ICARUS 130, 540–543 (1997)ARTICLE NO. IS975826

NOTE

Mystery of Callisto: Is It Undifferentiated?

William B. McKinnon

Department of Earth and Planetary Sciences and McDonnell Center for the Space Sciences, Washington University, St. Louis, Missouri 63130E-mail: mckinnon@wunder.wustl.edu

Received May 28, 1997; revised July 28, 1997

(1985), respectively; cf. Table IV in Burns (1986). For an undifferentiatedCallisto, I use both CI and PF-rock as plausible rock components (fromThe Galileo-determined moment-of-inertia factor for CallistoMueller and McKinnon 1988), representing greater and lesser degrees

of 0.406 6 0.039 (1s) is consistent with only a small amount of hydration and oxidation. Anhydrous rock is not used in the modeling,of ice–rock differentiation (,10%), because the moment-of- as dry rock would have had ample opportunity to hydrate over geologicinertia for a totally undifferentiated Callisto is 0.38 (not 0.40). time if intimately mixed with relatively warm water ice (e.g., McKinnonThe apparently high value for the moment-of-inertia may in- et al. 1997), and the thermochemical conditions for hydrated silicateclude nonhydrostatic contributions originating in Callisto’s formation in the protojovian nebula were favorable to begin with (Fegley

and Prinn 1989).lithosphere. The anhydrous rock/(rock 1 water–ice) mass ratioA typical temperature and density profile through Callisto is shown infor Callisto is P0.45, close to the theoretically predicted value

Fig. 1. This particular calculation is for a mix of PF-rock and water–ice,of P0.40. 1997 Academic Pressbut the results for a CI-rock/ice mix are quantitatively similar. The tem-Key words: Callisto; geophysics; interiors, satellites; planetaryperature profile is conductive near the surface and then becomes adiabaticformation; satellites of Jupiterin the convective interior, but the adiabatic temperature variation ismodest, ranging between p205 and 240 K depending on the ice phase

Introduction. The Galileo Orbiter passed within p1000 km of Cal- present. Adiabatic changes in mixed ice phase regions are calculatedlisto’s surface last November. Analysis of the radio tracking by Anderson according to the heats of transformation between the respective iceet al. (1997b) argues for an undifferentiated Callisto, consistent with this phases, weighted according to the ice mass fraction (Mueller and McKin-satellite’s deathly appearance (e.g., Moore et al. 1997). Assuming a perfect non 1988). The adiabatic temperature at the top of the convecting regionhydrostatic relationship between the second-degree gravitational mo- is determined by the parameterized convection formalism, utilizing thements J2 and C22, they derive a reduced or normalized moment-of-inertia extremum hypothesis of Stevenson (e.g., Friedson and Stevenson 1983,C/MR2 (where M and R are the satellite mass and radius) of 0.406 6 Kirk and Stevenson 1987, and see McKinnon et al. 1997 and McKinnon0.039, where 0.4 is the value for a uniform sphere. Their 1-s lower limit 1997 for discussions). Convection is assumed to carry the present-dayof 0.367 allows for some differentiation; a simple two-layer model with radiogenic heat flow in steady state, which is reasonable as the lithosphericice above and mixed ice–rock below (Anderson et al. 1997b) gives an thicknesses inferred (such as in Fig. 1) are not great. The preferredupper limit of p300 km for the ice layer thickness, which Anderson et al. Newtonian rheology in Table VI of Mueller and McKinnon (1988) is(1997b) argue is not consistent with differentiation, because there would adopted for the water–ice, with no stiffening due to rock particles (thisbe plenty of unseparated ice in the rock–ice interior in this model. A is justified in the Discussion).two-layer model is not realistic, however, in the sense that the separation Other minor ice phases (e.g., NH3) and carbonaceous materials areof rock from ice should ultimately lead to the formation of a rock core formally neglected in the structural models but can be considered sub-surrounded by a mixed ice–rock lower mantle and clean ice upper mantle sumed into the ice phase insofar as thermophysical properties are con-(Schubert et al. 1981, Lunine and Stevenson 1982, McKinnon and Parmen- cerned. Clathrate, which in the context of the protojovian nebula meanstier 1986, Kirk and Stevenson 1987). Partially differentiated Callisto mod- methane clathrate, is not expected, because the outer protojovian nebula,els (Mueller and McKinnon 1988) show that a 300-km ice layer actually thermally buffered by the solar nebula or solar radiation field, was notcorresponds to a full 40% differentiation by mass and the formation of cold enough for clathrate formation (Lunine and Stevenson 1982, 1985).a rock core .1000 km in radius. This is a rather substantial degree of Salts or sulfates (Kargel 1991) are also not considered, as these requireunmixing. So, is Callisto undifferentiated? If it is, I argue that it is a low-temperature aqueous alteration of the rock component, which isprofound mystery. unlikely in an undifferentiated ice–rock body.

