## Abstract

Radio Doppler data from four encounters of the Galileo spacecraft with the jovian moon Europa have been used to refine models of Europa's interior. Europa is most likely differentiated into a metallic core surrounded by a rock mantle and a water ice-liquid outer shell, but the data cannot eliminate the possibility of a uniform mixture of dense silicate and metal beneath the water ice-liquid shell. The size of a metallic core is uncertain because of its unknown composition, but it could be as large as about 50 percent of Europa's radius. The thickness of Europa's outer shell of water ice-liquid must lie in the range of about 80 to 170 kilometers.

The Galileo mission has provided four Europa encounters (E4, E6, E11, and E12; Table 1) at flyby distances close enough to reveal details of the satellite's gravitational field (1). Radio Doppler data were also generated from three more encounters (E13, E14, and E15) at altitudes of 3558, 1648, and 2519 km, but they are not included. Here, we removed all model ambiguities caused by previous inconsistent results (2) to yield a new suite of interior models based on a factor of 5 improvement in Europa's second-degree gravitational coefficients.

On the basis of radio Doppler data generated by the Deep Space Network (DSN) at three 70-m stations located at Goldstone, California (DSS14), near Madrid, Spain (DSS63), and near Canberra, Australia (DSS43), and nonlinear weighted least squares (3), we have determined coefficients in the standard spherical harmonic expansion of the gravitational potential *V* (4) to the third degree. All other higher degree harmonics have been set to zero. Our results reveal a satellite in hydrostatic equilibrium at the ±10-mgal level (5); hence, we have used the theory of equilibrium figures (6) to derive interior models consistent with the data. The data are not accurate enough (7) to determine the rigidity of materials within Europa by means of the method of periodic tidal deformations (8).

The flyby geometry for E4, E6, and E11 (Table 1), where along-track and cross-track components of the Doppler shift can be detected, is the most useful for determining gravitational perturbations. For E12 the spacecraft passed directly in front of Europa. Therefore, any gravitational perturbations for E12 are detected by the Europa-centered trajectory bending only, whereas for the other three encounters the bending and the velocity perturbation along the orbital path contribute to the measured Doppler shift. The E11 data were considered less reliable than the E12 data because there was a gap of ∼14 min in the data (starting 4 min before closest approach), an important fraction of the ∼60-min interval when the data were sensitive to the second-degree gravitational field.

We combined the Doppler data from all four encounters (Table 1), along with ground-based astrometric data on the positions of the four Galilean satellites and optical navigational data from the Voyager and Galileo missions to Jupiter, to obtain models of Europa's interior structure. This combined solution includes adjustments to the satellite ephemerides, obtained by numerical integration of their equations of motion. The E4 data were included for purposes of improving the Europa ephemeris, but these data had a negligible effect on the determination of the gravitational coefficients (Table 1). We included the possibility of an atmospheric drag deceleration acting during E12, when the spacecraft altitude was less than one Europa radius (4). We found that the E12 encounter data could be fit equally well with and without a drag model. Furthermore, a solution for the drag deceleration as a parameter in the model yields 0 ± 3 mm s^{–1} in integrated velocity change. The conclusion from the E12 data is that atmospheric drag is not detected, but for the adopted scale heights (240 km below 300 km altitude and 440 km above 300 km altitude), there is a 1σ upper limit on surface atmospheric density of 3 × 10^{–11} kg m^{–3}. This limit is consistent with radio occultation results (9).

Because the given orientation of the satellite's axes predates the Voyager mission, we included all five second-degree gravitational coefficients in the fit to the combined data. The two first-order harmonics *C*
_{21} and *S*
_{21} can be interpreted as corrections to the orientation of the polar axis, whereas the coefficient *S*
_{22} measures a rotation of the *x* and *y* axes about the polar axis*z*. By definition, the origin of coordinates is at Europa's center of mass; hence, the first-degree harmonics*C*
_{10}, *C*
_{11}, and*S*
_{11} are all zero and were not included in the fit. The seven third-degree coefficients were included in the fit, but it is the second-degree field that provides the important constraints on the interior structure, and those coefficients (in units of 10^{–6}) are *J*
_{2} = 435.5 ± 8.2,*C*
_{21} = –1.4 ± 6.0,*S*
_{21} = 14 ± 12, *C*
_{22}= 131.0 ± 2.5, *S*
_{22} = –11.9 ± 2.9, and μ = 0.993 (the coefficient μ represents the correlation between*J*
_{2} and *C*
_{22} from the post-fit covariance matrix).

The lack of a definite detection of *C*
_{21}and *S*
_{21} indicates that the orientation of Europa's polar axis needs no correction. If the *x* axis is aligned in the Europa-Jupiter direction, along the smallest principal moment of inertia *A*, then *S*
_{22} should be zero. The negative value of *S*
_{22} implies that the axis along *A* lies 2.60° ± 0.63° west of the nominal*x* axis (10).

The major inconsistencies between the combined fit and the separate fits to each encounter (Table 1) are the *J*
_{2} and*C*
_{22} values for E4. However, the a priori hydrostatic constraint ensures that *J*
_{2} is 10/3 of *C*
_{22} within the error limits; hence, we are actually concerned with only one inconsistency, the parameter*C*
_{22}. We have published plots of the Doppler residuals (observed Doppler minus model Doppler) for E4 and E6 using the fits of Table 1 (2). A similar plot of E4 residuals from the combined fit is essentially identical to the published plot. We conclude that the 2σ bias in the *C*
_{22} value from E4 (Table 1) is caused by systematic errors in the earlier fit to the E4 data, most likely low-frequency systematic errors in the noncoherent Doppler data.

