Gravity Field and Internal Structure of Mercury from MESSENGER

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Science  13 Apr 2012:
Vol. 336, Issue 6078, pp. 214-217
DOI: 10.1126/science.1218809

Mercury Inside and Out

The MESSENGER spacecraft orbiting Mercury has been in a ∼12-hour eccentric, near-polar orbit since 18 March 2011 (see the Perspective by McKinnon). Smith et al. (p. 214, published online 21 March) present the most recent determination of Mercury's gravity field, based on radio tracking of the MESSENGER spacecraft between 18 March and 23 August 2011. The results point to an interior structure that differs from those of the other terrestrial planets: the density of the planet's solid outer shell suggests the existence of a deep reservoir of high-density material, possibly an Fe-S layer. Zuber et al. (p. 217, published online 21 March) used data obtained by the MESSENGER laser altimeter through to 24 October 2011 to build a topographic map of Mercury's northern hemisphere. The map shows less variation in elevation, compared with Mars or the Moon, and its features add to the body of evidence that Mercury has sustained geophysical activity for much of its history.


Radio tracking of the MESSENGER spacecraft has provided a model of Mercury’s gravity field. In the northern hemisphere, several large gravity anomalies, including candidate mass concentrations (mascons), exceed 100 milli-Galileos (mgal). Mercury’s northern hemisphere crust is thicker at low latitudes and thinner in the polar region and shows evidence for thinning beneath some impact basins. The low-degree gravity field, combined with planetary spin parameters, yields the moment of inertia C/MR2 = 0.353 ± 0.017, where M and R are Mercury’s mass and radius, and a ratio of the moment of inertia of Mercury’s solid outer shell to that of the planet of Cm/C = 0.452 ± 0.035. A model for Mercury’s radial density distribution consistent with these results includes a solid silicate crust and mantle overlying a solid iron-sulfide layer and an iron-rich liquid outer core and perhaps a solid inner core.

The internal structure of a planet preserves substantial information regarding processes that have influenced thermal and tectonic evolution, and measuring a planet’s gravity field provides fundamental information for understanding that body’s internal mass distribution. Mapping Mercury’s gravity field is consequently a primary objective of the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) mission (1).

On 18 March 2011, the MESSENGER spacecraft was inserted into a ~12-hour, near-polar orbit around Mercury, with an initial periapsis altitude of 200 km, initial periapsis longitude of 60°N, and apoapsis at ~15,200 km altitude in the southern hemisphere. This highly eccentric orbit permits the mapping of regional gravitational structure in the northern hemisphere at the maximum resolution of a spherical harmonic model near periapsis but limits the recoverability of the gravity field to long wavelengths at southern latitudes. At the ascending and descending nodes of the orbit (on the equator), the altitude of MESSENGER is about 4900 and 1200 km, respectively.

During the first few weeks after orbit insertion, MESSENGER was tracked extensively at X-band (8 GHz) by stations of NASA’s Deep Space Network (DSN). After this initial period of nearly continuous tracking, the typical coverage was less frequent, limiting the number of direct periapsis passages that were observed. We have processed data from 18 March through 23 August 2011, a tracking period that spans more than two Mercury sidereal days (2) (fig. S1). We limited our analysis to 1-day arcs to reduce the modeling errors from the nonconservative forces, which grow quadratically with time. The aggregated normal equations developed from daily arcs were used to develop solutions of the gravity field of Mercury (2) to degree (l) and order (m) in spherical harmonics, a compromise between data sensitivity and global resolution.

