REPORTS
real-time FTIR as 1-propanol was added to a dilute[Bu4N][O2CCN]/IL solution. This peak rapidly
diminished during the addition, while concomitantly a peak corresponding to bicarbonate appeared at 1652 cm−1 (39). Over the course of
only 2 min, nasCO2 for cyanoformate disappeared
completely, while the bicarbonate peak reacheda steady absorbance. All of the observed experimental results are entirely consistent with the computationally based proposal of a stepwise process
for the decomposition and hydrolysis of the
cyanoformate anion.
The stability of cyanoformate, a simple anionof CN– coordinated to CO2, has been shown to
be dependent on the dielectric constant of its local
environment. We propose that this property allows it to shuttle toxic CN– away from the lowdielectric active site of the enzyme ACC oxidase
before its decomposition in higher dielectric media. In broader terms, the ability to manipulate
solution stability of otherwise unstable or transient species, through changes to the dielectric
constant, should find other important applications.
References and Notes
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105, 1814–1819 (2008).

9. S. Shima et al., Science 321, 572–575 (2008).
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11. D. R. Dilley et al., AoB Plants 5, plt031 (2013).
12. W.-K. Yip, S. F. Yang, Plant Physiol. 88, 473–476(1988).
13. J. M. Smith, R. N. Arteca, Physiol. Plant. 109, 180–187(2000).
14. D. Braga et al., Chem. Eur. J. 8, 1173–1180 (2002).
15. X. Zhang, U. Gross, K. Seppelt, Angew. Chem. Int.
Ed. Engl. 34, 1858–1860 (1995).
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17. U. Drück, W. Becker, G. Becker, Z. Kristallogr. 167,
131–134 (1984).
18. F. H. Allen, Acta Crystallogr. B 58, 380–388 (2002).
19. K. F. Purcell, J. Am. Chem. Soc. 91, 3487–3497 (1969).
20. N. W. Alcock, M. Pennington, G. R. Willey, Acta
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227, 85–86 (2012).
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12, 4321–4327 (2010).
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325–340 (1976).
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Chem. Commun. 2004, 112–113 (2004).
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54, 427–433 (1999).

34. A. M. Appel et al., Chem. Rev. 113, 6621–6658 (2013).
35. M. Shoukry, S. S. Hassan, Cent. Eur. J. Chem. 12,
318–324 (2014).
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38. F. Mani, M. Peruzzini, P. Stoppioni, Green Chem. 8,
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Acknowledgments: We thank the Natural Sciences andEngineering Research Council of Canada (through the
Discovery Grants Program to J.A.C.C.) and the Academy ofFinland (through its Research Fellowship to H.M.T.). J.A.C.C.
acknowledges generous support from the Canada Research
Chairs Program, the Canadian Foundation for Innovation, andthe Nova Scotia Research and Innovation Trust Fund. H.M.T.
acknowledges generous support from the Academy of Finland,
the Technology Industries of Finland Centennial Foundation,and the University of Jyväskylä. This work was also supported
in part by GreenCentre Canada, Encana Corporation(Deep Panuke Education and Training and Research andDevelopment Fund), Springboard, and the Magnus Ehrnrooth
Foundation (postdoctoral scholarship to J.M.). We are
grateful to NMR-3 (Dalhousie University) for NMR dataacquisition, Canadian Microanalytical Services for elemental
analyses, and the Finnish Grid Infrastructure consortium forcentral processing unit time. We also thank E. Plettner forher helpful discussions and T. S. Cameron and A. Linden for
their crystallographic insights. Metrical parameters for the
structure of tetraphenylphosphonium cyanoformate areavailable free of charge from the Cambridge Crystallographic
Data Centre, under reference number CCDC 986380.

