements that of the volcanoes. Whereas volcanoes concentrate near the sub-jovian point (0ºN, 0ºW) and its antipode, mountains are found around ±90ºW (Figure 1). These distributions apparently reflect the state of stress in Io's lithosphere: extensional at the crest of the tidal bulges, and compressional at the troughs. McKinnon et al. (2001) suggested that compressive heating, melting, and tilting form Io's mountains.

Asymmetries in surface mass distribution can cause a reorientation of a rotating body with respect to its spin axis, fixed in space. Goldreich and Toomre (1969) modeled the effect of mass inhomogeneities on a rotating Earth. The mass disturbance controls the position of the rotation as it tracks the maximum principal axis of the disturbing mass distribution. The reorientation positions excess mass around the equator, thus minimizing kinetic energy. They showed that on a rotating quasi-rigid body that small changes in the horizontal positions of the perturbing masses can result in large changes of the position of the spin axis with respect to the body’s surface, with a factor of Ö N, where N is the number of surface effects. All this depends on the ability of the rotational bulge of the planet to re-equilibrate as the rotation axis changes, that is, on the viscosity of the mantle. On Earth, true polar wander (TPW) has been proposed to account for the early Cambrian redistribution of continents and subsequent "explosion" of life (Kirschvink et al., 1997); in the early Tertiary it might have occurred in response to changing geometry of Pacific Ocean subduction zones (Jurdy, 1983).

Silicate volcanism on Io has the potential to cause significant mass redistribution in a short period of time. Eruption rates at Ra Patera estimated from slopes may be about 2000 m³ s^-¹, equivalent to the 1783 rate at Laki, Iceland, the largest observed on Earth; eruption rates at Io's Loki volcano may be 50 times larger (Schenk et al., 1997). With such high rates, it seems quite unlikely that Io's volcanoes would be isostatically compensated. On Earth, for comparison, the gravity signatures of the Hawaiian/Emperor seamounts persist for tens of millions of years. These massive outpourings over short time periods could cause instability in the rotation of Io and a reorientation of the satellite. Yamaji (1991) finds evidence for preferential chains in the volcanic hotspot distribution and argues for control by lithospheric fissures with characteristic spacing imposed by the thickness of the lithosphere. The mountain building process has been estimated to occur over time scales of ~1 m.y. (McKinnon et al., 2001), and thus is a much slower process than volcanic resurfacing. If also isostatically compensated these mountains are less likely to influence dramatic changes in spin axis orientation. To the first order, isostatically compensated features will have no inertia effects (Jurdy, 1983), and thus can not excite true polar wander.

To test the sensitivity of the current position of Io's spin axis to changing volcanic distribution, we have analyzed the current distribution and have modeled several random variations of that distribution. All models started with the current configuration of 351 volcanoes as determined from Voyager and Galileo images (Carr et al., 1998). We treat each volcano as a delta function valued only at its location (x, y), and from these determine an "Inertia Tensor."

A total inertia tensor is summed from the contributions of all volcanoes. For this calculation, we assume each volcano has a unit mass. Next, the inertia tensor, I, is diagonalized yielding 3 eigenvalues and eigenvectors. If the rotation or spin axis of a rotating body coincides with the location of the maximum principal axis of the inertia tensor then there is no excitation effect. Thus there is no excitation of TPW. Inertia tensor analysis, based solely on volcanoes as mass perturbations on an otherwise homogeneous Io, predicts that the location of the minimum principal axis lies near the sub-jovian point (6.3ºS, 21.6ºE), with the maximum moment pole close to the spin axis (73.6ºN, 313.5ºE). Similar analysis for Io's mountains gives a maximum pole at about 30ºN (Figure 2). This suggests that for the present time volcanic distribution may control the spin axis orientation of Io. Furthermore, the near equivalence of the magnitudes of the maximum and middle eigenvalues of the diagonalized matrix (0.2299, and 0.2280) means a small change in mass distribution could have a large effect on a body's orientation, by causing an interchange of the two eigenvectors. In other words, the body "flips" with respect to the orientation of the spin axis which is dynamically fixed in space. To investigate this we have modeled several random variations of the present volcano distribution.