The gravity anomalies and gravitational potential (geoid) of the spherical harmonic solution, here termed HgM002, are depicted in Fig. 1, A and B, respectively. The northern lowlands, ~2 km lower in elevation than surrounding terrain and approximately centered over the north pole (3), correspond to a broad gravity low (Fig. 2). At mid-latitudes, a west-southwest–east-northeast–trending, discontinuous upland that extends for nearly half the circumference of Mercury is marked by weakly positive gravity anomalies and thus must be largely balanced at depth by thicker-than-average crust or lower-than average densities. The gravity field in the northern hemisphere shows several regional anomalies that exceed 100 milli-Galileo (mgal) in amplitude. One such anomaly coincides with Mercury’s northern rise, a locally elevated region (centered at 68°N, 33°E) (3) within the northern lowlands and north polar gravity low. Another is associated with the Caloris impact basin (31°N, 160°E), where some of the anomalous mass correlates with and can be attributed to regions of high topography on the basin floor (3). A third positive anomaly is near the Sobkou impact basin (36°N, 226°E), but the gravity anomaly is centered on the southeast rim of that basin, complicating the relation between gravity and topography. Other positive gravity anomalies are not obviously associated with mapped impact basins at the current resolution of the gravity field. Attempts to resolve mass concentration (or mascon) anomalies similar to those seen at prominent basins on the Moon (4) and Mars (5) from tracking observations during MESSENGER’s first two Mercury flybys (6) and the third Mariner 10 flyby (7) have not produced definitive results. From harmonic solution HgM002, the only large, positive free-air gravity anomaly that is spatially well-correlated with an impact basin, the classical definition of a mascon (4), is that associated with the Caloris basin.

Fig. 1

Maps of Mercury’s (A) free-air gravity anomaly, (B) geoid anomaly, and (C) crustal thickness (cylindrical projections). The height of the geoid anomaly is calculated with respect to a surface given by the rotational and degree-2 zonal gravitational potential for which the average radius at the equator is 2440 km. The potential on the geoid is the sum of the even zonal harmonics in the potential to degree 20 and the rotational potential, under the convention that potential increases outward. The reference potential is 9.02956464 × 106 m2 s−2. In the crustal thickness map, the shaded area indicates a lack of altimetry (3) and weak gravity anomalies due to high spacecraft altitude (fig. S1).

Fig. 2

(A) The radial component of the gravitational acceleration vector resulting from a 20 by 20 spherical harmonic expansion of Mercury’s shape (3) given a density of upper crustal material of 3100 kg m−3. Results are shown in a polar stereographic projection north of 40°N. NR indicates the location of the northern rise. (B) The radial component of the gravitational acceleration vector resulting from the 20 by 20 HgM002 spherical harmonic gravity solution. In both plots, the solution shown has been limited to spherical harmonic terms with degrees 6 and greater to emphasize local- to regional-scale anomalies. The calculation demonstrates that gravity and shape are correlated and that the topography, except for the northern rise, is approximately compensated.

The surface that represents Mercury’s reference equipotential, or geoid (Fig. 1B), has a dynamic range of 200 m, and its largest anomaly is centered at Caloris. Because the spacecraft altitude over the southern hemisphere is much higher than in the northern hemisphere, the geoid error, projected from the full covariance of the HgM002 solution, is less than 20 m north of the equator but reaches 40 to 50 m in regions of mid- to high latitudes in the southern hemisphere. The presence or absence of large geoid features in the south cannot be confirmed with the present data.

The gravity field has been combined with topography from MESSENGER’s Mercury Laser Altimeter (MLA) (3) to produce a map of the crustal thickness of Mercury’s northern hemisphere (Fig. 1C). On the basis of surface compositional measurements (8, 9) from MESSENGER’s X-Ray Spectrometer (XRS) indicating that the crust is intermediate between basaltic and more ultramafic compositions, as well as melting experiments on candidate mantle compositions consistent with XRS measurements (10), we assume a density contrast between the crust and mantle of 200 kg m−3. On the basis of limits determined from flyby observations of gravity and topography (6, 11) and constraints from tectonic models for the depth extent of faulting (12), we adopt a mean crustal thickness of 50 km. The uncertainty in this mean value represents the largest uncertainty in the crustal thickness model. We also assume uniform values for the densities of the crust and mantle and that all signals in the gravity field not produced by topography are signatures of relief on the crust-mantle boundary. The resulting map of crustal thickness (Fig. 1C) indicates that the crust is generally thicker (50 to 80 km) near the equator and thins toward the north polar region (20 to 40 km), with the regionally thinnest crust located beneath the northern lowlands (3). The Caloris basin overlies an area of locally thin crust, consistent with the interpretation of mascon basins on the Moon (13) and Mars (14) that crustal thinning beneath basins contributes substantially to the observed gravity anomaly. The positive free-air gravity anomaly near Sobkou is associated with an adjacent topographic rise, and the anomaly extends in the directions of both the Sobkou and the Budh (17°N, 208°E) impact basins. If the gravitational effects of topography are removed from the free-air gravity anomaly map, the resulting Bouguer anomaly shows strong positive anomalies centered over the Sobkou and Budh basins and a weaker negative anomaly over the rise, indicating crustal thinning directly beneath the basins and thicker crust beneath the rise (Fig. 1C). Like Caloris, Sobkou and Budh also qualify as mascons on the basis of a crust-mantle boundary that is substantially elevated beneath these basins.