Supplementary Materials
www.sciencemag.org/content/344/6179/75/suppl/DC1
Figs. S1 to S33
Tables S1 to S17
References (40–62)
14 January 2014; accepted 24 February 201410.1126/science.1250808

tional estimates of tidal heating if Enceladus’ curThe Gravity Field and Interior Structure rent
orbital eccentricity represents a so-called“equilibrium” resonant state with other satellites(6). It indicates time-variability in its internal propof Enceladus
erties (7), in a resonant state with other nearby
L. Iess,1* D. J. Stevenson,2 M. Parisi,1 D. Hemingway,3 R. A. Jacobson,4 J. I. Lunine,5 F. Nimmo,3
J. W. Armstrong,4 S. W. Asmar,4 M. Ducci,1 P. Tortora6
The small and active Saturnian moon Enceladus is one of the primary targets of the Cassini mission. We
determined the quadrupole gravity field of Enceladus and its hemispherical asymmetry using Doppler
data from three spacecraft flybys. Our results indicate the presence of a negative mass anomaly in thesouth-polar region, largely compensated by a positive subsurface anomaly compatible with the presenceof a regional subsurface sea at depths of 30 to 40 kilometers and extending up to south latitudes of about
50°. The estimated values for the largest quadrupole harmonic coefficients (106J2 = 5435.2 T 34.9,
106C22 = 1549.8 T 15.6, 1s) and their ratio ( J2/C22 = 3.51 T 0.05) indicate that the body deviates
mildly from hydrostatic equilibrium. The moment of inertia is around 0.335MR2, where M is the mass and
R is the radius, suggesting a differentiated body with a low-density core.
fter Titan, Enceladus has been the mostobserved satellite by the Cassini spacecraft during its exploration of the Saturniansystem. Images of this small moon (252 km radius) revealed a large plume ejected from thesouth-polar region, with the source being long
fractures from which vapor and ice emerge as
discrete jets (1). Concurrent observations of sodium and potassium salts in the plume (2), andthe measured temperatures within the fractures (3),A

78strongly argue for the presence of liquid water inthe subsurface source region. The plume exhibitsa time variability well correlated to the predictedtidal stresses of the body (4).
The endogenic (nonsolar) power emitted fromthe south-polar region, derived from Cassini Composite Infrared Spectrometer data, is 15.8 GW, with
a 20% formal uncertainty (5). This is equivalent
to an average surface heat flux of ~20 mW/m2
and is an order of magnitude larger than conven-

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VOL 344SCIENCEmoons (8), or in the rate of heat transport. In any or
all of these cases, a plausible internal structure isthat of a liquid water ocean overlain by a (thermally conductive) crust (5).
The design of the Cassini spacecraft does notallow radio tracking from Earth during remotesensing observations. Therefore, only 3 of the
19 flybys of Enceladus completed so far havebeen used for gravity measurements. In these close
encounters, the spacecraft was continuously tracked
from ground antennas while flying within 100 kmof the moon’s surface, twice above the southern
1
Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza
Università di Roma, via Eudossiana 18, 00184 Rome, Italy.
2
California Institute of Technology, 150-21 Pasadena, CA
91125, USA. 3Department of Earth and Planetary Sciences,
University of California Santa Cruz, 1156 High Street, Santa
Cruz, CA 95064, USA. 4Jet Propulsion Laboratory, California
Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA
91109, USA. 5Department of Astronomy, Cornell University,
Ithaca, NY 14850, USA. 6Dipartimento di Ingegneria Industriale, Università di Bologna, I-47121 Forlì, Italy.

*Corresponding author. E-mail: luciano.iess@uniroma1.it

www.sciencemag.org

REPORTS
hemisphere (in the flybys labeled E9 and E19)and once over the northern hemisphere (E12) (9).
We determined Enceladus’ quadrupole gravity fieldand degree-3 zonal harmonic coefficient J3 frommeasurements of spacecraft range-rate. With a radius ~10 times smaller than that of Titan, andabout the same density, the gravitational signature of Enceladus in Doppler measurements ismuch weaker than that of Saturn’s largest moon.
However, the small perturbation due to J3 (about
0.2 to 0.3 mm/s) is still clearly detectable by the
Cassini tracking system, whose accuracy is 0.02
to 0.09 mm/s on a time scale of t ≈ 60 s.
Microwave links between the onboard transponder and ground stations of NASA’s DeepSpace Network enabled precise measurements ofthe spacecraft range-rate. In addition to gravitational forces, our analysis accounts for the main
nongravitational accelerations, most notably neutral particle drag exerted by the substantial gas
plume formed by the jets of the south-polar region. Flying by the moon at latitudes below –70°,
the spacecraft interacts with the plume at distances of up to 500 km from Enceladus’ surface,although most of the effect is localized within
20 s from closest approach. Given the uncertainties in the gas density along the spacecraft flight
path, and the short time scale of the interaction,
the effect of the drag can be modeled as an
unknown, impulsive, vectorial acceleration at
closest approach at E9 and E19 (9). The orbital solutions yielded a velocity variation almost
parallel to the spacecraft velocity, as expected fora drag force, of magnitude 0.25 mm/s for E9 and0.26 mm/s for E19, which are comparable with
the J3 signature. The inclusion of the neutral
particle drag in the south-polar flybys is therefore
essential for obtaining Doppler residuals free of any
signatures, which is essential for a faithful gravity
solution.
As in previous Cassini gravity analyses (10, 11),the solution for Enceladus’ gravity field (labeled
as SOL1 in Table 1) was obtained from a multiplearc analysis in which all data from the three flybys
were fitted by using separate initial conditions forthe spacecraft state vector at each arc (local parameters). The Enceladus state vector, the fivedegree-2 harmonic coefficients, and J3 were considered global parameters common to all arcs. To
Table 1. Solution for the gravity field ofEnceladus. Estimated gravity harmonic coefficients from the multiarc fit of E9, E12, and E19
Doppler data.
SOL 1
CoefficientCentral value T 1s