I note that in terms of the convective scaling analysis of SolomatovNew model satellite. I have calculated new undifferentiated interior(1995), Callisto is in the stagnant lid regime. Calibrated to the numericalmodels for Callisto, using the ICYMOON structural code developed byexperiments of Moresi and Solomatov (1995), the internal potential tem-S. Mueller and myself. This code can handle radially symmetric icy satel-peratures implied are similar to those derived here (perhaps up to 10 Klites built of one or more layers of water–ice, rock, mixed ice–rock, orwarmer), but there is actually no precise correspondence between themetal, with fixed temperatures in the layers or conductive or adiabaticscaling laws derived by Moresi and Solomatov (1995), for bottom heatedradial temperature gradients self-consistently determined from the rocksquare box convection with uniform material parameters (other than thecontent and geologic age, through the heat flow. The radius and mass

for Callisto are taken from Davies et al. (1992) and Campbell and Synnott viscosity), and Callisto’s case, convection in an internally heated self-

5400019-1035/97 $25.00Copyright 1997 by Academic PressAll rights of reproduction in any form reserved.

NOTE 541

FIG. 1. Temperature and density profiles for an undifferentiated Callisto model. The temperature rises on a conductive gradient from anassumed surface temperature of 130 K to P215 K; the temperature gradient at greater depths is adiabatic due to convection, tracking various icephase boundaries as they are crossed. The relatively shallow segments of the density profile correspond, from left to right, to layers of rock 1 iceI, rock 1 ice II, rock 1 ice VI, and rock 1 ice VIII. The relatively steeper segments are the corresponding mixed-phase regions, but with ice IIfirst transforming to ice V before both convert to ice VI.

gravitating sphere with temperature-dependent material parameters. Cal- palimpsest (600 km across), or a thicker sheet of pure ice created bylisto’s precise internal potential temperature does not, however, affect impact melting, if appropriately located, could contribute 8 3 1026 to J2.the conclusions herein. This could account for the excess in the nominal J2 determined by Ander-

As can be seen in Fig. 1, Callisto is significantly self-compressed due son et al. (1997b), 47.7 6 11.5 3 1026, compared with the purely hydrostaticto the extraordinary polymorphism of the water–ice phase. The density case, P40 3 1026 (see Fig. 4 in Mueller and McKinnon 1988). The impliedat the surface is p1.4 g/cm3 (rock 1 ice I) and increases to reach a stresses in Callisto’s lithosphere are only a few percent of the kbar-levelmaximum of p2.2 g/cm3 at the center (rock 1 ice VIII). The reduced stresses supported by the lunar lithosphere (Solomon 1986), and wouldmoment-of-inertia, for either CI- or PF-rock based models, is 0.38, signifi- be consistent with the long-term survival of 1–2 km of basin-generatedcantly lower than 0.40 and close to the lower limit of 0.367. Hence, there topography on Callisto as determined by stereo image analysis (Schenkis actually less leeway to accept a partially differentiated model, and the et al. 1997). This is not meant to suggest that the Valhalla palimpsest islarge moment-of-inertia derived by Anderson et al. (1997b) may appear to the source of Callisto’s excess second-degree gravity field. Rather, I sug-be something of an anomaly. Specifically, based on three-layer structural gest that even on an undifferentiated and apparently geologically deadcalculations, the lower limit of 0.367 restricts any ice upper mantle thick- satellite, impacts are a source of topographic and density variation (ice–ness to &75 km, and the corresponding degree of differentiation to be rock separation). Callisto, especially, may be cool enough that its outer&10% by mass (the 1-s limit is taken at face value; obviously a 3-s lower shell or lithosphere possesses the finite strength to support these variationslimit would admit any model, differentiated or undifferentiated). over geologic time.