For the first random model we allowed for a change of location for 10% of the volcano population for 1000 trials. For each trial, therefore, 316 volcanoes remain in their actual positions, and 35 - randomly selected in each individual run – are replaced with randomly determined positions. As expected, there is a wide range of positions of resultant maximum principal axes encircling the nearly invariant minimum axis (Figure 3(a)). The trials show that the maximum and middle eigenvalues (labeled as C and B, respectively in Figure 3(b)) always remain nearly equal, and significantly higher than the minimum (line A). In fact, the maximum and middle eigenvalues frequently switch positions, creating flips of the model body relative to the spin axis. Correspondingly, the position of the maximum principal axis jumps as much as 60º and more (Figure 3(b)).

A second model, essentially a random walk trial, was run in which a single volcano location out of 351 was randomly replaced for each of 1000 time steps. By the end of the 1000 changes, only 24 of the original volcano locations remained. (After each individual run, a new random volcano could replace any one member of the entire new volcano set, so it becomes less and less likely that an original volcano would be replaced.) The resulting polar wander path is shown in Figure 4(a). This assumes that the spin axis tracks the maximum principal axis. The positions of the maximum principal axis vary more than in the previous model, but the path still tends to center on a nearly invariant minimum principal axis. Large jumps in the position of the maximum principal axis still occur (Figure 4(b)), but less frequently than in the random 10% substitution model. Jumps in this random walk result from the change in position of a single "volcano." Note also that approximately 300 random position substitutions took place before the first of the major axis jumps.

Certainly Io's tidal bulge significantly limits reorientation of the body relative to its rotation axis. To model the possible effects of this bulge we heavily weight the sub-jovian point with 149 new "volcanoes" - each with unit mass identical to that used for the original 351 volcanoes. Compared to the previous models, the maximum and intermediate principal axes tend to form a more well-defined circle 90º in diameter about the virtually stationary minimum axis (Figure 5(a)). Large axis jumps, much rarer than in the previous models, require more time steps (nearly 600 substitutions) to initiate (Figure 5(b)).

Finally, to see how few new volcanoes locations were required to create a dramatic shift in the calculated inertia tensor, we relocated three volcanoes from near the minimum principal axis to near the maximum principal axis. This caused the positions of the maximum and intermediate axes to switch, thus flipping the model Io approximately 90º relative to its spin axis.

Io's mountains and volcanoes have complementary distributions with respect to longitude which resemble gaussian pulses along the equator. Volcanoes center about the sub-jovian point and its antipode, whereas mountains center about ±90ºW. The mountains of Io presumably form over long periods of time, and should therefore be isostatically compensated. The volcanoes, however, erupt quickly allowing for vertical redistribution of mass, and could significantly contribute to the inertia tensor of Io, presumably creating positive mass anomalies. Thus we might expect gravity anomalies associated with volcanoes, but not with mountains on Io. These mass anomalies could cause excitation of true polar wander, the reorientation of Io with respect to its spin axis. The maximum principal axis, as determined from the distribution of 351 equally-weighted volcanoes, roughly coincides with the satellite's spin axis, whereas the minimum axis lies near the subjovian point. This configuration is delicately balanced due to the near equivalence of the maximum and middle eigenvalues. Therefore, assuming an otherwise perfectly homogeneous Io, changes in location of even small numbers of non-isostatically compensated volcanoes may cause dramatic shifts in Io's orientation with respect to its axis. On the other hand, it is possible that it is the tidal flexing that controls the location of volcano formation - with preferential formation atop the tidal bulge. The viscosity of Io is of critical importance in allowing true polar wander to occur: a high viscosity would inhibit any rolling of Io in response to mass disturbance. Rubincam (personal communication) calculates Io's rotational bulge to be 2/3 its tidal bulge, noting that volcanoes would have to overcome the rotational bulge in order to roll, unless the viscosity were sufficiently low. Future observations of the evolution of Io's volcanoes and its orientation may resolve this issue.

Acknowledgments. We thank David Rubincam and Benjamin Chao for their thoughtful reviews, and Michael Stefanick for discussions on the manuscript. This research was partially supported by the Graduate School Fund for Research and Artistry at Northern Illinois University, and also by the New Ideas Fund and the Hinrichs gift fund of the Department of Geological Sciences.

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Paul R. Stoddard, Department of Geology and Environmental Geosciences, Northern Illinois University, DeKalb, IL 60115. (email: prs@geol.niu.edu)

Donna M. Jurdy, Department of Geological Sciences, Northwestern University, Evanston, IL 60208-2150. (email: donna@earth.northwestern.edu)

Copyright 2002 by the American Geophysical Union.

Paper #2001GL0145397170A