## Abstract

Doppler data generated with the Galileo spacecraft’s radio carrier wave during two Europa encounters on 19 December 1996 (E4) and 20 February 1997 (E6) were used to measure Europa’s external gravitational field. The measurements indicate that Europa has a predominantly water ice-liquid outer shell about 100 to 200 kilometers thick and a deep interior with a density in excess of about 4000 kilograms per cubic meter. The deep interior could be a mixture of metal and rock or it could consist of a metal core with a radius about 40 percent of Europa’s radius surrounded by a rock mantle with a density of 3000 to 3500 kilograms per cubic meter. The metallic core is favored if Europa has a magnetic field.

Before the Galileo mission to Jupiter there was little information on Europa’s interior structure. Its mean density of 3018 ± 35 kg m^{–3}, determined from previous Jupiter missions (1), is consistent with an interior of hydrated silicate minerals with a thin ice cover, or alternatively an interior of dehydrated silicate minerals with a thick ice cover (2). Here we report gravitational data from two close passes of Europa by the Galileo spacecraft, E4 and E6, that show that Europa has a more complicated internal structure. Recent Galileo data have shown that Ganymede is differentiated, most likely into a three-layer structure with a large metallic core, a silicate mantle and a thick outer layer of ice (3); Io has a large metallic core (4); and Callisto is essentially a uniform mixture of ice and rock (5).

The Galileo spacecraft flew by Europa on 19 December 1996 (E4) and 20 February 1997 (E6) and measured the Doppler shift in the spacecraft’s radio carrier wave. We analyzed these data by fitting a parameterized orbital model, including Europa’s gravitational field, to the radio Doppler data by weighted nonlinear least squares (6). Europa’s external gravitational field was modeled by the standard spherical harmonic representation of the gravitational potential (7). For the assumption that the origin of coordinates is at the center of mass and that the orientation of Europa’s principal axes is known because it rotates synchronously, only three gravity parameters are needed to specify the gravitational potential through the second degree and order (8).

For the two encounters (9) the two gravity coefficients are highly correlated, so we imposed the a priori hydrostatic constraint that *J*
_{2} is 10/3 of *C*
_{22}. Also, because of an inconsistency in results for E4 and E6, analyzed independently, we added two third- degree gravity coefficients*J*
_{3} and *C*
_{33} to the fitting model. The addition of these two harmonics makes the results (Table1) more consistent and possibly indicates that there are significant nonhydrostatic components in Europa’s gravitational field perturbing *J*
_{2} and *C*
_{22}. The Jupiter-Europa distance was 671,567,992 m during E4 and 671,569,331 m during E6, so the Jupiter tidal force at Europa’s surface differed by a fractional amount, 6 × 10^{–6}, between the two encounters. This difference is too small to account for the inconsistency in the results. Given that neither E4 nor E6 are ideal encounters for a gravity field determination, it is not possible to relax the *J*
_{2} = (10/3)*C*
_{22}a priori hydrostatic constraint or to explore the physical significance of the inconsistency between E4 and E6 in more detail. Additional close encounters with Europa, perhaps with a Galileo extended mission or a future orbiter mission, could reveal the true nature of this inconsistency.

Because of the a priori constraint, the values of*J*
_{2} and its uncertainty are nearly 10/3 of*C*
_{22} (Table 1). There is essentially 1 degree of freedom per encounter in the second-degree field. The measured gravity signals corresponding to the values of *J*
_{2},*C*
_{22}, *J*
_{3}, and*C*
_{33} (Table 1) for E4 and E6 (Fig.1) are above the noise level, even though the large Doppler shift between the preencounter and postencounter signals can be absorbed in a number of other parameters in the model, most notably*GM* and the spacecraft orbital parameters. The last column of Table 1 represents a five-dimensional weighted mean of results from E4 and E6. The weighted mean for *GM* is 3202.86 ± 0.072 km^{3} s^{–2}, where the error represents our best estimate of realistic standard error (1σ), as for all other errors reported here (10).

We used the theory of equilibrium figures for synchronously rotating satellites (11) to infer the internal structure of Europa, as has been done for Io, Ganymede, and Callisto (3-5). For a body in rotational and tidal equilibrium, *C*
_{22} is related to the rotational parameter *q*
_{r} by
(1)where *q*
_{r} is the ratio of centrifugal to gravitational acceleration at the satellite’s surface at its equator (*q*
_{r} = 4.97 × 10^{–4} for Europa). The parameter α is a dimensionless response coefficient that depends on the radial distribution of mass within the satellite (α = 0.5 for constant density).

Given the differences in the values of*J*
_{2} and *C*
_{22} derived from the two encounters with Europa, we separately explored the implications of each set of gravitational coefficients for the internal structure of Europa. We also considered the consequences of weighted mean values of*J*
_{2} and *C*
_{22}. We considered only those inferred internal structures that are robust or common to all the sets of *J*
_{2} and*C*
_{22} values as plausible interior models of Europa. For the E4, E6, and weighted mean values of*C*
_{22} (Table 1), we find, from (1), that α is 0.172 ± 0.082, 0.350 ± 0.034, and 0.310 ± 0.032, respectively. Values of α based on *J*
_{2}are essentially identical. These values of α imply, on the basis of equilibrium theory, that Europa’s axial moment of inertia*C*, scaled by *MR*
^{2}, is 0.264 ± 0.041, 0.347 ± 0.014, and 0.330 ± 0.014. All of these values are small compared with *C*/*MR*
^{2}values of 0.4 for a uniform density body, 0.4 for Callisto (5), 0.378 for Io (4), 0.334 for Earth, and 0.310 for Ganymede (3). The smaller the value of*C*/*MR*
^{2}, the larger is the density contrast between the near surface and deep interior of a body. It is clear from the possible values of*C*/*MR*
^{2} for Europa that the satellite is much denser at great depth.