A comparison of gravity anomalies that would result from Mercury’s shape alone with the gravity anomalies from the HgM002 solution is made in Fig. 2. High-standing terrain borders many parts of the northern lowlands (3), as is also evident in the broader-scale view of the equivalent gravity field (Fig. 2A). Mild gravity anomalies in this region (Fig. 2B) suggest a high degree of interior mass compensation. By contrast, the northern rise has a gravity anomaly nearly as strong as that due to shape alone (~150 versus ~170 mGal), indicating little mass compensation and a thick lithosphere. We have estimated the thickness, Te, of the effective elastic lithosphere beneath the northern rise by assuming that partial compensation takes place at the crust-mantle boundary and then finding model solutions that best fit the gravity anomaly in terms of crustal and elastic lithosphere thicknesses (Fig. 2). Over a crustal thickness range of 25 to 100 km, Te is 70 to 90 km, and the downward flexural deflection of the crust-mantle boundary is minor (3 to 5 km), consistent with the lack of a discernible crustal thickness anomaly at the northern rise (Fig. 1C). An elastic lithosphere is a surrogate for one with more complex temperature-dependent strength, but temperatures at a given depth in the lower crust and uppermost mantle vary approximately inversely with Te. The northern rise, part of the northern smooth plains volcanic complex (15), has been estimated from its impact crater size-frequency distribution to have a surface that formed ~3.7 to 3.8 billion years ago (Ga), substantially younger than that of the surrounding heavily cratered highlands (16). The greater level of apparent mass compensation of the highlands will yield, under similar assumptions, a thinner elastic lithosphere and higher crustal and mantle temperatures at the time of formation than the northern rise. The inference that Mercury’s interior generally cooled with time is in keeping with thermal evolution models for the terrestrial planets. Te estimates for Mars derived from gravity-topography relations for regions with ages of major topographic features similar to that of the northern rise, in contrast, are considerably smaller (17).

The major parameters of gravity field solution HgM002, including the product of the gravitational constant and Mercury’s mass (GM), are given in Table 1. The GM value is close to that given by the most recent previous model of Mercury’s gravitational field (HgM001), derived solely from the tracking of MESSENGER during its first two near-equatorial flybys (6).

Table 1

Normalized* low-degree gravity coefficients in the HgM002 gravity model for Mercury.

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The covariance matrix of solution HgM002 was used to generate clone models of the gravity field in order to analyze the error characteristics for the degree-2 coefficients and C30 (2) (fig. S5). The harmonic coefficients C20 and C22 are tightly bounded with small relative uncertainties, and C21 and S21 are small (Table 1).

The C20 and C22 terms provide important constraints on the interior structure of Mercury because they are directly relatable to the radial distribution of density. Earth-based radar measurements of Mercury’s pole position confirm that the planet occupies a Cassini state in which the axis of rotation remains coplanar with the orbit normal and the normal to the Laplace plane as the spin vector and the orbit normal precess together about the latter with an ~300,000-year period (18). Radar observations also show that the amplitude of the 88-day physical libration in longitude is so large that the mantle and crust must be librating independently of the core (18). This state allows the determination of Mercury’s normalized polar moment of inertia, C/MR2, where R is Mercury’s mean radius, and a measurement of the ratio of the polar moment of inertia Cm of the solid outer portion of the planet (6, 18) to that of the entire planet (19, 20). The values of C20 and C22 (Table 1), combined with Earth-based radar measurements of the amplitude of Mercury’s forced libration and obliquity (18) and ancillary data on the precession rate and pole position (21), provide the information necessary to estimate C/MR2 and Cm/C. A libration amplitude of 35.8 ± 2 arcseconds and a slightly revised obliquity value of 2.06 ± 0.1 arcmin (22) yields internal structure parameters C/MR2 = 0.353 ± 0.017 and Cm/C = 0.452 ± 0.035.