The value of *C*
_{22} and Europa's average density (11) can be used to infer the moon's internal structure if we assume, as in our previous report (2), that the source of Europa's spherical harmonic degree 2 gravitational field is an equilibrium ellipsoidal distortion of the satellite, a distortion produced by spin and tidal forces as Europa revolves around Jupiter in synchronous rotation with its orbital period. Under these conditions,*C*
_{22} is related to the rotational parameter*q*
_{r} by(1)where *q*
_{r} [the ratio of the centrifugal force to the gravitational force at Europa's equator (11)] is a measure of the forcing for rotational flattening of the satellite, and α is a dimensionless response coefficient that depends on the distribution of density with depth inside the satellite (α = 0.5 for constant density). For*C*
_{22} = 131.5 ± 2.5 × 10^{–6} (10), α = 0.3493 ± 0.0085, where the errors in *C*
_{22} and *q*
_{r}respectively contribute 1.9% and 1.5% to the error in α (11). From equilibrium theory and the value of α, it follows that Europa's axial moment of inertia *C*, normalized to *MR*
^{2}, is*C*/*MR*
^{2} = 0.346 ± 0.005. This value of *C*/*MR*
^{2} is less than 0.4, the value of *C*/*MR*
^{2} for a sphere of constant density, and it requires a concentration of mass toward the center of Europa (12).

The surface of Europa is covered by a layer of water ice, which may in turn overlie a liquid water ocean (13). The gravity experiment cannot distinguish between liquid water and ice because their densities are similar, but it is clear that the interior of Europa must have a density higher than the mean value (2). Because silicates and iron compounds are the only sufficiently abundant materials with densities in this range, we explore three-layer models consisting of a water ice or liquid outer shell, a rock layer composed of silicates or a silicate-metal mixture, and an optional metallic core composed of Fe or an Fe-FeS eutectic mixture.

Because only mean density and *C* constrain the models, there are too many unknowns to provide a unique inversion. We bound the parameter space with constraints on the densities of ice, including “dirty” ice-rock mixtures and some denser phases of ice that may exist near the bottom of the water ice layer, the densities of silicates and silicate-metal mixtures, the radius of the core, and the density of the core, which is either 8000 kg m^{–3} for Fe or 5150 kg m^{–3} for the Fe-FeS eutectic. We took a forward-modeling approach and solved Clairaut's equation for α to determine the family of model parameters that satisfied our combined fit to all the observations. All the models have water ice-liquid shell thicknesses between ∼100 and 200 km (Fig. 1).

Although two-layer models can be found that are consistent with the observations, we find these models implausible. Previously we argued for a metallic core on the basis of magnetic field perturbations observed during the E4 flyby (14). Subsequent observations have not confirmed an intrinsic Europan magnetic field, and are instead more consistent with plasma surrounding Europa and a time-varying induced magnetic field with a source near the surface (15). Although an intrinsic magnetic dipole would have provided powerful evidence for a metallic core, other lines of evidence allow us to use the gravity data to confirm the presence of a Europan core.

Models of Europa's interior that lack a metallic core are only consistent with the observed value of *C*
_{22} if the interior is a mixture of rock and metal with a density higher than 3800 kg m^{–3}. This density implies that Europa's interior is enriched in dense metallic phases relative to Io, which has a bulk density of 3529 kg m^{–3} (16). If the metal is Fe, the enrichment is 12%, and the enrichment is even greater for lower density metallic phases such as magnetite. We suggest that such degrees of enrichment in dense phases are unlikely for a smaller body forming farther out in the proto-jovian nebula than Io. It is more likely that this mixture would separate into a metallic core and rock mantle, because radiogenic heating in the silicates alone would raise Europa's interior to temperatures high enough for differentiation to occur (17), and tidal heating, though difficult to quantify, is potentially an important additional source of heating in the mantle. We therefore conclude that Europa has a differentiated metallic core, and we proceed to analyze three-layer models that can satisfy the constraint on the moment of inertia without requiring Fe enrichment in Europa relative to Io.

The three-layer models of Europa have Fe and Fe-FeS cores of varying sizes, depending on the density of the rock mantle; lower rock densities yield larger cores and thinner water ice-liquid outer shells (Figs. 1 and 2). The minimum thickness of the water ice-liquid outer shell in the three-layer models is ∼80 km. Smaller outer shell thicknesses are possible only for mantle densities lower than 3000 kg m^{–3}. Such low mantle densities are possible only if the mantle silicates are hydrated. In effect, the water in the outer shell is trading off with the water in hydrated mantle silicates. If the mantle density is sufficiently low (<3000 kg m^{–3}), there is enough density contrast between the mantle and the metallic core to account for the relatively small moment of inertia of Europa. Otherwise, a thick water ice-liquid shell (100 to 200 km) is needed to provide the requisite density contrast between the exterior and deep interior of a differentiated Europa. Hydrated silicates break down and release their water at temperatures between 700° and 800°C at the pressures in Europa's interior (18), making it unlikely that a thick Europan mantle would have an average density lower than 3000 kg m^{–3}. Furthermore, it is implausible that Europa would have differentiated a metallic core while retaining a hydrated silicate mantle.