J2 (×106)
C21 (×106)
S21 (×106)
C22 (×106)
S22 (×106)
J3 (×106)
J2/C225435.2 T 34.9
9.2 T 11.6
39.8 T 22.4
1549.8 T 15.6
22.6 T 7.4–115.3 T 22.9
3.51 T 0.05

avoid biased estimates, the a priori uncertainties
on the gravity coefficients were at least 30 times
larger than were the formal uncertainties obtained
from the orbital solution. The nongravitational accelerations due to anisotropic thermal emission
from the three radioisotope thermoelectric generators and solar radiation pressure were modeledby using values determined by the spacecraft navigation team from the past 8 years of the Saturntour. By processing the data into a multiple-arc
least-squares filter, we were able to estimate local
and global parameters (Table 1). Furthermore, thesolution was proven to be stable with respect toperturbations of the dynamical model, such as theestimation of a full degree-3 field (9).
The ratio J2/C22 differs from the value required for hydrostatic equilibrium (J2/C22 = 10/3),
suggesting that the satellite is not in a fully relaxedshape. The equipotential surface of the tidal,
rotational, and gravitational potential (the latter
limited to 2,0 and 2,2 harmonics) has semiaxis
differences of a-c = 6.00 km and b-c = 2.07 km.
The tesseral coefficients C21, S21, and S22 are nullwithin 3s, indicating that the adopted rotationalmodel (9) is correct and that the orientation of theprincipal axes is that expected for a tidally locked
body with a fully damped pole. The estimatedvalue of J3 implies a 2.5 mGal, negative gravity
anomaly at the south pole (Fig. 1).
The interpretation of Enceladus gravity presents a greater difficulty and uncertainty than usual,
given the strikingly different appearances of thenorthern and southern hemisphere and the apparent confinement of endogenic activity to the highsouthern latitudes. Still, the deviation of J2/C22
from 10/3 (the value for a laterally homogeneous body) is modest (of order 5%) and thenon–degree-2 gravity is small (of order 2% relative to J2), suggesting that there is some prospectof useful inferences.
The topography of Enceladus (12) is not thatof a relaxed hydrostatic body under the action oftides and rotation in a synchronous orbit. Comparisons of the geoid heights with actual topography
for the largest harmonics show differences of up
to 1.2 km (Table 2).

Fig. 1. Enceladus’s gravity disturbances. The gravity field due to C21, S21, S22, and J3 (SOL1) ismapped onto the reference ellipsoid. The negative anomaly at the south pole, representing the asymmetry
between the two hemispheres, is ~2.5 mGal.
Table 2. Comparison between Enceladus’s geoid heights and actual topography. The existing
differences for statistically nonzero harmonic coefficients result in contributions to Enceladus’ gravity
harmonics.