A more quantitative assessment of the radial profile of Europa’s internal density can be obtained by solving Clairaut’s equation (12) for the distortion of hydrostatic satellite models to the rotational and tidal driving forces experienced by Europa, determining values of α from the models, and constraining the models by comparison with the inferred value of α for Europa. Europa’s measured average density provides a second constraint on possible models, but the availability of only two constraints dictates that we consider only simple models of Europa with a minimum number of unknown parameters. Accordingly, we investigated two- and three-layer models of Europa.

The surface of Europa is known to be predominantly water ice, and it is thought that the ice extends to depths of up to perhaps 100 kilometers. A global liquid water ocean may lie beneath a relatively thin (about 10 kilometers thick) cover of ice (2). We therefore assumed that the outer shell in our models has a density appropriate to a predominantly water ice-liquid composition. The relatively low density of water ice-liquid compared to the density of the rocks and metal that lie beneath the water is in accord with the measured value of α.

The two-layer models of Europa require interior densities that are at the edge of the envelope of acceptable silicate densities (Fig. 2). For the E4/E6 mean value of*C*
_{22}, the density of the deep interior must be greater than about 4100 kg m^{–3}, too dense for a silicate core (the core must be a mix of rock and metal, with a substantial metal component). The radius of the core in this case is about 0.85*R*
_{E} (*R*
_{E} is the radius of Europa). Smaller, denser cores with larger metal fractions, combined with thicker water ice-liquid shells are possible. For the E6 value of*C*
_{22}, the minimum core density is about 3800 kg m^{–3}, just at the outer edge of possible silicate densities (3). The E4 value of *C*
_{22} is so small that Europa would have to be similar to a sphere of Fe surrounded by a shell of water ice-liquid. Based on these two-layer models we conclude that Europa must have a water ice-liquid shell at least about 150 km thick surrounding a dense interior with a substantial amount of metal (density ≥ about 4000 kg m^{–3}).

In the three-layer models of Europa (Fig.3), we assume that the core has the density of Fe (8000 kg m^{–3}) or Fe-FeS (5150 kg m^{–3}). The Galileo magnetometer measured magnetic field perturbations at its initial encounter with Europa that are consistent with the satellite possessing an intrinsic magnetic field (13) and thus a metallic core. For the E4/E6 mean value of *C*
_{22} and silicate densities of 3000 to 3500 kg m^{–3}, an Fe core would have a radius of 0.4 to 0.3 *R*
_{E}, whereas an Fe-FeS core would have a radius of 0.6 to 0.4 *R*
_{E} (Fig. 3B). The water ice-liquid shells in these models have thicknesses between about 150 and 200 km. For mantle densities in excess of about 3800 kg m^{–3}, Fig. 3B and the two-layer model results show that smaller metallic cores are possible, but a substantial amount of metal must be mixed into the mantle to achieve the required high density of the mantle. Three-layer model results for the E6 value of*C*
_{22} (Fig. 3A) are similar; the main differences are that the water ice-liquid shell thickness is smaller (about 100 to 150 km) and that the core is smaller or the mantle has less metal. The value of *C*
_{22} is so small for E4 (Fig. 3) that only models with Fe cores of radius 0.6 to 0.5*R*
_{E} and outer water ice-liquid shells between 300 and 400 km thick are possible.

For a three-layer model with a mantle density of 3300 kg m^{–3}, typical of dehydrated silicates, and the E4/E6 mean value of *C*
_{22} (Fig. 4, A and C), the core radius would be 0.4 to 0.3 *R*
_{E} for an Fe core or 0.65 to 0.45 *R*
_{E} for an Fe-FeS core, independent of the actual density of the water ice-liquid shell. For the Fe core, the water ice-liquid shell is 125 to 250 km thick, and for the Fe-FeS core the water ice-liquid layer is 125 to 300 km thick. The smaller Fe cores in these models make up about 11 to 21% of Europa’s mass, whereas the larger iron–iron sulfide cores in the models are about 18 to 47% of Europa’s mass. The cores in the E6 models (Fig. 4, B and D) are smaller than those in the E4/E6 models, and the water ice-liquid layer thicknesses are also smaller in the E6 models. The E4 models with Fe cores have large cores and thick water ice-liquid shells (Fig. 4D), whereas E4 models with Fe-FeS cores are only possible for the +1σ value of *C*
_{22}.

Although a large suite of three-layer Europa models is possible depending on the actual value of *C*
_{22}, the core density, and the densities of the water ice-liquid shell and rock mantle, the gross features of these models are all similar. In these models, Europa has a metallic core about 0.4*R*
_{E} in radius and a water ice-liquid shell about 150 km thick. Although Io is somewhat larger than Europa, a possible model of Europa is an Io-like interior surrounded by a shell of water ice-liquid. Europa could have a subsurface liquid water ocean; our determination of the low degree and order gravitational coefficients cannot distinguish if the water in the outer shell is solid or liquid. Instead of a metallic core, Europa could have a dense deep interior that is a mixture of metal and rock, but the presence of a europan magnetic field, as implied by the magnetometer data (13), would argue in favor of a metallic core in Europa as a necessary site for magnetic field generation.