Even this level of differentiation is dubious, however, as the heat flows Mueller and McKinnon (1988) also pointed out that a nonhydrostaticearly in solar system history would have been high enough to cause the contribution by the rock core of a fully differentiated Callisto could allowice and ice–rock layers to convect separately. The thermal structure in a differentiated Callisto to mimic (or even exceed) an undifferentiatedsuch a three-layer model guarantees that the ice–rock layer is hotter and one, in terms of J2 and C22. The hydrostatic J2 of a differentiated Callistosusceptible to further ice melting; melting and differentiation should be would be only about 2.5 3 1025, so the magnitude of the nonhydrostaticself-sustaining to at least the pressure level of the ice III–V transition, contribution would need to be larger than that discussed above, *2 3and anything other than a trivial amount of differentiation (2%) would 1025, to account for the value determined by Anderson et al. (1997b). Ahave been subject to this runaway ice melting (Mueller and McKinnon nonhydrostatic contribution due to core mass anomalies, when appropri-1988). This argument is even more stringent if the rock that initially ately scaled from the lunar value (2 3 1024), could, however, easily beseparates forms a metastable layer or ‘‘carapace’’ above the primordial, of this size.ice–rock interior (see discussion in Kirk and Stevenson 1987). The tem- Anderson et al. (1997b) cannot address these nonhydrostatic possibili-perature at the base of the rock layer, once steady-state thermal conditions ties because they assume Callisto is hydrostatic: J2 and C22 are presumedare reached, must exceed that at the bottom of the overlying ice layer, to be in their hydrostatic ratio of 10/3, as noted earlier, and higher degreeand hence the ice–rock interior should be driven to even higher convective terms are neglected. This modeling approach finds some support in thetemperatures; ice melting and further ice–rock differentiation are even results for Ganymede, in which two Galileo passes were analyzed sepa-more likely. rately, one more sensitive to J2 and one more sensitive to C22 (Anderson

et al. 1996). J2/C22 was fixed at 10/3 for each pass, but the best fits forDiscussion. It is possible for the derived reduced moment-of-inertiaeach pass were consistent and similar to within p2 3 1026. The implicationof a body to exceed 0.4 in the absence of a global density inversion ifis that any nonhydrostatic components, which would contribute to differ-there are unmodeled nonhydrostatic components of sufficient strength.ences between the two fits, are similarly small. Ostensibly, this inferenceMueller and McKinnon (1988) argued that nonhydrostatic contributionsapplies to any putative Callisto core as well, although the errors on theto J2 of the order 1 3 1025 were possible for an undifferentiated Callisto,Ganymede fits could mask a greater nonhydrostatic contribution. On thedue to uncompensated topography and/or density structure in Callisto’s

icy lithosphere. For example, a 2-km depression the size of the Valhalla other hand, Ganymede’s core may indeed be close to hydrostatic, perhaps

542 WILLIAM B. MCKINNON

as a result of earlier tidal heating reducing the internal strength of core of the composition and density of rock 1 ice condensed from solarcomposition gas under conditions of thermochemical equilibrium.rock. In this regard, though, the discrepant gravity results from the first

two Europa encounters (Anderson et al. 1997a) should give one pause.The inferences for Callisto could likewise change depending on results

ACKNOWLEDGMENTSfrom additional encounters.To summarize to this point, a straightforward interpretation of the

I thank J. Lunine and C. Yoder for helpful reviews and O. Cromwellmeasured C22 and J2 for Callisto is that the satellite is indeed undifferenti-for continuing inspiration. This research supported by NASA Planetaryated, but the magnitude of the gravitational moments suggests that nonhy-Geology and Geophysics Grant NAGW-432/NAG5-3657.drostatic contributions may be important. Analysis of additional encoun-

ters by the Galileo Orbiter should help determine if this is so byindependently fitting J2 and C22 as well as higher degree terms in the

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Kargel, J. S. 1991. Brine volcanism and the interior structures of asteroidsto the densities of the middle-sized satellites of Saturn. This uncompressedand icy satellites. Icarus 94, 368–390.density yields a rock volume fraction at the surface of 0.20 (for PF-rock)

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NOTE 543

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