Harmonic

Topography* (km)Equipotential
height†(km)–C20 (or J2)
C22–C30 (or J3)

3.85 T 0.02
0.92 T 0.02
–0.38 T 0.01

2.680 T 0.010
0.780 T 0.007–0.030 T 0.003

Difference
Dh(km)

Contribution ofdifference togravity harmonics‡(×106)

1.17 T 0.03
0.13 T 0.03
–0.35 T 0.01

1606 f20
183 f22–349 f30*From (12), 2s error bars.
†From Table 1, 2s error bars (9).
‡The geoid-to-topography ratio (GTR) for uncompensatedtopographic relief is 3rc=ð2l þ 1Þ r for degree l, where rc is the crustal density (~0.93 g/cm3 is assumed) and r is the mean density(1.61 g/cm3), so GTR (l = 2) ≅ 0.35, and GTR (l = 3) ≅ 0.25. Here, f is the factor (different for each harmonics) by which the gravity due tothe excess topography is compensated by a mass deficit or excess beneath the surface. For Airy compensation, f = 1 – (1 – d/R)l, where dis depth of compensation, R = 252 km, and l is harmonic degree. The entries in the final column are given by Dh *GTR* f/(252km).

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REPORTS
Either J2 and C22 are fortuitously close to having ratio 10/3, or the nonhydrostatic contributions
are small because of compensation ( f is small).
The degree-3 gravity, uncontaminated by tides
and rotation, provides an estimate: f30 ≅ 115.3/
349 ≅ 0.33, implying an Airy depth of compensation of ~32 km. This would in turn imply f20 ≅0.23 (and f22 should equal f20 if compensation isisotropic); hence, the part of C22 arising from thetopographic excess is ~43 × 10−6. Assuming thatthe hydrostatic contribution to this harmonic isthen the remainder, 1507 × 10−6, we infer that themost likely moment of inertia (MOI) of Enceladus is 0.336MR2, where M is the mass and R is
the radius (9). If we choose the value of f20 = f22
such that the hydrostatic part of J2 is exactly 10/3
the hydrostatic part of C22, we obtain f ≅ 0.27,
implying a depth of compensation of ~37 km anda moment of inertia of ~0.335MR2.
If we instead use an iterative approach to selfconsistently separate the hydrostatic and nonhydrostatic parts of both gravity and topography[(9), section S3.5], we obtain converging estimates of f20 and f22 (~0.25) when the moment ofinertia is 0.335MR2, suggesting a compensation
depth of ~34 km. The convergent f20 = f22 is close
to the value predicted on the basis of the observed
f30, confirming that the assumption of isotropic
compensation is reasonable.
When we included elastic flexure as a meansof supporting topography in our model, we foundthat in order to be consistent with the observed
gravity-to-topography ratios, the elastic thickness
must be less than 0.5 km, a value consistent withother estimates made from flexural analysis (13)and relaxation studies (14).
Results in this MOI range are compatible witha differentiated structure (15). For example, avalue of 0.335MR2 can arise from a model witha relatively low core density of ~2.4 g/cm3 and a
H2O mantle of density of 1 g/cm3and thicknessof 60 km (9). The high heat flow and plume activity strongly suggests a differentiated structure,
which is compatible with these results.
The data imply a great deal of compensation;
if our assumption of Airy isostasy is correct, theinferred compensation depth of 30 to 40 km is
most simply explained as the thickness of the ice
shell overlying a liquid water layer. The large
compensation excludes a very different kind ofmodel, in which the main effect is the tidal androtational response of a body with a nonradialsymmetry of material properties. The tidal androtational response of a body with a degree-1
variation in properties could introduce topography and gravity at degree 3, an example ofmode coupling (16); but if this were responsible
for the topographic distortion, then it would predict a much larger gravity distortion than is observed (yielding f ~ 1 instead of the observedmuch smaller values). For the same reason, afrozen-in tidal and rotational bulge from an earlier epoch (17) will not explain the observed gravity if that bulge has persisted in the ice mantle. A
frozen-in deformation of the core (18) could in