Resulting moment of inertia parameters for more than 1 million Monte Carlo models that include a silicate crust and mantle, as well as an Fe-rich core that may contain solid and liquid layers are shown in Fig. 3. These models are constrained only by the mean radius (2440 km) and bulk density of Mercury [5430 kg m−3, e.g., (23)]. Comparison of the internal structure models with the measured moment of inertia parameters indicates that the outer radius of the liquid portion of the core under the adopted modeling assumptions is 2030 ± 37 km (1 SD), and the density of the outer shell overlying the liquid core is 3650 ± 225 kg m−3. The procedure does not provide a size estimate for any solid inner component of the core.

Fig. 3

(A) Outer radius of Mercury’s liquid core. (B) Average density of the solid shell that overlies the liquid core. The stars represent the central values for C/MR2 and Cm/C, and the black bars denote ± 1 SD.

The large average bulk density inferred for Mercury’s solid outer shell is surprising given that measurements by the MESSENGER XRS determined an upper bound on the average surface abundance of Fe of ~4 weight percent (8). Although uncertainty in the density of the solid shell permits a wide range of possibilities, the nominal value provides an important constraint on the planet’s bulk composition. The low Fe abundance in volcanic rocks at Mercury’s surface suggests that Mercury’s silicate mantle is also low in iron and cannot account for the outer shell density. Relatively low surface abundances of Ti and Al (8) are also inconsistent with substantial amounts of such high-density mantle minerals as ilmenite and garnet. A deeper reservoir of high-density material is therefore needed to account for the large solid-shell density and moment of inertia. One possibility is a dense silicate layer, possibly Fe-bearing, that has not substantively participated in the generation of Mercury’s crust.

Alternatively, Mercury may have a solid layer of FeS at the top of the core. The highly reducing chemical conditions implied for Mercury’s precursory materials by the low Fe and high S content of surface rocks (8, 9) suggest that Mercury’s core likely contains substantial Si as well as S (24). Fe-S-Si alloys are subject to liquid immiscibility at pressures less than ~15 GPa (25), resulting in the buoyancy segregation of S-rich liquids at the top of the core. The density of solid FeS is sufficiently low that for a broad range of conditions the solid form would likely remain at the top of the core. There is a strong, albeit poorly constrained, trade-off between the thickness of a basal solid FeS layer and the density of the silicate mantle, although the basal layer could be a few tens of kilometers to as much as ~200 km in thickness. The thickness of the outer silicate portion of the planet would, under this interpretation, be thinner than the nominal 410-km depth to the solid-liquid boundary. A solid FeS layer at the base of the mantle would place strong constraints on the present thermal structure of Mercury. Moreover, a static, electrically conducting layer at the top of the core would act to decrease the overall strength of the field observable at or above the planetary surface and would attenuate harmonic components of the magnetic field increasingly strongly with increasing degree (26).

The gravity field results point to a much different interior structure for Mercury from that heretofore anticipated and from those of the other terrestrial planets. These results will require reconsideration of models for Mercury’s interior thermal (27) and tectonic (28) evolution.

Supporting Online Material

Materials and Methods

Figs. S1 to S7

References (3037)

References and Notes

  1. Materials and methods are available as supporting material on Science Online.
  2. Acknowledgments: The MESSENGER project is supported by the NASA Discovery Program under contracts NAS5-97271 to The Johns Hopkins University Applied Physics Laboratory and NASW-00002 to the Carnegie Institution of Washington. We acknowledge the contributions of the MESSENGER spacecraft team and the radio science and MLA instrument teams in acquiring the observations used herein. We are also grateful to three anonymous reviewers for comments that improved the manuscript.
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