80

principle explain the gravity, but the topography
would still have to be highly compensated.
The presence of at least a regional south polar
subcrustal sea suggests a model in which themean temperature of the ice beneath the southpole is warmer than elsewhere, perhaps leading
to a lower mean density of ~1% (corresponding
to 100 K temperature excess and a coefficient ofthermal expansion of ~10−4 K−1). But to satisfy
the observed gravity, it is then necessary to insert
a region of higher-density material roughly twiceas large as that needed to offset the topographic
depression alone and at a depth at least as great as
the previous compensation depth estimates. If
this material is water and is 8% denser than thesurrounding ice, then a layer ~10 km thick isrequired, diminishing in thickness toward thelower southern latitudes. The total hydrostaticpressure at the base of this region would be inbalance with the pressure at the same depth,
plausibly at or near the base of the ice shell, in
adjacent non–south polar regions that lack water,thus reducing the tendency for this layer to spreadlaterally. A highly concentrated mass anomaly at
the south pole would predict J3 = –J2,nh. The data
(Table 2) suggest J3 ~ –0.35J2,nh, and this could
be explained by a mass anomaly that extends
from the pole to roughly 50° south latitude (9).
However, the limitations of the data preclude highconfidence in this inference.
Although the gravity data cannot rule out aglobal ocean, a regional sea is consistent with thegravity, topography, and high local heat fluxes(19) and does not suffer from the thermal problems that a global ocean encounters (19, 20). A
global ocean would yield larger and potentiallydetectable longitudinal librations than are predicted
for a solid body (21). The gravity coefficients andinferred MOI of Enceladus are not consistent with aforced 4:1 secondary libration (17, 22) at the 2s
level (9).

References and Notes
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8. K. Zhang, F. Nimmo, Icarus 204, 597–609 (2009).
9. Materials and methods are available as supplementarymaterials on Science Online.
10. L. Iess et al., Science 327, 1367–1369 (2010).
11. L. Iess et al., Science 337, 457–459 (2012).
12. F. Nimmo, B. G. Bills, P. C. Thomas, J. Geophys. Res. 116,
E11001 (2011).
13. B. Giese et al., Geophys. Res. Lett. 35, L24204 (2008).
14. M. T. Bland, K. N. Singer, W. B. McKinnon, P. M. Schenk,
Geophys. Res. Lett. 39, L17204 (2012).
15. G. Schubert, J. D. Anderson, B. J. Travis, J. Palguta, Icarus
188, 345–355 (2007).
16. S. Zhong et al., J. Geophys. Res. 39, L15201 (2012).
17. C. C. Porco et al., Science 311, 1393–1401 (2006).
18. W. B. McKinnon, J. Geophys. Res. 118, 1775 (2013).
19. G. Tobie, O. Cadek, C. Sotin, Icarus 196, 642–652(2008).
20. J. H. Roberts, F. Nimmo, Icarus 194, 675–689 (2008).
21. N. Rambaux, J. C. Castillo-Rogez, J. G. Williams,
Ö. Karatekin, Geophys. Res. Lett. 37, L04202 (2010).
22. J. Wisdom, Astron. J. 128, 484–491 (2004).
Acknowledgments: L.I., M.P., M.D., and P.T. acknowledge
support from the Italian Space Agency. D.H., F.N., andJ.I.L. are grateful to NASA for support through the Cassini
Project. The work of R.A.J., J.W.A., and S.W.A. was carriedout at the Jet Propulsion Laboratory, California Institute ofTechnology, under a contract with NASA. The Doppler data
and ancillary information used in this analysis are archived
in NASA’s Planetary Data System.

Supplementary Materials
www.sciencemag.org/content/344/6179/78/suppl/DC1
Materials and Methods
Supplementary Text
Figs. S1 to S6Tables S1 to S7
References (23–36)
8 January 2014; accepted 24 February 201410.1126/science.1250551

Geophysical and Geochemical
Evidence for Deep Temperature
Variations Beneath Mid-Ocean Ridges
Colleen A. Dalton,1*† Charles H. Langmuir,2 Allison Gale2,3
The temperature and composition of Earth’s mantle control fundamental planetary properties, including
the vigor of mantle convection and the depths of the ocean basins. Seismic wave velocities, ocean
ridge depths, and the composition of mid-ocean ridge basalts can all be used to determine variations inmantle temperature and composition, yet are typically considered in isolation. We show that correlations
among these three data sets are consistent with 250°C variation extending to depths >400 kilometers andare inconsistent with variations in mantle composition at constant temperature. Anomalously hot ridge
segments are located near hot spots, confirming a deep mantle-plume origin for hot spot volcanism.
Chemical heterogeneity may contribute to scatter about the global trend. The coherent temperature signal
provides a thermal calibration scale for interpreting seismic velocities located distant from ridges.

M

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antle convection controls the evolutionof the planet’s interior and results in the
motion of tectonic plates. The charac-

VOL 344SCIENCEteristics of this convection are governed by thedensity and viscosity of the mantle, which arefunctions of both temperature and composition.

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